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A study of the radiative capture of ⁴He by 12C below 4 MeV

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A study of the radiative capture of ⁴He by 12C below 4 MeV
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Jaszczak, Ronald Jack
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vii, 108 leaves : ill. ; 28 cm.

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Alkynes ( jstor )
Alpha particles ( jstor )
Carbon ( jstor )
Crystals ( jstor )
Energy ( jstor )
Gamma ray spectrum ( jstor )
Gamma rays ( jstor )
Neutrons ( jstor )
Particle interactions ( jstor )
Particle resonance ( jstor )
Astrophysics ( lcsh )
Helium ( lcsh )
Nuclear physics ( lcsh )
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bibliography ( marcgt )
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non-fiction ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 103-107.
General Note:
Manuscript copy.
General Note:
Vita.
Statement of Responsibility:
by Ronald Jack Jaszczak.

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Full Text















A STUDY OF THE RADIATIVE CAPTURE
OF 4He BY "1C BELOW 4 MeV













By

RONALD JACK JASZCZAK


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA
1968













ACKNOWLEDGEMENTS


The author wishes to express his deepest and most

sincere gratitude to Dr. F. E. Dunnam. Without his direction

the experiment would have been an exhausting toil.

A special thank-you goes to Dr. J. L. Duggan for his

guidance concerning target preparation and to Dr. T. A.

Tombrello for the use of his calculations. Thanks go to

Dr. H, A. Van Rinsvelt for his help (including the design of

the target holder) and for checking portions of the manuscript;

to Dr. R. A. Dlue for valuable suggestions concerning

electronics; and to Professor A. E. S. Green for his cclments

on the theory section.

Acknowledgement is made to other members of the

laboratory, including K, E. Baker, R. E. Daniel, R. Stein

and especially R. C. Johns for his generous assistance

during design and construction of the acetylene cracking

apparatus.

Finally, the author expresses his gratitude to the

graduate students who assisted in the data acquisition and.

to his wife for typing the manuscript.
















TABLE OF CONTENTS


ACKNOWLEDGEMENTS s .

LIST OF TABLES .

LIST OF FIGURES .

INTRCDUCTION .

Nuclear Astrophysical Interest

Prior Results .

Intent of Experiment .

CHAPTER


S

S

S

S

S

S

S


I. THEORY .

Nuclear Processes in Stars .

Radiative Alpha Capture .

Radiative Capture of Alpha Particles
by 1 0 .

Angular Distributions .

Absolute Yields .

Radiative Width Determination .

Nuclear Reaction Rates in Stars .

II, EXPERIMENTAL METHOD ,

Energy Analyzing System .

Cold Trap and Target Assembly .


Detectors and Circuitry ,


. 0 0 a ii

. .. Y

vi

. 1i


* I 9 S 3











S, 16


* 19


20
. 20


* 25

a 27

. 31

* 36

*, 36

. .9 37


9 0 0 a 0


iii














Background Radiation .

Target Preparation .

Synthesis of Barium Carbonate

Synthesis of the Carbide .

Synthesis of Acetylene .

The High-Frequency Cracking of
Acetylene .


* .

* 0 0

* 6 6

I 6

* 6 0


* 6 0


CHAPTER

III. EXPERIMENTAL RESULTS .

Excitation Functions .

The 9.85 MeV Level in 10 ..

Cross Sections and the 9.59 MeV Level

IV. DISCUSSION .

Resonances .

Target Deterioration ..

Cross Sections .
12 16
The C(a,y)16 0 Reaction Rate at
Effective Stellar Energies .

APPENDIX . .

GAMMA RAY DETECTION EFFICIENCIES OF
NaI(Tl) CRYSTALS .

Total Incident Intrinsic Efficiency .

Source Full Energy Peak Efficiency

LIST OF REFERENCES .

BIOGRAPHICAL SKETCH .


. 60

. 62

* 66

. .' 72

. 84
S. 84


. 85

. 86


* 0 6

* 6 6


* 6

* 6

* 0 6

* 6

* 6 0


87

90


91

91

97

103

108













LIST OF TABLES


1. Nuclear reactions in the proton-proton chain. 10
2. Attenuation coefficients. 24

3. Radiative widths for ground state and cascal
radiations from the 9.85 MeV (2+) level in -0. 70
4. Possible causes of error. .. 71

5. Radiative width for the 0 P-- 1-(9.59 MeV) EL 0+
transition. .. .. 80
6. The 12C(a,y)160 reaction cross section 83














LIST OF FIGURES


1. "Smoothed" abundance curve of the elements. 8

2. Nuclear reactions in the helium
burning process .. 12

3. Energy levels of 160. 13
4. Theorethical angular distributiDns for
0+1--- 1--->- 0 and 0--- 2+-E- 0
radiative transitions. 22

5. In-line cold trap assembly. 39
6. Target chamber. . 41

7. NaI(T1) crystal and lead shield. 43
8.. Schematic electronic circuit for NaI(Tl)
detector. . 45

9. Electronic pile-up elimination circuit. 47
10. Ge(Li) detector electronic circuit. 48

11. Barium carbonate apparatus. 53

12. Acetylene apparatus. ... 56

13. High-frequency discharge apparatus. 57
14. Enriched 12C excitation function in the
region of the E. = 3.58 MeV resonance 61
12
15. Excitation function for enriched 12C target. 63
16. Excitation function for natural carbon target. 64

17. Excitation function for enriched 13C target. .. 65














18. Gamma ray spectrum from Nai(Tl) detector
at Ea = 3.58 MeV. .

19. Gamma ray spectrum from Ge(Li) detector
at E. = 3.58 MeV. .

20. Branching ratios of 9.85 MeV level in 160.

21. Gamma ray spectrum from NaI(Tl1 detector
at Ea = 3.24 MeV for enriched 2C target.

22. Gamma ray spectrum at E = 2.95 MeV for
enriched 13C target. .

23. Gamma ray spectrum at E. = 2.95 MeV for
natural carbon target. .

24. Gamma ray1~pectrum at E = 2.95 MeV for
enriched C target. .

25. Gamma ray spectrum at E = 2.14 MeV for
enriched 1C target, .


26. The 1C(a,y) 160 reaction cross section values.

27. The parameters involved in the calculation
of NaI(Tl) crystal efficiencies. .

28. Gamma ray spectrum from the 13C(p,y)14N
reaction (Ey = 9.17 MeV).. .


vii


. 67


. .

. S


S







S


. 100


*













INTRODUCTION


Nuclear Astrophysical Interest


The 12C(a,y)160 reaction is of considerable interest

in nuclear astrophysics, especially in studies of stellar

nucleosynthesis and models of stellar interiors. This

reaction occurs in the helium burning sequence and has

a direct influence on the relative abundances of oxygen

and carbon. The helium is produced from hydrogen burning

by the proton-proton and carbon-nitrogen-oxygen cycles (1, 2).

After the hydrogen is consumed by these processes, the

core is heated due to gravitational contraction and at a
8 o
temperature of about 10 K (corresponding to an effective

thermal energy of about 200 keV), helium burning is initi-

ated. The parameters for the 3a-reaction leading to 12C

are known to a fair degree of accuracy, and hence the

rates of these reactions have been determined (3).

The 12C(a,) 160 reaction in the helium burning

chain is believed to proceed through the 7.12 MeV (1~)

level in 160 which is about 40 keV below the threshold.

Very little is known about this state, especially the

reduced alpha particle width which is necessary in the

determination of the 12C(a,y)160 reaction rate at stellar

1






2

temperatures. The reduced alpha particle width Oa2 in units

of the Wigner limit is defined here by Oa2 = ya2(3h2/2M2)-1

The quantity ya2 is related to the partial width Fa by the

expression F = 2y A2 where A2 is the penetrability. Alpha

particle model calculations (where the 160 nucleus is assumed

to be formed by four alpha particles at the corners of a

tetrahedron) indicate that the reduced width for the 7.12 MeV

state is near unity (4); Cluster model calculations by Roth

and Wildermuth indicate a larger variation for the reduced

alpha width (5). The value of the reduced width for states

obtained by assuming a 12C + He cluster (in their ground

states) is about 0.6. If the 12C nucleus is in the
4.43 MeV (2+) state then the reduced width is about 0.02.

Roth and Wildermuth assign the 7.12 MeV level to the 12C + 4He

cluster, indicating that the reduced width is nearer the

value 0.6. Since the final abundances of 12C and 0 will

depend critically on the 12C(a,y) 160 reaction rate (and hence

on 2), a more accurate determination of the reduced alpha

particle width of the 7.12 MeV level is required. It is

possible to obtain some information on ea 2 by examining the
12C(a,y)160 reaction cross section at alpha particle bom-

barding energies near 2 MeV. Because there were no accurate

estimates of this reduced alpha width, Deinzer and Salpeter

(6), and also Fowler and Hoyle (7), calculated the final
abundance of 12C in the core of a helium burning star for

various assumed values of 9 2






3
Prior Results


Prior results on the 12C(a,y)160 reaction have been
limited to work done by Allan and Sarma (8), Bloom et al, (9),

Meads and McIldowie (10), and Larson and Spear (11, 12). In
the preliminary work done by Allan and Sarma, alpha particles

(Ea = 1.6 MeV) were used to bombard thick carbon targets
while observing the high energy gamma rays with a 5.08 cm

thick NaI(T1) crystal. The yields were determined by comparing
the counting rates in the high energy region with the known

counting rate due to the 4.43 MeV gammas from the 9Be(a,ny)12C
reaction. They obtained the value 3 x l0-5 barns for the

integrated cross section at Ea = 1.6 MeV. It is now felt that
the correct cross section is much smaller than this.

Bloom et al. examined the 1" state in 10 at 9.59 MeV.
They were investigating isotopic spin mixing of this T = 0

state, from which the ground state radiation should be inhib-
ited. The radiative width Fy for this state was found to be
0.006 eV corresponding to IMj2(E1) = 1 x 10-5 in Weisskopf

units. From this it was concluded that there was some T = 1

mixing present.

Meads and McIldowie studied the 2+ excited states in
160 at 9.85 MeV and 11.52 MeV in order to obtain the radiative

widths of these states. Using enriched 12C targets and a

10.2 cm x 10.2 cm NaI(Tl) crystal, the values 0.02 + 0.01 and

0.9 0.2 eV were obtained for these radiative widths,
respectively. The state at 9.59 MeV was observed, but the
radiative width was not found for this state,






4
Larson and Spear examined the region E. = 2.8 to 8.3 MeV
in some detail with enriched 12C targets using a 10.2 cm by

10.2 cmr NaI(T1) detector. The region of interest for the

present experiment includes principally the resonances at

Ea = 3.24 and 3.58 MeV corresponding to excited states in
160 at 9.59 MeV (1-) and 9.85 MeV (2+), respectively. The

radiative width for the 9.59 MeV state was given by Larson

as 0.022 + 0.005 eV, and the value of the radiative width

for the 9.85 MeV state was 0.0059 + 0.0006 eV. Also, the

cross section at E. = 3.24 MeV was given as 36 nb (10-9 barns)

(11). The disagreement of Larson with the results of
Bloom et al. was explained by assuming the latter had inad-
vertently lost data due to their background subtraction or

renormalization. Larson and Spear were in better agreement
with the expected isobaric spin impurity predicted by

Wilkinson (13). It was not possible for them to determine

the capture cross section for lower alpha particle bombarding

energies. Cascade radiation of about 7 MeV was observed

from the 9.85 MeV state; however, it was impossible to

determine whether this cascade proceeded through the 7.12 MeV

(1-) state or the 6.92 MeV (2+) state in 160. A width of

0.0012 + 0.0004 eV was given for this radiation, assuming an
isotropic distribution.

A recent endeavor on the 12C(a,y)160 reaction was
presented at the 1968 American Physical Society Meeting in

Washington byAdams et al. (14). Using time-of-flight methods
to discriminate against the neutron background, a value of






5
10 nb was obtained for the capture cross section at

Ea = 2.75 MeV. Data accumulation was hindered somewhat by

low yields resulting from the detector being relatively far

from the target and by low beam currents from the tandem

accelerator employed in the experiment.


Intent of Experiment


At the time this experiment was first proposed it was

hoped that absolute cross section measurements could be

extended to an alpha particle bombarding energy below 1.5 MeVi

however, this did not prove feasible because of the extremely

low yield from the 12C(a,y)160 reaction, and the lowest

bombarding energy at which the cross section was determined

was 1.9 MeV.

Because of the discord between the results of Larson

and those of previous experimenters concerning the radiative

widths of the 9.59 MeV and 9.85 MeV excited states, it was

felt that these radiative widths should be measured. Also,

since Larson was not able to determine the state through

which the cascade radiation from the 9.85 MeV state in 160

proceeded, it appeared desirable to examine this cascade

radiation using a 20 cm3 Ge(Li) detector.














CHAPTER I


THEORY



Nuclear Processes in Stars



In search of an understanding of the origin of the

elements in the universe, many theories have been formulated.

So far the theories fall into two classes. One class assumes

that the elements were formed in a primordial state of the

universe. Two examples of this class are the non-equilibrium

theory of Alpher and Herman (15) and the poly-neutron theory

of Mayer and Teller (16). The other type proposes that stars

are the principal instrument in element formation. A

relatively complete theory of this type has been formulated

by Burbidge, Burbidge, Fowler, and Hoyle (17). Primordial

theories distribute the elements on a cosmic scale; however,

the theories imply that the distribution should be independent

of time. This is contrary to what is observed since, for

example, anomalies (such as the presence of technetium)

have been observed in certain stars. Stars may distribute

material by ejection (such as the explosion of a supernova)

which would result in a distribution of the elements on a

cosmic scale.






7
The theories must all be able to explain the relative

abundance distribution of the elements. Suess and Urey have

constructed a "smoothed" abundance curve by employing data

obtained from terrestrial, meteoritic, and solar measurements

(18). It is impossible to say unequivocally that such a

curve is universal. Thus, one only attempts to explain the

origin of the material that is observed. The general

feature of the abundance curve is that it decreases exponen-

tially from A = 1 to about A = 100 (figure 1). This is

from Burbidge et al. (17). Other principal features include

the change in slope at A = 100, the scarcity of D, Li, Be and

B, the relatively high abundance of alpha particle nuclei

such as 160, 20Ne, 4Ti, large peaks centered at A equal to

about 85, 134, 202, and finally the small abundance of

proton-rich heavy nuclei. Any complete theory must be able

to explain all of these features.

Burbidge, Burbidge, Fowler, and Hoyle proposed eight

processes in stars that would account for these features in

the abundance curve (17). A few modifications to the theory

have occurred since the original article, and the number of

processes has increased. The processes are labeled hydrogen

burning, helium burning, carbon and oxygen burning, the alpha

process, the equilibrium process, the s-process, the r-process,

the p-process and the f-process. It will be shown that the
12C(a,Y)160 reaction is in the helium burning chain of reac-

tions. However, to better understand the motivation behind
this experiment it is desirable to examine the over-all

















































ATOMIC WEIGHT



Figure 1. "Smoothed" abundance curve of the elements.
Burbidge et al. (17).






9
theory slightly. Also, all of the separate processes inter-

connect to form the complete theory. It is for these reasons

that a brief description of the individual processes will be

given.

The f-process is introduced to explain the formation

of the elements lithium, beryllium, and boron. These elements

are rapidly reduced to helium through numerous nuclear reac-

tionswith protons in stellar interiors; thus, it appears

that they must be produced near the surfaces of magnetic

stars through spallation of carbon by highly energetic protons.

The p-process is employed to explain the existence of

certain proton-rich nuclides found in the heavy elements.

These proton-rich elements are formed by (p,y) or (y,n)

reactions on the elements along the nuclear stability line.

Hydrogen burning is the synthesis of helium from

hydrogen (table 1) (19). The alternate endings seem to

depend on the temperature of the region where the hydrogen

burning is occurring. The quantity So is the cross section

factor at stellar temperatures (19). The cross section

factor is directly proportional to the reaction rate which

determines abundances. The cross section factor S is

related to the cross section a by


S(E) = o(E)Eexp(31.28 Z1ZoA E ) keV barns,


where a(E) is the cross section in barns (10-24 cm2)
measured at the center-of-mass energy E in keV (17).













00



I o o
0 0H




S000- 0 0 r- I
c ) > CM 0 0 l 0
4 ,M H M M 8 v H m
0 0 O r 4 1 O 1 B
? CO a H OC n I IP
0
O o


0
A 03 G0 o
0 H
) o o o N
0 r0 0
0 H H


4- C

03 m O \O 0 0n O

0 H H H &
) I U CI




0
SM 0







- r + 4 .0 N
+e +





H+ ) m +
C 0 +W
+ +
+ PQ +

N NC n 0 H0

I 0 2, 4 El m P, r
+ +-




E- + + +






r-i C4 n Ell.- CO cO 4
aS 0f +e ?- +
E-4 0j11 I- +





11
Z1 and Zo are the charges of the interacting particles in

units of proton charge, and A = A1Ao(A1 + Ao)-1 is the reduced

mass of the system in atomic mass units. S results after

effects due to resonances and barrier-penetration have been

eliminated in the expression for the cross section.

In stars that contain enough carbon, nitrogen, or
oxygen, helium may be produced from hydrogen through the

carbon-nitrogen-oxygen cycle. The cycle starts with radiative

proton capture on 12C and progresses to the reaction
15N(p,a)12C. After the hydrogen in the core has been exhausted,

the core begins to contract due to gravity. As this occurs

the temperature rises from the 107 OK that was present during

the hydrogen burning process.

When the temperature is about 108 oK the core begins
to burn helium. The principal reactions involved are shown

in figure 2 (19). The 0+ ground state in 8Be and the 0+

state at 7.65 MeV in 12C allow the first two reactions to

proceed at a reasonable rate. The formation of 160 appears

to be caused mainly by the 1- state at 7.12 MeV (figure 2).

This is about 40 keV below the 12C + He threshold. Using

resonance fluorescence, Swann and Metzger found the mean
lifetime of this state to be about 1.0 x 10-14 s (as corrected
from their previously obtained value), corresponding to a

radiative width of about 0.065 eV (20). The alpha particle

width for this state remained unknown. If the reaction is

due to a single resonance (as is the case for 12C(a,Y)160),
then it can be shown that the cross section factor So is



















( -0094 j -B-.

He4 Be8


Figure 2.
process.


Nuclear reactions in the helium burning
Barnes (19).


a


O16


















!2 S5 c5 "

124 3 N t


!22 3 e7Z16 --J
V3 ':I -- He' -a


I j I _/I'_ .4 -


i -...~~--- ~~.








N, .-- .;


i
_2 ;-_ -- _-





9 27.1 2







a-n
ii J=^ a.4 -> .

.1.0S --
0 d^o O x -10







0 I t
Si Cle i 1 ( -'1 I.- 1-2.








\_ ,_ .____


Figure 3. Energy levels of 160. Lauritsen and
Ajzenberg-Selove (21).


46
JcA6.-


f
C
Sr4 "
N"le


N"'a -d









proportional to 92 (the reduced particle width of that state)

(17). Thus, it is evident that a determination of the
reaction rate requires a determination of that reduced width.

Figure 3 shows the energy levels of 160 (21). It is
possible for the broad (Fcm = 645 keV) 1" level at 9.59 MeV

to interfere with the 1- level at 7.12 HeV. This inter-

ference will either enhance or decrease the capture cross

section in the region between these resonances, depending

on whether the interference is constructive or destructive,

respectively. If the relative sign of the amplitudes of

these states is minus, constructive interference will occur.

If the sign is positive, destructive interference will occur.

Thus, a dete7inration of 0 2 is possible by fitting the

observed cross section in the region Ea = 1.5 to 3 MeV to

calculated values of the cross section (for assumed values

of e 2, and computing both destructive and constructive
values), A calculation of this type has been done by

Tombrello (22). It is therefore necessary to measure the
capture cross section in this region in order to determine
the reduced alpha particle width ea2. Larson has measured

the cross section at an alpha particle bombarding energy

of 3.24 MeV, but this does not allow a determination of
the interference effects (11),

The relative abundance of 160 to 12C will depend on
the cross section of this reaction at stellar temperatures;

thus, the necessity for a better extrapolation forms an
incentive for the present experiment. The main difficulty






15

in performing the experiment, besides the extremely low cross

section values for the 12C(a,y)160 reaction, is the relatively

large cross section (20-100 mb) for the 13C(an) 60 reaction,

since NaI(T1) detectors are quite sensitive to neutrons.

After the helium has burned, the core again contracts,

and the stars will begin burning the carbon and oxygen.

In this way nuclides up to 281 may be formed.

As the temperature rises (2 x 109 OK) photodisintegra-

tion occurs producing alpha particles, protons, and neutrons.

Since the thresholds for (y,p) and (y,n) processes on nuclei

with A = 2Z = 2N are higher than for other nuclei, there

tends to be an increase in abundance for nuclides with

A = 2Z = 2N, These give the appearance of being composed

of alpha particles. This is known as the alpha process.

As the temperature rises to about 4 x 109 OK, many

nuclear reactions are occurring so rapidly that a statis-

tical equilibrium is created. This is known as the e-process.

Since electron capture can occur quickly at this tempera-

ture, there is a shift to nuclei that have N slightly larger

than Z in the vicinity of the "iron peak."

The terms "r-and s-processes" refer to rapid and

slow neutron capture, respectively. The s-process is the

capture of neutrons such that there is enough time between

captures to permit beta decay. The necessary neutrons for

the s-process are produced by (aCn) reactions on nuclei such






16
as 13C and 21Ne. Since certain elements beyond bismuth have

decay times that are short compared to the characteristic

time for the s-process, the elements heavier than bismuth

could not be produced by the s-process. But neutron capture

at a rapid rate (the r-process) could produce the heavy elements

such as uranium, etc. Since the cross section in the

r-process and s-process are small at neutron magic numbers,

the abundances are large at these points. The r-process

produces the peaks in the abundances curve at lower values of

A than the s-process, of course, since the r-process occurs

to the neutron rich side of the stability (N = Z) line; thus,

the formation of the double peaks observed in the abundance

curve may be explained by these processes.

As the iron-group nuclei increase, the star again

contracts and the core implodes; however, nuclear reactions

are still occurring in the outer part of the star. This

implosion creates the supernova. This also produces a rapid

increase in temperature, causing an emission of a large

part of the star; furthermore, neutrons are produced profusely

and are thus convenient for the execution of the r-process.

In this way evolution of the star is completed.



Radiative Alpha Capture


Radiative alpha capture has often been employed for

determining detailed information (such as the energy, spin,

parity, etc.) on excited states of nuclei (23, 24). These






17

parameters (along with others such as radiative widths,

branching ratios of gamma rays, mixing parameters, etc.)

are required in comparing nuclear models and extending

their usefulness. The alpha particle capture reaction is

different from proton capture in that the alpha particle

is spinless; thus, there is a simplification in angular

correlation meaurements. If the target nucleus is also spin-

less, as is the case for even-even nuclei such as 160, a

further simplification occurs. In this case only the relative

motion of the interacting particles may contribute to the

spin of the compound state. This requires that the possible

values of spin (J) are limited to J = 1, 2, 3. .

These are simply the eigenvalues (f) of the orbital angular

momentum operator. The concept of parity is determined by

the behavior of the wave function for the system upon

reflection of spatial coordinates (25). If upon this reflec-

tion the spatial part of the wave function does not undergo

a sign change, the parity (n) is even (+). If the sign

changes, the parity is odd (-). Furthermore, it is known

that the parity is determined by the orbital angular

momentum eigenvalue (f). If I is even (0, 2, 4, .),

than the sign of the wave function will not change upon

spatial reflection, and the parity will be even (+). If

I is odd (1, 3, ), the sign will change, and the

parity will be odd (-). Hence, in cases where the pro-

jectile and target are both spinless, the spin (J) and
parity (r) of the states that can be excited are limited






18
to J" = 0+, 1-, 2+, 3-. These are the so-called

states of "natural" parity.

For this experiment the concept of the compound

nucleus is also useful (25). Here the incident particle is

captured and a compound system is formed, with the energy

shared among all the particles of the compound system. A

relatively long time elapses before sufficient energy is

concentrated onto a particle to allow it to escape. This

time is long compared to the "characteristic nuclear time,"

which is the time required for the incident particle to

traverse the target nucleus without interacting. Since the

decay time is long compared the the "characteristic time,"

the compound nucleus "forgets" its method of formation, If

there is sufficient energy, the compound nucleus can decay

though particle emission in addition to gamma emission.

The states excited in this way are called virtual states.

If there is not sufficient energy to allow particle emission,

the compound nucleus can decay by gamma emission or by

internal conversion. In any case conservation laws are

obeyed.

In gamma ray emission, the angular momentum of the

gamma ray for the ground state transition must be equal to

the angular momentum of the compound system, which is equal

to the orbital angular momentum in the particular case where

the spin of the interacting particles is zero. A light

quantum has an angular momentum equal to hf(f + 1)i. The

maximum projection is Ph. The multiple order of radiation






19
is 2 ; thus, for example in the case where the interacting

particles are spinless, p-wave capture will result in

electric dipole radiation for the ground state transition.

Since the radiation is transverse, there cannot be an I = 0
multiple. This is the reason that 0+ ---> 0+ radiative

transitions are strictly forbidden.


Radiative Capture of Alpha Particles by 160


The two resonance levels in 160 that can be reached

by the present experiment are the 2+ level at 9.85 MeV and
the I1 level at about 9.59 MeV (figure 3). These occur at

incident alpha particle energies of 3.58 and 3.24 MeV,

respectively.

The level at 9.85 MeV has a total width rem of 0.75 keV

(26, 27). This narrow resonance proved quite useful for
determining the target thickness. The thickness of the

target is essential in the determination of cross sections

and radiative widths. Also, because of the large cross

section for the 13C(a,n)160 reaction immediately preceding

this resonance, the 12C enrichment was indicated through a

comparison of the excitation function for a natural carbon

target with that from an enriched 1C target.

Unfortunately a broad peak due to the 13C(a,n)160
reaction is located in the same alpha particle energy region

as the 9.59 MeV peak (28). This makes the gamma radiation
from the 9.59 MeV level extremely difficult to observe.






20
The 9.59 MeV level is a broad resonance having a total

width rcm of 645 keV (26). Hence, the peak extends over a

considerable energy region, but the determination of the

off-resonance yield is hampered by the sensitivity of the

NaI(Tl) spectrometer to neutrons originating in the
13C(a,n)160 reaction.

Below about Ea = 2.9 MeV the main process is nonreso-
nant capture. Here the cross section for the 12C(a,y)160

reaction is extremely small (<10 nb), while the 13C(a,n)160

reaction remains relatively large (-20-100 mb). Thus, it is

even more difficult to determine the nonresonant reaction

cross section at the lower energies. Around E. = 2.0 MeV
interference effects between the 7.12 MeV and the 9.59 MeV 1-

states in 160 become important. The cross section will be

increased or decreased depending on whether this interference

is constructive or destructive. The magnitude of this effect

is dependent upon the parameters of the states involved.

Tombrello has calculated this effect assuming 2 = 0.1;

however, without knowing the relative sign of the amplitudes

it is impossible to determine whether this effect is con-

structive of destructive (22).



Angular Distributions


In the appendix the efficiency of the NaI(Tl) crystal
is derived assuming an isotropic distribution of gamma

radiation. It is necessary to determine the effects of an






21
anisotropic distribution on these results. Gamma radiation

resulting from transitions between natural states, i.e.

0+, 1-, 2+. will have an angular distribution given

by W(e) = anPn(cose), where Pn(cose) is the nth order Legendre

polynomial, and e is the angle between the emitted photon and

the incident particle. Since the ground state of 160 is 0+,

the observation of radiation Yo to the ground state resulting
from the capture of an alpha particle in most cases indicates
that the spin and parity of the resonance state is either 1"

or 2'. J = 0 would not decay to the 0+ ground state, and

J = 2 is more likely to decay to higher excited states which

would then decay to the ground state in 160. In particular,

for 0 d 2+ E2 0+ and 0+ P 1 El 0+ transitions the
-) ----4 -4- ---
theoretical angular distributions will be of the form


W(e) sin2e -1l-P2(cose) (J=l")


W(e)- sin22e0 -+(5/7)P2(cose)-(l2/7)P4(cose) (JT=2+).


From figure 4 it can be seen that these distributions are

entirely distinguishable. The simplicity of these distri-

butions results from the fact that there can be no radiation

mixing, channel spin mixing, or orbital angular momentum
mixing for these transitions. However, the distribution

resulting from the transition between the 2+ states at

9.85 MeV and 6.92 MeV in 160 (0_ d 2+ M2lE2 2+) is
--4 --4
complicated by the fact that Ml E2 radiation mixing is

.possible. In this case it is possible to obtain from the


















































0.0 0 0. 0.4 0.6 0.8 1.0
Cos 2



Figure 4. Theorethical angular distributions for
0-+ 1 i-- 0+ and 0--J 2 -2- 0 radiative
transitions.






23
angular distribution the value of the mixing parameter X,

where X = S(E2)/S(M1),. S(E2) and S(M1) are the amplitudes of

the E2 and Ml transition probabilities, respectively (29).

In determining the total yield (and therefore radiative'

widths, cross sections, and branching ratios) it is essential

to have a knowledge of the angular distribution of the gamma

radiation. If a measurement is taken at only a single angle,

then inaccurate determination of the yield can be obtained

only with the aid of a prior knowledge of the angular distri-

bution, unless the detector is so close to the target that

the distribution appears isotropic.

The observed angular distribution Wobs(G) is then

"smoothed" by the large solid angle subtended by the detector.

This means that the larger the solid angle subtended (the

larger the detector or the nearer the detector to the target),

the smaller the angular variations will be. In other words,

the observed angular distribution will have a decreased

dependency on higher order Legendre polynomials. Wobs(q)

has the form


Wobs(O) = anbnPn(cos9), bnlS 1.


The coefficents bn are the attenuation coefficients described

by Rose (30). They are given by bn = Jn/Jo where Jn is the

nth order integral defined in the appendix. These integrals

were evaluated numerically through the use of a subprogram
(forming a part of a program that determines angular cor-

relation parameters) (31) (table 2). In general, the values






































*


0
-p





HH



E-o -
0




4
"p


<1)
-p
-P


0\
r-t
0
C;
'o0


0 0


CO
o


,o*







F- H
( V3





r-1
0\
0
'. 0

0
Lo O






0
0




0o
4-




N t

Vl'
0 N

0


r4




0


43.--%
(y 0

(d 0
+-


O
60 4




8 *d
F4 O


r-N Ce.'
H V.
El- cr\

00





S0\


CO CO 0

vx V- o






25
of Jn and b. decrease rapidly with increasing n for large

solid angles. It is obvious that the proximity of the detector

to the target determines how rapidly the bn approach zero

with increasing n. If the detector is very close to the

target, the observed distribution will be quite independent

of higher order terms.


Absolute Yields


The absolute total yield of a nuclear reaction is

defined here as the number of disintegrations per incident

particle. In the following discussion the notation adheres

to that used in the appendix. The yield may be related to

Nobs(e) (the number of counts in the spectrum peak observed
at the laboratory angle 0 per incident particle, corrected

for background and dead-time) by employing the ideas derived

above and in the appendix. The number of counts in the

peak (here defined as the region (Ex 1.02 MeV) to 1.1Ex)

at angle e per steradian per incident particle, is given by



Nobs(e)/4T = np x (Y/4n) Wobs(e)/ao,


where rp = REt = R(fqT) = R(Jo/2)


R = peak-to-total ratio





26
R= solid angle subtended by detector


lp = source full energy peak efficiency


rt = source intrinsic efficiency


9T = source incident intrinsic efficiency


Jo = the zeroth-order integral as defined in the
appendix.


The absolute total yield is denoted by Y; hence, Y/4n is the
average yield per steradian. Thus, from the above equation,
it is seen that the yield is


Y = Nobs(e)(R(Jo/2) x J(an/ao)(Jn/Jo)Pn(cose))'1


The expression Nobs(e)/4n may be defined as the "ob-
served differential" yield and denoted by nobs(e). Similarly,
the expression N(e)/4n may be defined as the actual differ-
ential yield and set equal to n(e). Using the expression
derived for the yield it is easy to show that the relation
between n(e) and nobs(e) is

nobs(e) X(an/ao)Pn
n(e) = x
R(Jo/2) (an/ao) (Jn/J o)Pn








Radiative Width Determination


For a resonant radiative capture reaction the cross

section a is assumed to depend on the energy according to

the single-level dispersion formula (25). Explicitly for an

(a,Y) reaction this has the form


(E En)2 r2/
(E El)2+ F2/4


where u = statistical weight = (2J + 1)/((2I + 1)(2S + 1))


J = total angular momentum of system (spin of state)


I = spin of target nucleus


S = spin of incident particle


I = total width of resonance



y = radiative width


r = particle width


S= h(2mE)-2 = wavelenght of interacting particles


m = reduced mass of system = (AaAT/(Aa + AT))1.66x10-24g


Aa = incident particle mass (atomic mass units)






28

AT = target mass (atomic mass units)


E = center-of-mass energy = (T/(Aa + AT)) x Elab


Elab = incident particle energy in laboratory.


At resonance, a is given by


oR = T X2 x /(2/4).


Hence, a may be expressed in the form

UR( r 2/4)
(E ER)2 + r2/F

The relation between the yield and the cross section, assuming

the Breit-Wigner formula is applicable, has often been cited

in the literature (32, 33, 34, 35). The relation is given by


E
Y = -
E-6


(o/e)dE,


where 6 is the target thickness in energy units and


e is the stopping cross section for the incident

particle per disintegrable nucleus in the target

material.






29
The relationship between and the stopping power is


S= l/n(dE/dx),


where -(dE/dx) = the stopping power of the target material


-1l
n = gpNAM-1 = number of disintegrable nuclei per cm3 of

target nuclei


p = the density of target material in grams per cm3


NA = Avogadro's number


M = the molecular mass of target material


g = the fraction of disintegrable nuclei in target

material.


If it is assumed that 6 and e are independent of E over the
resonance, then 6 = (dE/dx)t = net, where t is the target

thickness in centimeters. The integral for Y may now be
evaluated analytically. The result is


2n X2 )o1 [ (E-ER) (E-ER )6
Y = 2 x arctan -arctan ,
e F 1F2 r/2







FoR a (E-ER) (E-ER-6)
or Y arctan arctan .
2 r/2 r/2

It can be shown that this expression has an observed width

r' given by


= (r2 + 62)


Thus, the thickness of the target tends to broaden the

observed width. When the target thickness is determined

(as is often the case) by examining the excitation function

across a narrow resonance, errors enter through such factors

as accelerator instability, energy-defining slits, etc. The

final observed width will thus be the square root of the

sums of the squares of all of these contributions. It is

evident from the above expression for the yield that a

maximum occurs at the energy E = ER + 6/2; thus, the observed

resonance energy is shifted to the higher energy side by

approximately 6/2. This is only approximate because in the

derivation it was assumed that the parameters in the formula

for the cross section were independent of energy over the

energy integration. This shift in resonance energy is one

of the reasons why it is very desirable to have an extremely

thin target for resonance spectroscopy measurements; however,

there are situations where it may be more desirable to have

a thick target (for example, to increase data acquisition rate).

The maximum yield is given by


Ymax = (aR rF/)arctan(6/r).








In terms of measured quantities the resonance cross section

OR has the form


STrmax(e)
aR = x
arctan(6/F) R(Jo/2) (an/ao) (Jn/Jo)Pn(cose)


where Nmax(e) is the maximum counts observed in the peak

at the laboratory angle e. Using the expression relating

aR with the radiative width Fy, it can be shown that Fy is

given by


r Nmax( )
Iy = x
y 4TT rFaarctan(5/r) R(Jo/2) (an/ao) (Jn/Jo)Pn(cose)

This is the expression that was used to obtain the radiative

widths from the observed counting rates. For off-resonance

cross section measurements, a and eare assumed constant in

the integral over the energy interval (E 6) to E.


Nuclear Reaction Rates in Stars


At a temperature T the number of collisions (coll cm-3s )

between nuclei of types 0 and 1, having a center-of-mass

energy between E and E + dE is proportional to

nonlE2exp(-E/kT)dE, where ng and n1 are the number densities

of particles 0 and 1, respectively. The mean reaction rate

(reactions per cubic centimeter per second) of a thermonuclear

process is thus proportional to the integral (36).









fonnlE2exp(-E/kT)P(E)S(E)dE,


where E is the center-of-mass energy, Eiexp(-E/kT) is the
Boltzmann factor (probability for the interaction energy E),
P(E) is the barrier penetration factor, and S(E) is the
cross section factor (defined previously in section 1). The
quantity S is a slowly varying function of the energy E for
off-resonant reactions. It can be shown that the product
of exp(-E/kT) and P(E) has a fairly strong maximum centered
at an energy Eo given by.


Eo = 26.29(Z12Zo AT82) 1 keV,


where Z1 = charge (in units of proton charge) of interacting

particle 1


Zo = charge of particle 0


A = A1Ao/(A1 + Ao) = reduced atomic mass number of

interacting particles


T8= stellar temperature in units of 108 oK.


The quantity Eo is the effective thermal energy used by
Burbidge et al. (17). For reactions such as those normally
found in the helium burning process, the effective thermal
energy is much larger than the mean kinetic energy.






33
This means that the region of interest occurs in the high

energy tail of the Maxwell-Boltzmann distribution of velocities.

The number densities no and ni are related to the
abundances Xo and X1, expressed as the fractional amounts

(by weight) of the interacting nuclei:


ni = NAXi P/Ai*


where ITA is Avogadro's number, p is the density in g cm-3, and
Ai is the atomic mass number of species i. The mean reaction
rate Pl(0) per nucleus of type 0 (expressed in terms of So)
for the interaction with nuclei of type 1 is explicitly

given by


1 o 01 pX1
Pl(0) = 1/r1(0) = 3.63 x 107S ofo ---
AT8 Al

where 0 = 9.15(ZL2Z 2A/T8 .


The quantity T1(0) in the above expression is the mean
lifetime (seconds) of the nuclei of type 0 for interaction
with nuclei of species 1. The quantity fo is the correction
due to electron screening of the bare nuclei as explained
by Salpeter (37). This is a result of the spherical

polarization of the electron gas immediately surrounding
the bare nucleus.
If the reaction rate is due principally to a single

resonance at Er (not in the range of the effective thermal
energy), then an expression for So can be obtained by using






34
the Breit-Iigner single level formula for a. The result

is (17)


2
3 01 1 aYE
So = 3.10 x 10 -
A [K21+ 1(Z)


Eo 2 ER
2 2
(E0 Er) + /4


where 012 = reduced particle width


z = 2(Bo/ER)


2
Be = Coulomb barrier height = ZZ1oe2/R


Eg = h2/2MR2


K21 + 1(z) is the modified Bessel function of order
21 + 1.


The quantity a, is the function of z defined by Burbidge
et al. (17). Values for the modified Bessel function have
12 16
been tabulated (38). For the C(a,Y) 0 reaction (assuming
the state at 7.12 MeV n 160) the expression for S
the 1 state at 7.12 MeV in 0) the expression for S0 is


1.17 x 105 a 2(7.12)
So =
( 2 2
(5T38 + 1)


keV barns,


where the following values have been used


F2/4 << (Eo Er)2


r2 = fy = 0.065 ev







Er 40 keV


Eo = 200 T8 s.


The reaction rate is given by


p(12C) = (C(12C))-


1.69 x 1012Xo 2 12c p

T8 (5T8S+ 1)2


exp(-69.2 T8" ) s-.













CHAPTER II


EXPERIMENTAL METHOD


Energy Analyzing System


Singly charged helium ions at energies up to 4 MeV

were available from the University of Florida Van de Graaff

accelerator. Beam currents for the present experiment were

between 1.5 and 3 ,A. Some preliminary experiments were

carried out using beam currents in the range of 4-7 pA;

however, the rate of target deterioration was intolerable

with these currents. The singly ionized 4He beam was

deflected through a 900 arc by the use of a momentum analyz-

ing magnet (of radius 45.72 cm). The magnetic field B

determined the energy of the He+ beam traversing the slit

system of the analyzer. This magnetic field was determined

by the usual nuclear magnetic resonance (NMR) methods (23, 39).

The NMR fluxmeter (Varian Model F-8A) was supplied by

Varian Associates of Palo Alto, California. Its upper limit

of measurement is 52 kG. This easily surpasses the upper

limit requirements of 12.6 kG for 4 MeV alpha particles.

The NMR unit was calibrated using the 2.4374 MeV and

3.1998 MeV resonances in the 2Mg(a,y) Si reaction (40, 41).








The calibration has also been examined using the 7Li(p,n)7Be

threshold at 1.8807 NeV. The calibrations were accurate to

within 1 keV (112). A Fortran program for tabulating NMR

frequencies versus alpha particle energies in 5 keV intervals

was employed in this experiment (39). Energy variations

due to the finite apertures of slits introduces some error

into the determination of alpha particle energies. It was

assumed that this error was + 0.2 per cent. The magnitude

of the error is not important for off-resonance yields

(since thick targets were used) and enters mainly through

the determination of the target thickness using the 9.85 MeV

level in 160. Current integration was accomplished through

the use of an Elcor current integrator (Model A309B) (calibrated

for an accuracy of 1 per cent or better). The target was

cooled with "refrigerated" water that was demineralized,

thereby minimizing the possibility of current leakage to

ground. This precaution appeared desirable due to the high

mineral content of the water normally supplied to the

laboratory.


Cold Trap and Target Assembly


Initial experiments with natural carbon targets

were performed in order to test target preparation tech-

niques. Data were also later compared with enriched 12C

spectra. The initial target chamber was a 9.1 cm inside
diameter (I. D.) glass "T," separated from the main vacuum







38
system by an in-line liquid nitrogen cold trap. This

apparatus has already been described in some detail by

Bruton (39). It essentially consisted of a holder (cooled

by water) with accommodations for 3 targets plus a quartz

viewer. It was possible to slide the holder (on Viton 0-rings)

in a vertical direction (permitting the positioning of targets

without opening the system to atmospheric pressure). Pressures
-6
were around 106 torr on the oil diffusion pump side of the

in-line cold trap. "Teflon" gaskets were used throughout

except on the target holder and in-line cold traps, where

Viton 0-rings were employed. Carbon deposition from organic

vapors was not apparent with this system, but several improve-

ments were devised to insure better results with the enriched
2C targets.

The improved in-line cold trap (designed by Dr. F. E.

Dunnam and Dr. H. A. Van Rinsvelt) had several features

which would minimize contamination of the target region by

organic vapors (figure 5). This consisted of an in-line

liquid nitrogen cold trap from Sulfrian Cryogenics, Inc.

(Model 338-1), to which a collimating system and a 36 cm

long polished copper tube have been added. The collimator

holders were mounted on the inside of copper couplers that

connected the cold trap to the vacuum system. Except for

the Viton 0-rings on the in-line cold trap the vacuum

gaskets for the beam transport system were of indium, which

is inherently free of organic contamination. The long

copper tube (2.8 cm outside diameter) was in good thermal




























1








contact with the flanges on the cold trap. The collimating

system consisted of three 20 mil Ta discs, one on the diffusion

pump side of the cold trap and two on the target side. The

initial collimating aperture was 0.5 cm in diameter, followed

by 0.4 cm and 0.3 cm apertures on the target end. This system

made it impossible for the beam to strike the long copper

tube; furthermore, the maximum diameter beam spot on the

target was limited to about 0.3 cm by the collimators.

The target holder was designed by Dr. H. A. Van Rinsvelt

and is based on one used at Utrecht (figure 6). "Refrigerated"

water flowing between the outer and inner copper cylinders

cooled the copper endplate (0.02 cm thick) which then cooled

the target backing by conduction. The endplate wias at 550

with the beam axis. The outer cylinder was 4.8 cm in

diameter, the inner was 2.15 cm. A Ta insert fitted into

the inner copper sleeve. This insert had a circular hole

in one end that was slightly smaller in diameter (1.77 cm)

than the target backing. Extremely thin Ta fittings on this

end held the target in position. This insert (and therefore

the target backing) was pressed against the copper endplate

by tightening the bushing (lined with Ta on the beam side).

A greaseless Viton 0-ring sealed the target holder to the

glass reducer. An annulus of thin "Teflon" was placed

between the glass and the inner surface of the flange. This

limited the flow of any organic vapors (originating from the

Viton 0-ring) into the target region. The cold trap and
target holder assembly have the following characteristics
























Sca

0d 4) 4
d
0 (D


o p
koo
S(dr $
S0 pl.p m

S0 B






04 0
c -, +s







C0 d H
1go B


Se |E t4 0
0 I3 >












/0 0 0 q

4^ %0



\o 0% O
p^ S-i-*^^'






42

a) The beam traverses a relatively long path through
an effective cold trap before reaching the target
chamber.

b) The target holder is easily and quickly removed
from the system.

c) The target backings are effectively cooled to
insure maximum target life with relatively
large beam currents.

d) The detector may be located close to the target
in taking excitation runs (about 0.1 cm).

e) It is possible to outgas the interior of the target
chamber by heating the surfaces prior to the
performing of an experiment.

This assembly effectively minimized carbon deposition on the

target. Pressures on the diffusion pump side were typically

2-4 x 10-7 torr. The enriched 12C data were acquired with

this apparatus.


Detectors and Circuitry


The NaI(T1) crystal (12.7 cm x 12.7 cm) was enclosed

in a 28 cm diameter lead shield in order to minimize room

background (figure 7). This was mounted on a table that

allowed the detector to be rotated about the target in a

horizontal plane. When the Ge(Li) and NaI(T1) detectors

were used simultaneously this rotation was not allowed. In

this case the detectors were set at fixed angles of 550

with the beam axis.

The detector used for most of the measurements was

a 12.7 cm x 12.7 cm NaI(T1) crystal mounted on an RCA-8055
photomultiplier tube. A 20.1 cm3 Ge(Li) detector (Ortec































NaI(TI)


Figure 7. NaI(Tl) crystal and lead shield.






'44
Model 8101-20) was used in determining the 7 MeV cascade

radiation. The resolution of the IHaI(T1) spectrometer was

12 per cent for the 1.33 MeV gamria rays from 60Co. For this

experiment, resolution is defined as the full width (in MeV)

at half-maximum divided by the energy (in MeV) of the peakl
position. The Ge(Li) detector had a resolution of 0.5 per

cent for this gamma ray.

The NaI(T1) spectra were measured with a Nuclear
Data 512 channel pulse height analyzer (Series 130) (figure 8).

The signal from the photomultiplier went through a pre-

amplifier and then to an Ortec Selectable Active Filter
Amplifier (Model 440). The first two single channel analyzers

(Ortec Model 413) were set to sum over the 9 MeV and 7 MeV
radiation. The third single channel analyzer was used

(in conjunction with the gate generator (Ortec Model 406)
and the linear gate (Ortec Model 409)) to eliminate the

lower portion of the spectrum. In this way dead time
corrections (from the multi-channel analyzer) to the spectra

were less than two per cent. A pulse stretcher (inserted

after the linear gate) was employed on some of the runs.

The calibration and linearity of the analyzer was checked
often during the experiment using a pulser and several
known gamma rays. The following gamma rays were employed
for this purposes

a) 0.662 MeV photopeak frcm 137Cs

b) 1.17 and 1.13 MeV photopeaks from 60Co
c) 2.50 MeV sum peak from 60CO






















-J
w W
LJ
C Z r


:<
0 'z


liJ
I-

X -
>- 0
.I -
4


y


< :3
IO. 0-__
)J o,


m t
0



-z

z
[0-


CO


_J






46
d) 2.75 MeV photopeak from 24Na
e) 2.225 and 4.432 MeV peaks from a Pu-Be neutron
source and its paraffin shield
f) 8.66 MeV (9.17 MeV-e) escape peak from the
13 14
C(p,y) IT reaction

g) 9.34 MeV (9.85 MeV-e) escape peak from the
12 16
C(a,y) 0 reaction.
The base of the photomultiplier tube was modified to
obtain a fast signal (from a circuit obtained from Dr. R. A.

Blue). A negative fast signal (rise time of about 40 ns)

was obtained from the anode of the 8055 tube. The slow

signal was taken from dynode 9 and therefore was positive.

The purpose of the fast signal was to eliminate electronic

pile-up problems using an EG & G Pile-Up Gate (Model GP100).

The fast circuit components (all EG & G) were set-up to

eliminate all pulses coming within 2 (s of one another

(figure 9). Although this circuit was employed for most

of the measurements, the count-rate was small, and thus this

circuit was not essential for the execution of this experiment.

The signal from the Ortec Ge(Li) detector (20.1 cm3
active volume) went into its matched Ortec Model 118A preamp-

lifier. The signal was then amplified by an Ortec Selectable

Active Filter Amplifier (Model 440) and processed by 1024
channels of a Technical Measurement Corporation 4096 channel

analyzer (figure 10). In addition to the calibration points
used for the NaI(T1) spectrometer the Ge(Li) spectrometer was

also calibrated using the second escape peaks of gamma rays
















CI)
I-.

0
0.


V)
-0 F-


00









































L&J
LI
0:
<
rTt


0
I-


o -






49
from the reaction 24Mg(a,y)28Si. The following gamma rays

were observed:

11.72 MeV (12.74 MeV(Yo)-2e)

9.95 MeV (10.97 MeV(yl)-2e).
The ADC of the 1024 channel analyzer was not linear for

the larger pulses; however, itdidappear to be linear up

to at least 10 MeV. Another problem was a slight drift with

time in the gain of the ADC of the analyzer. This resulted

in a slight broadening of peaks in the spectra obtained from

long runs. The results should still be valid, even though

theseproblems were present.


Background Radiation


Although there are obvious advantages in using the

spinless alpha particle as the projectile, there still

exists an important disadvantage. This disadvantage is
the prolific neutron background produced by the bombardment

of 13C by alpha particles. The carbon is usually in the

form of organic deposits on the vacuum system, walls, on

slits, on collimators, and on the target itself. Neutrons

produced by the 13C(a,n)160 reaction are captured by the
NaI(Tl) crystal, resulting in an exponentially decreasing

background spectrum extending to about Ey = 9 MeV. The

neutron background from the NaI(T1) detector results from

the radiative capture (by such reactions as 23Na(n,y)24Na
and 127I(n,y)128I) in the crystal (1). This is probably






50
the principal difficulty in performing an (a,y) experiment

using a NaI(Tl) detector. The cross section for the 13C + a

reaction in the region E. = 2 to 5 MeV ranges between 20 and

100 mb (43, 44, 45, 46, 47, 48, 28). This is indeed an

extremely large cross section compared to the 12C + 4He

capture cross section, and it was thus necessary to avoid
13C contamination. Methods employed included the preparation

of enriched (- 99.4 per cent) 12C targets and minimizing

natural carbon contamination of the system.

Room background is also a problem. For resonance
measurements the room background was not too important;

however, when off-resonant values were obtained, it increased

in significance. Shielding the detector or using an anti-

coincidence annulus will minimize this source of background

(49-). A plastic anti-coincidence annulus surrounding a

12.7 cm x 12.7 cm NaI(T1) detector had been constructed at
this laboratory by D. R. Wulfinghoff, but was not operational

when this experiment was performed. Lead shielding was

provided for the detector, and it was felt that room back-

ground did not negate the results of this experiment.


Target Preparation


Gamma rays experience little attenuation in passing
through matter; therefore, self-supported targets are unneces-

sary in gamma spectroscopy. This is a considerable advantage
in target preparation and handling. However, because of the







51
prolific neutron background resulting from the 13C(a,n)160

reaction it was necessary to make targets enriched in
12C. The cost of enriched 12C isotope limits the total amount

available; thus, methods of preparation were desired which

would require a very small quantity (of the order of 10-20 mg)

of enriched 12C isotope. Two methods were investigated.

These were the thermal decomposition and gaseous (high-

frequency) discharge methods. In the thermal decomposition

process (50, 51) the target backing (10 mil Ta) is heated by

a flow of current through it. When the foil has heated and

the pressure reaches a steady value of about 5 x 106 torr,

the system is isolated and methyl iodide (CH3I), or acety-

lene (C2H2), is allowed to enter the system until the pres-

sure is about 50 torr. The carbon forms as a thin, uniform

film on the Ta backing. The thickness of the film is a

function of thedecomposition time and CH3I (C2H2) pressure.

The temperature of decomposition is quite different for the

two gases. The methyl iodide cracks readily when the foil

is heated to a very dull red, while the acetylene requires

a bright yellow glow of the foil to crack properly. The

latter high temperature causes the Ta backing to become

brittle, and the carbon film tends to peel from the backing

unless handled carefully. Targets thus could be prepared

using acetylene, but extreme caution had to be observed.

Targets could be easily prepared with the methyl iodide by

this method, and many of these (along with a few prepared
from thermally cracked acetylene) were used in preliminary
experiments on natural carbon.







52
It later became apparent that acetylene would be
easier to synthesize than methyl iodide (52). The gaseous

discharge method allows the efficient use of acetylene in

carbon target preparation (53). This method was finally

chosen in preparing the enriched 12C targets and, for this

reason, will be discussed in detail. Many of the techniques

involved (such as the preparation of carbides, the synthesis

of acetylene and the high-frequency discharge method) were

suggested by Dr. J. L. Duggan of Oak Ridge National Labora-

tory during a visit (supported by Oak Ridge Associated

Universities, Inc.) to the laboratory by the author,

The target preparation method is conveniently
subdivided into four separate steps which may be labeled

1) synthesis of barium carbonate (BaC03)

2) synthesis of the carbide

3) synthesis of acetylene
4) and the cracking of acetylene onto the target
backing.


Synthesis of Barium Carbonate


The enriched 12C (99.94 per cent) used in the prepara-
tion of the targets was obtained from Oak Ridge National

Laboratory in the form of graphite. The apparatus involved

in the production of BaCO3 from elemental carbon is shown

in figure 11. This mainly consists of a quartz combustion

tube coupled to a fretted glass bubbling tube. The carbon
(about 20 mg) is contained in an Al-foil capsule placed in












02


Ba(OH)


Figure 11. Barium carbonate apparatus.






54

the "plugged Teflon" stopcock at the top of the system.

Ta wire mesh in the center of the combustion tube holds

the Al capsule after it is released from the stopcock.

Oxygen flows into the system through the glass "T." The

carbon is heated forming C02 that then reacts readily with

the Ba(OH)2 contained in the test tube at the bottom of

the apparatus. The barium carbonate is formed as a white

precipitate in this test tube. This is then recovered by

vacuum filtration and dried. The efficiency (by weight)

of this process was typically greater than 70 per cent.


Synthesis of the Carbide


The carbide is prepared by placing equal amounts by

volume of the barium carbonate and clean calcium filings in

a small quartz test tube. Glass wool is positioned above

the mixture in order to confine the contents during the

reaction. The quartz tube (containing the BaCO3-Ca mixture)

is connected to a vacuum pump and heated slightly with a

Bunsen burner. The system is then isolated and heated

vigorously with an oxygen-acetylene flame. The carbide

forms a black deposit inside the quartz test tube,


Synthesis of Acetylene


Acetylene is produced by the addition of water to

the carbide (54). This process is carried out employing








the apparatus shown in figure 12. This consisted of a

waterreservoir (upper beaker), a reaction chamber and a series

of cold traps. The first two cold traps (A and B) were

alcohol-dry ice traps. The purpose of these traps is

to limit the flow of water vapor from the reaction chamber,

Acetylene (subliming at -830C) would not be removed by these

traps (having a temperature of -780C); however, it would be

quickly recovered by trap C (a liquid nitrogen trap at about

-1960C) (55). The final liquid nitrogen trap D served to

limit the possibility of contamination from the vacuum pump.

The procedure consists of breaking the quartz tube

containing the carbide (obtained from the previous process)

and immediately placing the pieces in the reaction chamber

which is then evacuated and isolated from the vacuum pump

by closing the stopcock farthest from the reaction chamber.

Distilled water is then allowed to enter the reaction

chamber. Acetylene is rapidly produced and captured as

a white solid by trap C.


The High-Frequency Cracking of Acetylene


The production of carbon targets by a high-frequency

(h. f.) discharge is described in the references (53).
The apparatus used in the present experiment was designed

so that it would rest on the base of a conventional

evaporation system (thereby using the diffusion pump, cold
trap and associated electronics of the evaporator) (figure 13).

































W-J

O
>- 0

0.<


0


w
0 V,
cuIJw


LQJ
2w


W 3:





















































Figure 13. High-frequency discharge apparatus.







58
The target backings (10 mil Ta) were placed in the 34.5 cm

long by 3,8 cm I. D. "Pyrex" tube. The tube could accommodate

four backings (three resting in the horizontal tube and one

attached to the endplate) without affecting the cracking

process. A Tesla coil furnished the h. f. discharge, The
_'7
system is evacuated to a pressure of about 3 x 10- torr,

then isolated from the diffusion pump. The Tesla coil is

activated, and acetylene is admitted into the cracking

chamber through the "side-arm" from trap C (which was removed

from the apparatus used to produce the acetylene). The C2H2

was allowed to sublime by removing the trap from the liquid

nitrogen and placing it in an alcohol-dry ice slush, thereby

allowing acetylene to enter the cracking chamber. To make

uniform targets required careful control of the C2H2 vapor

pressure. This was done by using a stopcock to limit the

flow of C2H2. Experience showed that the most efficient

pressure could be determined by the color of the glow dis-

charge. This optimum pressure is indicated by a pale green

glow with no visible striations. After the acetylene has

completely cracked, the color of the glow discharge

changes to blue, characteristic of nitrogen. At this point

the process could be halted (producing very thin targets)

or repeated several times (producing thicker targets). It

was observed that the target attached to the endplate was

thicker than the ones resting in the glass tube. It was

found that by starting with 20 mg of enriched 12C it was

possible to produce eight targets. Four were thin, three








were of intermediate thickness (15-30 keV for 3.6 MeV alpha

particles), and one was relatively thick (about 55 keV for

3.6 MeV alpha particles).

Targets prepared by this procedure were able to with-
stand beam currents of about 3 1A; furthermore, the spectra

indicated a significant enrichment in 12C (see next section).

The advantage of this procedure was that after the method

was perfected a sizable number of enriched 12C targets

was available at minimal cost. Of course, the above procedure

could also by employed to produce targets enriched in isotopes

of carbon other than 12C.













CHAPTER III


EXPERIMENTAL RESULTS


The yield curves which follow were obtained with
the 12.7 cm x 12.7 cm NaI(T1) crystal fixed at a 550 angle
with respect to the alpha particle beam. This detector was

usually 0.5 cm from the target; however, some long runs were
obtained with the detector at 2.5 cm from the target. Since
the detector was quite close to the target, summing of
cascade gamma rays may occur. A 20.1 cm3 Ge(Li) detector
was also employed in examining the 7 MeV cascade radiation
from the 9.85 MeV level in 160.

The target thicknesses were determined by employing
the narrow level (Fcm = 0.75 keV) in 160 at an excitation
of 9.85 MeV (26, 27). This part of the excitation function
for the target used for the 9.85 MeV measurements is shown
in figure 14. No corrections have been made to this curve.
By determining the full width at half-maximum, the target
thickness was found to be 25 keV for 3.6 MeV alpha particles
incident at 550 to the surface. Using standard methods the
thicknesses were extrapolated to the lower alpha particle
energies as required. A thicker target (55 keV for
3.6 MeV alpha particles incident at 550) was used for most

60


















240




180-

I0
I-
Z

0 120




60



I I I I
3.50 3.55 3.60 3.65
Ea(lab) (MeV)


Figure 14. Enriched 12C excitation function in the
region of the Ea = 3.58 MeV resonance.






62
off-resonance cross section measurements. Some off-resonance
cross sections were also determined with a 30 keV (for

3.6 MeV alpha particles) target.


Excitation Functions


The excitation functions in the region Ea = 2.7-3.7 MeV
for targets of enriched 12C, natural carbon and enriched 13C
are shown in figures 15, 16 and 17, respectively. The
ordinate in figures 15 and 16 represents the number of counts
per 300 p Coulombs of singly charged helium ions within the
region Ey = 8.7 MeV to 10.8 NeV. In the excitation function
for the enriched 13C target the ordinate represents the
number of counts (in the same sum region as for the natural
carbon and enriched 12C targets) per 150 Coulombs. Beam
currents were usually between 1.5-3 pA. The detector was at
a distance 0.5 cm from the target and at an angle of 550
with the beam axis. The enriched 12C target was 15 pg/cm2
thick, the natural carbon target was 22 pg/cm2 thick and
the enriched (probably 15-25 per cent enrichment) 13C target
was 14 pg/cm2 thick. The enrichment of 12C is indicated by
comparing the resonance at E. = 3.58 MeV in the three figures.
The broad peak in the enriched 1C spectrum at E, = 3.24 MeV
is in the region of the 9.59 MeV excitation energy in 160;
however, most of this yield is probably due to the 13C(an)160
reaction. It is difficult to determine the actual enrichment
of 12C, since some of the background is due to neutrons































>t
\> u
a) ('4




-f
H







04
w-








0 00

0 00 0




0 0 0 0























3

,o


0








0


0o

WO
0


&








If Wj
a,
0 0 0








-O


o 0 0 0 0
O O O O
O O O O
r N

-1-o o<002 /Si




























Il)
rto













w
a)
0





oj


o 0 0 0
0 0 0 0
(0 N cO V,


"1 noo9'


091 /S13


bo

0
4)
CH

S3








r'l
.0
0










r-4
-I
4H


P4






66
originating at collimators, etc. Certain runs on tantalum

backings (at Ea = 3.24 MeV) indicate that this source of

background may be as much as 30 per cent of the total back-

ground.

An indication of a resonance due to the 12C(a,y)160
reaction at Ea = 3.48 MeV was observed in the excitation
functions for the enriched 12C and natural carbon targets.

This structure was not observed in the excitation function

for the enriched 13C target. No attempt was made to determine

conclusively whether this structure could be attributed to

the 12C(ty)160 reaction.



The 9.85 MeV Level in 160


The level at E = 3.58 MeV corresponds to a level in
160 at 9.85 MeV (2+). This level has been observed through

the 12C(ay)160 reaction by Meads and Mclldowie, and Larson and

Spear (10, 12). A spectrum taken at E = 3.58 MeV is shown

in figure 18. No corrections have been made. Larson had
observed 7 MeV cascade radiation in the spectrum from his

thick target (11). This 7 MeV radiation is also visible in

figure 18. Because of the resolution of the NaI(T1) detector

it is difficult to determine the level in 160 through which

this cascade proceeds. For this reason the level was
examined using a 20.1 cm3 Ge(Li) detector. A spectrum from

the 1024 channels of the TMC analyzer is shown in figure 19.
This is a point-by-point sum of individual runs of













































150 200


500


500 400
CHANNEL NUMBER


Figure 18. Gamma ray spectrum from NaI(T1) detector at
Ea = 3.58 MeV, The three arrows correspond to the positions
of the photopeak and the two escape peaks,












/ .
*/ ''

.** 1.

N ,
In
u> .7
ro
., ____ -.... ---,----
m





N)














I:
'.. "








'..










*r' *\
.ir1






.. .?'





- /



IDI


0
( *


0
0

SI NOO


- --~-?-- ---T


SIJ

I1








r"




I


//
i-

^



.d


f


f.





4 -.
P







i'





N L4. .
^ -~









0
.I 'C













o 0
o 0
O_ -




N>

SINACJ'


0
co

t1~
ag







0
vC


a




4)






O
o

4)
M


Ql






Sr
4,
0
0



0






pd
02

1.4








I
0

0%









4)
i



r4
0e


IE








0.09, 0.05 and 0.12 Coulomb. The (9.85 MeV-2e) peak is
clearly visible. The smaller peak is from the (6.92 MeV-2e)

radiation. The peak corresponding to the 2+_ 2+ transition

((9.85 6.92) MeV-2e) is also evident. The other peaks
apparently correspond to various background gamma rays. From

this it appears reasonable that the cascade radiation proceeds

through the 2+ level at 6.92 MeV in 160. The results for

the radiative widths (determined from NaI(Tl) data) for the

9.85 MeV ground state and cascade transitions are given in
table 3. The value Fy = 0.0050 eV corresponds to

IMI2 = 2.76 x 102, where IMI2 is the ratio of r to the
radiative width calculated from an extreme single particle

model (F'). Fy is the so-called Weisskopf limit. In deter-
mining the radiative width for the cascade radiation, Larson

assumed an isotropic distribution since he was not able to
determine the identity of the intermediate level (11).

The sources of error are given in table 4. Errors
due to current integration, extrapolation of stopping cross

sections to different energies, and geometry have been

combined and listed in the column labeled "other". The total

error is the square root of the sum of the squares of the

individual errors. From table 4 it can be seen that no error

is listed under "target thickness" for the 9.85 MeV radiations.
Due to the extremely narrow total width of this state
(Fcm = 0.75 keV) the factor arctan(6/r) in the expression
for the radiative width reduces to n/2 and is not a source
of error. The difficulty in extracting the 9.85 MeV cascade

















0
0





0
+0

0u


S0
0





0
'dO













0

0C
43'







m0
(d












4 0
0
OSv






w 4
O



od

.4

$ad
4 0-
Nl-


0
Q4
cc 0

-p
W'



043
g r
o
C^ ^


0





O
0



Id
0







)
0


.-

















0
rE-
4.






0




0O
90
0,


c- o
E4 0

C)


0

P4
p4


0



NHG)
.* r
0

0


o3
0
"H
Co

Od





00

0 0
0 0.

Co-4


0-
0
Co





co

o.







M


< 0\ o rN f^ 3 cO r p













SO O VI O H v c O
Sr4 rr C N rN1









co o o\ o\ o\ o\ 0\ o\ o\ %o\ "


Hn H 4 N C 4 N 4 N C 'O


I r


S-I H H H H H H r-H r- i-


0 N N N C0-N 0\N N- C- o I I






N .
N
N 4 0 N 4 0c 0
n N H 0O C NEl U% n' H O\ WN V%
* 4 4 r A
C C^ CO f N N N N N H lCM C^






72
radiation in the presence of the strong ground state

radiation caused a 10 per cent error for "background sub-

traction" for the cascade radiation. The brancing ratios

for the 9.85 MeV level are given in figure 20.


Cross Sections and the 9.59 MeV Level


The 1" state at 9.59 MeV excitation in 160 was

examined with the 29 pg/cm2 thick target. This level is

very broad, having a center-of-mass width of 645 keV (26).

Figure 21 shows a spectrum from the NaI(T1) crystal at

E = 3.24 MeV. There were no corrections made to this

spectrum. The detector was 0.5 cm from the target and

at an angle of 550. The total amount of charge collected
was 5.5 x 10 o Coulombs of singly ionized helium. The arrows

indicate the expected positions of the photopeak and escape

peaks. For comparison purposes a spectrum at E. = 2.95 MeV

obtained from the enriched 13C target (14 pg/cm2) is shown

in figure 22. Spectra obtained at Ea = 3.24 MeV with this

target have the same general appearance. The spectrum

from the 13C is exponentially decreasing under the radiation

from the 9.59 MeV level. This same feature is also observed
in the spectra from a natural carbon target (figure 23).

The 9.59 MeV yield was obtained by subtracting

fractional parts of the 9.85 MeV spectrum from the 9.59 MeV

spectrum. The resulting spectrum was then compared with a
13C(,n)160 spectrum to determine ts fit with the background
C(cxn) 0 spectrum to determine its fit with the background.























9.85 M eV Z


6,92 MeV


17


















0
0?


10


Figure 20. Branching ratios of 9.85 MeV level in 160
The energy levels are not drawn to scale.

























O






102






10


200


Figure 21. Gamma
Ea = 3.24 MeV for


300
CHANNEL


400
NUMBER


ray spectrum from NaI(T1) detector at
enriched 12C target.


500










10s







104





0





10










10
I0


200 300 400


Figure 22.
13C target.


CHANNEL


NUMBER


500


Gamma ray spectrum at Ez = 2.95 MeV for enriched






























U)
-1 9.37 MeV
ZI







00

000
00
102 o





go3t
0 o


10- I I I
200 300 400 500
CHANNEL NUMBER
Figure 23. Gamma ray spectrum at E = 2.95 MeV for natural
carbon target.















ENRICHED 12C
E,= 2.95 MeV

104 45000 pCOULOMBS





CO)
h 9.37 MeV

0 b r
oo







102 O0





150 200 300 400 500

CHANNEL NUMBER
Figure 24. Gamma ray spectrum at E. = 2.95 MeV for enriched
12C target.


























z 103
10

0









10 -I ..I .I,

200 300 400 500
CHANNEL NUMBER
Figure 25. Gamma ray spectrum at E = 2.14 MeV for enriched
12C target,






79
This same method was also used in determining the off-

resonance yields. This procedure gave a value of

0.021 + 0.004 eV for the radiative width. A comparison with

previous results is given in table 5. The present work

agrees well with the value given by Larson (11). The value

Ty = 0.021 eV gives a value of 5.5 x 10-5 for IM12.

Although there is some indication of 7 MeV cascade

radiation in the 12C spectrum near channel 280, this feature

is also seen in the 13C spectrum. It is felt that the

spectrum peak in channel 280 is the result of the capture

of thermal neutrons by the 23Na in the NaI(Tl) crystal.

When a paraffin shield was installed between the detector

and the collimators, the spectrum peak became more pronounced.

The curves shown in figures 21, 22 and 25 were obtained

with this shield, while the data shown in figures 23 and 24

were obtained without the paraffin shield. There was some

indication that although this shield increased the 7 MeV

background, it decreased the background in the 9 MeV region.

It has been observed that 9 MeV radiation (resulting

from the 1C(d,y) N reaction) may also present a background

problem in a 12C + a experiment (11). The reason presented

is that if deuterons exist in the ion beam, the beam energy

analyzing magnet will permit the target to be bombarded with

deuterons having one-half the energy of the alpha particles,

since molecular D2+ ions will have nearly the same path as
4 12
singly ionized He. The bombardment of C by 1.65 MeV
deuterons produces 9.4 MeV cascade radiation to the 2.31 MeV































co


0 0

C o

O


ad
0
0
0




o o
+1
O %
00
0 0


+
0





o

0o
u\





-1


0




*0
4J







*d
4-


Co
a )


p4








first excited state in 1N. The r. f. source bottle used

for this experiment has never been used to ionize any

hydrogen isotope; hence, it was assumed that the contribution

from deuteron-induced reactions was negligible in the present

experiment.

The off-resonance cross sections were determined from

spectra such as the one shown in figure 24. The 52 Ag/cm2

thick target was used for this data. The ground state

radiation is clearly visible in channels 355-390. A

comparison with figure 22 shows that the number of counts in

the corresponding channels for the 13C spectrum is decreasing

almost exponentially. For the spectrum at E = 2.95 MeV

(as for the other cross section measurements) the 12.7 cm by

12.7 cm NaI(T1) detector was at a 550 angle with respect to

the beam axis, and was located 0.5 cm from the target. The

ground state radiation is more visible at EC = 2.95 MeV

(figure 24) than at the peak Ea = 3.24 MeV (figure 21). Two

factors contribute to this appearance. First, the average

number of counts per channel in figure 21 is about 10 times

that in figure 23; hence, on the logarithmic scale the peak

is not as evident. Also, the 13C(a,n)160 cross section is

about 5 times as large at Ea = 3.24 MeV as at Ea = 2.95 MeV

(43). Thus, the ground state radiation is more difficult
to observe at the resonant energy because of the increased

neutron background.

The yield spectra for the other data points are

similar to the spectrum shown in figure 24. As the alpha








particle bombarding energy decreases, the spectra resemble

the 13C background more closely. For example, at Ea = 2.14 MeV

there is only a slight indication of the ground state radiation.

This is shown in figure 25, where the data were obtained with

the 28.8 jg/cm2 thick target. Because of this the error

caused by extracting the yields from the backgrounds are

relatively large for the cross section meaurements made at

low bombarding energies (table 4). The amount of singly

ionized helium collected was typically between 0.045 and

0.16 Coulomb.

The yield at each of the experimental points was

normalized to that at 3.58 IeV by multiplying the total number

of counts in the capture spectrum peak by the ratio of the

number of channels enclosing the peak to the number of channels

in the standard spectrum peak. The values of the cross

section are listed in table 6. The errors shown were computed

from the values given in table 4.













Table 6
The 12C(ay) 160 reaction cross section.


He energy Cros- section
(MeV) (10-' barns)


3.37 32.0 + 6.1
3.24 35.0 + 6.1
3.22 35.0 + 6.1
3.10 29.0 + 5.8
3.07 19.8 + 3.8
2.95 15.2 t 3.0
2.92 11.9 + 2.4
2.76 8.0 + 1.8
2.54 4.3 + 1.3

2.35 3.5 1.2
2.14 1.5 + 0.5
1.90 0.3 + 0.1













CHAPTER IV


DISCUSSION


'Resonances



In this experiment the radiative capture of alpha

particles by 12C below Ea = 3.6 MeV has been examined. The

7 MeV cascade radiation from the 9.85 MeV (2+) level in 160

was determined to proceed through the 6.92 MeV (2+) level.

It would be of interest to examine this (0+_ d 2+ MIE2 2+)
--____--_@)

transition using angular distribution methods to determine

the mixing parameter X, where X = S(M1)/S(E2). S(M1) and

S(E2) are amplitudes for dipole and quadrupole emission,

respectively (29). Further study of this state would

probably best be accomplished through angular correlation

methods. At the time this experiment was performed, a new

correlation table was being designed and constructed by

members of the laboratory. This table will be able to make

the above measurements accurately. For this reason no

determination of the mixing parameter X was attempted using

the present apparatus.

The radiative width measurements agree in general
with the results of Larson (the errors overlap); however,
the values tended to be slightly smaller than the values
84








obtained by Larson. This may be due in part to the method

used in determining the peak-to-total ratio for the present

experiment.


Target Deterioration


Target deterioration was present only at higher beam

currents (about 4-7 ;A).- At these beam currents the carbon

was dissipated, and the tantalum backing became quite pitted.

Carbon deposition was not observed on the target, even after

the relatively long bombarding times. In order to observe

this more carefully, several relatively long runs (greater

than 0.04 Coulomb) were made on clean Ta backings using

both low (1-3 ~A) and high (4-8 1A) beam currents. No

deposition of organic material was observed for either of

these currents. However, the higher beam currents did cause

the tantalum to change color at the spot which had been

bombarded by the beam. This spot was gold in color on both

sides of the backing. This is believed to be caused by the

tempering of the tantalum by the concentration of heat on the

beam spot. This same effect was observed during preliminary

experiments in target preparation by thermal cracking methods.

When the Ta backing was outgassed by heating the backing to

a bright yellow glow in a vacuum, the Ta backing would have

the characteristic gold color and be very rigid when removed

hence, it seemed that the backing had been tempered by the
high temperature used in the outgassing process. It might






86
be noted here that there was some evidence (using the natural

carbon target made by h. f. cracking) to indicate that

backings that had been outgassed in a vacuum produced targets

which exhibited greater resistance to deterioration (by

high beam currents) than targets produced from backings that

had not been outgassed. Enriched 12C targets were made using

Cu backings, but these were not used in this experiment,

These may be able to withstand higher beam currents than

those made with tantalum backings.


Cross Sections


The cross section for the 12C(a,y)160 reaction at low
alpha particle bombarding energies is necessary for an accurate

extrapolation to effective stellar energies. The Coulomb

barrier Bc for the 12C + 4e can be approximated by


Bc = Z1Zoe2/ ,
1 1

where R = 1.4 x (A13 + Ao3 ) x 10-13 cm.


The prescription gives the value 3.18 MeV for B ; hence,

below 3 MeV barrier penetration becomes increasingly important.

Tombrello has computed the effect of interference
between the 1- states at 7.12 MeV and 9.59 MeV in 160.

Using a value a2 = 0.10 for the reduced width of the 7.12 MeV
state, he has calculated the values of the capture cross







section for both constructive and destructive interference

(22), Since the signs of the amplitudes were unknown, it
was impossible to determine whether the interference was

constructive or destructive.

The values for the 12C(a,y)160 reaction cross section
obtained from the present experiment, and those computed by

Tombrello (assuming ea2 = 0.1) are plotted in figure 26.
The value obtained for the capture cross section at

Ea = 3 MeV is slightly smaller than that calculated by
Tombrello; while at Ea = 1.9 MeV it is about 1.5 times as
large as the calculated value. The results of this experi-

ment indicate that the interference is constructive and that

Oa2 is between 0.1 and 0.3,


The 12C(a,)160 Reaction Rate
at Effective Stellar Energies


The reduced alpha particle width 0a2 of the 7.12 MeV
level in 160 is essential in the determination of the
12C(a,y)160 reaction rate at stellar temperatures (see the

section on theory). This reaction rate is important in
stellar model calculations since it determines the relative
abundances of 12C and 160 and hence the further evolution of
the star.

This experiment indicates the cross section factor So
at a typical stellar temperature of 108 OK has the value


So(12C(a,y)160) = (0.65 0.32) x 103 keV barns,





88



2
,o "=--'------------------------
10






10 T
a 0.1
x CONSTRUCTIVE
o 09.59 MeV LEVEL
/$ Ad DESTRUCTIVE
S 4 FROM- TOMBRELLO
C= CALCULATED (22)
Q / /* PRESENT WORK
o0 / aREF. (11)
/ / REF (14)
b"

/y/ (-cE 12)
S/ o'/(E) u S(E) e



c = 31.28 Z ZoA 1/2

/

,01-2 I -TI l-I
2.0 2.5 3.0
E a (lab) M eV
Figure 26. The 12 16
Figure 26. The 12(ay) 0 reaction cross section values.
The solid line has been drawn through the calculated points.






89
2
using 8 = 0.2 + 0.1. Similar (using the equations derived

in the section on theory), the present experiment yields

the following value for the 12C(a,y)160 reaction rate at a

stellar temperature of 108 OKI


p (12C) = (0.84 + 0.42) x 10-20X Pf2C s-1


where Pis the density of the core in g cm-3 (-105), X is

the abundance (-1) by weight of He and f12 is the screening
C
factor (37). Although the above errors on So and p may
appear large, it should be noted that prior to this experiment,
2
0 could only be estimated to within a factor of 10 at best.

Also, it is quite probable that the errors will be further

reduced as revised fits are obtained to the measured values

of the capture cross section.

A determination of 12C + He capture cross sections

at lower bombarding energies than those employed in this

experiment would also produce a better value for the reaction

rate. Experimental procedures that could reduce the

13C(a,n)160 background would be necessary. Using-a more
highly enriched 12C target, and time-of-flight methods to

eliminate neutron background originating from the collimators

may be the most useful procedure since it appeared that same
of the neutron background resulted from the beam striking

collimators and slits on which carbon had deposited.


































APPENDIX














GAMMA RAY DETECTION EFFICIENCIES OF NaI(T1) CRYSTALS


Total Incident Intrinsic Efficieny


The "total incident" intrinsic efficiency, 7T(Ey), of

a NaI(Tl) crystal in the form of a right cylinder for gamma

rays of energy E is defined as the probability for the

detection of a gamma ray that is incident on the face of the

crystal (56, 57). This is equal to the ratio of the total

number of gamma rays detected per second to the total number

of gamma rays incident on the face of the crystal. In the

form of an equation, this is


NT
1T(E) = -
Nof

where NT is the total number of gamma rays of energy E

detected per second, No is the total number of gamma rays
of energy E emitted per second by an isotropic source, and

f is the fraction of 4v that the solid angle of the crystal

face subtends. Stated differently, f is defined by





where 9 is the solid angle subtended by the crystal.

91






92

It is evident that NT/I'o is simply the fraction of the

gamma rays detected, and f is simply the probability that a

gamma ray from an isotropic source will strike somewhere on

the face of the crystal. The geometry for the case of an

isotropic point source of gamma rays of energy E located

on the axis of a right cylinder of radius R and thickness t

is shown in figure 27.

The parameter x2(e') is the path length in the NaI(T1)

crystal. The parameter xl(e') is the path length in any

absorbing material preceding the crystal. The quantities

x2 and x1 have the following explicit dependency on e':


xl(e') = d sece', for 0 < d

R
x2(e') = t sece', for 0 e < e = arctan
t+d



x2(e') = R csce' d sece', for ei < eo = arctan -d


The intensity of the source will be attenuated by a

factor exp(- L1(E)xl(e')) in traversing the absorbing material

preceding the crystal. 1 is the total linear absorbing

coefficient for a gamma ray of energy E in the absorbing

material (58). In traversing the NaI(T1) crystal the gamma

ray intensity will be attenuated by a factor exp(- L2(E)x2(e')),

where I2(E) is the total linear absorption coefficient for

a gamma ray of energy E in NaI(T1).

N /4rT is the intensity per unit solid angle (the number





























E-4








o
r-4
0

0






4.3


4E

W4










o
'o



.4


00

C0


C-4





qU4




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A STUDY OF THE RADIATIVE CAPTURE
OF ’He BY 12C BELOW 4 MeV
By
RONALD JACK JASZCZAK
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY'
UNIVERSITY OF FLORIDA
1968

ACKNOWLEDGEMENTS
The author wishes to express his deepest and most
sincere gratitude to Dr. F. E, Dunnam. Without his direction
the experiment would have been an exhausting tell.
A special thank-you goes to Dr. J, L, Duggan for his
guidance concerning target preparation and to Dr. T. A.
Tombre11o for the use of his calculations. Thanks gc to
Dr. H, A. Van Einsvelt for his help (including the design of
the target holder) and for checking portions of the manuscript
to Dr, H. A. Blue for valuable suggestions concerning
electronics; and to Professor A, E. S. Green for his comments
on the theory section.
Acknowledgement is made to other members of the
laboratory, including K. E. Baker, R. E, Daniel, R. Stein
and especially R. C. Johns for his generous assistance
during design and construction of the acetylene cracking
apparatus.
Finally, the author expresses his gratitude to the
graduate students who assisted in the data acquisition and
to his wife for typing the manuscript.
il

table op contents
ACKNOWLEDGEMENTS . .
LIST OF TABLES
LIST OF FIGURES
INTRODUCTION
Nuclear Astrcphysical Interest ,,,,,,
Prior Results
Intent of Experiment
CHAPTER
I. THEORY ,
Nuclear Processes in Stars
Radiative Alpha Capture , . .
tive Capture of Alpha Particles
0
Angular Distributions . .
Absolute Yields . .
Radiative Width Determination .......
Nuclear Reaction Rates in Stars ......
II. EXPERIMENTAL METHOD
Energy Analyzing System
Cold Trap and Target Assembly ,
Detectors and Circuitry
Radia
by
ii
V
vi
1
1
3
6
6
16
19
20
25
27
31
36
36
37
42
ill

Background Eadiation , 49
Target Preparation ..... 50
Synthesis of Barium Carbonate 52
Synthesis of the Carbide 5^
Synthesis of Acetylene . 54
The High-Frequency Cracking of
Acetylene 55
CHAPTER
III. EXPERIMENTAL RESULTS 60
Excitation Functions ... 62
The 9.05 MeV Level in l60 66
Cross Sections and the 9.59 MeV Level . .* . 72
IV. DISCUSSION 84
Resonances ........... 84
Target Deterioration , 85
Cross Sections 86
The ^C(a,Y)^0 Reaction Rate at
Effective Stellar Energies 87
APPENDIX 90
GAMMA RAY DETECTION EFFICIENCIES OF
Nal(Tl) CRYSTALS 91
Total Incident Intrinsic Efficiency .... 91
Source Full Energy Peak Efficiency .... 97
LIST OF REFERENCES 103
BIOGRAPHICAL SKETCH 108
iv

LIST OF TABLES
1. Nuclear reactions In the proton-proton chain. . , 10
2. Attenuation coefficients, . , ..... 24
3. Radiative widths for ground state and cascade
radiations from the 9.85 MeV (2+) level in -*-60, . 70
4. Possible causes of error. ...... 71
5. Radiative width for the 0+-E> 1 (9.59 MeV)JEÜ> 0+
transition 80
■^2 ló
6. The C(afy) 0 reaction cross section 83
v

LIS? OF FIGURES
1."Smoothed” abundance curve of the elements. , . 8
2. Nuclear reactions In the helium
burning process
3. Energy levels of
4.
Theorethical angular distributions for
0+—P~> l”-Íí-> 0* and 0+—~> 2+—-> 0+
radiative transitions,
12
13
22
5, In-line cold trap assembly 39
6, Target chamber 4l
7, Nal(Tl) crystal and lead shield, ........ 43
8., Schematic electronic circuit for Nal(Tl)
detector. 45
9. Electronic pile-up elimination circuit 4?
10. Ge(Li) detector electronic circuit 48
11. Barium carbonate apparatus 53
12. Acetylene apparatus. . $6
13. High-frequency discharge apparatus 57
14. Enriched C excitation function in the
region of the Ea = 3.58 MeV resonance 6l
12
15. Excitation function for enriched C target. . . 63
16. Excitation function for natural carbon target. . 64
12
17. Excitation function for enriched C target, , . 65
vi

18. Gamma ray spectrum from Nal(Tl) detector
at Ea =3.58 HeV '. 67
19. Gamma ray spectrum from Ge(Li) detector
at Ea = 3.58 HeV 68
20. Branching ratios of 9.85 HeV level In ^0. ... 73
21. Gamma ray spectrum from Nal(Tl) detector
at Ea = 3.24 HeV for enriched -*-2C target, ... 74
22. Gamma ray spectrum at Ea = 2.95 HeV for
enriched target. . 75
23. Gamma ray spectrum at Ea = 2.95 HeV for
natural carbon target 76
24. Gamma ray spectrum at Ea = 2.95 HeV for
enriched ¿C target 77
25. Gamma ray spectrum at Ea = 2,14 HeV for
enriched -*-2C target. 78
12 l6
26. The C(a,y) 0 reaction cross section values. . 88
27. The parameters involved In the calculation
of Nal(Tl) crystal efficiencies. ... 93
28. Gamma ray spectrum from the '^C(p,y)1/+N
reaction (Ey = 9.17 MeV). 100
vll

INTRODUCTION
Nuclear Astrophyslcal Interest
12 1 ó
The ¿C(a,y) 0 reaction is of considerable interest
in nuclear astrophysics, especially in studies of stellar
nucleosynthesis and models of stellar Interiors. This
reaction occurs in the helium burning sequence and has
a direct influence on the relative abundances of oxygen
and carbon. The helium is produced from hydrogen burning
by the proton-proton and carbon-nitrogen-oxygen cycles (1, 2).
After the hydrogen is consumed by these processes, the
core is heated due to gravitational contraction and at a
8 o ,
temperature of about 10 K (corresponding to an effective
thermal energy of about 200 keV), helium burning is inlti-
12
ated. The parameters for the 3a-reactlon leading to C
are known to a fair degree of accuracy, and hence the
rates of these reactions have been determined (3).
12 ló
The ¿C(a,y) 0 reaction in the helium burning
chain is believed to proceed through the 7.12 KeV (1~)
level in ^0 which is about 40 keV below the threshold.
Very little is known about this state, especially the
reduced alpha particle width which is necessary in the
12 16
determination of the u(a,y) 0 reaction rate at stellar
1

2
2
temperatures. The reduced alpha particle width 0a in units
of the Wigner limit is defined here by 0a^ = y ^(3h^/2MR^)
o
The quantity ya is related to the partial width Ta by the
2 2 2
expression Ta = 2y^ Ap , where Ap is the penetrability. Alpha
particle model calculations (where the iO0 nucleus is assumed
to be formed by four alpha particles at the corners of a
tetrahedron) indicate that the reduced width for the 7.12 MeV
state is near unity (4); Cluster model calculations by Roth
and Wildermuth indicate a larger variation for the reduced
alpha width (5). The value of the reduced width for states
-i 2 4
obtained by assuming a + He cluster (in their ground
1 2
states) is about 0.6, If the C nucleus is in the
4.43 MeV (2+) state then the reduced width is about 0.02.
Roth and Wildermuth assign the 7.12 MeV level to the + ^He
cluster, indicating that the reduced width is nearer the
value 0.6, Since the final abundances of and ^0 will
depend critically on the ^C(a»y)^0 reaction rate (and hence
on 0a }, a more accurate determination of the reduced alpha
particle width of the 7.12 MeV level is required. It is
possible to obtain some information on 0a^ by examining the
12C(a»y)^0 reaction cross section at alpha particle bom¬
barding energies near 2 MeV, Because there were no accurate
estimates of this reduced alpha width, Delnzer and Salpeter
(6), and also Fowler and Hoyle (7)» calculated the final
12
abundance of C in the core of a helium burning star for
various assumed values of 0

3
Prior Results
i a "J
Prior results on the x¿C(a,y) 0 reaction have "been
limited to work done by Allan and Sarma (8), Bloom et al. (9),
Heads and Mclldowie (10), and Larson and Spear (11, 12). In
the preliminary work done by Allan and Sarma, alpha particles
(Ea =1,6 KeV) were used to bombard thick carbon targets
while observing the high energy gamma rays with a 5.08 cm
thick Nal(Tl) crystal. The yields were determined by comparing
the counting rates in the high energy region with the known
counting rate due to the 4.43 KeV gammas from the 9Be(a,ny)^2C
reaction. They obtained the value 3 x 10“^ barns for the
Integrated cross section at Ea = 1.6 MeV. It is now felt that
the correct cross section is much smaller than this.
Bloom et al, examined the 1" state in ^0 at 9.59 MeV.
They were investigating isotopic spin mixing of this T = 0
state, from which the ground state radiation should be inhib¬
ited. The radiative width T^ for this state was found to be
0.006 eV corresponding to |H|2(E1) = 1 x 10“^ in Welsskopf
units. From this it was concluded that there was some T = 1
mixing present.
Heads and Mclldowie studied the 2+ excited states in
1^0 at 9.85 MeV and 11.52 MeV in order to obtain the radiative
widths of these states. Using enriched ^2C targets and a
10,2 cm x 10,2 cm Nal(Tl) crystal, the values 0,02 + 0.01 and
0.9 + 0.2 eV were obtained for these radiative widths,
respectively. The state at 9,59 MeV was observed, but the
radiative width was not found for this state.

4
Larson and Spear examined the region Ea = 2,8 to 8,3 HeV
in some detail with enriched ^G targets using a 10.2 cm by
10,2 era Nal(Tl) detector. The region of interest for the
present experiment Includes principally the resonances at
Ea = 3.24 and 3.58 MeV corresponding to excited states in
1^0 at 9.59 MeV (1“) and 9.85 MeV (2+), respectively. The
radiative width for the 9.59 MeV state vras given by Larson
as 0,022 + 0.005 eV, and the value of the radiative width
for the 9.85 MeV state was 0.0059 ± 0.0006 eV. Also, the
cross section at Ea = 3.24 MeV was given as J6 nb (10~9 barns)
(11). The disagreement of Larson with the results of
Bloom et al. was explained by assuming the latter had inad¬
vertently lost data due to their background subtraction or
renormalization. Larson and Spear were in better agreement
with the expected isobaric spin impurity predicted by
Wilkinson (13). It was not possible for them to determine
the capture cross section for lower alpha particle bombarding
energies. Cascade radiation of about 7 MeV was observed
from the 9.85 MeV state; however, it was impossible to
determine whether this cascade proceeded through the 7,12 MeV
(1~) state or the 6.92 MeV (2+) state in ^&0. A width of
0.0012 + 0,0004 eV was given for this radiation, assuming an
Isotropic distribution,
A recent endeavor on the ^C(a,Y)^^0 reaction Tras
presented at the 1968 American Physical Society Meeting in
Washington by Adams et al. (14), Using time-of-flight methods
to discriminate against the neutron background, a value of

5
10 no was obtained for the capture cross section at
Ea = 2.75 MeV. Data accumulation was hindered somewhat by
low yields resulting from the detector being relatively far
from the target and by low beam currents from the tandem
accelerator employed in the experiment.
Intent of Experiment
At the time this experiment was first proposed it was
hoped that absolute cross section measurements could be
extended to an alpha particle bombarding energy below 1.5 MeV;
however, this did not prove feasible because of the extremely
"IP T
low yield from the C(a,v) 0 reaction, and the lowest
bombarding energy at which the cross section was determined
was 1.9 MeV.
Because of the discord between the results of Larson
and those of previous experimenters concerning the radiative
widths of the 9.59 MeV and 9.85 MeV excited states, it was
felt that these radiative widths should be measured. Also,
since Larson was not able to determine the state through
which the cascade radiation from the 9.85 MeV state in ^0
proceeded, it appeared desirable to examine this cascade
radiation using a 20 cnP Ge(Li) detector.

CHAPTER I
THEORY
Nuclear Processes In Stars
In search of an understanding of the origin of the
elements in the universe, many theories have been formulated.
So far the theories fall into two classes. One class assumes
that the elements were formed in a primordial state of the
universe. Two examples of this class are the non-equilibrium
theory of Alpher and Herman (15) and the poly-neutron theory
of Mayer and Teller (16). The other type proposes that stars
are the principal instrument in element formation. A
relatively complete theory of this type has been formulated
by Burbidge, Burbidge, Fowler, and Hoyle (17). Primordial
theories distribute the elements on a cosmic scale; however,
the theories imply that the distribution should be independent
of time. This is contrary to what is observed since, for
example, anomalies (such as the presence of technetium)
have been observed in certain stars. Stars may distribute
material by ejection (such as the explosion of a supernova)
which would result in a distribution of the elements on a
cosmic scale.
6

7
The theories must all be able to explain the relative
abundance distribution of the elements. Suess and Urey have
constructed a "smoothed" abundance curve by employing data
obtained from terrestrial, meteoritlc, and solar measurements
(18). It is impossible to say unequivocally that such a
curve is universal. Thus, one only attempts to explain the
origin of the material that is observed. The general
feature of the abundance curve is that it decreases exponen¬
tially from A = 1 to about A = 100 (figure 1). This is
from Burbldge et al, (17). Other principal features include
the change in slope at A = 10C, the scarcity of D, Li, Be and
B, the relatively high abundance of alpha particle nuclei
such as ^°0, ^®Ne, ^^Ti, large peaks centered at A equal to
about 85, 13^» 202, and finally the small abundance of
proton-rich heavy nuclei. Any complete theory must be able
to explain all of these features.
Burbldge, Burbidge, Fowler, and Hoyle proposed eight
processes in stars that would account for these features In
the abundance curve (17). A few modifications to the theory
have occured since the original article, and the number of
processes has increased. The processes are labeled hydrogen
burning, helium burning, carbon and oxygen burning, the alpha
process, the equilibrium process, the s-process, the r-process,
the p-process and the P-process. It will be shown that the
^C(a»Y)^0 reaction is in the helium burning chain of reac¬
tions. However, to better understand the motivation behind
this experiment it is desirable to examine the over-all

8
Figure 1. "Smoothed." abundance curve of the elements»
Burbidge et al, (17).

9
theory slightly. Also, all of the separate processes Inter¬
connect to form the complete theory. It is for these reasons
that a brief description of the individual processes will be
given.
The 7-process is introduced to explain the formation
of the elements lithium, beryllium, and boron. These elements
are rapidly reduced to helium through numerous nuclear reac¬
tions with protons in stellar interiors; thus, it appears
that they must be produced near the surfaces of magnetic
stars through spallation of carbon by highly energetic protons.
The p-process is employed to explain the existence of
certain proton-rich nuclides found in the heavy elements.
These proton-rich elements are formed by (p,y) or (y,n)
reactions on the elements along the nuclear stability line.
Hydrogen burning is the synthesis of helium from
hydrogen (table 1) (19). The alternate endings seem to
depend on the temperature of the region where the hydrogen
burning is occurring. The quantity SQ is the cross section
factor at stellar temperatures (19). The cross section
factor is directly proportional to the reaction rate which
determines abundances. The cross section factor S is
related to the cross section a by
S(E) = a(E)Eexp(31.28 Z-j_Z0A^E“^) keV barns,
where a(E) is the cross section in barns (10“^ cm^)
measured at the center-of-mass energy E in keV (17).

Table 1, Nuclear reactions In the proton-proton chain. Barnes (19)
The p-p reactions
XH + 2S —
2D + XH —
3He + \e
2 +
• D + 3 + v
3
: He + Y
4 1
-> He + 2 H
or
3*4
•'He + He
X
7Be + e”
Be + y
7
7Li + %
LI + v + y
4
2 He
or
8,
8
Be + H > B + y
8 * +
* Be + 0 + v
B —
8^ *
Be -
4
2 He
Energy release
1.19 x 2
5.49 x 2
2.38 MeV
10.98
12.86
26,22 (2$ v^-loss)
19.1 (29# iz-loss)
S (keV-barns) or ”
o
3.5 x 10
3.0 x 10
1.1 x 10‘
-22
-4
0.47
t s 120 days (solar core)
120 (nonres)
H
o
30 x io“3
T = 1.1 S
no"16
10 s
41H
He
Total = 26.73 MeV

11
Z-j_ and Z0 axe the charges of the Interacting particles In
units of proton charge, and A = A-j_A0(A]_ + A0)-1 Is the reduced
mass of the system in atomic mass units, S results after
effects due to resonances and barrier-penetration have been
eliminated In the expression for the cross section.
In stars that contain enough carbon, nitrogen, or
oxygen, helium may be produced from hydrogen through the
carbon-nitrogen-oxygen cycle. The cycle starts with radiative
proton capture on ^2C and progresses to the reaction
-^Nip.cxJ-^C. After the hydrogen in the core has been exhausted,
the core begins to contract due to gravity. As this occurs
the temperature rises from the 10? °K that was present during
the hydrogen burning process.
When the temperature Is about 10® °K the core begins
to -burn helium. The principal reactions involved are shown
in figure 2 (19). The 0+ ground state in ®Be and the 0+
state at 7.65 MeV in ^2C allow the first two reactions to
proceed at a reasonable rate. The formation of ^®0 appears
to be caused mainly by the 1" state at 7.12 MeV (figure 2 ).
This is about 40 keV below the C + ^He threshold. Using
resonance fluorescence, Swann and Metzger found the mean
lifetime of this state to be about 1.0 x 10“^ s (as corrected
from their previously obtained value), corresponding to a
radiative width of about 0.065 eV (20). The alpha particle
width for this state remained unknown. If the reaction is
due to a single resonance (as is the case for ^C(a»y)^0)
then it can be shown that the cross section factor SQ Is
»

12
( -0.094)
He4
Figure 2
process.
?.9
T- r~V/> XV*
9.61
(7 37) 0+
a __
7.65
0+
Be8'
y
4.43 ’
2+
y
e*
(7.15) 1
'
o+
J
9 59 I*
12
8.87
2*
7.12 <
!~
o .i.' i
6.14
6~C6
2
“’Ó
::p+
0
ie
a
—
Nuclear reactions in the helium burning
Barnes (19). ^

13
Figure 3. Energy levels of -^0. Laurltsen and
AJzenberg-Selove (21).

14
proportional to 92 (the reduced particle width of that state)
(17), Thus, it is evident that a determination of the
reaction rate requires a determination of that reduced width.
Figure 3 shows the energy levels of ^0 (21). It is
possible for the broad (rclü = 645 keV) 1“ level at 9.59 MeV
to Interfere with the 1" level at 7.12 ileV. This inter¬
ference will either enhance or decrease the capture cross
section in the region between these resonances, depending
on whether the interference is constructive or destructive,
respectively. If the relative sign of the amplitudes of
these states is minus, constructive Interference will occur.
If the sign is positive, destructive interference will occur.
Thus, a determination of Ga2 is possible by fitting the
observed cross section in the region Ea = 1.5 to 3 MeV to
calculated values of the cross section (for assumed values
of ea2, and computing both destructive and constructive
values), A calculation of tills type has been done by
Tombrello (22). It is therefore necessary to measure the
capture cross section in this region in order to determine
O
the reduced alpha particle width 0a . Larson has measured
the cross section at an alpha particle bombarding energy
cf 3.24 MeV, but this does not allow a determination of
the interference effects (11).
The relative abundance of ^0 to -^C will depend on
the cross section of this reaction at stellar temperatures;
thus, the necessity for a better extrapolation forms an
incentive for the present experiment. The main difficulty

15
in performing the experiment, besides the extremely low cross
section values for the -^Cia.Y)"00 reaction, is the relatively
large cross section (20-100 mb) for the 13c(a,n)1^0 reaction,
since Nal(Tl) detectors are quite sensitive to neutrons.
After the helium has burned, the core again contracts,
and the stars will begin burning the carbon and oxygen.
p Q
In tills way nuclides up to Si may be formed.
As the temperature rises (2 x 10^ °K) photodisintegra¬
tion occurs producing alpha particles, protons, and neutrons.
Since the thresholds for (y,p) and (y,n) processes on nuclei
with A = 2Z = 2N are higher than for other nuclei, there
tends to be an Increase in abundance for nuclides with
A = 2Z = 2N, These give the appearance of being composed
of alpha particles. This is known as the alpha process.
As the temperature rises to about 4 x 10^ °K, many
nuclear reactions are occuring so rapidly that a statis¬
tical equilibrium is created. This is known as the e-process.
Since electron capture can occur quickly at this tempera¬
ture, there is a shift to nuclei that have N slightly larger
than Z in the vicinity of the "iron peak."
The terms "r-and s-processes" refer to rapid and
slow neutron capture, respectively. The s-process is the
capture of neutrons such that there is enough time between
captures to permit beta decay. The necessary neutrons for
the s-process are produced by (a,n) reactions on nuclei such

16
1 ^ 21
as JC and. Ne, Since certain elements beyond bismuth have
decay times that are short compared to the characteristic
time for the s-process, the elements heavier than bismuth
could not be produced by the s-process. But neutron capture
at a rapid rate (the r-process) could produce the heavy elements
such as uranium, etc. Since the cross section in the
r-process and s-process are small at neutron magic numbers,
the abundances are large at these points. The r-process
produces the peaks in the abundances curve at lower values of
A than the s-process, of course, since the r-process occurs
to the neutron rich side of the stability (N = Z) line; thus,
the formation of the double peaks observed in the abundance
curve may be explained by these processes.
As the iron-group nuclei increase, the star again
contracts and the core implodes; however, nuclear reactions
are still occurring in the outer part of the star. This
implosion creates the supernova. This also produces a rapid
Increase in temperature, causing an emission of a large
part of the star; furthermore, neutrons are produced profusely
and are thus convenient for the execution of the r-process.
In this way evolution of the star Is completed.
Radiative Alpha Capture
Radiative alpha capture has often been employed for
determining detailed Information (such as the energy, spin,
parity, etc.) on excited states of nuclei (23» 24). These

17
parameters (along with others such as radiative widths,
branching rauios of gamma rays, mixing parameters, etc.)
are required in comparing nuclear models and extending
their usefulness. The alpha particle capture reaction is
different from proton capture in that the alpha particle
is spiniess; thus, there is a simplification in angular
correlation meaurements. If the target nucleus is also spin-
less, as is the case for even-even nuclei such as -^0, a
further simplification occurs. In this case only the relative
motion of the interacting particles may contribute to the
spin of the compound state. This requires that the possible
values of spin (J) are limited to J = 1, 2, 3* • • •
These are simply the eigenvalues (f) of the orbital angular
momentum operator. The concept of parity is determined by
the behavior of the wave function for the system upon
reflection of spatial coordinates (25). If* upon this reflec¬
tion the spatial part of the wave function does not undergo
a sign change, the parity (tt) is even ( + ). If the sign
changes, the parity is odd (-). Furthermore, it is known
that the parity is determined by the orbital angular
momentum eigenvalue (7). If Í is even (0, 2, 4, . , .),
than the sign of the wave function will not change upon
spatial reflection, and the parity will be even (+), If
l is odd (1, 3» • • •)» the sign will change, and the
parity will be odd (-), Hence, in cases where the pro¬
jectile and target are both spinless, the spin (J) and
parity (rr) of the states that can be excited are limited

18
to J™ = 0+, 1“, 2+, 3”. . . . These are the so-called
states of "natural" parity.
For this experiment the concept of the compound
nucleus is also useful (25). Here the incident particle is
captured and a compound system is formed, with the energy
shared among all the particles of the compound system, A
relatively long time elapses before sufficient energy is
concentrated onto a particle to allow it to escape. This
time is long compared to the "characteristic nuclear time,"
which is the time required for the incident particle to
traverse the target nucleus without interacting. Since the
decay time is long compared the the "characteristic time,"
the compound nucleus "forgets" its method of formation. If
there is sufficient energy, the compound nucleus can decay
through particle emission in addition to gamma emission.
The states excited in this way are called virtual states.
If there is not sufficient energy to allow particle emission,
the compound nucleus can decay by gamma emission or by
internal conversion. In any case conservation laws are
obeyed.
In gamma ray emission, the angular momentum of the
gamma ray for the ground state transition must be equal to
the angular momentum of the compound system, which is equal
to the orbital angular momentum in the particular case where
the spin of the Interacting particles is zero, A light
quantum has an angular momentum equal to + 1)^. The
maximum projection is Stfi. The multipole order of radiation

19
o
is 2 ; thus, for example In the case where the interacting
particles arc spinless, p-wave capture will result in
electric dipole radiation for the ground state transition.
Since the radiation is transverse, there cannot be an Í = 0
multipole. This is the reason that 0+ > 0+ radiative
transitions are strictly forbidden.
Radiative Capture of Alpha Particles by ~^0
The two resonance levels in ^0 that can be reached
by the present experiment are the 2+ level at 9.85 MeV and
the 1” level at about 9.59 MeV (figure 3). These occur at
incident alpha particle energies of 3-58 and 3.24 MeV,
respectively.
The level at 9.85 MeV has a total width Tcm of 0.75 keV
(26, 27). This narrow resonance proved quite useful for
determining the target thickness. The thickness of the
target is essential in the determination of cross sections
and radiative widths. Also, because of the large cross
section for the 'L^C(a,n)^^0 reaction immediately preceding
this resonance, the C enrichment was indicated through a
comparison of the excitation function for a natural carbon
target with that from an enriched target.
Unfortunately a broad peak due to the ^^C(a,n)^^0
reaction is located in the same alpha particle energy region
as the 9.59 MeV peak (28). This makes the gamma radiation
from the 9.59 MeV level extremely difficult to observe.

20
The 9.59 MeV level Is a broad, resonance having a total
width rcm of 645 keV (26). Hence, the peak extends over a
considerable energy region, but the determination of the
off-resonance yield is hampered by the sensitivity of the
Nal(Tl) spectrometer to neutrons originating in the
~3c(a,n)-^0 reaction.
Below about Ea = 2.9 MeV the main process is nonresc-
nant capture. Here the cross section for the '^C(a,y)'^0
reaction is extremely small (<10 nb) , while the ^°C(a,n)^0
reaction remains relatively large (~-20-l00 mb). Thus, it is
even more difficult to determine the nonresonant reaction
cross section at the lower energies. Around Ea = 2.0 MeV
Interference effects between the 7.12 MeV and the 9.59 MeV 1“
states in ^0 become Important. The cross section will be
increased or decreased depending on whether this Interference
is constructive or destructive. The magnitude of this effect
is dependent upon the parameters of the states involved.
Tombrello has calculated this effect assuming 0 ^ = 0.1}
however, without knowing the relative sign of the amplitudes
it is impossible to determine whether this effect is con¬
structive of destructive (22),
Angular Distributions
In the appendix the efficiency of the Nal(Tl) crystal
is derived assuming an isotropic distribution of gamma
radiation. It is necessary to determine the effects of an

21
anisotropic distribution on these results. Gamma radiation
resulting from transitions between natural states, i.e.
0+, 1“, 2+, . . , will have an angular distribution given
by Vi(e) = anPn(cose), where Pn(cos0) is the nth order Legendre
polynomial, and 6 is the angle between the emitted photon and
the Incident particle. Since the ground state of xo0 is 0 ,
the observation of radiation y0 to the ground state resulting
from the capture of an alpha particle in most cases Indicates
that the spin and parity of the resonance state is either 1“
or 2+. J = 0 would not decay to the 0+ ground state, and
J = 2 is more likely to decay to higher excited states which
would then decay to the ground state in in particular,
for 0+_l> 2+ E2 ^ 0+ and 0+ ^ ^ 1" ^1 ^ 0+ transitions the
theoretical angular distributions will be of the form
tf(e) - Sin2e -l-P2(cose) (Jn=l“)
W(0) ~sln226 ^l+(5/7)P2(cose)-(12/7)P4(cose) (J"=2+).
From figure 4 it can be seen that these distributions are
entirely distinguishable. The simplicity of these distri¬
butions results from the fact that there can be no radiation
mixing, channel spin mixing, or orbital angular momentum
mixing for these transitions. However, the distribution
resulting from the transition between the 2+ states at
9.85 MeV and 6.92 MeV in ^0 (0+ ^ 2+ K1E2 2+) is
complicated by the fact that Ml - E2 radiation mixing is
possible. In this case it is possible to obtain from the

22
Figure 4. Theorethical angular distributions for
0+—L» rJÜ* 0+ and o -Í* 2+-l^ 0+ radiative
transitions

23
angular distribution the value of the mixing parameter X,
where X = S(S2)/S(M1), 3(S2) and S(M1) are the amplitudes of
the S2 and Ml transition probabilities, respectively (29).
In determining the total yield (and therefore radiative
widths, cross sections, and branching ratios) it is essential
to have a knowledge of the angular distribution of the gamma
radiation. If a measurement is taken at only a single angle,
then an accurate determination of the yield can be obtained
only with the aid of a prior knowledge of the angular distri¬
bution, unless the detector is so close to the target that
the distribution appears isotropic.
The observed angular distribution W^gíO) then
"smoothed" by the large solid angle subtended by the detector.
This means that the larger the solid angle subtended (the
larger the detector or the nearer the detector to the target),
the smaller the angular variations will be. In other words,
the observed angular distribution will have a decreased
dependency on higher order Legendre polynomials. wobs^0^
has the form
Wobs(9) — an^n^n^cos®)» |^n|^
The coefficents bn are the attenuation coefficients described
by Rose (30). They are given by bn = Jn/JQ. where Jn is the
nth order integral defined in the appendix. These integrals
v/ere evaluated numerically through the use of a subprogram
(forming a part of a program that determines angular cor¬
relation parameters) (31) (table 2). In general, the values

Table 2
Attenuation coefficients.
Target detector
distance (cm)
ey
(MeV)
Jo
J2
J4
J6
b2
°4
b6
5.08
10
0.1753
0.1149
0.0317
-0.0091
0.6553
0.1806
-0.0519
5.08
7
0.1712
0.1125
0.0314
-0.0085
O.6569
0.1837
-0.0499
0.50
9
0.5371
0.0865
-O.0223
0.0138
0.1610
-0.0415
0.0257

25
of Jn and bn decrease rapidly with increasing n for large
solid angles. It is obvious that the proximity of the detector
to the target determines how rapidly the bn approach zero
with increasing n. If the detector is very close to the
target, the observed distribution will be quite independent
of higher order terms.
Absolute Yields
The absolute total yield of a nuclear reaction is
defined here as the number of disintegrations per Incident
particle. In the following discussion the notation adheres
to that used in the appendix. The yield may be related to
N0bs(8) (the number of counts In the spectrum peak observed
at the laboratory angle 6 per Incident particle, corrected
for background and dead-time) by employing the ideas derived
above and in the appendix. The number of counts in the
peak (here defined as the region (Ex - 1.02 KeV) to 1.1EX)
at angle e per steradian per incident particle, is given by
•^obsi 9 )/*hr = 4p x (Y/4tt) ^obs(®)/^o»
where »7p = B»?t = fUff/pO = R(J0/2)
B = peak-to-total ratio
f = £2/4tt

26
solid angle subtended by detector
*7^ = source full energy peak efficiency
nt = source intrinsic efficiency
T?rp -- source incident intrinsic efficiency
JQ = the zeroth-order Integral as defined in the
appendix.
The absolute total yield is denoted by Y; hence, Y/4rr is the
average yield per steradian. Thus, from the above equation,
it is seen that the yield is
I = Nobs(e)(H(Jo/2) * S(an/a0)(Jn/J0)Pn(cose))-1.
The expression Nobg(e)/4rr may be defined as the "ob¬
served differential" yield and denoted by nobs(e). Similarly,
the expression U(0)/4rr may be defined as the actual differ¬
ential yield and set equal to n(0). Using the expression
derived for the yield it is easy to show that the relation
between n(e) and nobs(e) is
n(e) =
nobs(®>
(an/a0)Pn
x
B(Jq/2)
^(an/ao)(n

27
Radiative Width Determination
For a resonant radiative capture reaction the cross
section a is assumed to depend on the energy according to
the single-level dispersion formula (25). Explicitly for an
(a.y) reaction this has the form
a =
ttX ojTy Ta
(E - ER)2+ r2/^
where a> =
statistical weight = (2J + 1)/((2I + i)(2S + 1))
J =
total angular momentum of system (spin of state)
I =
•
spin of target nucleus
S =
spin of incident particle
r =
total width of resonance
rY
= radiative width
r =
■‘a
particle width
X =
h(2mE)“- = wavelenght of interacting particles
m =
reduced mass of system = UaAT/(Aa + AT))1.66xl0~24g
A :
a
= incident particle mass (atomic mass units)

28
A£ = target mass (atomic mass units)
E = center-of-mass energy = (Ai'/(Aa + A^)) x Sia-b
Elab - incident particle energy in laboratory.
At resonance, a is given by
aH = tt x2íü ra ry/( r2/4).
Hence, a may be expressed in the form
oB( r2/4)
(J = X •
(e - eh)2 + rv^
The relation between the yield and the cross section, assuming
the Breit-Wigner formula is applicable, has often been cited
in the literature (32, 33* 3^* 35). The relation is given by
rE
Y = (o/£)dE,
E-6
where 6 is the target thickness in energy units and
£ Is the stopping cross section for the incident
particle per dislntegrable nucleus in the target
material

29
The relationship between £ and the stopping power is
£ = l/n(dE/dx) ,
where -(dE/dx) = the stopping power of the target material
n = gpN^M”^ = number of disintegrable nuclei per cm^ of
target nuclei
p = the density of target material in grams per cm^
Na = Avogadro's number
M = the molecular mass of target material
g = the fraction of disintegrable nuclei in target
material.
If it is assumed that 6 and £ are independent of E over the
resonance, then 6 = (dE/dx)t = n£t, where t is the target
thickness in centimeters. The integral for Y may now be
evaluated analytically. The result is
Y = 2TT*2a>rqry
£ r
(e-er)
arctan
r/2
r/2 J’
X
arctan

30
or Y =.
arctan - arctan
(E-Er-6)
2£
r/2
r/2
It can be shown that this expression has an observed width
T' given by
Thus, the thickness of the target tends to broaden the
observed width. When the target thickness is determined
(as is often the case) by examining the excitation function
across a narrow resonance, errors enter through such factors
as accelerator instability, energy-defining slits, etc. The
final observed width will thus be the square root of the
sums of the squares of all of these contributions. It is
evident from the above expression for the yield that a
maximum occurs at the energy E = ER + 6/2; thus, the observed
resonance energy is shifted to the higher energy side by
approximately 6/2. This is only approximate because in the
derivation it v/as assumed that the parameters in the formula
for the cross section were independent of energy over the
energy integration. This shift in resonance energy is one
of the reasons why it is very desirable to have an extremely
thin target for resonance spectroscopy measurements; however,
there are situations where it may be more desirable to have
a thick target (for example, to increase data aquisition rate).
The maximum yield is given by
Ymax = r/£)arctan(6/ r)

31
In terms of measured quantities the resonance cross section
gr has the form
£ ^max(9)
cth = x .
arctan(6/r) R(JQ/2) (an/aQ)(Jn/JQ)Pn(cose)
where e) Is the maximum counts observed in the peak
at the laboratory angle 6. Using the expression relating
or with the radiative width Ty, it can be shown that ry is
given by
£ r kTmax (® 5
Fy = x ,
4tt £bi raarctan(6/r) R(J0/2) (an/aQ)(Jn/J0)Pn(cose)
This is the expression that was used to obtain the radiative
widths from the observed counting rates. For off-resonance
cross section measurements, a and £ are assumed constant in
the integral over the energy interval (E - 5) to E.
Nuclear Reaction Rates in Stars
At a temperature T the number of collisions (coll cm“3s“l)
between nuclei of types 0 and 1, having a center-of-mass
energy between E and E + dE is proportional to
n0niE-2eXp(-E/kT)dE, where ng and nj are the number densities
of particles 0 and 1, respectively. The mean reaction rate
(reactions per cubic centimeter per second) of a thermonuclear
process is thus proportional to the integral (36)

32
r i
In n-LE^expí-E/kTjPÍEjSÍEjcLE:,
Jo 0
where E Is the center-of-mass energy, E^exp(-E/kT) is the
Boltzmann factor (probability for the Interaction energy E),
P(E) is the barrier penetration factor, and S(E) is the
cross section factor (defined previously in section 1), The
quantity S is a slowly varying function of the energy E for
off-resonant reactions. It can be shown that the product
of exp(-E/kT) and P(E) has a fairly strong maximum centered
at an energy E0 given by.
E0 = 26.29(Z12Z02ATq2)* keV,
where Z-j_ = charge (in units of proton charge) of interacting
particle 1
ZQ = charge of particle 0
A = A]A0/(Aq + A0) = reduced atomic mass number of
interacting particles
Tq= stellar temperature in units of 10® °K,
The quantity EQ is the effective thermal energy used by
Burbldge et al, (17). For reactions such as those normally
found in the helium burning process, the effective thermal
energy is much larger than the mean kinetic energy.

33
This means that the region of interest occurs in the high
energy tail of the Naxwell-Boltzmann distribution of velocities.
The number densities n0 and nq are related to the
abundances XQ and Xq, expressed as the fractional amounts
(by weight) of the interacting nuclei*
ni = NAxi p/Ai•
where is Avogadro's number, p is the density in g cm”3f and
Ai is the atomic mass number of species i. The mean reaction
rate Pq(0) per nucleus of type 0 (expressed in terms of SQ)
for the interaction with nuclei of type 1 is explicitely
given by
Pl(0) = l/x^O) = 3.63 x I07sof(
lZo
PX1
e ,
An
where 0 = 9. 15(Zq2Z02A/Tg)* .
The quantity in the above expression is the mean
lifetime (seconds) cf the nuclei of type 0 for interaction
with nuclei of species 1. The quantity f is the correction
due to electron screening of the bare nuclei as explained
by Salpeter (37). This is a result of the spherical
polarization of the electron gas immediately surrounding
the bare nucleus.
If the reaction rate is due principally to a single
resonance at Er (not in the range of the effective thermal
energy), then an expression for SQ can be obtained by using

34
the Breit-l/igner single level formula for o. The result
is (1?)
03 ^2ER
(Eo ” Er)2 + f2/4
where 8]_ = reduced particle width
*
z = 2(Bc/E£)2
2
B^ = Coulomb barrier height = 2-j_ZQe /R
ER = h2/2MR2
+ 1^ is the mcKiified- Bessel function of order
2/ + 1.
The quantity is the function of z defined by Burbidge
et al. (17). Values for the modified Bessel function have
12 16
been tabulated (38). For the C(a»y) 0 reaction (assuming
the 1” state at 7.12 MeV in ^0) the expression for SQ is
1.17 x 105 ea2(7.12)
S0 = keV barns,
(5T8 t + l)2
where the following values have been usedt
Tz/k « (E0 - Er)2
r2 = ry = 0.065 ev

35
Er ^ 40 keV
Eq =r 200 Tg T.
The reaction rate is given by
pa(12c) = (to(120))-1
l.69 X 1012xaeg2f12e P
Tg 'í (5Tgi + l)2
exp(-69.2
T8't)

CHAPTER II
EXPERIMENTAL METHOD
Energy Analyzing System
Singly charged helium ions at energies up to 4 MeV
viere available from the University of Florida Van de Graaff
accelerator. Beam currents for the present experiment viere
between 1.5 and 3 /¿A. Some preliminary experiments were
carried out using beam currents in the range of 4-7 //A;
however, the rate of target deterioration was Intolerable
with these currents. The singly ionized ^He beam was
deflected through a 90° arc by the use of a momentum analyz¬
ing magnet (of radius 45.72 cm). The magnetic field B
determined the energy of the He+ beam traversing the slit
system of the analyzer. This magnetic field was determined
by the usual nuclear magnetic resonance (NMR) methods (23» 39).
The NMR fluxmeter (Varian Model F-8A) was supplied by
Varian Associates of Palo Alto, California. Its upper limit
of measurement is 52 kG. This easily surpasses the upper
limit requirements of 12.6 kG for 4 MeV alpha particles.
The NMR unit was calibrated using the 2.4374 MeV and
o/. 28
3.1998 MeV resonances in the Mg(a,y) Si reaction (40, 4l),
36

37
7 7
The calibration has also been examined using the Li(p,n) Be
threshold at 1.8807 heV. The calibrations were accurate to
within 1 keV (¡12). A Fortran program for tabulating NMH
frequencies versus alpha particle energies in 5 keV intervals
was employed in this experiment (39). Energy variations
due to the finite apertures of slits introduces some error
into the determination of alpha particle energies. It was
assumed that this error was +0.2 per cent. The magnitude
of the error is not Important for off-resonance yields
(since thick targets were used) and enters mainly through
the determination of the target thickness using the 9.85 MeV
level in "^0, Current Integration was accomplished through
the use of an Elcor current integrator (Model A309B) (calibrated
for an accuracy of 1 per cent or better). The target was
cooled with "refrigerated" water that was demineralized,
thereby minimizing the possibility of current leakage to
ground. This precaution appeared desirable due to the high
mineral content of the water normally supplied to the
laboratory.
Cold Trap and Target Assembly
Initial experiments with natural carbon targets
were performed In order to test target preparation tech-
12
ñiques. Data were also later compared with enriched C
spectra. The initial target chamber was a 9.1 cm inside
diameter (I. D.) glass "T,"
separated from the main vacuum

system by an in-line liquid nitrogen cold trap. This
apparatus has already been described in some detail by
Bruton (39). It essentially consisted of a holder (cooled
by water) with accommodations for 3 targets plus a quartz
viewer. It was possible to slide the holder (on Viton 0-rlngs)
in a vertical direction (permitting the positioning of targets
without opening the system to atmospheric pressure). Pressures
were around 10~^ torr on the oil diffusion pump side of the
in-line cold trap. "Teflon" gaskets were used throughout
except on the target holder and in-line cold traps, where
Viton 0-rings were employed. Carbon deposition from organic
vapors was not apparent with this system, but several improve¬
ments were devised to insure better results with the enriched
12C targets.
The Improved in-line cold trap (designed by Dr, F, E,
Dunnam and Dr, H. A, Van Rlnsvelt) had several features
which would minimize contamination of the target region by
organic vapors (figure 5). This consisted of an in-line
liquid nitrogen cold trap from Sulfrian Cryogenics, Inc.
(Model 338-1), to which a collimating system and a 36 cm
long polished copper tube have been added. The collimator
holders were mounted on the Inside of copper couplers that
connected the cold trap to the vacuum system. Except for
the Viton O-rlngs on the in-line cold trap the vacuum
gaskets for the beam transport system were of indium, which
is inherently free of organic contamination. The long
copper tube (2,8 cm outside diameter) was in good thermal

Figure 5. In-line cold trap assembly.

contact with the flanges on the cold trap. The collimating
system consisted of three 20 mil Ta discs, one on the diffusion
pump side of the cold trap and two on the target side. The
initial collimating aperture was 0,5 cm in diameter, followed
by 0.4 cm and 0,3 cm apertures on the target end. This system
made it impossible for the beam to strike the long copper
tube; furthermore, the maximum diameter beam spot on the
target was limited to about 0.3 cm by the collimators.
The target holder was designed by Dr, H, A. Van Rinsvelt
and is based on one used at Utrecht (figure 6), "Refrigerated"
Ttfater flowing between the outer and inner copper cylinders
cooled the copper endplate (0.02 cm thick) which then cooled
the target backing by conduction. The endplate was at 55°
with the beam axis. The outer cylinder was 4.8 cm in
diameter, the inner was 2.15 cm. A Ta insert fitted into
the inner copper sleeve. This insert had a circular hole
in one end that was slightly smaller in diameter (1,77 cm)
than the target backing. Extremely thin Ta fittings on this
end held the target in position. This insert (and therefore
the target backing) was pressed against the copper endplate
by tightening the bushing (lined with Ta on the beam side).
A greaseless Viton 0-ring sealed the target holder to the
glass reducer. An annulus of thin "Teflon" was placed
between the glass and the inner surface of the flange. This
limited the flow of any organic vapors (originating from the
Viton C-rlng) into the target region. The cold tra.p and
target holder assembly have the following characteristics:

IN
Figure 6. Target chamber. The letters in the figure correspond to the
following: (a) outer copper cylinder, (b) inner copper cylinder,
(c) tantalum Insert, (d) target and backing, (e) tantalum-faced bushing,
(f) "Teflon" annulus, (g) oopper endplate, (h) "Pyrex" reducer and
(i) Viton O-ring.

w¿
a) The beam traverses a relatively long path through
an effective cold trap before reaching the target
chamber.
b) The target holder is easily and quickly removed
from the system.
c) The ta.rget backings are effectively cooled to
insure maximum target life with relatively
large beam currents.
d) The detector may be located close to the target
in taking excitation runs (about 0,1 cm).
e) It is possible to outgas the interior of the target
chamber by heating the surfaces prior to the
performing of an experiment.
This assembly effectively minimized carbon deposition on the
target. Fressures on the diffusion pump side were typically
2--4 x lO”"'7 torr. The enriched data were acquired with
this apparatus.
Detectors and Circuitry
The Nal(Tl) crystal (12.7 cm x 12.7 cm) was enclosed
in a 28 cm diameter lead shield in order to minimize room
background (figure 7). This was mounted on a table that
allowed the detector to be rotated about the target in a
horizontal plane. When the Ge(Li) and Nal(Tl) detectors
were used simultaneously this rotation was not allowed. In
this case the detectors were set at fixed angles of 55°
with the beam axis.
The detector used for most of the measurements was
a 12,7 cm x 12,7 cm Nal(Tl) crystal mounted on an RCA-8055
photomultiplier tube. A 20,1 cm^ Ge(Li) detector (Ortec

43
FíStjt
e ?.
ÃœzI(Tl)
crystal
and
lead ^ieia.

44
Model 8101-20) was used in determining the 7 MeV cascade
radiation. The resolution of the Nal(Tl) spectrometer was
12 per cent for the 1.33 MeV gamma rays from ^°Co. For this
experiment, resolution is defined as the full width (in MeV)
at half-maximum divided by the energy (in MeV) of the peak
position. The Ge(Li) detector had a resolution of 0.5 per
cent for this gamma ray.
The Nal(Tl) spectra were measured with a Nuclear
Data 512 channel pulse height analyzer (Series 130) (figure 8).
The signal from the photomultiplier went through a pre¬
amplifier and then to an Ortec Selectable Active Filter
Amplifier (Model 440). The first two single channel analyzers
(Ortec Model 413) were set to sum over the 9 MeV and 7 MeV
radiation. The third single channel analyzer was used
(in* conjunction with the gate generator (Ortec Model 406)
and the linear gate (Ortec Model 409)) to eliminate the
lower portion of the spectrum. In this way dead time
corrections (from the multi-channel analyzer) to the spectra
were less than two per cent, A pulse stretcher (inserted
after the linear gate) was employed on some of the runs.
The calibration and linearity of the analyzer was checked
often during the experiment using a pulser and several
known gamma rays. The following gamma rays viere employed
for this purpose»
a) 0.662 MeV photopeak from
b) 1.17 and 1.13 MeV photopeaks from
c) 2.50 MeV sum peak from ^CO

Figure 8. Schematic electronic circuit for Nal(Tl) detector

46
Q ft
d) 2.75 HeV photopeak from “Na
e) 2.225 and 4.432 HeV peaks from a Pu-Bs neutron
source and Its paraffin shield
f) 8.66 HeV (9.17 MeV-e) escape peale from the
13 14
C(p,y) IT reaction
g) 9.3^ HeV (9.85 HeV-e) escape peak from the
12 16
C(a,y) 0 reaction.
The base of the photomultiplier tube tras modified to
obtain a fast signal (from a circuit obtained from Dr. B, A.
Blue). A negative fast signal (rise time of about 40 ns)
teas obtained from the anode of the 8055 tube. The slow
signal was taken from dynode 9 and therefore was positive.
The purpose of the fast signal was to eliminate electronic
pile-up problems using an EG & G Pile-Up Gate (ITodel GP100).
The fast circuit components (all EG & G) were set-up to
eliminate all pulses coming within 2 (is of one another
(figure 9). Although this circuit was employed for most
of the measurements, the count-rate was small, and thus this
circuit was not essential for the execution of this experiment.
The signal from the Ortec Ge(Li) detector (20.1 cm^
active volume) went into its matched Crtec Hodel 118A preamp¬
lifier. The signal was then amplified by an Grtec Selectable
Active Filter Amplifier (Hodel 440) and processed by 1024
channels of a Technical Measurement Corporation 4096 channel
analyzer (figure 10). In addition to the calibration points
used for the Nal(Tl) spectrometer the Ge(Li) spectrometer was
also calibrated using the second escape peaks of gamma rays

TOTAL
COUNTS
1 O ns
1/2 PILE-UP ALLOWED
COUNTS COUNTS
-p-
-o
Figure 9. Electronic pile-up elimination circuit

00
Figure 10. Ge(Li) detector electronic circuit

from the reaction 2^Mg(a.iY)2^si* The following gamma rays
were observed:
11.72 HeV (12.74 MeV(y0)-2e)
9.95 KeV (10.97 MeV(Yl)-2e).
The ADC of the 1024 channel analyzer was not linear for
the larger pulses; however, it did appear to be linear up
to at least 10 MeV. Another problem was a slight drift with
time in the gain of the ADC of the analyzer. This resulted
in a slight broadening of peaks in the spectra obtained from
long runs. The results should still be valid, even though
these problems were present.
Background Radiation
Although there are obvious advantages in using the
spinless alpha particle as the projectile, there still
exists an Important disadvantage. This disadvantage is
the prolific neutron background produced by the bombardment
of 1^C by alpha particles. The carbon is usually in the
form of organic deposits on the vacuum system, walls, on
slits, on collimators, and on the target Itself, Neutrons
produced by the -1-^C(a»n)'1'^0 reaction are captured by the
Nal(Tl) crystal, resulting in an exponentially decreasing
background spectrum extending to about Ey = 9 MeV. The
neutron background from the Nal(Tl) detector results from
the radiative capture (by such reactions as ^Na( n, y) ^Na
and -*-2?I(n,Y)'''2^I) in the crystal (1). This is probably

50
the principal difficulty in performing an (a.y) experiment
using a Nal(Tl) detector. The cross section for the + a
reaction in the region Ea = 2 to 5 KeV ranges between 20 and
100 mb (43, 44, 45, 46, 47, 48, 28). This is indeed an
extremely large cross section compared to the + 4^
capture cross section, and it was thus necessary to avoid
-^c contamination. Methods employed included the preparation
of enriched 99.4 per cent) -^C targets and minimizing
natural carbon contamination of the system.
Room background is also a problem. For resonance
measurements the room background was not too Importanti
however, when off-resonant values were obtained, it increased
in significance. Shielding the detector or using an anti-
coincidence annulus will minimize this source of background
(49*) o A plastic anti-coincidence annulus surrounding a
12,7 cm x 12,7 cm Nal(Tl) detector had been constructed at
this laboratory by D. R. Wulfinghoff, but was not operational
when this experiment was performed. Lead shielding was
provided for the detector, and it was felt that room back¬
ground did not negate the results of this experiment.
Target Preparation
Gamma rays experience little attenuation in passing
through matter; therefore, self-supported targets are unneces¬
sary in gamma spectroscopy. This is a considerable advantage
in target preparation and handling. However, because of the

51
prolific neutron background resulting from the ^-3c(a,n)-^0
reaction it was necessary to make targets enriched in
12C. The cost of enriched 12C isotope limits the total amount
available; thus, methods of preparation were desired which
would require a very small quantity (of the order of 10-20 mg)
of enriched 1-C Isotope. Two methods were investigated.
These were the thermal decomposition and gaseous (high-
frequency) discharge methods. In the thermal decomposition
process (50, 5D the target backing (10 mil Ta) is heated by
a flow of current through it. When the foil has heated and
the pressure reaches a steady value of about 5 x 10“^ torr,
the system is Isolated and methyl iodide (GH^I), or acety¬
lene (C2H2), is allowed to enter the system until the pres¬
sure is about 50 torr. The carbon forms as a thin, uniform
film on the Ta backing. The thickness of the film Is a
function of the decomposition time and CH^I (C2H2) pressure.
The temperature of decomposition Is quite different for the
two gases. The methyl iodide cracks readily when the foil
is heated to a very dull red, while the acetylene requires
a bright yellow glow of the foil to crack properly. The
latter high temperature causes the Ta backing to become
brittle, and the carbon film tends to peel from the backing
unless handled carefully. Targets thus could be prepared
using acetylene, but extreme caution had to be observed.
Targets could be easily prepared with the methyl iodide by
this method, and many of these (along with a few prepared
from thermally cracked acetylene) were used in preliminary
experiments on natural carbon.

52
It later became apparent that acetylene would be
easier to synthesize than methyl iodide (52). The gaseous
discharge method allows the efficient use of acetylene in
carbon target preparation (53). This method vías finally
chosen in preparing the enriched ^-2C targets and, for this
reason, will be discussed in detail. Kany of the techniques
Involved (such as the preparation of carbides, the synthesis
of acetylene and the high-frequency discharge method) were
suggested by Dr. J. L. Duggan of Oak Ridge National Labora¬
tory during a visit (supported by Oak Ridge Associated
Universities, Inc.) to the laboratory by the author.
The target preparation method is conveniently
subdivided into four separate steps which may be labeled:
1) synthesis of barium carbonate (BaCO^)
2) synthesis of the carbide
3) synthesis of acetylene
4) and the cracking of acetylene onto the target
backing.
Synthesis of Barium Carbonate
The enriched 12C (99.94 per cent) used in the prepara
tion of the targets vías obtained from Oak Ridge National
Laboratory in the form of graphite. The apparatus involved
in the production of BaCO^ from elemental carbon Is shown
in figure 11. This mainly consists of a quartz combustion
tube coupled to a fretted glass bubbling tube. The carbon
(about 20 mg) Is contained in an Al-foil capsule placed in

53
o
o
O
o
Ba(OH)
Figure 11. Barium carbonate apparatus

the "plugged Teflon" stopcock at the top of the system.
Ta wire mesh in the center of the combustion tube holds
the A1 capsule after it is released from the stopcock.
Oxygen flows into the system through the glass "T." The
carbon is heated forming CO2 that then reacts readily with
the Ba(0K)2 contained in the test tube at the bottom of
the apparatus. The barium carbonate is formed as a white
precipitate in this test tube. This is then recovered by
vacuum filtration and dried. The efficiency (by weight)
of this process was typically greater than 70 per cent.
Synthesis of the Carbide
The carbide is prepared by placing equal amounts by
volume of the barium carbonate and clean calcium filings In
a small quartz test tube. Glass wool is positioned above
the mixture in order to confine the contents during the
reaction. The quartz tube (containing the BaCO^-Ca mixture)
is connected to a vacuum pump and heated slightly with a
Bunsen burner. The system is then isolated and heated
vigorously with an oxygen-acetylene flame. The carbide
forms a black deposit inside the quartz test tube.
Synthesis of Acetylene
Acetylene is produced by the addition of water to
the carbide (5*0. This process is carried out employing

55
the apparatus shewn in figure 12. This consisted of a
water reservoir (upper beaker), a reaction chamber and a series
of cold traps. The first two cold traps (A and B) were
alcohol-dry ice traps. The purpose of these traps Í3
to limit the flow of water vapor from the reaction chamber.
Acetylene (subliming at -83°C) would not be removed by these
traps (having a temperature of -?8°C); however, it would be
quickly recovered by trap C (a liquid nitrogen trap at about
-196°C) (55). The final liquid nitrogen trap D served to
limit the possibility of contamination from the vacuum pump.
The procedure consists of breaking the quartz tube
containing the carbide (obtained from the previous process)
and immediately placing the pieces in the reaction chamber
which is then evacuated and isolated from the vacuum pump
by closing the stopcock farthest from the reaction chamber.
Distilled water is then allowed to enter the reaction
chamber. Acetylene is rapidly produced and captured as
a white solid by trap C.
The High-Frequency Cracking of Acetylene
The production of carbon targets by a high-frequency
(h, f.) discharge is described in the references (53).
The apparatus used in the present experiment was designed
so that it would rest on the base of a conventional
evaporation system (thereby using the diffusion pump, cold
trap and associated electronics of the evaporator) (figure 13).

REACTION DRY ICE DRY ICE
CHAMBER ALCOHOL ALCOHOL L,Q N,T L,Q NIT
v^n
o\
Figure 12. Acetylene apparatus

57
FI glare 13. High-frequency discharge apparatus

58
The target backings (10 nil Ta) were placed in the 3^.5 cm
long by 3*8 cm I. D. "Fyrex" tube. The tube could accommodate
four backings (three resting in the horizontal tube and one
attached to the endplate) without affecting the cracking
process, A Tesla coll furnished the h, f. discharge, The
_7
system is evacuated to a pressure of about 3 x 10 torr,
then isolated from the diffusion pump. The Tesla coil is
activated, and acetylene is admitted into the cracking
chamber through the "side-arm" from trap C (which was removed
from the apparatus used to produce the acetylene). The £¿^2
was allowed to sublime by removing the trap from the liquid
nitrogen and placing it in an alcohol-dry ice slush, thereby
allowing acetylene to enter the cracking chamber. To make
uniform targets required careful control of the C2H2 vapor
pressure. This was done by using a stopcock to limit the
flow of C2H2. Experience showed that the most efficient
pressure could be determined by the color of the glow dis¬
charge. This optimum pressure is indicated by a pale green
glow with no visible striations. After the acetylene has
completely cracked, the color of the glow discharge
changes to blue, characteristic of nitrogen. At this point
the process could be halted (producing very thin targets)
or repeated several times (producing thicker targets). It
was observed that the target attached to the endplate was
thicker than the ones resting in the glass tube. It was
found that by starting Tilth 20 mg of enriched it was
possible to produce eight targets. Four were thin, three

59
were of Intermediate thickness (15-30 keV for 3.6 MeV alpha
particles), and one was relatively thick (about 55 keV for
3.6 MeV alpha particles).
Targets prepared by this procedure were able to with¬
stand beam currents of about 3 /¿A; furthermore, the spectra
indicated a significant enrichment in (see next section).
The advantage of this procedure was that after the method
was perfected a sizable number of enriched C targets
vías available at minimal cost. Of course, the above procedure
could also by employed to produce targets enriched in Isotopes
of carbon other than C.

CHAPTER III
EXPERIMENTAL RESULTS
The yield, curves which follow were obtained with
the 12.7 era x 12,7 cm Nal(Tl) crystal fixed at a 55° angle
with respect to the alpha particle beam. This detector was
usually 0.5 cm from the target; however, some long runs were
obtained with the detector at 2.5 cm from the target. Since
the detector was quite close to the target, summing of
cascade gamma rays may occur. A 20,1 cm3 Ge(Li) detector
was also employed in examining the 7 MeV cascade radiation
from the 9.85 MeV level in -^0.
The target thicknesses were determined by employing
the narrow level (rcm = 0.75 keV) in ^0 at an excitation
of 9.85 MeV (26, 27). This part of the excitation function
for the target used for the 9.85 MeV measurements is shown
in figure 14. No corrections have been made to this curve.
By determining the full width at half-maximum, the target
thickness was found to be 25 keV for 3.6 KeV alpha particles
incident at 55° to the surface. Using standard methods the
thicknesses wTere extrapolated to the lov:er alpha particle
energies as required. A thicker target (55 keV for
3.6 MeV alpha particles incident at 55°) was used for most
60

COUNTS
61
Figure 14. Enriched 12C excitation function in the
region of the Ea = 3.58 MeV resonance.

62
off-resonance cross section measurements. Some off-resonance
cross sections were also determined with a 30 keV (for
3.6 MeV alpha particles) target.
Excitation Functions
The excitation functions in the region Ea = 2.7-3.7 MeV
for targets of enriched natural carbon and enriched
are shown In figures 15» 16 and 17, respectively. The
ordinate in figures 15 and 16 represents the number of counts
per 300 n Coulombs of singly charged helium ions within the
region Ey = 8.7 MeV to 10.8 MeV. In the excitation function
for the enriched -^C target the ordinate represents the
number of counts (in the same sum region as for the natural
carbon and enriched ^2C targets) per 150 n Coulombs. Beam
currents were usually between 1.5-3 /¿A.. The detector was at
a distance 0.5 cm from the target and at an angle of 55°
with the beam axis. The enriched ^-2C target was 15 ns/cm^
thick., the natural carbon target was 22 ^g/cm2 thick and
the enriched (probably 15-25 per cent enrichment) target
was 14 ns/cm2 thick. The enrichment of 12C is indicated by
comparing the resonance at Ea = 3.58 MeV in the three figures.
The broad peak in the enriched C spectrum at Ea = 3.24 MeV
is in the region of the 9.59 MeV excitation energy in 1^0;
however, most of this yield is probably due to the ~^C(a,n)^0
reaction, it is difficult to determine the actual enrichment
of C, since some of the background is due to neutrons


E„(lab) MeV
Figure 16, Excitation function for natural carbon target.

2.7 2.9 3.1 3.3 3.5
E a (lab) MeV
13
Figure 17. Excitation function for enriched C target.

66
originating at collimators, etc. Certain runs on tantalum
backings (at Ea = 3.24 MeV) Indicate that this so\irce of
background may be as much as 30 per cent of the total back¬
ground.
An indication of a resonance due to the •^C(a,y)'^0
reaction at Ea = 3.48 MeV was observed in the excitation
functions for the enriched and natural carbon targets.
This structure was not observed in the excitation function
for the enriched target. No attempt was made to determine
conclusively whether this structure could be attributed to
the 12C(a,Y)1^° reaction.
The 9.85 MeV Level in l60
The level at E^ = 3.58 MeV corresponds to a level in
^0 at 9.85 MeV (2+), This level has been observed through
the C(a,y) 0 reaction by Meads and Mclldowie, and Larson and
Spear (10, 12). A spectrum taken at EQ = 3*58 MeV is shown
in figure 18. No corrections have been made. Larson had
observed 7 MeV cascade radiation in the spectrum from his
thick target (11). This 7 MeV radiation is also visible in
figure 18. Because of the resolution of the Nal(Tl) detector
it is difficult to determine the level in ^0 through which
this cascade proceeds. For this reason the level was
examined using a 20.1 cm^ Ge(Li) detector, A spectrum from
the 1024 channels of the TMC analyzer is shown in figure 19.
This is a point-by-polnt sum of individual runs of

COUNTS
6?
CHANNEL NUMBER
Figure 18, Gamma ray spectrum from Nal(Tl) detector at
Ea = 3,58 MeV, The three arrows correspond to the positions
of the photopeak and the two escape peaks.

COUNTS COUNTS
200
100
400
500
600
100 200 300
CHANNEL NUMBER
o.
03
Figure 19. Gamma ray spectrum from Ge(Ll) detector at Ea = 3.58 MeV,

69
0,091 0.05 and 0,12 Coulomb, The (9.85 KeV-2e) peak is
clearly visible. The smaller peak is from the (6,92 KeV~2e)
radiation. The peak corresponding to the 2 ^ 2 transition
((9.85 - 6.92) MeV-2e) is also evident. The other peaks
apparently correspond to various background gamma rays. From
this it appears reasonable that the cascade radiation proceeds
through the 2+ level at 6.92 MeV in ^0. The results for
the radiative widths (determined from Nal(Tl) data) for the
9.85 MeV ground state and cascade transitions are given in
table 3. The value = 0.0050 eV corresponds to
I Ml^ = 2.76 x 10“2, where IHi 2 is the ratio of r to the
radiative width calculated from an extreme single particle
model (F-^). Fy is the so-called Welsskopf limit. In deter¬
mining the radiative width for the cascade radiation, Larson
assumed an Isotropic distribution since he was not able to
determine the identity of the intermediate level (11),
The sources of error are given in table 4. Errors
due to current Integration, extrapolation of stopping cross
sections to different energies, and geometry have been
combined and listed in the column labeled "other". The total
error is the square root of the sum of the squares of the
Individual errors. From table 4 it can be seen that no error
is listed under "target thickness" for the 9.85 MeV radiations.
Due to the extremely narrow total width of this state
(Fcm = 0,75 keV) the factor arctan(6/D in the expression
for the radiative width reduces to tt/2 and is not a source
of error. The difficulty in extracting the 9.85 MeV cascade

Table 3
Ground state
transition
Cascade
Radiative widths for ground state and cascade
radiations from the 9.85 MeV(2+) level in lo0.
Present work
T (eV)
Y
0.0050 t 0.0007
0.0011 t 0.0002
Other results
rY(ev)
0.0059 t 0.006a
0,0012 t 0.0004a
Other result
rY(ev)
0.020 t 0.001
aLarson and Spear (12), bMeads and Mclldowie (10),

Table 4
Possible causes of error.
He+ energy
(MeV)
Target
thickness
Deteotor
efficiency
Statistics
Angular
correction
Background.
subtraction
Other
Tota
3.37
9%
12%
1%
Q%
9%
3%
19%
3.24(3.22)
7
12
1
8
10
3
19
3.10
7 .
12
4
9
10
4
20
3.0?
9
12
2
9
7
4
19
2.95(2.92)
9
12
3
9
8
4
20
2.76
7
12
4
9
15
4
23
2.54
9
12
2
9
25
4
31
2.35
7
12
4
9
27
5
33
2.14
7
12
7
9
29
5
34
1.90
9
12
6
9
33
5
38
3.58ÍG.S.)
-
12
-
4
1
2
13
3.58(Cas.)
-
12
1
5
10
3
17

72
radiation in the presence of the strong ground state
radiation caused a 10 per cent error for "background sub¬
traction” for the cascade radiation. The brancing ratios
for the 9.85 MeV level are given in figure 20.
Cross Sections and the 9.59 MeV Level
The 1" state at 9.59 MeV excitation in ^0 was
exaimined with the 29 Mg/cm^ thick target. This level is
very broad, having a center-of-mass width of 645 keV (26).
Figure 21 shows a spectrum from the Nal(Tl) crystal at
Ea = 3.24 MeV. There were no corrections made to this
spectrum. The detector was 0.5 cm from the target and
at an angle of 55°. The total amount of charge collected
was 5.5 3C 10^ fi Coulombs of singly ionized helium. The arrows
indicate the expected positions of the photopeak and escape
peaks. For comparison purposes a spectrum at Ea = 2.95 MeV
obtained from the enriched ^C target (14 fxg/cm^) is shown
in figure 22. Spectra obtained at Eq = 3.24 MeV with this
target have the same general appearance. The spectrum
from the -^C is exponentially decreasing under the radiation
from the 9.59 MeV level. This same feature is also observed
in the spectra from a natural carbon target (figure 23).
The 9.59 MeV yield was obtained by subtracting
fractional parts of the 9.85 MeV spectrum from the 9.59 MeV
spectrum. The resulting spectrum was then compared with a
TO -l £
^C(a»n)iO0 spectrum to determine its fit with the background.

73
Figure 20.
The energy

COUNTS
74
Figure 21. Gamma ray spectrum from Nal(Tl) detector at
2a = 3.24 MeV for enriched target.

sjiwnoo
75
Figure 22. Gamma ray spectrum at Ea = 2.95 MeV for enriched
1^C target.

C.OUNTS
76
Figure 23. Gamma ray spectrum at E = 2.95 MeV for natural
carbon target.
,00

COUNTS
77
CHANNEL NUMBER
Figure 24. Gamma ray spectrum at Ea = 2.95 for enriched.
^2C target.

COUNTS
78
200 300 400 500
CHANNEL NUMBER
Figure 25. Gamma ray spectrum at E = 2.14 MeV for enriched
i2C target.

79
This same method was also used in determining the off-
resonance yields. This procedure gave a value of
0,021 + 0,004 eV for the radiative width. A comparison with
previous results is given in table 5. The present work
agrees well with the value given by Larson (11). The value
ry = 0.021 eV gives a value of 5*5 x 10"^ for |H|2.
Although there is some indication of 7 MeV cascade
radiation in the ^2C spectrum near channel 280, this feature
is also seen in the spectrum. It is felt that the
spectrum peak in channel 280 is the result of the capture
of thermal neutrons by the 2-^Na in the Nal(Tl) crystal.
When a paraffin shield was installed between the detector
and the collimators, the spectrum peak became more pronounced.
The curves shown in figures 21, 22 and 25 were obtained
with this shield, while the data shown in figures 23 and 24
were obtained without the paraffin shield. There was some
indication that although this shield increased the 7 MeV
background, it decreased the background in the 9 MeV region.
It has been observed that 9 MeV radiation (resulting
12 i4
from the C(d,y) N reaction) may also present a background
problem in a x C + a experiment (11). The reason presented
is that if deuterons exist in the ion beam, the beam energy
analyzing magnet will permit the target to be bombarded with
deuterons having one-half the energy of the alpha particles,
4.
since molecular D£ ions will have nearly the same path as
4 12 ,
singly ionized He. The bombardment of C by 1.65 MeV
deuterons produces 9.4 MeV cascade radiation to the 2.31 MeV

Table
Radiative width for the 0* ^ -> 1
Present work
rY(eV)
0.021 - 0.004
pi 4*
(9.59 MeV)——> 0 transition.
Other results
rY(ev)
0.022 t 0.005a
0.006b
co
o
Parson (11), bBloom et al, (9).

first excited, state in 1^N. The r. f. source bottle used
for this experiment has never been used to ionize any
hydrogen isotope; hence, it was assumed that the contribution
from deuteron-induced reactions was negligible in the present
experiment.
The off-resonance cross sections were determined from
spectra such as the one shown in figure 24. The 52 /zg/cnr
thick target was used for this data. The ground state
radiation is clearly visible in channels 355-390. A
comparison with figure 22 shows that the number of counts in
11
the corresponding channels for the spectrum is decreasing
almost exponentially. For the spectrum at Ea = 2.95 MeV
(as for the other cross section measurements) the 12,7 cm by
12.7 cm Nal(Tl) detector was at a 55° angle with respect to
the beam axis, and was located 0.5 cm from the target. The
ground state radiation is more visible at Ea = 2.95 MeV
(figure 24) than at the peak Ea = 3*24 KeV (figure 21). Two
factors contribute to this appearance. First, the average
number of counts per channel in figure 21 is about 10 times
that in figure 23; hence, on the logarithmic scale the peak
is not as evident. Also, the ^Cia.nJ^O cross section is
about 5 times as large at Ea = 3.24 KeV as at E& = 2.95 MeV
(43). Thus, the ground state radiation is more difficult
to observe at the resonant energy because of the increased
neutron background.
The yield spectra for the other data points are
similar to the spectrum shown in figure 24. As the alpha

82
particle bombarding energy decreases, the spectra resemble
the 13C background more closely. For example, at Ea = 2,l4 MeV
there is only a slight indication of the ground state radiation.
This is shown in figure 25» where the data were obtained with
the 28.8 ¿ig/cm2 thick target. Because of this the error
caused by extracting the yields from the backgrounds are
relatively large for the cross section meaurements made at
low bombarding energies (table 4). The amount of singly
ionized helium collected was typically between 0,045 and
0,16 Coulomb.
The yield at each of the experimental points was
normalized to that at 3.58 KeV by multiplying the total number
of counts in the capture spectrum peak by the ratio of the
number of channels enclosing the peak to the number of channels
in the standard spectrum peak. The values of the cross
section are listed in table 6. The errors shown were computed
from the values given in table 4.

83
The
He
Table 6
12 l6
C(a»y) 0 reaction cross section.
energy
(MeV)
Cross section
(10“9 barns)
3.37
3.24
3.22
3.10
3.07
2.95
2.92
2.76
2.54
2.35
2.14
1.90
32.0 + 6.1
35.0 + 6.1
35.0 + 6.1
29.0 + 5.8
19.8 + 3.8
15.2 + 3.0
11.9 + 2.4
8.0 + 1.8
4.3 ± 1.3
3.5 ± 1.2
1.5 ± 0.5
0.3 + 0.1

CHAPTER IV
DISCUSSION
'Resonances
In this experiment the radiative capture of alpha
particles by ^C below Ea = 3.6 MeV has been examined. The
7 MeV cascade radiation from the 9.85 MeV (2+) level in ^0
vías determined to proceed through the 6,92 MeV (2+) level.
It would be of Interest to examine this (O-'' ^ 2+ M1E2 ^ 2+)
transition using angular distribution methods to determine
the mixing parameter X, where X = S(M1)/S(E2). S(M1) and
S(E2) are amplitudes for dipole and quadrupole emission,
respectively (29). Further study of this state would
probably best be accomplished through angular correlation
methods. At the time this experiment was performed, a new
correlation table vías being designed and constructed by
members of the laboratory, This table will be able to make
the above measurements accurately. For this reason no
determination of the mixing parameter X vías attempted using
the present apparatus.
The radiative width measurements agree in general
with the results of Larson (the errors overlap)} however,
the values tended to be slightly smaller than the values
84

85
obtained by Larson. This may be due in part to the method
used in determining the peak-to-total ratio for the present
experiment.
Target Deterioration
Target deterioration was present only at higher beam
currents (about 4-7 m A) .• At these beam currents the carbon
was dissipated, and the tantalum backing became quite pitted.
Carbon deposition was not observed on the target, even after
the relatively long bombarding times. In order to observe
this more carefully, several relatively long runs (greater
than 0,04 Coulomb) were made on clean Ta backings using
both low (1-3 ^A) and high (4-8 /zA) beam currents. No
deposition of organic material was observed for either of
these currents. However, the higher beam currents did cause
the tantalum to change color at the spot which had been
bombarded by the beam. This spot was gold in color on both
sides of the backing. This is believed to be caused by the
tempering of the tantalum by the concentration of heat on the
beam spot. This same effect was observed during preliminary
experiments in target preparation by thermal cracking methods.
When the Ta backing was outgassed by heating the backing to
a bright yellow glow in a vacuum, the Ta backing would have
the characteristic gold color and be very rigid when removed»
hence, it seemed that the backing had been tempered by the
high temperature used in the outgassing process. It might

36
be noted here that there was some evidence (using the natural
carbon target made by h. f. cracking) to Indicate that
backings that had been outgassed in a vacuum produced targets
which exhibited greater resistance to deterioration (by
high beam currents) than targets produced from backings that
had not been outgassed. Enriched x C targets were made using
Cu backings, but these were not used in this experiment.
These may be able to withstand higher beam currents than
those made with tantalum backings.
Cross Sections
The cross section for the -^Cia, y) ^0 reaction at low
alpha particle bombarding energies is necessary for an accurate
extrapolation to effective stellar energies. The Coulomb
barrier Bc for the ^C + ^He can be approximated by
Bc = Z-jZoe^/Rf
-L ± n
where R = 1.4 x (Ax3 + A03 ) x lO"^ cm.
The prescription gives the value 3.18 KeV for B.j hence,
o
below 3 MeV barrier penetration becomes increasingly important.
Tombrello has computed the effect of Interference
between the 1" states at 7.12 MeV and 9.59 KeV in 1^0.
p
Using a value ea = 0.10 for the reduced width of the 7.12 MeV
state, he has calculated the values of the capture cross

87
section for both constructive and destructive interference
(22), Since the signs of the amplitudes were unknown, it
was impossible to determine whether the interference was
constructive or destructive.
The values for the ^2C(a,Y)^0 reaction cross section
obtained from the present experiment, and those computed by
Tombrello (assuming ea =0,1) are plotted in figure 26,
The value obtained for the capture cross section at
Ea = 3 KeV is slightly smaller than that calculated by
Tombrello; while at Ea = 1,9 MeV it is about 1.5 times as
large as the calculated value. The results of this experi¬
ment indicate that the interference is constructive and that
p
9a is between 0,1 and 0.3#
The 12g(atV)l6Q Reaction Rate
at Effective Stellar Energies
p
The reduced alpha particle width ea of the 7,12 MeV
level in ^0 is essential in the determination of the
-^C(a,y)^0 reaction rate at stellar temperatures (see the
section on theory). This reaction rate is important in
stellar model calculations since it determines the relative
abundances of ~2C and ^0 and hence the futher evolution of
the star.
This experiment indicates the cross section factor S0
Q
at a typical stellar temperature of 10 °K has the value
So(12C(a,Y)l60) = (0.65 + 0,32) x 103 keV barns,

88
E a (lab) MeV
Figure 26. The ^C{a,y)^0 reaction cross section values.
The solid line has been drawn through the calculated points.

89
p
using 0 = 0.2 + 0.1. Similary (using the equations derived
a “
in the section on theory), the present experiment yields
the following value for the ^C(a,y)^^0 reaction rate at a
g
stellar temperature of 10 °K*
p (12C) = (0.84 + 0.42) x 10"20X Pf,, s"1,
01
where Pis the density of the core in g cm“^ (—10^), X is
4 a
the abundance (~1) by weight of He and f1C) is the screening
factor (37). Although the above errors on SQ and p& may
appear large, it should be noted that prior to this experiment,
2
0^ could only be estimated to within a factor of 10 at best.
Also, it is quite probable that the errors will be further
reduced as revised fits are obtained to the measured values
of 1¡he capture cross section.
ip h,
A determination of C + He capture cross sections
at lower bombarding energies than those employed in this
experiment would also produce a better value for the reaction
rate. Experimental procedures that could reduce the
^C(a »n)^0 background would be necessary. Using-a more
12
highly enriched C target, and time-of-flight methods to
eliminate neutron background originating from the collimators
may be the most useful procedure since it appeared that some
of the neutron background resulted from the beam striking
collimators and slits on which carbon had deposited.

APPENDIX

GAMMA HAY DETECTION EFFICIENCIES OF Nal(Tl) CRYSTALS
Total Incident Intrinsic Efflcleny
The "total incident" intrinsic efficiency, ^(Ey), of
a Nal(Tl) crystal in the form of a right cylinder for gamma
rays of energy E is defined as the probability for the
detection of a gamma ray that is incident on the face of the
crystal (56, 57). This is equal to the ratio of the total
number of gamma rays detected per second to the total number
of gamma rays incident on the face of the crystal. In the
form of an equation, this is
Nt
ME) = ,
N0f
where N is the total number of gamma rays of energy E
detected per second, N0 is the total number of gamma rays
of energy E emitted per second by an Isotropic source, and
f is the fraction of 4rr that the solid angle of the crystal
face subtends. Stated differently, f is defined by
where £2 is the solid angle subtended by the crystal.
91

92
It Is evident that %/!>! is simply the fraction of the
gamma rays detected, and f is simply the probability that a
gamma ray from an isotropic source will strike somewhere on
the face of the crystal. The geometry for the case of an
isotropic point source of gamma rays of energy E located
on the axis of a right cylinder of radius R and thickness t
is shorn in figure 27.
The parameter X2(e*) is the path length in the Nal(Tl)
crystal. The parameter x-j_(e') is the path length in any
absorbing material preceding the crystal. The quantities
Xg and x-j_ have the following explicit dependency on 0 ' i
TJ
Xt (e ') = d sece ', for 0 < 0' < e_ = arctan ,
0 d
R
Xo(e ') = t sece ', for 0 < e ' < 6, = arctan
t + d
R
Xo(e') = R csc0' - d sece', for e,< e'< e = arctan .
i o d
The intensity of the source will be attenuated by a
factor exp(- Mp(E)x^(0 *)) in traversing the absorbing material
preceding the crystal. is the total linear absorbing
coefficient for a gamma ray of energy E in the absorbing
material (58). In traversing the Nal(Tl) crystal the gamma
ray intensity will be attenuated by a factor exp( - M 6 '))»
where /¿2(E) is the total linear absorption coefficient for
a gamma ray of energy E in Ral(Tl).
N /4tt is the intensity per unit solid angle (the number

Figure 27. The parameters involved in the calculation of Nal(Tl)
crystal efficiencies.

94
of disintegratlons per second per unit solid angle) of the
isotropic source. The number of gamma rays emitted per
second into the small solid angle AO' about O' is (NQ/4n)A 0*.
In the small solid angle AO’the number of gamma rays traversing
the crystal without interacting is equal to the quantity
Hence, the total number of gamma rays, emitted by
an isotropic source of Intensity N not interacting with
the crystal is given by
4rr ‘'crystal
The number Ninc of gamma rays Incident on the face of the
crystal is given by
Therefore, N,j, (the number of gamma rays detected per second,
assuming that each interaction produces an observable pulse)
Is obtained from the followings
Nrp _ Nj_nc - Nn, or

95
Using the relation derived for NT, the total incident intrinsic
efficiency >7 j is given by
» (E ) = — re°( 1 - e“ M2X2)e- ^lxl Sin e'de\
1 Y 2f J0
where f = £2/4n = (l/4rr) C dñ* = J(l-d(R^ + d^)~2).
‘'crystal
It is often convenient to define a "source" intrinsic
efficiency, ^(E), as the product of f and *7
(771 = fr?T = NT/N0) • In this case the geometry factor f is
accounted for in the computation of the source intrinsic
efficiency. Hence, the absolute intensity N of a source
is obtained by dividing the observed counting rate N.p by
*1 f If we introduce Legendre polynomials Pn(cose')> we will
be* able to relate the source intrinsic efficiency t)¡- to the
integrals
Jn = —L_ f Pn(cose')e~ ^^(l - e- m2X2) dfi*.
2rr ''crystal
These are the integrals defined by Rose (30). Therefore,
NT _ _J_o
N0 " 2
is the source intrinsic efficiency.
In general is much larger than an(^ It is possible
to calculate values of >7t using ft-^ = 0. Values of »?T
(computed at Oak Ridge with = 0) and values of *1^

96
(computed by Wolicki with ¡i^ = 0) are compiled in Mott and
Sutton for several different crystal sizes and source-
detector geometries (56, 59). Mor other geometries and
crystal sizes one may interpolate between given values-. More
curves for i?,p may be found in the article by Rivers (60),
These calculations have been further extended by Heath to
include disc and line sources (61, 62). Values of absorption
coefficients for photons have been compiled by Grodstein (63).
The pulse spectrum for mono energetic gamma rays is
complicated by pulses from externally scattered.photons in
addition to the spectrum resulting from the primary photons
of the source. The scattered radiation results from the
Compton gamma rays scattered into the crystal by shielding,
wall, target or source holders, etc. This radiation has
a peak which occurs at an energy corresponding to 180° Compton
scattering, and hence is due mainly to backscattered photons
emerging from the photomultiplier window (56, 58).
Thus, in order to measure absolute yields the spectrum
of pulses must be corrected accordingly. In general it is
relatively easy to obtain the yield for monoenergetic gamma
rays. However, it is much more difficult to accurately
determine the absolute yields if two or more gamma rays
of different energies are present. The analysis of a spectrum
containing gamma rays of several energies is accomplished
by "spectral decomposition" (6¿0. That is, the spectrum is
broken into its individual components. After corrections
have been made for background and backscatterlng, the

97
"response function" (the detailed shape of the spectrum of
a single gamma ray energy) of the gamma ray having the
largest energy is obtained and subtracted from the spectrum.
The process is repeated for the residual spectrum. This is
repeated until the response functions for all of the gamma
rays have been obtained. These individual "component spectra"
may then be analyzed separately.
Source Full Energy Peak Efficiency
Since a pulse height spectrum depends so strongly on
the particular experimental arrangement, it is desirable to
choose a portion of the spectrum that Is somewhat less
sensitive to scattered radiation and background (56, 59* 64),
Now, the shape of the photopeak is relatively insensitive
to radiation scattered into the Nal(Tl) crystal, and back¬
ground corrections are usually small. Furthermore, the
shape of the photopeak is very similar to a normal curve
(Gaussian), and thus the total number of counts in the
peak (which is equal to the area under the peak) may be
related to certain parameters of the Gaussian (peak counting
rate, full width at half-maximum, energy interval per
channel) (65* 66). Hence, the problems encountered in
relating an observed counting rate to the absolute intensity
Nq of a given source are greatly simplified if one employs
the total number lip of counts in the full energy peak instead
of employing Nrp.

98
The "incident" intrinsic peak efficiency (not the
source full energy peak efficiency r¡ (E)), may now be defined
x-'
as the probability that a gamma ray of energy E incident on
the Nal(Tl) crystal will produce a pulse lying in the full
energy peak. Stated differently, the "Incident" intrinsic
peak efficiency is the ratio of the number of counts per
second lying in the photopeak to the number of gamma rays
of energy E incident per second on the face of the crystal
(assuming Mq = 0). Thus, the "Incident" intrinsic peak
efficiency is given by
"peak = VV-
It is now possible to define the source full energy
peak efficiency tj^ as a product of f and t
*7p(E) = f^peak = ^p/^o*
It is quite difficult to calculate directly from
the theory because a pulse lying in the photopeak may have
been caused by the summing of several successive processes
in the stopping of a single gamma ray. For example, a
photon may be absorbed by a Compton scattering followed by
pair-production followed by annihilation of the positron.
If all quanta and electrons are absorbed, the resulting
light from the scintillator will produce a pulse lying in
the photopeak. This is possible since the time required for

99
collecting the light is long compared to the time required
by the scintillator to absorb the gamma ray. This pulse
would then be indistinguishable from one due to a single
photoelectric process. Hence, it is extremely difficult
to determine the actual absorption coefficient ¡i that would
be required in the calculation of n , However, by defining
a suitable ratio R it is possible to relate rjto the
calculated source intrinsic efficiency 17^. The ratio S is
determined experimentally as a function of the gamma ray
energy E^. R(E) is defined as the ratio of the number Np
of counts under the photopeak (area of photopeak) to the
total number under the entire pulse spectrum (corrected
for background, backseattering, and spectrally decomposed).
Hence, the relation between the source full energy peak
efficiency »7p and is given by
The "peak-to-total" ratio R may be determined by analyz
ing spectra from standard sources (if the energy of interest
is low). If the energy range of the gamma rays is higher,
then one must resort to certain nuclear reactions where
there is a predominant gamma ray present in this range. In
this experiment the 9.17 KeV gamma ray resulting from the
13c(p,y)^ N reaction was employed (figure 28). The 9.85 MeV
I p “l ¿1
gamma ray resulting from the C(a,y) 0 reaction was also
used in determining R,

100
Figure 28, Gamma ray spectrum from the (p,y)reaction
(Ey = 9,17 MeV). The dashed line indicates the horizontal
extrapolation used in the present experiment to determine
the peak-to-total ratio R. This gives the value R = 0.¿0.

101
Although the spectrum exhibits a strong gamma ray of
the energjr indicated, there is some background present.
Furthermore, the low energy portion is hidden due to back¬
ground pulses (Compton scattering, bremsstrahlung, random
amplifier and detector noise, etc.). To determine the exact
shape of the spectrum for monoenergetic gamma rays requires
that an estimate be made for the shape of the low energy
region (even after the background has been subtracted). This
estimate is needed to compute the total number of counts
in the spectrum,
In order to obtain the shape of the spectrum for low
energy pulses it is necessary to consider the different
processes that have been employed in reproducing a spectrum,
by empirical methods. There are two basic procedures. Cne
is the Monte Carlo method which attempts to generate the
spectrum by tracking individual photons through a crystal
using a computer (67, 68, 69). Zerby and Moran assumed that
the source was in a vacuum, thus eliminating background.
Also, the calculations are first carried out as if the crys¬
tal produced a sharp line in response to the energy deposited
in the crystal. The response spectrum is subsequently
spread out by a semi-empirical C-aussian broadening. The
physical processes that gamma rays undergo in passing
through the crystal are simulated by this method. The Monte
Carlo calculation is started by determining the direction
of incidence of the gamma ray by systematically sampling
the isotropic, monenergetic, point source within the cone
subtended by the crystal. The different interactions

102
(photoelectric, pair, Compton) are then systematically-
sampled. In relation to their probabilities of occurring
Zerby and Horan argue that the intercept of the
spectrum with the zero pulse-height value can be calculated.
They note that photons which are forward scattered only
once before escaping can be the only ones that contribute
in the limit of zero pulse-height. They obtain an expression
for this. Unfortunately, it does not agree well with the
actual zero-intercept observed in carefully performed
experiments. It is consistently lower. Thus, some difficulty
in determining the zero-intercept exists.
The second approach is to employ the method of least-
squares to fit the observed spectrum using known or suspected
energy components as a first approximation (70, 71). These
known spectra have been carefully compiled by Heath and
others using stringent laboratory conditions which minimize
the effects of background (72, 73). The idea is to use a
program to fit the observed spectra using a complete set of
functions. It is then desirable to be able to adjust the
parameters so that the spectrum response for any energy
gamma ray can be generated. In this case Heath has shown
that the low energy region can be approximated by a linear
extrapolation to the zero energy axis from the known,
rather flat Compton distribution. For the present experiment a
horizontal extrapolation has been employed.

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BIOGRAPHICAL SKETCH
Róñala Jack Jaszczak vras born August 23» 19^2, in
Chicago Heights, Illinois. He was graduated in June, I960,
from Eunnell High School in Bunnell, Florida. In September,
i960, he enrolled in Daytona Beach Junior College in
Daytona Beach, Florida. He received the Engineering Award
in June, 1962, when he graduated with the degree of
Associate of Arts. He enrolled in the University oí' Florida
in September, 1962. In 1963» he received a Radio Corporation
of America Scholarship. He majored in Physics and earned
the degree of Bachelor of Science with High Honors in
April, 1964, In September of that year he enrolled in
the Graduate School of the University of Florida and has
pursued his work toward the degree of Doctor of Philosophy.
He was the recipient of a National Aeronautics and Space
Administration Traineeship from September, 1964, to
August, 196?. From that time until the present he has
held a Graduate School Fellowship,
He is a member of Phi Beta Kappa, Phi Kappa Phi,
Sigma Tau Sigma, and Sigma PI Sigma.
Ronald Jack Jaszczak is married to the former
Nancy Jane Bober of Chicago Heights, Illinois.
108

This dissertation vras prepared under the direction
of the chairman of the candidate's supervisory committee
and has "been approved by all members of that committee.
It lias submitted to the Dean of the College of Arts and
Sciences and to the Graduate Council, and was approved
as partial fulfillment of the requirements for the degree
of Doctor of Philosophy.
August, 1953
Dean, Graduate School

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UNIVERSITY OF FLORIDA
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