• TABLE OF CONTENTS
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 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Experiment
 Calculations and results
 Discussion
 Conclusions
 Bibliography
 Biographical sketch
 Copyright














Title: Nuclear reaction cross sections from the nitrogen bombardment of sulfur.
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
    List of Tables
        Page v
    List of Figures
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Experiment
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
    Calculations and results
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
    Discussion
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
    Conclusions
        Page 61
        Page 62
    Bibliography
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
    Biographical sketch
        Page 68
        Page 69
    Copyright
        Copyright
Full Text











NUCLEAR REACTION CROSS SECTIONS

FROM THE NITROGEN BOMBARDMENT

OF SULFUR










By
DAVID E. FISHER


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
June, 1958


















ACKNOWLEDGEMENTS


The successful performance of the radiochemical

studies involved in this project was made possible by the guidance

and aid of Dr. John J. Pinajian, who gave unflinchingly of his time

and skill in laboratory technique.

Dr. Alexander Zucker, the author's research director,

supervised the entire project from its conception until its comr- *-

pletion. Nothing could have been accomplished without his

thoughtful direction.

Dr. Armin Gropp, of the University of Florida, was instru-

mental in making the arrangements for the ORINS fellowship whi h

sponsored this work, as well as in guiding the author through the

precarious first years of graduate study. His proficiency in cutting

red tape is gratefully recognized. In addition, Dr. Gropp provided

the necessary liason-between the Oak Ridge National Laboratory

and the University of Florida.

Dr. Donald Lafferty, also of the University of Florida,

was responsible for introducing the author to the proper research

personnel at the Oak Ridge National Laboratory. Gratitude is also

due to Drs. Alfred Chethain-Strode and Morton Gordon for their

continued interest and encouragement; Dr. Chetham-Strode pro-

ii














vided consultation and guidance throughout this research project,

while Dr. Gordon's contribution n dates back to his introduction of

the author to quantum mechanics.

A special debt is owed to Dr. Robert S. Livingston, dir-

ector of the Electronuclear Research Division of the Oak Ridge

National Laboratory, who permitted the author to impose upon

the personnel and equipment under his jurisdiction. This

dissertation could never have been finished on time without the

special help and sober interest of Mrs. Martha Armstrong, who

typed devotedly and well, and of Dr. Frederick T. Howard, who

corrected the manuscript.

The research for this project was supported by the Oak

Ridge Graduate Fellowship Program of the Oak Ridge Institute

of Nuclear Studies. The work was performed at the Oak Ridge

National Laboratory, which is operated by the Union Carbide Nuc-

lear Company for the United States Atomic Energy Commission.

Finally, it is a distinct pleasure for the author to acknowl-

edge-.his Brobdingnagian indebtedness to his delightful wife, Leila

L., for her distinctly personal contributions.












TABLE OF CONTENTS




Page
ACKNOWLEDGEMENTS --------------------------- i

LIST OF TABLES ------------------------------- v

LIST OF FIGURES ---------- -------------------- vi

Chapter

1. INTRODUCTION ----------------------- 1

Previous Work

Present Experiment

II EXPERIMENT ----------------------- 15

Bombardment Techniques

Chemical Techniques

Counting Techniques

III. CALCULATIONS AND RESULTS --------- 34

IV. DISCUSSION --------------------------- 44

V .. CONCLUSIONS ------------------------- 61

BIBLIOGRAPHY ----------------------------------- 63

BIOGRAPHICAL NOTE ----------------------------- 68



















LIST OF TABLES


Table Page
46
1 Possible Reactions from the V Compound 12
Nucleus

2 Assigned Half-Lives 25

3 Measured Cross Sections 43

4 Comparison of Results 58


















LIST OF FIGURES


Title

Energy Determination Apparatus

Ra-DEF Calibration

Typical Ti45 Decay Curve
44
Typical Sc44 Decay Curve

Scandium Gamma Spectrum

Rb Gamma Spectrum
Typical K38 Decay Curve
Typical N13 Decay Curve

Yields vs Nitrogen Energy
14 13
Yield vs Nitrogen Energy for (N N ) Reaction

Stopping Power of ZnS for Nitrogen Ions vs
Nitrogen Energy
Cross Sections vs Nitrogen Energy

Cross Section vs Nitrogen Energy, (N N3)

Positions of Nuclides

Schematic Diagram for Evaporation Calculations

Cross Sections for Neutron Transfer Reactions
vs E -B.+ 1/2 Q
- cm


Figure

1

2

3

4

-5

6

7

8

9

10

11

12

13

14

f5

16


Page

17

23

27

28

29

31

32

33

36

37

40

41

42

53

55

60



















CHAPTER I

INTRODUCTION

One of the earliest models of nuclear reactions is that of the

compound nucleus, first put forth by Niels Bohr(1) in 1936. According

to this model the incident particle strikes the target and fuses with it

to form a compound nucleus; the kinetic energy of the projectile is

shared among all the constituents. The main assumption of the model

is that the nuclear reaction can be divided into two states -the formation

of. a compound nucleus and its subsequent decay-and that these two

stages are independent of each other.

During the following years Weisskopf and co-workers formu-

lated a statistical theory describing the decay of the compound nucleus(2).

As had been suggested by Frenkel(3), the nucleus was thought of as a

number of nucleons in thermodynamic equilibrium, losing its excitation

energy by the evaporation of particles. A "nuclear temperature" was

defined which governs the energy distribution of the emitted particles.

The theory attempts to describe the nuclear level density, the energy

spectra of particles emitted in a nuclear reaction, .and thus predict

reaction cross sections. Experiments testing the theory may deal,

then, with any of these phenomena.











2

Previous Work

Early qualitative investigations of the theory of nuclear

reactions were described by Bethe (4) and by Konopinski and Bethe (5)

without any detailed determination of the quantities involved.

Experimental evidence concerning the statistical decay of a

compound nucleus is difficult-to collect because of the possibility of

direct interaction between.the bombarding projectile and the target

nucleus. At high bombarding energies this direct interaction may over-

shadow the compound nucleus mnechanism. Yet at low incident

energies the statistical theory may be invalidated inasmuch as it

requires that the compound nucleus be excited highly enough so that

a great many energy levels are involved.

Peaslee, in his survey (6) on intermediate energy nuclear

reactions, reports the following: Barschall(7) measured total cross

sections for the neutron bombardment of many elements ranging in

mass number from 50 to 230, for incident energies in the range 0. 1-

3.0:Mev. The theory predicted a monotonic decrease in cross section

with increasing energy. Barschall did not observe this. Miller et al. (8)

bombarded 3. elements from iron to bismuth with neutrons of 0. 05-

3. 2 Mev and measured total cross sections. Their results agreed

with.those of Barschall. Walt et al. (9) continued the above experi-

ments on nine more elements in the same mass region and got the

same results. Okazaki et al. (10) extended the experimental work to

include the bombardment of neodymium, samarium, erbium,











3

ytterbium and hafnium with neutrons of 0. 06-3. 0 Mev. Their results

agree with the others. Weisskopf and co-workers (11) modified the

theory to account for the above results on the basis of a single particle

interaction. The new theory accounted for the gradual change in

cross section with atomic weight.

Paul and Clarke (12) bombarded 57 elements with 14. 5-Mev

neutrons. They found that for mass numbers greater than 100, experi-

mental cross.sections for (n, p) and (n, a) reactions were as much as

104 times greater than predicted by theory. The (n, 2n) cross sections,

however, agreed with theoretical values. They concluded that a

direct interaction mechanism was operating in the (n, p) and (n, a)

/reactions. Brolley et al. (13) measured (n, Zn) reactions from the

bombardment of Cu and Mo9 .with neutrons at energies from thres-

hold to 27 Mev. They found good correlation with theory up to 16-18

Mev, where the.experimental cross sections dipped rapidly. They

concluded that at this energy tertiary reactions became important.

Gugelot (14) reports that Hirzel and Wtffler(15) measured

1r(y,p)/r(y, n) ratiosand found that the (y, p) reaction is 103 times

larger than the theory would predict. An explanation of.this by

Schiff (16) was that the residual nuclei did not have all states excited

due to the peculiarities of y-ray absorption. Levinger and Bethe (17)

explained (y, p) reactions by the direct interaction of the photon with

one of the protons of a nuclear alpha particle. Nabholz et al. (18), '

from (y, a) reactions on Br79 81 and utilizing experimental (y, n)











4

results, gave good theoretical correlation for (y, a)/(y,n) cross

sections. Toms and Stephens (19) measured photoprotons from cobalt,

initiated by bremsstrahlung x-rays, and found good correlation with

theory if it was assumed that 10% of the protons came from a direct

interaction mechanism.

Bradt and Tendham(20) bombarded silver and rhodium with

alpha particles at 15-20 Mev and measured (a, n) and (a, 2n) cross

sections. They made the assumption that the sum of these two cross

sections would give the total cross section for alpha particles on the

targets considered, and compared this value to that predicted by theory.

The theoretical value agreed with their measured value. Kelly and

Segre (21) bombarded bismuth with 38-Mev alpha particles and 19-Mev

deuterons. The deuteron excitation functions were explained by

Peaslee (22) on the basis of a non-compound nucleus stripping reaction.

Cross sections for (a, 2n) and (a, 3n) reactions were measured and

compared to,statistical theoretical predictions. Agreement was found.
109
Bleuler et al. (23) bombarded Ag09 with 19. 5-Mev alpha particles

and measured (a, n) and (a, 2n) excitation functions. In their calcul-

tions they neglected possible proton emission. Their calculated cross

sections..agree with their measurements.

According to the statistical theory, a ratio of particle emis-

sions (such as the ratio of protons emitted as compared to neutrons

emitted) from a given compound nucleus should be independent of

the mode of formation of that nucleus. Peaslee (6) reports that











5

these relative probabilities may change by an order of magnitude

depending on the nature of the incident particle. Experiments

quoted by Peaslee with y-induced reactions (15) at 17 Mev and

neutron-induced reactions (12, 24) at 14 Mev showed that the frac-

tion of proton emission compared.to neutron emission from a com-

pound nucleus was 100 times larger than predicted by the statistical

theory. It is possible that a knock-on process here has obscured

the statistical results. The fraction seems to increase with

increasing Z while statistical theory predicts that proton emission

will fall off as Z increases past 40.

On the other hand, Cohen et al. (25) compared the (p, 2p)
25 14 12
reaction on a Mg target with the (N 2p) reaction on aC Ctar-
26
get. Both reactions involve the Al compound nucleus. After

corrections for barrier penetrations were applied, the cross sec-

tions were "quite comparable". However, the (N a) and (N14, 2a)

cross sections were about.two and four times larger, respectively,

than those for the (p, a) and (p, Za) reactions. This was possibly

related to the original alpha particle structure of the C1Z target.

Ghoshal (26) bombarded Ni60 with 40-Mev alpha particles
63
and Cu63 with 32-Mev protons, in each case forming the compound
64
nucleus Zn According to the theory, the probability of this com-

pound nucleus forming specific reaction products is the same in

each case, providing corrections are taken into account which re-

cognize that different excitation energies are involved in each case.











6

Ghoshal obtained experimental results giving better than fair agree-

ment with theory, and until 1950 this experiment was among the

most conclusive in favor of the compound nucleus. However, his

experimental cross sections for the (a, 2n) reaction are about 4

times less than for the (a, pn). This result is not at all what one

would expect from the theory. It might be explained (7) on the

basis that the residual nucleus from the (a,pn) process is Cu62

an odd-odd nuclide, whereas Zn ,6 the (a, 2n) product, is even-

even. Odd-odd nuclei are known to have level densities larger

than those of even-even nuclei by a factor of approximately 12,

and the level densities eater into,the statistical theory quite heavily.

This point is not considered in the calculations by Ghoshal.

SSkyrme and Williams (27) bombarded tungsten and carbon

with 157-Mev protons. They measured.the differential cross

sections for neutron emission at.various energies and found that

the shape of the curve agreed "fairly well" with theoretical pre-

dictions. They assumed some direct interaction was present.,

Feld (28) interpreted the data of Barschall et al. (29) on energy

distributions from the inelastic scattering of neutrons at energies

from 1. 5 to,3. 0 Mev. The data from tungsten targets correlated

with statistical theory; that from lead and iron targets did not fit

the theory. He presented a theory which accounted for the lead

and iron data on the basis that only a few energy levels were in-

volved. Graves and Rosen (30) measured the energy distribution













of neutronsinelastically scattered from carbon, aluminum, iron,

copper, zinc, silver, cadmium, tin, gold, lead, and bismuth.

The neutrons emitted in the energy range 0.5 to 4. 0 Mev had a

Maxwellian distribution, as ,expected from the statistical theory,

but the energetic dependence of the level density did not.vary with

the mass of the residual nucleus.asthe theory predicts it should.

Graves and Rosen concluded that the excitation energy of the com-

pound nucleus was not shared by all the particles. Gugelot (14)

measured the energy spectra of neutrons emitted from reactions

initiated by 16-Mev protons on beryllium, aluminum, iron, rhodium,

gold, and tellurium. His values for nuclear temperature agreed

with those of Graves and Rosen. Cohen (31) found that the angular

distribution of neutrons from alpha-induced reactions could be

approximately reproduced by statistical theory, but it was evident

to him that some other process was also effective.

Levinthal et al. (32) measured the energy distributions of

protons inelastically scattered from carbon and aluminum. The

incident energy was.31 Mev. The distribution was correlated

with theory and fit the predictions "fairly well" at excitation energies

.above 15 Mev. Below this energy, the observed values deviated from

predictions, Eisberg and Igo (33) bombarded lead, gold,, tantalum,

and..tin with 31-Mev protons and measured the inelastic .scattering

energy distributions, angular distributions, and total cross sections.

They.took measurements at 30, 45, 60, 90, and 135 degrees. The














,energy distributions were not Maxwellian; statistical theory predicts

they should be. The differential cross-sections were peaked forward;

statistical theory gives.an isotopic distribution. The total cross

sections were larger than predicted. They concluded that the inci-

dent proton may hit the rim of the target and be scattered from

there without forming a compound nucleus.

Eisberg et al. (34) measured the energy spectra of emitted

protons from the alpha bombardment of gold, silver, and copper, at

40 Mev. Their results agreed with the predictions of statistical

theory for proton energies above about 4 Mev. Below this energy,

they concluded,, some other process interfered. Gugelot (35) bom-

barded aluminum, iron, nickel, copper, silver, tin, platinum, and

gold with 18-Mev protons and measured the energy distribution of

the inelastically-scattered particles. The distribution agreed with

statistical theory at high excitation energies. He also found an

anisotropic particle distribution.which lead him to believe that a

direct interaction was present. In an attempt to eliminate this

interference he measured the energy distribution at 150 deg and

calculated.the level densities. Using these values he calculated

values of r(n,p) and o(n, 2n) for rhodium and platinum and compared

these values with the experimental results of Paul and Clarke (12).

He obtained good agreement. His observed .(p, n) reaction for

silver targets, however, differed by an order of magnitude from

his calculated value.












9

Millar(36) bombarded silver and bromine with 70-Mev brems-

strahlung and measured the energy spectra of emitted alpha particles.

The statistical theory correctly predicted the shape of the curve and

the position of the peak.

Experiments testing the statistical decay, of the compound

nucleus by the usual methods of nuclear physics are, then, hampered

by the interference of various direct interaction mechanisms. These

mechanismsare expected to become ever more important as the

incident energy is increased, but even at low bombarding energies

they may obscure the compound nucleus process. Bombardments

with 14o-Mev neutrons by McManus et al. (37) measuring the energy

distribution of emitted protons, show that a surface proton may

receive nearly all the incident energy and leave the nucleus immediately.

This type of reaction was considered by the authors to be most

important at 10 to 30 Mev. Below 10 Mev,. such a reaction may take

place throughout the entire nucleus, competing with formation of a

compound nucleus (38). A further discussion of surface reactions is

given by Austern et al. (39).

Many of the afore-mentioned experiments (those dealing with

the emission of high energy particles) are discussed by Cohen (40).

He concludes either that some non-compound nucleus process is

operative, or that some unknown selection rules are important.

Eisberg (41) cites evidence in support of the contention that a direct

interaction, preferably with surface nucleons, is the explanation.












10

Heavier bombarding projectiles which travel at the same velocity

as light particles produce compound nuclei with greater excitation

energy. Inaddition, this energy is shared among many incident nucleons;

therefore, the probability of energy exchange with the target nucleons is

much greater than in the foregoing experiments. The utilization of a

heavy ion as the bombarding projectile has the further advantage that

the nuclear binding energy of the incident ion will enter into the excita-

tion energy of the compound nucleus. In the case of nitrogen on sulfur

this may account for nearly half the total excitation energy. Heavy ion

bombardments, then, are a logical method of obtaining experimental

results at higher excitation energies.

Chackett etW:l.l(42) have utilized a nitrogen accelerator which

produces a continuous energy distribution up to 1.25 Mev, the beam

intensity falling off rapidly above 50 Mev. They put forth a-"buckshot"

theory to account for their results with aluminum targets (42). This

theory assumes, in general,. that only part of the nitrogen projectile

fuses with the target. Souch, (43) analyzing the C138/C134 ratio

formed in.the aluminum bombardments, concluded that the buckshot

theory is more valid than is-the compound nucleus hypothesis.

Greenlees and Souch (44) bombarded chlorine and reported that their

data from this experiment could be made to fit either theory. They

suggested that more information is necessary and may be obtained

from monoenergetic heavy ions.

Nitrogen ions are accelerated to 28 Mev in the Oak Ridge












11

National Laboratory. 63-inch cyclotron, with a full widthat half

maximum 600 Kev in the deflected beam. A nitrogen ion at this

energy has a velocity equal tothat of a 2-Mev proton. The low

incident velocity should make direct interactions unlikely; the

nitrogen should completely fuse with the target to form a compound

nucleus in which the excitation energy will be shared equally among

all the nucleons. If this is so then, according to the assumptions

proposed by Bohr (1), the decay of this nucleus will not depend on

the manner in.which it was formed. These ions would.seem to be

ideal for testing the theory.

Zucker and.co-workers have for the past several years been

conducting such experiments on a series of targets. A systematic

survey of nuclear reactions induced by nitrogen ions has been under-

taken (45). Various correlations with theory have been computed.

In this experiment a more complete comparison is attempted.


Present Experiment

Natural sulfur was bombarded with nitrogen ions at incident

energies ranging from 20 to 28 Mev. At this latter energy the V46

compound nucleus is excited to 33. 3 Mev.

The reactions listed in Table 1 were computed to be possible

results of evaporation from a compound nucleus. The half-lives in

this table refer in each case tothe first nuclide listed. The Q-values

were computed from the table of masses by Wapstra(46). Q"values












12

TABLE 1

POSSIBLE REACTIONS FROM THE V46 COMPOUND NUCLEUS



Product Nuclei Half life Q


'45
Ti +p
44
Sc44 + 2p
44m
Sc4 + 2p

Ca43 + 3p

K42 + 4p
V45 +
V +n
44
Ti4 + pn

Ti43 + p2n

Sc43 + 2pn

Ca42 + 3pn

Sc42 +
38m+
K + 2a

K38 + Za

Cl34 + 3a

Sc41 + na
41
Ca + pa
40
Ca + pna

Ka40 + 2pa

A3 + p2a


3. 09 hours

3.9 hours

2.44 days

stable

12. 5 hours

1 second

20 years

0.6 seconds

3. 9 hours

stable

0. 66 seconds

7. 7 minutes

1 second

32.4 minutes

0. seconds

10 years

stable

stable

35 days


+8. 66

+1.8

+1.55

-6.582

-17.41

+10.34





-9.58

-14.52

+8.0

+0.808

+0. 808

-6.03

-4.45

+2.3

-6.07

-6.61

-4.28











13

for nuclides not listed in these tables were computed from the semi-

empirical data of Cameron (47).

Not all the listed reactions were observed. In some cases the

residual nucleus is stable, or its half-life is either too long or too

short for convenient study. In other cases the reaction was energeti-

cally forbidden. The following reactions were observed:

S (N14, p) Ti45 (1)
32 14 44
S (N1, 2p) Sc (2)

S32 (N14, 2pn) Sc,3 (3)
32 14 38
s3 (N 4,Z) K. (4)

In addition the reaction:
32 (N14 13 33 (5)
46
was observed. It does not appear to go through the V46 compound

nucleus, is identified as a transfer reaction and is treated separately.

In the case of each reaction to be studied, the radioactive pro-

duct nuclei were chemically separated and their yields measured by

absolute beta counting. Smooth curves drawn through the yield vs

energy curves were differentiated to obtain excitation functions. The

cross sections at 27 Mev for reactions (1), (2), and (4) were then com-

pared with predictions based on statistical decay theory of the compound

nucleus. In the theoretical calculations, the procedure as set forth by

Blatt and Weisskopf (48) was extended by including both odd-even

effects (49) and shell structure effects (50) on the nuclear level densities,

and by including in the theory the possibility of compound nucleus deexc-

itation by gamma. emission. In addition, the effect of nuclear spins of












14

the emitted particles was taken into account.

There are certain assumptions which are included ,in the

original theory, such as specific values for nuclear radii and. a

certain prescribed dependence of level densities on energies. In

this experiment the nuclear radius was not.varied but calculations

were made for two values of the energy dependence of the level

densities.



















CHAPTER I

EXPERIMENT



Bombardment Techniques

Targets were made by pressing ZnS at a pressure of five

tons/in. 2 into brass molds 3/4 in. in diameter. ZnS was chosen as

the target material primarily because of the ease with which it

could be handled chemically, as compared to sulfur powder.

Nuclear reactions on the zinc were prohibited by the Coulomb

barrier of 31.4 Mev, calculated from the relation
2 1/3 1/3
B = Z1Z e2 /(A/3 + A ) r (6)

where B is the Coulomb barrier; Z1 and A1 refer to the nuclear

charge and mass, respectively, of the nitrogen ions; Z and A2

refer to the target nucleus; and ro is equal to 1. 5 x 101 cm. The

most energy available in the center-of-mass system was 23 Mev.

The targets were approximately 0. 1 in. thick, that is, infinitely

thicker than the range of energetic nitrogen ions. The ZnS was

obtained from the General Chemical Division of Allied Chemical

and.Dye Corporation and was reagent grade. The sulfur was nat-
32
ural sulfur, containing 94. 06% of S3. The ZnS was thoroughly
15












16

dried in an oven before pressing, and the targets were stored in a

desiccator. The targets as used presented.a hard uniform surface

which did not change under bombardment and which was found to be

stable at bombardment tempe ratures.

The target for each run was placed in the external beam of the

63-inch cyclotron and bombarded for periods ranging from ten minutes

for product potassium to three hours for scandium.

The energy of the incident beam was measured by observing

the energy of. recoil protons. The experimental apparatus is shown in

Fig. 1, taken from Reynolds et al. (51). The recoil protons pass

through a 9. 5 mg/cm nickel foil and then through a collimator which

permits passage of only those protons having an angle less than five

deg to the incident beam. The protons then pass.through 42. 76

mg/cm2 aluminum and.1.3 cm of air into an Ilford.C-2 nuclear emul-

sion. The range of the protons.in.the emulsion was measured. From

the known range-energy relations for protons in the emulsion(52); in

air, aluminum, and nickel (53); for nitrogen ions.in nickel (51); and

from the energy relations of nitrogen and recoil protons, the incident

nitrogen energy was calculated. The energy of nitrogen is related to

that of recoil protons at zero degrees, from conservation of energy

and momentum relationships, by

EN = 3.99.Ep. (7)

The incident energy was found to vary from 27. 2.to 28 Mev from day














UNCLASSIFIED
ORNL-LR-DWG 29339


ILFORD C-2 PLATE




ALUMINUM
ABSORBER FOILS-



COLLIMATOR-


PLATE HOLDER


ALUMINUM FOIL


S- EXIT FOIL

r ^i


TO MANOMETER


ENTRANCE FOIL


BEAM


Fig. 1. Energy Determination Apparatus.












18

to day, with about a.0.6 Mev full width at half maximum.

The energy of the incident beam was degraded by placing

nickel foils, in steps of approximately 0. 5 mg/cm2, between the beam

and the target. From the range-energy relations of nitrogen in

nickel (51) the energy of the beam hitting each target was calculated.

The beam current was integrated with a vibrating reed electrometer;

it was usually about 0.3 microamperes.


Chemical Techniques

According to Eqs. 1-5 the following elements were to be

isolated chemically: potassium, titanium, scandium, and nitrogen. In

addition, it was deemed necessary to add vanadium holdback carrier

in all cases. A slight amount of vanadium might have been formed by

the reactions:

S34 (N14,) V48 (8)

S34 (N14,n) V47 (9)

Zinc was present from the ZnS target.

It was determined that both scandium and titanium could be

removed from the same target. The technique, as follows, was modi-

fied from that given by Stevenson and Folger(54):
45
Titanium and.Scandium: The half-life of Ti45 is 3.09 hours.

The metastable state of Sc44 has a 2. 44 day half-life; the half-life of
the ground state is 3.9 hours. The half-life of43 is 3.9 hours.
the ground state is 3. 9 hours. The half-life of Sc is 3. 9 hours.












19

The target was dissolved in concentrated HC1 and heated to drive off

all HZS. Titanium and scandium carriers equivalent to about 10 mg of

each element were added along with holdback carriers. Scandium was

precipitated with saturated oxalic acid. The remaining solution was

scavenged five times with oxalic acid, then TiO2 was precipitated with

KBrO4. This was washed several times with hot water, then.redis-

solved in.concentrated HC1. TiOZ was precipitated again with conceh-

trated ammonia. The precipitate was washed with hot water, ignited

at 800* C in a muffle furnace for thirty minutes (55), cooled, and

weighed after transfer to a counting cup. Time: 2 hours. Yield:

40-60%. The scandium precipitate was washed with hot water and'

then with oxalic acid. It was dissolved in concentrated nitric acid.

The scandium was then precipitated as the oxide with concentrated

ammonia. It was washed with hot water, ignited in platinum in a

muffle furnace at 700 C forty minutes (55), cooled, and weighed after

transfer to a counting cup. Time: 2 hours. Yield: 30-80%.

The technique for potassium was taken from the Oak Ridge

National Laboratory Master Analytic Manual, No. 1-216451, and is as

follows:

Potassium: The half-life of K38 is 7. 7 minutes. The target

was dissolved in a test tube containing concentrated HC1 and about 5

mg potassium carrier. Holdback carriers were added. Twenty ml of

pH 2. 8 buffer.were added, 10 ml of 0.6% sodium tetraphenyl boron












20

reagent were added and the potassium precipitated as potassium tetra-

phenyl boron, K(C6H5)4B. The precipitate was washed once, dried,

transferred and counted. It was weighed after counting. Time: 15

minutes. Yield: 45-80%.

The nitrogen technique was modified from that used for potas-

sium and is as follows:

Nitrogen: The half-life of N13 is 10.1 minutes. The target

was dissolved in concentrated HC1 and carriers were added. 6N

NaOH was added and the solution was boiled. NH3 escaped and was

distilled into a cooled solution containing pH 2. 8 buffer and 0. 6%

sodium tetraphenyl boron. The nitrogen precipitated as NH4(C 6H)4B.

It was washed once, dried, transferred, and counted. It was weighed

after counting. Time: 20 minutes. Yield: 30-60%.

Carriers were prepared as follows:

Titanium: Approximately 20 g of TiC14 was dissolved in

enough water to give about 500 ml of solution. The solution was then

assayed. Ti(OH)4.was precipitated from 5 ml of the solution by the

addition of concentrated ammonia. The precipitate was filtered and

washed with water containing a few drops of ammonia. It was ignited

in a platinum crucible in a muffle furnace at above 700 C for 30

minutes (55), then cooled in a desiccator and weighed. Results gave

10.42 mg of titanium per ml of solution, with an error of + 1.5% for

a standard deviation from a series of measurements.

Scandium: 1. 6947 g of Sc 03 was dissolved slowly in hot con-











21

centrated HCl to a volume of about 100 ml. The solution was assayed

as follows: 2 ml of the solution was diluted with 0. 5 ml of water and

Sc(OH)3 was precipitated with 2. 5 ml concentrated ammonia. The

precipitate was centrifuged and the supernatant decanted. The preci-

pitated was washed with water containing a few drops of ammonia and

ignited in a platinum crucible in a muffle furnace for thirty minutes

at 600-700 C (55). Results gave 10. 54 mg of scandium per ml of

solution, with an error of : 3. 72% for a standard deviation from a

series of measurements.

Potassium: 9. 5383 g of KC1 was dissolved in water and taken

to 500 ml-volume in a volumetric flask. This gave 10.005 mg potas-

sium per ml and was felt to be more accurate than an assay would be.

Nitrogen: 1. 202 g of NH4Cl was dissolved in water and taken

to 500 ml of solution in a volumetric flask. This gave 0..6297 mg

nitrogen per ml of solution and was thought to be more accurate than

an assay would be.

Vanadium: 17. 848 g of VO05 was dissolved with difficulty in

concentrated HCi and the volume brought to 500 ml. Two ml of this

solution was diluted with one ml water and 4 drops 30% H20zZ. It was

evaporated in an oven at 110* C for thirty minutes (55). It was a blue

liquid which solidified immediately upon removal from the oven. It

was cooled and weighed, and gave 19.495 mg vanadium per ml of

carrier solution if the residue was,V205. Some V205 powder was

obtained from the stock room and heated to above 650* C for thirty














minutes. Upon removal from the muffle furnace it was identical with

the above. Since the carrier was to be used solely for holdback pur-

poses, it was not thought worthwhile to spend more time on the problem

of assaying it.



Counting Techniques

In general the counting technique was the same for all residual

nuclei studied. After each bombardment the target was removed

from the cyclotron, chemically processed, and then counted.

Calibration

Each nuclide was counted in a stainless steel cup, supported

by cardboard plates, beneath end-window Geiger counters enclosed

in lead shields. Geometry was maintained as constant as possible for

all samples, and constant with that of a Ra-DEF standard which was

used to calibrate each counter. The standard was obtained from the

National Bureau of Standards and was certified to have had an activity

of 201.8 disintegrations per second on March 1, 1950.

The calibrations were performed by counting the standard

with various amounts of aluminum absorber between it and the

counter and extrapolating the -ate on semi-log paper to zero absorber.

Such a plot is shown in Fig. 2. The Ra-DEF source has radiation
210
consisting of negatons with a 22. 2-year half-life from Pb alpha

particles of half-life equal to 2.6 x 10 years from Bil0, and 138-day

alpha particles from Po20. The absorbers cut out the alpha activity





























UNCLASSIFIED
ORNL-LR-DWG 29340

















S-0-- -
.....


mg/cm2 Al ABSORBER


Fig. 2. Ra-DEF Calibration.


U 50
0
o

LJ
I-



z 20
I-
z
0
0

40












24

while their effect on the negatons emitted was small. The absorbers

used ranged from 1. 63 to 20. 8 mg/cm2 of aluminum. A back-scatter

correction factor of 1.54 was applied to the calibration. No correc-

tions were applied for air scattering, scattering by the sides of the

lead shield, or window absorption. Window thicknesses varied about

2. 0 mg/cm2 of .iica. A back-scatter correction factor of 1.6 was

applied to all nuclides counted in accordance with experiments per.~

formed in this laboratory by M. L. Halbert. Burtt (56) has shown

that the saturation back-scatter correction is independent of the maxi-

mum beta energy if that energy is above 0. 5 Mev. Preliminary

experiments done in this laboratory by J. J. Pinajian showed that self-

absorption of beta particles at these energies, and for the amount of

material being counted, could be neglected. Corrections were made
32
for K-capture branching ratios and for isotopic abundance of S3 in

the target material. The background rate in each counter was about

0.4 counts per second and was measured to a statistical accuracy of

one per cent.

Experimental values

Half-lives were assigned to the nuclides as shown in Table 2.

These half-life values are the best available in the opinion of the

author.



















TABLE 2

ASSIGNED HALF-LIVES



Nuclide Half-life Reference


3. 09 hours

2. 44 days

3. 9 hours

3. 9 hours

.7. 7 minutes

10. 1 minutes


H. E. Kubitschek

Hibdon, Pool, and Kurbatov

Hibdon, Pool, and Kurbatov

Hibdon, Pool, and Kurbatov

Green and Richardson

Siegbahn and Slatis


Ti45
Sc44m

Sc44
Sc43

K38

N13


(57)

(58)
(58)

(58)

(59)

(60)


I- -












26
In each case a straight line corresponding to the best half life

was drawn through the experimentally determined points. This line

was fitted to the points visually, and was later extrapolated to deter-

mine the activity of each nuclide at the end of bombardment. Each

nuclide was counted down to background level to ascertain whether
45
any long-lived nuclide was present. A typical decay curve for Ti45

is shown in Fig. 3, Points shown are counting rates minus back-

ground, with standard deviations as indicated on typical points.

A decay curve characteristic ofSc44 is shown in .Fig. 4. Two

activities are present: a 2.44-day activity due to the metastable
44 44 43
state of Sc, .and. a 3. 9-hour activity due to both Sc and Sc A

straight line with half-life .equal to.2.44 days was drawn through the

lower points as shown and extrapolated back to end of bombardment.

The activity due to this state was then subtracted from the total to

determine the 3. 9-hour counting rate.
44 43
To determine the relative yield of the Sc 4and Sc4 isotopes

of 3. 9-hour half-life, several scandium samples were gamma counted

on a scintillation spectroscope with a sodium iodide crystal.. Sc44

has..a l.47-Mev position and a 1.16-Mev gamma ray. Sc43 has a

1.19-Mev position and only low energy gamma rays. A graph showing

the gamma counting rate as a function of gamma energy was expected,

then, to show a peak due to annihilation photons from both isotopes,

plus a peak at 1. 16 Mev due to both states of the Sc44 isotope. Such a

graph is shown in Fig. 5, showing the activity at two times. The peak









UNCLASSIFIED
ORNL-LR-DWG 29344






N.* '\_____________________


N ______
*.
==.. ^^=
___________--^_-,,,._

----------------------------"--^---------------





--------.-..


TIME (hr)
Fig. 3. Typical Ti45 Decay Curve.
















5X.402




2



402


0 40 20 30


40 50 60


70 80 90 100 110
TIME (hr)


Fig. 4. Typical Sc44 Decay Curve. Crosses indicate total counting rate. Dots indicate rate after sub-
traction of 2.44-day activity.


UNCLASSIFIED
ORNL-LR-DWG 29342


















X
qx
X




X





3.92 hr Sc 2.44 day Sc -x
X *X


120 430














UNCLASSIFIED
ORNL-LR-DWG 28264R


1-4 I 7


____ ____ I ____ ____ ____ ____ 1]


40
CHANNEL


50


10 20


Fig. 5. Scandium Gamma Spectrum.


Dck6~


c


5

2

10-i


60


I I I I ...- I


j


0\












30

at channel 57 is due to the 1. 16-Mev gamma.

The observed gamma counting rate at a particular time t'
44m 44
indicated the activity due to Sc and Sc at that-time, where
0
44m 44
Sc is.the metastable state and Sc is the ground state. From

the decay curve plotted on the basis of geiger counting, as in Fig. 4,
44m 44 43
the activity due to Sc and that due to (Sc + Sc ) was known at
44m
time t' Then subtracting the activity due to Sc from the gamma
44
activity gave that due solely to,Sc This was compared to the
0
activity due to both Sc 44and Sc43 measured by the geiger counting to

determine the relative activities of each isotope.

The efficiency of the scintillation apparatus was determined

with a Rb86 source obtained from the Radioisotopes Division of the

Oak Ridge National Laboratory. The Rb8 has a 1. 77-Mev negaton

and a 1. 08-Mev gamma ray. It was precipitated from HC1 solution

by sodium tetraphenyl boron, with KC1 carrier, and was beta counted

to determine its disintegration rate. The ratio of gamma to beta

disintegrations was taken from Nuclear Level Schemes (61). A graph
8f6
of the Rb standard is shown in Fig. 6.

Decay curves for K and N3 are shown in Figs. 7 and 8.

The potassium showed a small amount of long-lived activity which

was assigned tothe ground state of Sc44. This activity was therefore

subtracted from the observed rate as is indicated on the graph. The

curve thus obtained fitted the K38 decay rate.




















UNCLASSIFIED
4 ORNL-LR-DWG 29343


10



5
5 --------- -




2


3
10 -



5




02
o 2 0080

2


o .
40




I-

t0
z
2
z


10

S2 --- -- -- -- --- --- -- ---
5







2







0.5 -




0.2



0. -
5 10 45 20 25 30 35 40 45
CHANNEL


50 55 60 65 70 75


Fig. 6. Rb86 Gamma Spectrum.

















UNCLASSIFIED
ORNL-LR-DWG 29344


456


36 56 76 96 446 436
TIME (min)


Fig. 7. Typical K38 Decay Curv. Dots indicate total counting rate. Crosses
indicate rate after subtraction of Sc activity.















































































0 8 46 24 32 40 48 56
TIME (min)



Fig. 8. Typical N13 Decay Curve.


UNCLASSIFIED
ORNL-LR- DWG 29345


64 72 80


















CHAPTER IIl

CALCULATIONS AND RESULTS

Each nuclide was beta counted for a length of time equal to

about ten half-lives. As each nuclide was counted, the disintegrations

were automatically recorded on a tape. The counting rate for each

nuclide, corrected for background, was plotted on semi-log paper.

Straight lines with slopes determined by the assigned half lives were

drawn through the experimental points, as shown in Figs. 3, 4, 7, and

8. These lines were extrapolated to the end of bombardment.

The yield of nuclear reactions formed per incident particle was

then calculated for each run by the equation

(dN/dt) (10)
E E R B K I(1-4 t)
c p k
where (dN/dt) = counts per second at end of bombardment,

E = chemical efficiency,

E = counter efficiency,

R = N+3 beam current expressed as the number of nitrogen

ions hitting the target per second,

Bk = backscatter correction = 1.6,

K = K-capture branching ratio,
32
I = isotopic target abundance of S 0. 94,

\ = decay constant,











35

t = length of bombardment.

The chemical efficiency.was determined by weighing each

separated sample and assuming that complete chemical exchange

took place between reaction products and carrier. At the counting

rates involved, a maximum of 80 counts per second, .no correction

was needed for resolving time of the counters. The K-capture
45 44
branching ratio.for Ti and Sc44 was taken from Nuclear Level

Schemes (61), for K38 from Endt and Kluyver (62), and for N13 from

Ajzenberg and Lauritsen (63).

Nuclear reaction yields were determined at several energies

for each nuclide. In each case, the incident energy was degraded

.until activity could no longer be measured. The yields were plotted
44
.against energy as shown in .Figs. 9 and .10. Relative yields of Sc4
0
43
and Sc43 were determined as described in the previous section.
44
Sc accounted for 84% of the total 3. 9.hour activity. The yield as
44
7ishown for Sc44 is the sum of the yields due tothe ground state and.to

the metastable state.

The thick target yield measured, at any incident energy E is

expressed as

Y = n o(E) dE. (11)

Therefore to,determine the excitation functions. smooth curves

drawn through the. experimentally determined yield vs energy points

were differentiated. The equation for the cross-sections was derived

as follows:

















1-6
10


UNCLASSIFIED
ORNL-LR-DWG 28267R


5



2








-88
44
5



2

-8









10
5



2




545 38 _


5 -Ti K



2
-10-


5



2


10
18 20 22 24 26
NITROGEN ENERGYLAB (Mev)

Fig. 9. Yields vs Nitrogen Energy.


28 30
















UNCLASSIFIED
ORNL-LR-DWG 28269R


20 22 24 26 28
NITROGEN ENERGYLAB (Mev)


Fig. 10. Yield vs Nitrogen Energy for (N14, N13) Reaction.


0-8





5






-2


0
0.
S0

C







4-O
c



10
_1




2




-10





5x10
-t













Y = no, (12)

over a small interval dE, where

r = cross section in cm and
2
n = number of target atoms per cm.

Then

dY dn
_Y = -- (13)
dE dE

if is considered to be constant over the small energy interval

dE, as is nearly the case.

To determine dn/dE the following argument was used:

Range-energy relationships are usually given in terms of dE/dx.

Then

dn _dx N-*ID (14)
dE dE A 10
ZnS
where

D = density of ZnS in mg/cmZ

x = range of nitrogen in ZnS in cm,

N = 6.023 103 = number.of sulfur atoms per mole

of ZnS,

I = isotopic abundance of S32

AZnS = molecular weight of ZnS.

The stopping power.,S was defined as,equal to dE/dx for par-

ticles i incident on material j. The quantity needed for Eq. 14 is

SN .This was determined, according to the discussion by Allison
and Warshaw (64), from
and Warshaw (64), from












1 AZn + As
N A N N (15)
ZnS ZnS Zn AZnS S S
N N
Zn was taken as equal to SNi, whiih was. taken from the
N
data of Reynolds,. Scott, and Zucker (51); S was taken from the

relative stopping powers of sulfur and nickel for protons of the
P
same velocity. .-SNi was taken from the data of Allison and War-

.shaw (64); S was interpolated from the same-data.
S
A plot of.the stopping power of ZnS for nitrogen ions vs

nitrogen energy is shown in Fig. 11. This method of calculating the

range of nitrogen ions in target materials has been previously checked

by Reynolds and Zucker (45) for aluminum. Then

dY dE AZnS l.. (
E E N I D (N 16)

These -cross sections are plotted against incident nitrogen ion energy

in the laboratory system in Figs.. 12 and 13 and.are listed at. various

incident energies in Table 3.

The.errors in the absolute yields ,are on the order of 20%,

due mainly to the-inherent difficulties of Geiger tube calibrations.

Statistical errorsassociated with low counting rates became impor-

tant at thelowest incident energies. This fact is shown on the yield

curves in Figs. 9.and 10. No errors were plotted-on the cross sec-

tion curves as these were obtained by differentiating the smooth

curves drawn to fit the experimental yield points.


















UNCLASSIFIED
ORNL-LR-DWG 29346
5.0








E -*

E

S4.0












3.0
3 .0 -------------------------------------------------
40 12 14 16 18 20 22 24 26 28 30 32
NITROGEN ENERGYLAB (Mev)


Fig. 11. Stopping Power of ZnS for Nitrogen Ions vs Nitrogen Energy.


















UNCLASSIFIED
ORNL-LR-DWG 28266R


10-27

5


2

10-28

5x 40-29
16 18 20


22 24 26 28 30


NITROGEN ENERGYLAB (Mev)


Fig. 12. Cross Sections vs Nitrogen Energy.


-25
2 x 1025

10-25

5


2

10-26

5


2















UNCLASSIFIED
ORNL-LR-DWG 28270R


-029 I I
18 20 22 24 26 28
NITROGEN ENERGYLAB (Mev)


Fig. 13. Cross Section vs Nitrogen Energy for (N14, N 3) Reaction.


5xO-27
5x10





2



-27
10




5


-28
10




5















TABLE 3

MEASURED CROSS SECTIONS



Nuclide C-ross Sectionin --illibarns
Nuclide Cross Section in millibarns


20 Mev


22 Mev


24 Mev


26 Mev


27 Mev


44
Ti45 0.108 0.59 1.84 2.49

Sc44 0. 45 2.64 18.5 68.5 101

K38 0.46 1.83 2.22

N13 0.09 0.375 1.19 1.89


















CHAPTER IV

DISCUSSION

Niels Bohr, in.the formative paper (1) on compound nucleus

decay, postulated that.it is possible to divide a nuclear reaction into

,two distinct steps:

1. The formation of a compound nucleus, and

2. The disintegration of this nucleus.

The following assumption has been made: that these two

steps can be considered independently, that is, the disintegration

of the compound nucleus will not depend on the manner in which it

was formed (neglecting the spins and orbital angular moment

involved).

Bohr bases his assumption on a nuclear model consisting of

a group of nucleons with short-range forces but with strong inter-

actions over thpse short ranges. The process canbe visualized as

follows: the bombarding projectile hits the target nucleus and fuses

into it. Its energy is quickly shared among all the nucleons present,

in what is now a compound nucleus. The formation that has just been

described depends on such factors as the nature of target and projectile,

the projectile energy, et cetera, The compound nucleus will, however,

disintegrate in a manner independent of its formation.

44











45

Then.the cross section of a nuclear reaction can be written as

a(ab) = -c(a) P(b), (17)

where the reaction we are considering is initiated by projectile a inci-

dent on the target and is concluded by the evaporation ( or fission, or

splitting, et cetera) or particle b from the compound nucleus. The

factor c (a) is the "capture" cross section for the formation of the

compound nucleus by the interaction of projectile a and target. P(b)

is the probability that the compound nucleus, once formed, will decay

by emitting particle b. In this paper, a is the nitrogen ion and b may

be an alpha particle, neutron, proton, or photon. For purposes of

this discussion deuteron and tritium emission has been neglected.

The quantity c (a) for nitrogen ions incident on sulfur is not

well known; existing tables do not cover the wide range of parameters

needed due to the large masses involved. Correlation with experiment

is thus most meaningful when ratios of total crosssections are

computed:

cr(ab) c(a) P(b) P(b)
ac) (a) P(c) Pc
c

It is, ,then,the probability of a particular particle being emitted that

is of most.theoretical concern to this experiment. An expression

for P(b) can be derived by making use of.the "reciprocity theorem":

So-(ba) (19)



where >a is the wave. length corresponding to the energy of incident
a













particle -a, --as

a = (2MaE') 1/2 (20)

where M is the reduced mass of a and E' is the incident energy in
a a
the center-of-mass system. Then expressing P(b) as

P(b) = G(b)/G, (21)

where G may be considered as a level width [that is, G/t is.a decay

rate; G(b)/t being the rate of decay by emission of particle b,. and

.G = cG(c) and referring to Eqs. 17 and 19 we find

cc(b) k
P(b) = (22)
S:.k. c (i)

where k. = 1/W, and the sum is extended over all possible particle

emissions.

Each particle b that is emitted from the compound nucleus will

come off with a certain energy given by

b = E' + Q, (23)
b a
where E' is the center-of-mass energy carried in by particle a, and
a
Q is the energy released. in the (a,b) reaction. Recoil energy of the

residual nucleus is neglected. b can be given by

E = bm E (24)
13 bm bs
where bm is the maximum kinetic energy that particle b can carry

off, and Eb is.the energy left in the residual nucleus as excitation
energy. If E is large enough further particle emission can occur.
,energy. If Eb is large enough further particle emission can occur.














The shape of the energy distribution for particles b emitted with an

energyb between Eb and Eb + d-b is given by


P () de= 2.P(b), (25)

where the sum includes all final states of particle b within the interval

dE. The number of terms in this sum is given by the number of levels

of the residual nucleus with an energy Eb which lies between Eb and

Eb de. This number of terms is designated by w(Eb )dE, and

w(Eb ) is called the level density. The relative energy distribution of

the outgoing particle b can be calculated from Eqs. 22 and 25 as


N(eb)dl= constEb c(b,e)w(Eb*) (2s+l)d&b, (26)

where c (b) is now the inverse cross section for the emission of b

from the compound nucleus; that is, it is the cross section for the

formation of the compound nucleus by particle b, with energy Eb'

incident on the residual nucleus. The quantity s is the nuclear spin,

withvalues of 1/2 for proton and neutron, 0 for alpha particles.

Sc(b) for protons, neutrons, and alpha-particles can be interpolated

from the graph and tables given by Blatt and Weisskopf. The existing

data for charged particles do not cover energies of emission greater

than twice the Coulomb barrier. At these energies, an asymptotic













equation is used:


where


To calculate the

is introduced as


1/3
R =rA +D
o
-13
r =1.5x10 cm
o
-13
D = 1. 2 x 10 cm, for alpha particles and

= 0 for protons

Eb = energy of particle b in the center of mass
system

B = Coulomb barrier.

probability of particle emission, the "F-factor"


Fb =5-k- o (i), (27)
b11 c

where the sum is extended over all energies at which particle b can be

emitted. The sum is expressed as an integral as
2Mb
Fb(Ebm) :-2 b +m(2s +1)b 'cb,a)Eb )d% (28)

and the probability can be expressed as

P(b) = Fb/iFi, (29)

where the sum is extended over all particles emitted. In this paper

i includes protons, neutrons, alpha particles, and photons. To cal-

culate the probability of gamma emission an F-function was determined


(c (b ) = (R + >2 1 R B '
c1 (R + k)'b















for photons from Eq. 27 and analogous to Eq. 28 as

F (e ) = ("c), Eym aZ c (y,E)w(E *)dE .(30)


When proper unit conversion factors are utilized, this F=function is

additive with those defined in Eq. 28. The factor c(e y) in Eq. 30 is

the capture cross section for photons on the residual nuclei. This

was calculated from the approximate equations for magnetic dipole and

electric quadrupole radiation given in Blatt and Weisskopf. The

giant resonance due to electric dipole radiation was not included in

the final calculations, although preliminary consideration showed it

would not change the final results by more than a few per cent. The

remaining factor in Eqs. 28 and 30 is the level density, an expression

for which can be approximately derived by considering the logarithm

S(E) = log w(E), (31)

and defining

dS =1 (32)



T will then have energy dimensions and is considered to be a "nuclear

temperature" by analogy with thermodynamics. S is analogous to the

entropy of the residual nucleus, S being the logarithm of the level

density, and Eq. 32 then corresponds to the thermodynamic relation

between temperature and entropy. Omission of the Boltzmann constant

from the original definition of S leaves T with energetic dimensions.












.50 -.

Then dE/dT must equal zero at T = 0, extending the analogy to

include the third law of thermodynamics. If we assume that E(T)

can be expanded in a power series around T = 0, it must therefore

begin with a quadratic term. The further assumption is made that

all higher powers of T can be neglected in the expansion. Then

E = aT2 and

S = fdE/T = 2(aE)1/Z + const and

w(E) = C exp 2(aE)1/2. (33)

Absolute values of C do not enter into the calculations since ratios are

involved. The value of a, however, is extremely important. The values

given in Blatt and Weisskopf have not been supported by experiment.

Porges (65) bombarded silver and copper with 40-Mev alphas and calcu-

lated a value of a equal to about 2 Mev1 and independent of A, where

A is the mass number of the residual nucleus. Comparisons between

theory and (a, 2n) cross sections determined by Temmer (66) and

Kelly and Segre (21) give the same result. Slow neutron resonance

measurements (67) of level spacings give larger values of a, values

which are strongly functions of A. Energy emission spectra (30, 33, 35)

from inelastic scattering of protons and neutrons give high values of a

which are less dependent on A, Excitation function experiments (13, 23)

give low values for a. A discussion of possible errors and causes for

the variety of results are found in Porges (65).















/Eisberg et al. (34) bombarded several elements with 40-Mev alphas

and observed evaporated protons. They got a value of a which is

low and not a function of A. Igo and Wegner (68) summarize the

above papers. They arrive at two main estimates of a: one giving a

as relatively constant and equal to approximately 2, the other giving

a as function of A (as would be expected from a Fermi gas model) not

in disagreement with Lang and Le Couteur's (69) dependence on

A/10. 5.

A previous analysis of cross sections from nitrogen on sodium

(45) shows that values of a = A/10. 5 provide fair agreement between

experiment and theory. Further nitrogen-induced experiments by

Zucker (70) and by Goodman and Need (71) give results in agreement

with a = A/10. 5. On the basis of the above papers, two values of a

seem to emerge; namely a = 2, and a = A/10. 5 which was chosen for

the calculations described in this experiment and which was felt to be

the more valid of the two. The calculations were then duplicated

using a = 2.

The constant C in Eq. 33 is related to both even-odd and shell

structure characteristics of the residual nucleus. Even-odd effects

were taken into account by utilizing the averaged empirical relation-

ship of Brown and Muirhead (49):

w w w
oo oe ee (
T2- -'5- "- (34)











52

For example, C. for an odd-odd residual nucleus was taken to be

12/5 that for an odd-even nucleus. Shell structure effects were cal-

culated from the work of Newton (50) who arrives at the following

equation

DO =A5/3( +1)1/2(z 1) 1/(Eb + 3t)2
S7 1/ (35)
exp 8. 75-0.4982(n +tz + 1)1 /2A/3Eb /

where wD =1, and 3 are averaged angular momentum quantum
o n z
numbers, Eb is the excitation energy of the nucleus, and

t = (6r2 G -1Eb )/2 where G is a shell-dependent factor given in

Fig. 4 of the paper by Newton. The reciprocals of ratios of D -values

for a set of nuclei were taken to be the ratios of the constant C. All

the quantities in Eqs. 28 and 30 could now be numerically estimated.

Fig. 14 is a diagrammatic representation of the evaporation

process, Calculations were made in a step-wise procedure as follows:
32
A 27-Mev nitrogen ion incident on S32 yields a compound nucleus of

V46 with E = 32. 6 Mev, E being the excitation energy given by

E = E'N + Q, (35)

where E'N is the center-of-mass nitrogen energy and Q is calculated

from the masses of nuclides involved.

Considering first reactions (1) and (2), (the and 2p out reactions),

the probability that V46 at this excitation energy would emit a proton,

neutron, or alpha particle was calculated from Eqs.28 and 29.
















UNCLASSIFIED
ORNL-LR-DWG 28265

45 n 46
Vqs V




1\
4%



a

45
Ti3.0h
42
Sc0.6





43 n 44
Sc h Sc d
3.9 2.4
3.9h


38
K7.7


Fig. 14. Diagram Showing Position of Nuclides.















The quantity under the integral was evaluated at different energies

Eb and then graphically integrated. It was found that 65.3% of the

V46 nuclei formed would decay by proton emission. The energy

spectra of emitted protons were calculated from Eq. 26, and thus

the density of occupied states in Ti45 was found. Results of the cal-
45
culation are illustrated in Fig. 15. A further contribution to the Ti4

yield would be expected to come from the (N n) reaction leading to

V45 which emits positrons, forming Ti45, with a half life on the order

of one second. Calculations similar to the above show that only 21%

of the V6 decays by neutron emission. The preponderance of initial

proton emission is due to the Q-values involved. Further calculations
45
show that contributions to the total Ti45 yield from this reaction should

amount to 1-3% and have therefore been ignored in the remainder of

this discussion. This low value is due to the Q-values involved in
45
further particle emissions from the V45 nucleus which make such

reactions extremely likely, and the yield of V45 only about 2% of the

Ti45 yield.
45
The available states of Ti45 were arbitrarily broken into level
45
widths 4-Mev wide, and the fraction of emitted protons that left Ti4

in each band was calculated. That portion of occupied states lying

below the energetic barrier for further particle emission will remain
45
as Ti45. These states are shown in the shaded portion of Fig. 15.

All higher occupied states will again emit particles or gamma rays.















UNCLASSIFIED
ORNL-LR-DWG 29347














n OUT
Sc43


p OUT a OUT
Ca43 K40


Sc44


Ti45


Fig. 15. Diagram Showing Schematics of Evaporation Calculations.


32.6


5.14


a OUT
Ca44












56

Each level band was treated as a separate compound nucleus.

The top most level band was considered first: the probability that it

would evaporate a proton, neutron, alpha particle, or photon was
45
calculated. Photon emission would leave again a Ti residual

nucleus, but in a lower energy state, one corresponding to the energy

of the emitted photon. Thus, an additive correction was made to each

lower lying level band. The next lowest band was then treated in the

same fashion, and so on. It was found that gamma emission increased

the portion of Ti45 remaining below the energetic barrier from

2.3 x 10-4 to 6. 8 x 10-3; that is, of each Ti45 nucleus formed from

V 4, 0. 68% remained as Ti45 while 99. 32% emitted another particle

and formed another nuclide.
45 44
Some 65. 9% of the Ti emitted a proton to form Sc This

nuclide was treated in an analogous manner, the level bands being
44
made 2-Mev wide in this case. The final portion remaining as Sc,

after particle and gamma emissions were considered, was found to

be 0. 363; that is, of the Sc44 nuclei formed from the proton emission
45 44
of Ti45, 36. 3% remained as Sc44

In an analogous manner, a and 2a emission from the V46 nucleus

was considered: 13.4% of the V46 emitted an alpha to form Sc42

and 1.99% of this emitted another alpha to form K3; 31. 7% of this

remained as K3















Comparison of Results

Cross sections for each nuclide relative to the capture cross

section of nitrogen on sulfur were calculated by multiplying the

fraction of the original V46 which decayed into the nuclide times the

fraction so formed that remained as the nuclide. Ratios of cross

sections were calculated as in Eq. 18 and compared to experimental

results.

Calculations were made for two values a, and for two circum-

stances: gamma emission was included in one set, and excluded in

the other. Results are shown in Table 4.

It is seen that when gamma emission is included in the calculations,

according to Eq. 30, then a value of a = A/10. 5 gives good correlation

with experiment for the Sc44 /Ti45 ratio. Experimental yields of

K38 are much greater than those predicted by the theory. Actually,

since the ground state of K38 has a one second half-life and was thus

not counted, its total cross section is still higher. The value a = 2

does not give agreement with experiment.

If gamma emission is not considered, then a = A/10. 5 does not

seem to be valid, while a = 2 gives results in.agreement with the

measured values for QSc44 /Ti4

A careful examination of the processes involved leads to the

conclusion that gamma emission should be considered in the calcu-

lations. The above results show that a lack of this consideration may















TABLE 4

COMPARISON OF RESULTS


Experimental


.024




45


Theoretical
Gamma Emission No Gamma
A A
a=TU a=2 a= =


.025




185


.16




18


Emission
a=2


.0047


105


Nuclides


Ti45


SSc44

S44
Sc

K














lead to low values of a, as found in previous papers (13, 21, 23, 65, 66).

In all these papers gamma emission was not considered.

The neutron transfer reaction (5) gives results in agreement with

those of similar reactions previously studied in this laboratory (72).

G. Breit (73) has indicated that if the cross section of such a reaction

is plotted against an E defined by

E* = E' B + 1/2 Q, (36)

where E' is the incident center-of-mass energy and B is the barrier

energy, then a plot will be obtained which is independent of target

nucleus and will vary from one target to another depending only on

angular momentum changes in the transferred nucleon. Such a plot

for several target elements is shown in Fig. 16. Cross sections for

all elements other than S32 are taken from the paper by Zucker

et al (72). The targets do tend to group themselves in distinct bands,

with the exception of Na 7, in general accordance with the theory.









UNCLASSIFIED
ORNL-LR- DWG 28268R


1.0

0.5


0.2 --

0.1

0.05
-6 -5 -4 -3 -2 -1


0 1 2 3 4 5


E*


Fig. 16. Cross Sections for Neutron Transfer Reactions vs E* = Ecm B + 1/2Q.












CHAPTER VII

CONCLUSIONS


Four nuclear reactions initiated by the nitrogen bombardment

of natural sulfur were experimentally observed, excitation functions

were measured, and the cross sections of three of these at a bom-

barding energy of 27 Mev were compared with predictions based on the

statistical theory of compound nucleus decay. One of the reactions was

a nucleon transfer mechanism and its cross section was compared to

similar reactions; the comparison gave qualitative agreement.

The predictions of the statistical theory were calculated for two

values of the parameter a. The value a = A/10. 5 gave good agreement
14 14
with theory for the(N 14,p) and (N 14, 2p) reactions in view of the

approximations necessary. The predicted value of the (N14, 2a) reaction

was at least four times less than the experimental value. It had been

noted in a previous paper (25) that alpha-out reactions from the

nitrogen bombardment of C12 are higher than predicted. A possible

explanation may be related to the "alpha particle structure" of C12

in that the compound nucleus retains a "memory" of the original target.

Sulfur-32 may also exhibit this property, and this mpy account for the

variation from theory. However there is no real evidence for such an

explanation, and the variation may be simply a failure of the theory.

The ratios of cross sections calculated with a = 2 did not agree with

the experimental values when gamma emission was considered.

61












62

When the emission of gamma-rays was not included in the calculations,

a = 2 gave better correlation than did a = A/10. 5.

The work done here indicates that a compound nucleus process is

operative in the nitrogen bombardment of sulfur, in the energy region

considered. The statistical theory of compound nucleus decay gives

predictions in agreement with observed results, with the exception

of the alpha-out process. It is assumed that another mechanism,

such as an incomplete compound system formation, may be involved

in this reaction.















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BIOGRAPHICAL NOTE


David E. Fisher was born on June 22, 1932, in

Philadelphia, Pennsylvania, and received his early education in

that city. He graduated from Central High School of Philadelphia

in January, 1950.

He studied at Trinity College in Hartford, Connecticut,

receiving the Bachelor of Science degree in June, 1954.

Graduate studies were undertaken in September, 1954, at

the University of Florida. While there he was employed by the

Department of Chemistry, first as a graduate assistant, then as

a teaching assistant.

In August, 1957, he went to the Oak Ridge National Labora-

tory under the terms of an Oak Ridge Institute of Nuclear Studies

fellowship to undertake the research for this dissertation.

He is a member of Sigma Pi Sigma honorary fraternity,

of the American Chemical Society, and of the American Physical

Society.













This dissertation was prepared under the direction of the

chairman of the candidate's supervisory committee and has been

approved by all members of that committee. It was submitted to

the Dean of the College of Arts and Sciences and to the Graduate

Council, and was approved as partial fulfillment of the require-

ments for the degree of Doctor of Philosophy.



June 9, 1958





Dean, College of Arts and Sciences



Dean, Graduate School


SUPERVISORY COMMITTEE









\I, a Lir
A IF 711










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TITLE: Nuclear reaction cross sections from the nitrogen bombardment of
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PUBLICATION DATE: 1958


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