NUCLEAR REACTION CROSS SECTIONS
FROM THE NITROGEN BOMBARDMENT
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
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
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-
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
ACKNOWLEDGEMENTS --------------------------- i
LIST OF TABLES ------------------------------- v
LIST OF FIGURES ---------- -------------------- vi
1. INTRODUCTION ----------------------- 1
II EXPERIMENT ----------------------- 15
III. CALCULATIONS AND RESULTS --------- 34
IV. DISCUSSION --------------------------- 44
V .. CONCLUSIONS ------------------------- 61
BIBLIOGRAPHY ----------------------------------- 63
BIOGRAPHICAL NOTE ----------------------------- 68
LIST OF TABLES
1 Possible Reactions from the V Compound 12
2 Assigned Half-Lives 25
3 Measured Cross Sections 43
4 Comparison of Results 58
LIST OF FIGURES
Energy Determination Apparatus
Typical Ti45 Decay Curve
Typical Sc44 Decay Curve
Scandium Gamma Spectrum
Rb Gamma Spectrum
Typical K38 Decay Curve
Typical N13 Decay Curve
Yields vs Nitrogen Energy
Yield vs Nitrogen Energy for (N N ) Reaction
Stopping Power of ZnS for Nitrogen Ions vs
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
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.
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,
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)
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
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.
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
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-
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
and Cu63 with 32-Mev protons, in each case forming the compound
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.
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.
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.
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
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.
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
POSSIBLE REACTIONS FROM THE V46 COMPOUND NUCLEUS
Product Nuclei Half life Q
Sc44 + 2p
Sc4 + 2p
Ca43 + 3p
K42 + 4p
Ti4 + pn
Ti43 + p2n
Sc43 + 2pn
Ca42 + 3pn
K + 2a
K38 + Za
Cl34 + 3a
Sc41 + na
Ca + pa
Ca + pna
Ka40 + 2pa
A3 + p2a
3. 09 hours
12. 5 hours
3. 9 hours
0. 66 seconds
7. 7 minutes
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)
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
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
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-
ural sulfur, containing 94. 06% of S3. The ZnS was thoroughly
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
ILFORD C-2 PLATE
S- EXIT FOIL
Fig. 1. Energy Determination Apparatus.
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.
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
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):
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.
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
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
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-
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.
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.
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
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
mg/cm2 Al ABSORBER
Fig. 2. Ra-DEF Calibration.
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
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.
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
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
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
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.
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
Fig. 3. Typical Ti45 Decay Curve.
0 40 20 30
40 50 60
70 80 90 100 110
Fig. 4. Typical Sc44 Decay Curve. Crosses indicate total counting rate. Dots indicate rate after sub-
traction of 2.44-day activity.
3.92 hr Sc 2.44 day Sc -x
1-4 I 7
____ ____ I ____ ____ ____ ____ 1]
Fig. 5. Scandium Gamma Spectrum.
I I I I ...- I
at channel 57 is due to the 1. 16-Mev gamma.
The observed gamma counting rate at a particular time t'
indicated the activity due to Sc and Sc at that-time, where
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
time t' Then subtracting the activity due to Sc from the gamma
activity gave that due solely to,Sc This was compared to the
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
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.
4 ORNL-LR-DWG 29343
5 --------- -
o 2 0080
S2 --- -- -- -- --- --- -- ---
5 10 45 20 25 30 35 40 45
50 55 60 65 70 75
Fig. 6. Rb86 Gamma Spectrum.
36 56 76 96 446 436
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
Fig. 8. Typical N13 Decay Curve.
ORNL-LR- DWG 29345
64 72 80
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
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,
I = isotopic target abundance of S 0. 94,
\ = decay constant,
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
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
.against energy as shown in .Figs. 9 and .10. Relative yields of Sc4
and Sc43 were determined as described in the previous section.
Sc accounted for 84% of the total 3. 9.hour activity. The yield as
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
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
545 38 _
5 -Ti K
18 20 22 24 26
NITROGEN ENERGYLAB (Mev)
Fig. 9. Yields vs Nitrogen Energy.
20 22 24 26 28
NITROGEN ENERGYLAB (Mev)
Fig. 10. Yield vs Nitrogen Energy for (N14, N13) Reaction.
Y = no, (12)
over a small interval dE, where
r = cross section in cm and
n = number of target atoms per cm.
_Y = -- (13)
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.
dn _dx N-*ID (14)
dE dE A 10
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
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
Zn was taken as equal to SNi, whiih was. taken from the
data of Reynolds,. Scott, and Zucker (51); S was taken from the
relative stopping powers of sulfur and nickel for protons of the
same velocity. .-SNi was taken from the data of Allison and War-
.shaw (64); S was interpolated from the same-data.
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.
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.
16 18 20
22 24 26 28 30
NITROGEN ENERGYLAB (Mev)
Fig. 12. Cross Sections vs Nitrogen Energy.
2 x 1025
-029 I I
18 20 22 24 26 28
NITROGEN ENERGYLAB (Mev)
Fig. 13. Cross Section vs Nitrogen Energy for (N14, N 3) Reaction.
MEASURED CROSS SECTIONS
Nuclide C-ross Sectionin --illibarns
Nuclide Cross Section in millibarns
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
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
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.
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
cr(ab) c(a) P(b) P(b)
ac) (a) P(c) Pc
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":
where >a is the wave. length corresponding to the energy of incident
particle -a, --as
a = (2MaE') 1/2 (20)
where M is the reduced mass of a and E' is the incident energy in
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
P(b) = (22)
S:.k. c (i)
where k. = 1/W, and the sum is extended over all possible particle
Each particle b that is emitted from the compound nucleus will
come off with a certain energy given by
b = E' + Q, (23)
where E' is the center-of-mass energy carried in by particle a, and
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:
To calculate the
is introduced as
R =rA +D
r =1.5x10 cm
D = 1. 2 x 10 cm, for alpha particles and
= 0 for protons
Eb = energy of particle b in the center of mass
B = Coulomb barrier.
probability of particle emission, the "F-factor"
Fb =5-k- o (i), (27)
where the sum is extended over all energies at which particle b can be
emitted. The sum is expressed as an integral as
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)
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.
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 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)
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
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:
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.
45 n 46
43 n 44
Sc h Sc d
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-
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
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
further particle emissions from the V45 nucleus which make such
reactions extremely likely, and the yield of V45 only about 2% of the
The available states of Ti45 were arbitrarily broken into level
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
as Ti45. These states are shown in the shaded portion of Fig. 15.
All higher occupied states will again emit particles or gamma rays.
p OUT a OUT
Fig. 15. Diagram Showing Schematics of Evaporation Calculations.
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
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.
Some 65. 9% of the Ti emitted a proton to form Sc This
nuclide was treated in an analogous manner, the level bands being
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
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
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
COMPARISON OF RESULTS
Gamma Emission No Gamma
a=TU a=2 a= =
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.
ORNL-LR- DWG 28268R
-6 -5 -4 -3 -2 -1
0 1 2 3 4 5
Fig. 16. Cross Sections for Neutron Transfer Reactions vs E* = Ecm B + 1/2Q.
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
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.
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.
(1) N. Bohr, Nature 137, 344 (1936).
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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
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
\I, a Lir
A IF 711
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TITLE: Nuclear reaction cross sections from the nitrogen bombardment of
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