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University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 46106 A Xerox Education Company 73-11,464
BULTHAUP, Donald Carl, 1930- GAM4A DECAY OF ANALOG RESONANCES IN 6 5 Ga,
6 7 Ga, AND 6 9 Ga.
The Ohio State University, Ph.D., 1972 Physics, nuclear
University Microfilms,A XEROX Company, Ann Arbor, Michigan GAMMA DECAY OF ANALOG
RESONANCES IN 6 5 Ga, 6 7 Gaf and 69Ga
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Donald Carl Bulthaup, B .S., M.S. * * * * #
The Ohio State University 1972
Approved by
■S'. U'-ftx 1V^ 1 Adviser Department of Physics PLEASE NOTE:
Some pages may have
indistinct print.
Filmed as received.
University Microfilms, A Xerox Education Company ACKNOWLEDGEMENTS
I would like to express my thanks to Dr. S. Leslie
Blatt, my advisor, whose help in planning and completing this research is greatly appreciated. His dedication to his work marks him as an outstanding researcher and teacher.
1 would also like to thank Dr. Donald D*Amato,
Arnold Vlieks, Robert Maute, and Chu-Nan Chang for their
* assistance in the collection of data and Dr. James Kent for many helpful discussions about Isobaric Analog
Resonances and for suggesting the project. In addition, thanks are due Mrs. Pauline Swaney for her patience in typing the manuscript. Finally, I would like to express my sincere appreciation to my wife, Barbara, whose encourage ment and patience have made this work possible.
The partial support of The Ohio State University
Physics Department and Van de Graaff Laboratory is greatly appreciated as well as the support of Otterbein College
in granting a sabbatical leave.
ii VITA
March 3, 1930...... Born - Indianapolis, Indiana
1952...... ,.B.S. degree - Mathematics Indiana Central College
1952-195 3 ...... Attended Florida State University - Meteorology
1953-195 6 ...... Weather Officer - U. S . Air Force
1956-195 7 ...... High School Teacher - Mathematics
1957-196 3 ...... Instructor - Physics - General Motors Institute - Flint, Michigan
1958-196 3 ...... Part-Time graduate student - Physics - Michigan State University
1962...... M.S degree - Physics Michigan State University
1963-Present...... Assistant Professor - Physics Otterbein College
1969-197 1 ...... Full Time Graduate Study, The Ohio State University
1970-197 1 ...... Graduate Research Assistant, Van de Graaff Laboratory, The Ohio State University
iii PUBLICATIONS
"Measurements on the Decay of ^^Hg," A. A. Bartlett, D. C. Bulthaup, and K. Mohan* Bull. Am. Phys. Soc. 1_, 37 (1967).
"Analog Resonances in ^Mo(p,p*) J. J. Kent, S. L. Blatt, D. C. Bulthaup, and D. P. D'Amato. Bull. Am. Phys. Soc. 15, 1690 (1970).
"®^Zn(p, y) Reaction over Analog Resonances," J. J. Kent, D. C. Bulthaup, D. P. D'Amato, A. E. Vlieks, and S. L. Blatt. Bull. Am. Phys. Soc. 16, 1174 (1971).
"39K(p, Y0 ) Angular Distributions," D. P. D'Amato, S. L. Blatt, J. J. Kent, D. C. Bulthaup, and A. E. Vlieks. Bull. Am. Phys. Soc. 17, 91 (1972).
FIELD OF STUDY
Major Fields Physics TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS...... 11
VITA...... ill
LIST OF TABLES...... Vi
LIST OF ILLUSTRATIONS...... vli
Chapter
I. INTRODUCTION...... 1
II. EXPERIMENTAL PROCEDURE...... 21
III. ANALYSIS OF THE 6 4 Zn{p, y) RESONANCES 32
IV. ANALYSIS OF THE 6 6 Zn(p, Y) AND 6 8 Zn(p, Y) RESONANCES...... 61
V. CONCLUSIONS AND ERROR ANALYSIS...... 89
Appendix
A. COMPUTATION OF ANALOG RESONANCE ENERGIES... 93
B. EFFICIENCY CALIBRATION AND RESONANCE STRENGTH DETERMINATION...... 96
REFERENCES...... 104
V LIST OF TABLES
Calculated Ml Single-Nucleon Transition
Strengths......
Summary of the Predictions of the Maripuu
Rules......
Comparison of Computed ”*^9/2 Transition Strengths in 5^cu to Observed Values......
Summary of 6 4 Zn{p, y) Results..,......
Summary of 6 6 Zn(p, y) Results......
Proton Energies Necessary to Excite Isobaric
Analog Resonances...... LIST OP ILLUSTRATIONS
Page 1. Level Schemes of ^C, ^N, ^ O ...... 4
2 . Graphic Representation of Analog States...... 9
3. Decay of the 9.40 MeV Level of 31p ...... 15
4. Target Chamber...... 23
5. Gamma Group Experimental Station...... 26
6. Calibration Curve...... 30
7. Gamma Ray Yield Curve - 1.90 MeV Resonance
in 65Ga...... 34
8 . Spectra - 1.90 MeV, 1.95 MeV, and 2.04 MeV
Resonances in 63Ga...... 37
9. Gamma Ray Yield Curve - 1.95 MeV Resonance
in 65Ga...... 40
10. Gamma Ray Yield Curve - 2.04 MeV Resonance
in 6 5 Ga...... 42 1 1 . Spectra - 2.95 MeV Resonance in ®^Ga...... 45 12. Gamma Ray Yield Curve - 2.95 MeV Resonance
in 65Ga...... 4 7
13. Full-Energy Peak - 2.95 MeV Resonance in
65G a ...... 50
14. Separated Doublet ~ 2.95 MeV Resonance in
65G a ...... 52
vii LIST OP ILLUSTRATIONS (continued)
Page
15. Spectra - 3.25 MeV Resonance in ...... 5 5
16. Angular Distribution - 9 9 / 2 ** 99/2
Transition in ^ G a ...... 5 9
17. Spectra - 2.76 MeV Resonance in ®7Ga...... 63
18. Spectra - 2.83 MeV Resonance in ^ G a ...... 65
19. Gamma Ray Yield Curve - 2.76 MeV and 2.83 MeV
Resonances in 67Ga (Transition to 0.355 MeV
State)...... 67
20. Gamma Ray Yield Curve - 2.76 MeV and 2.83 MeV
Resonances in ^7Ga (Transition to Ground
State)...... 69
21. Spectra - 3.17 MeV Resonance in ®7 Ga....».... 73
22. Gamma Ray Yield Curve - 3.17 MeV Resonance
in *>7Ga (Transition to Ground State)...... 75
23. Gamma Ray Yield Curve - 3.17 MeV Resonance
in ®7Ga (Transition to 0.355 MeV State) 77
24. Spectra - 3.36 MeV Resonance in 6 7 Ga...... 80
25. Gamma Ray Yield Curve - 3.36 MeV Resonance
in 67Ga...... 82
26. Angular Distribution - 9g/2 * 99/2*****..... 85 27. Curves of Stopping Power for Protons vs.
Proton Energy and Atomic Number of Target.... 102
viii Chapter I
Introduction
The concept of isospin was introduced by Heisenberg in
1932, just after the discovery of the neutron. This intro duction formalized the hypothesis that neutrons and protons are different states of the same particle but was little more than a labeling scheme. Since Heisenberg did not believe that nuclear forces were charge independent, isospin could not have been a good quantum number. By 1937, much evidence had been gathered to support the existence of a charge independent nuclear force and in that year Wigner(l) introduced the concept of isospin for complex nuclei as it is known today. In that paper he emphasized that charge in dependent nuclear forces were necessary if the theory was to be valid.
To the extent that nuclear forces are charge independ ent, isospin is conserved and takes its place with spin and parity in the description of a nuclear state. The z-compo- nent of isospin is defined as
T 2 * 1/2 (Z - N) where N is the number of neutrons and Z the number of pro
tons in a nucleus. For any nucleus, this gives a single
1 value, and is directly a measure of the number of protons in excess of the number of neutrons. In analogy with the quantum mechanical treatment of angular momenta, for a given total isospin T, T_ must have one of a set of values 2 T, T-l, T-2...-T+1, -T and therefore a given Tz could be » the z-component of any one of several different isospins.
It is apparent, then, that the clear understanding of Tz will not help to attach a descriptive meaning to total isospin. Unlike ordinary spin, the isospin vector does not lend itself to description by a semi-classical model and therefore remains an abstract quantity.
The existence of isospin vectors with the above rules for z-projections implies the existence of isospin multiplets. Members of these multiplets have all quantum numbers except Tz the same and so have the same number of nucleons. It follows then that AT_ =» ±1 for adjacent mem- bers of multiplets. Because the members of these multiplets have different numbers of protons, the Coulomb energy is different for each. This energy difference plus the small mass difference between a proton and a neutron produces an energy shift between the various states of the multiplet.
An example of an isospin triplet is shown in Figure 1 where simplified energy level schemes are shown for 1 4 C, 1 4 N, and
^■*0. Note that the levels of and ^ 0 have been shifted 3
Figure 1. Simplified level schemes for and ^0.
The vertical positions of the three level
schemes have been shifted so that levels which
are members of the isospin triplet are in line. o = ! L i— !L N*,
i V O j t
+o z/r* w o ors J= ± T-J. r= x
j i H ’£
! £ L t t h 0 = J - u£ - ors 0 *J. by the amount of the coulomb plus proton-neutron mass energy difference so that the states which are members of the isospin triplet are in line. This identification of the levels belonging to the triplet is made by considering the following facts:
a. All three levels have the same spin and parity.
b. The energy differences between the levels are con
sistent with calculated values of Coulomb energy
differences plus proton-neutron mass differences.
(See Appendix A)
c. The f3+ decay of the level in 140 is 99.4% to the
indicated level in instead of to the ground
state. This is consistent with the fact that the
wave functions of the members of an isospin
multiplet must be closely similar.
Isospin multiplets of this type have been identified in many lighter nuclei# but as nuclei of higher Z are encoun
tered the identification becomes more difficult.
Prior to the discovery of isospin multiplets in heavi
er nuclei, it was generally believed that isospin would not
be a good quantum number for other than light nuclei. The
argument was that for heavy nuclei the Coulomb force would
become large enough to contribute significantly to the to
tal force between nucleons. Since this force is not charge independent, the condition established by Wigner for good isospin was felt to be violated. In addition the Coulomb energy of the higher T z members of T-multiplets is large enough to make these states unbound and positioned in a sea of other states. Because of this it was believed that even if T somehow managed to be a good quantum number it was doubtful that the higher Tz states could be observed. It came as a surprise, then, when analog states (i*e. higher Tz members of a T-multiplet) were identified in 5 % i in 1961 by Anderson and Wong (2) and in and ®®Zr in 1964 by Pox,
Moore, and Robson(3). Since that time a considerable
amount of effort has gone into the study of analog states
in heavier nuclei.
At higher A, the ground state of a nucleus is always
the member of a T-multiplet with the largest negative value
of Tz (i.e. Tz « ~T) (4). This is because the Coulomb
effects cause the excess neutrons to have their isospin
vectors aligned. The isobaric analog to this state is
always a highly excited state in the nucleus with one more
proton and one less neutron. For most heavier nuclei it is
an unbound state and could appear as a resonance in a
reaction. In many cases several low-lying states of a
nucleus have the same isospin as the ground state. Ac
cording to French(5) any state in which all protons are in orbits which are filled for neutrons will satisfy the con dition T » |t z |. These states serve as "parent" states
{T « |t 2 | members of an isospin multiplet) for analog re
sonances in the isobar with one more proton. The simplest
description of these states is accomplished with a single
particle shell model. In many cases spectroscopic factors measured in {d, n) reactions indicate that these resonances
closely approximate such single particle states. A con
venient way to describe these states graphically is shown
in Figure 2. Note that both the parent and the analog
state contain the same "core," which, in this simple model
is assumed to be inert.
Since the analog resonances described above are un
bound states, the predominant decay is by particle emission.
Some decay by gamma emission does occur, however, and has
been studied both theoretically and experimentally. It is
to be expected that transition matrix elements for gamma
decay will be largest between states which are most nearly
identical. If the model shown in Figure 2 is assumed,
an isospin doublet different from those previously dis
cussed should be observed. This doublet is produced by the
coupling of the T * 1/2 single particle to the core. The
members of this doublet will have all quantum numbers
identical except for T, which will differ by 1 in the two 8
Figure 2. Graphic Representation of Analog States. The
rectangular portion represents an inert "core^of
neutrons and protons while the dots above re
present "active"particles.
v Act/ve P articles
■
P r o t o n s N eu tro ns P r o t o n s N e u t r c n s
I n e r t C ore I n e r t C ore
Parent State Analog State 10
states. This concept was first discussed by Macfarlane and
French (6 , 7) who showed that the members of this doublet would differ in energy by about 1 MeV per excess neutron
in the nucleus. The low energy member of this doublet, which is sometimes termed the ’'anti-analog" state, is
a likely final state for the decay of the analog resonance.
Since the two states have the same parity, the radiation
which would produce the transition could be Ml or E2.
Radiation of lower multipolarity is, in general, more proba
ble, but E2 strengths are often comparable with Ml strengths.
However, for the analog to anti-analog transitions, the
primary radiation is expected to be Ml. This has been
observed to be the case in several experiments. The exist- « - ence of isospin doublets in a nucleus and the preferential
decay of the analog resonance to the other member of the
doublet also explains why it is possible to see these
resonances in (p, y) reactions. In heavy nuclei the analog
resonances lie in a region where the density of states is
very high. If the decay of these resonances were not very
selective then the total strength would be dissipated in
many decays and the gamma rays lost in the background
created by the decay of surrounding states. Since the
decay of analog resonances is primarily to a single final
state, the gamma rays can be identified, and their reso
nance properties observed. , In 1969, Maripuu published the results of some shell- model calculations of Ml transition probabilities from ana
log states (8 ). For odd-A nuclei in which the core particles
couple to = 0 he found Ml transition strengths as listed
in Table 1. Two important observations can be made about
these values. First, the strengths of transitions between
states with / = L + 1 / 2 are one to two orders of magnitude
stronger than those between states with / *= t - 1/2. Sec
ond, for any given orbit the transition strength decreases
as the isospin increases. For these calculations it was
assumed that the core was inert and that there existed
a pure isospin doublet from the coupling of the single
particle to the core. Prior to this work it had been
shown that the strengths of some lower-isospin members
of doublets (often referred to as T-lower states) were
fragmented (9) . This is because the core state may change
when a particle is added unless the core-particle coupling
is weak(10). When this happens the T-lower states mix,
causing a modification of the wave function describing the
states and hence a change in the transition strengths. In
the same paper referred to above, Maripuu presented the
results of a calculation on 31p in which two T-lower states
were mixed and the positions of the transition strengths to
these states were computed. This calculation started with
a 28Si inert core and 3 active particles, which produce the \ in CM T> T< Sl/2 P3/2 pl/2 d5/2 d 3/2 f7/2
3/2 1/2 1.95 1.59 0.071 1.85 0.051 2.24 0.0105 5/2 3/2 1.40 1,15 0.052 1.36 0.037 1.62 0.0076 7/2 5/2 1.07 0.88 0.039 1.02 0.028 1.24 0.0058 9/2 7/2 0.87 0.71 0.032 0.82 0.023 1.00 0.0047 11/2 9/2 0.72 0.59 0.027 0.69 0.019 0.84 0.0039
Table 1. Calculated Ml single-nucleon transition strengths, in Weisskopf units,
within isobaric-spin doublets.(8 ) T> and T< are the isospins of the
analog and anti-analog states respectively. The &i/2' ^3/2' etc« are
the orbital and total angular momenta of both members of the doublet. 13 7— following configurations for a — state 2
C ( s '/j I ^ 4, a j a , 3A
\_(S a ) o,,
\ j S A )l,c $7/*, y*]r/Z) I/a.
The first subscript represents the spin and second the iso spin for the particle or group. The first two configura tions can be easily identified as members of an isospin doublet since the quantum numbers are all the same except for total isospin which differs by one. The last configur ation, on the other hand, is similar to the T-lower member of the doublet except that the pair of S^^-P^^icles couple to spin 1 instead of zero. This means that the inert core plus these two particles couple to spin 1 and this group is then referred to as a "core-polarized" state. Using this simple model improved the agreement with • experimental evidence considerably, as can be seen in Figure 3. It should be noted that the effect of considering the mixing of the core-polarized state is to increase the transition
strength to the isospin doublet state, A corresponding
decrease of the transition strength to the core polarized 14
Figure 3. Decay of the 9.40 MeV Level of ^p. This dia
gram by Maripuu(8 ) compares the results of two
different calculations for transition strengths
with experimentally determined values. The mix
ing of core polarized states in the calculation
produced much better agreement with experimental x re s u lts . S tren gth
9.2 1 "
7 ~
7 -
7 -
2.23
E x p e r i m e n t
H Ul 16 state should also be noted* This explains the observed predominant decay of analog states to a single lower state.
The above arguments suggested that all Ml transitions between members of isospin doublets were strong. Experi mental evidence did not indicate that this was true so mod ifications to this theory were proposed by Maripuu in a follow-up paper(11). In this paper it is assumed that "a valence nucleon, in an orbit £ 2 /2 * coupled to a core which is assumed to consist of a doubly closed inert part and an even number, n, of active nucleons in an orbit
In addition the core is assumed to have a neutron excess so that its isospin is not zero. With these assump tions, single nucleon transition strengths were derived which included the effects of core-polarized states to a greater degree than previous calculations. This calcula tion yielded the rule that single-nucleon transitions are
expected to be strong only if fa = £ 2 + 1 / 2 • If this con dition is met, the calculation further predicts that cancel
lation of the transition strength due to core polarization will be strong if » £^ + 1/2. Table 2 shows the applica
tion of these rules to nuclei in the region of zinc. Exper
imental evidence is in qualitative agreement with these
miles except in the case of gcj/2 ^9 / 2 transitions. These transitions should be at least partially inhibited by core
polarization but experiments with Cu and Ga nuclei(12, 13) Expected Configuration Typical Nuclei Allowed Shell Involved Analog b y Polarization Core Resonance i2^ 2+ 1 / 2 Cancellation
s-d
Upper Part 3 4 S, 3 5 C1 W 3/2n lf7/2 Yes
Yes a o a o 2p3/2
f-p Lower Part 4V 52Cr lf7/2n 2P3/2 Yes Yes
lf5/2 No
f-p 64 66 68 Upper Part If ^ No . — Zn, Zn, Zn 5/2 2Pl/2 Partial 2P3/22 lg9/2 Yes
Table 2. Summary of the predictions of the Maripuu rules. The table shows the groups
of nuclei in which core polarization is expected to reduce the strengths of
analog to anti-analog transition.
M -J 18 have shown that strong transitions of this type occur. In
an attempt to explain this discrepancy, Maripuu,
Manthuruthil, and Poirier(15) performed a shell model cal
culation for using four active shells with a ^®Ni
inert core. Single particle and two-shell calculations were also performed for this nucleus. The results of these
calculations are shown in Table 3. Mote that the Ml
transition strength calculated with four active shells is
very close to the experimental value reported by Fodor
et al.(13). Calculations of this type have not been done
on nuclei above 59cu . This is because such calculations
become too large for computers to handle as the number of
particles outside the ^6Ni core increases.
The present investigation was undertaken to extend
knowledge about gamma transitions between members of iso
spin doublets in the region beyond ^Cu. The specific
goals were:
1. Search for isobaric analog resonances in (p, y)
reactions on ®*Zn, ®®Zn» and ^®Zn.
2. Compare the resonating gamma rays observed with
the Maripuu rules given above.
3* Determine resonance strengths for observed reso
nances .
4. Find branching ratios for the gamma decay of ob
served resonances. Theory Single Experiment Particle 2 -shell 4-shell
Ml strength in w. U. — for the go/o IAS ■+■ AIAS CQ transition in a:7Cu 1.5 ± 0.3b 2.74 0.30 1.53
Table 3. Comparison of the <3g/2 ** g9/2 ^ 'trans^-ti°n strengths in 5^Cu
computed by Maripuu with the experimental value found by Fodor
et al.(13)
H VO 20
5. Compare the angular distribution of major observed
gamma rays with that for pure Ml radiation*
This information can then serve to test future calculations as techniques are developed to handle the computations for nuclei with 65 or more nucleons. Chapter II
Experimental Procedure %
This experiment was performed using a proton beam from the Model CM Van de Graaff Accelerator of The Ohio State
University, The beam was magnetically analyzed to an absolute accuracy of ±10 Kev. Two target chambers were especially designed for particle-gamma ray experiments.
Each consists of a 2 3/8 inch diameter cylinder mounted with its axis vertical. One chamber is designed so that a
Faraday cup can be mounted, which allows the beam to be stopped eight feet behind the chamber (see Figure 4).
The other chamber is identical except that no Faraday cup extends out the rear. This allows the freedom to position the detector at any angle from 0° to 135° for angular distribution measurements. The beam enters through a 1
inch diameter pipe welded to the chamber and is collimated
by a set of adjustable slits mounted in the beam line six
feet from the chamber. An evaporation chamber for making
targets which cannot be exposed to air is mounted on top of
the target chamber but was not needed for this experiment.
The target chamber is mounted on and is coaxial with
21 22
Figure 4, Target Chamber. This diagram shows the target
chamber which has the Faraday cup attached. An
other chamber which is identical except for the
presence of a Faraday cup is also used with this
apparatus, f
M U» a column which serves also as the support and axis of rota tion for two radial, horizontal tracks (see Figure 5).
Each of these tracks is capable of supporting a detector and shielding up to a total weight of 5000 pounds on a cart which rolls radially along the track. Each detector can have its radial position varied from the chamber surface to a distance of four feet. The angular position of each de tector is variable from zero to 135 degrees to the beam direction* For this experiment only one detector was used; it was a Ge(Li) detector manufactured by Princeton Gamma-
Tech Corporation. The active volume was 80 cubic centi meters and the resolution during the first part of the ex periment was 2.6 keV for the 1.33-MeV 6®Co gamma ray. For the second part of the experiment the resolution had deteri orated to 5.0 keV for the same gamma ray. The electronics used consisted of a Princeton Gamma-Tech pre-amplifier and an Ortec 450 amplifier. The signals were then fed to a
Northern Scientific Model 625 analog-to-digital converter and on to an IBM 1800 computer which was used as a multi channel analyzer*
The energy calibration of the spectrum was accomplished using a 228^ source. By using the known Q value for the reaction being studied(14) and the energy of the bombarding particle# it was possible to determine the maximum-energy gamma ray to be expected. The gain of the amplifier was 25
Figure 5. Gamma Group Experimental Station. The target
chamber and both detector systems, Ge(Li) and
Nal(Tl), are shown. 26
Ul to 2 7 then adjusted until the 2.61-MeV gamma ray from the 22®Th appeared in the proper position to insure that the computed maximum energy gamma ray would be near the high end of the pulse height analyzer scale.
The targets used in this experiment were rolled by
Microfoils, Inc., Argonne, Illinois from material pur chased from Oak Ridge National Laboratories, Separated
Isotope Division. Each foil was rolled to a thickness of
0.5 milligrams per square centimeter and enriched in a particular isotope of zinc as follows:
64Zn - 99.85 ± 0.04% 66Zn - 99.35 + 0.05%
68Zn - 98.5 ± 0.1%
At the beam energies used these targets were on the order
of 30 kev thick and, 3 ince each of the resonances had a width of the same order of magnitude or less, were clas
sified as thick targets.
The excitation curves were taken with the detector as
close as possible to the chamber and at an angle of 125° to
the beam direction. The proton energy needed for each re
sonance was computed with the known Q value for the reaction
and the positions of analog resonances computed from known
low-lying states in the parent nucleus (see Appendix A).
The proton energy was varied in 10 keV steps starting 20
keV below the expected resonance and continuing until the 28 data indicated that the flat top of the thick-target yield curve had been reached. This was normally no more than 20 to 30 keV above the resonance energy. This procedure was repeated for each known or expected resonance.
To determine the resonance strength the entire detec tion system had to be calibrated. This was accomplished by using resonances in 1 3 C(p, y)14N and 2 7 Al(p, v)28Si reac tions for which resonance strengths were known.(17, 18)
The gamma rays from these calibration reactions were known
to have angular distributions with Pq (cos 9) and P2 (cos 0 )
components but with negligible contributions from other
terms in the expansion. By placing the detector at an ang ular position of 125° to the beam direction, which is a zero
of the P 2 (cos 9) term, only the gamma ray components which
are independent of angle were detected. Since the p 2 (cos 6 )
contribution integrated over all angles is zero, the meas
ured radiation was proportional to the total gamma yield
of the reaction. This information, along with the known
branching ratios for the gamma decay of the compound nuclei,
allowed a computation of the detection system efficiency
for each gamma ray energy. A calibration curve was then
drawn (see Figure 6 ) and efficiencies taken from this curve
were used to make calculations of resonance strengths and
branching ratios in the zinc experiments.
When the calibration data were first plotted, it was 29
Figure 6 . Calibration Curves. System efficiency curves
used for both the ^Zntp# y) experiment (curve
A) and the 6 6 Zn(p, y ), 68Zn(pr Y) experiments
(curve B) are shown. The calibration was
achieved using ^C(Pr y) and ^^Al(p, y) reac
tions for which resonance strengths were known. t 31 discovered that the points lay in such positions that it was possible to draw a smooth curve through the points from 13 the C(p, y) reaction and a different but parallel curve through the points from the 2 ^Al(p, y ) reaction. However, the correct values for the isotopic composition of the *3C target were in some doubt. In addition, the information about the resonance strengths for *3 C(p, Y) resonances was neither as recent nor as weli-confirmed as the information about the 2 ^Al(p, y) resonances. For these reasons the efficiencies computed from the ^*3 C(p, y) data, which should be internally consistant with each other, were normalized to the efficiencies computed from the yj data, taken as the standard for absolute values. This task was facil itated by the fact that one gamma ray from the *3c experi ment had nearly the same energy as one from the 2 ^Al(p, y) experiment. A complete discussion of the calibration and resonance strength determinations can be found in Appendix
B. Chapter XII
Analysis of the ® 4 Zn(p, y) Resonances
In the 6 4 Zn(p, y) 65Ga reaction a total of five res onances were observed. These were analogs of the ground state and four of the lowest five excited states in ^5 Zn.
The analog of the 0.865-MeV state in 6 J>Zn was not found in this reaction. For each of the observed resonances, decay to more than one low-lying state of ®^Ga was observed but these were not of equal strength and were generally weak.
The one exception was a strong 9/2+ to 9/2+ transition in the decay of the analog of the 1.064-MeV *^Zn state.
The analog of the *^Zn ground state was excited at a proton energy of 1.90-MeV. A graph of gamma ray yield vs. bombarding energy is shown in Figure 7. From this curve an accurate lower bound can be placed on the resonance energy; since the shape of the curve indicates that the target is thick enough to use thick target techniques for resonance strength determinations (see Appendix B), this energy is, within the basic calibration uncertainty, a good estimate of the true resonance position. This resonance was observed to decay to two low-lying states in
®®Ga, the ground state and the state at Ex»0.192-MeV. A
32 Figure 7. Gamma Ray Yield Curve - 1.90 MeV Resonance
The total net number of counts under the gamma
ray peak is plotted as a function of proton
energy. The gamma ray from the decay to the
state at 0.192 MeV was used. 34
6 4 Zn ( p,/)
200 f2 Z 8 150 o
Q uj 100 > ” <
< 5 0 CD
L88 1.90 1.92 1.94 p PROTON ENERGY (MeV) 35
series of spectra showing the resonance of the gamma rays
emitted in these decays is shown in Figure 8 . By using the
equation (2J+ >) £ £ = (jjgrfz (22> I) tgffr § £
as described in Appendix B with each of these gamma rays
the total resonance strength was found to be 0.713 eV. In
all resonance strength calculations, isotropy of the meas ured gamma rays was assumed since the detector was placed
at 125°. This is a zero for P 2 (cos 0) and the same argu ment used in the discussion of the calibration applies.
The resonance strength calculations also yielded branching
ratios of 25.5% to the ground state and 74.5% to the
0.192 MeV state. This favoring of the 0.192 MeV state is
consistant with an identification of this state as the
anti-analog for this resonance. A study of the spins and
parities of the states involved reveals another fact which
is consistent with that identification. The ground state
of *>5Zn has J1T = 5/2“ (18) which means that its analog in
65Ga also has J7* = 5/2“. The decay of this analog state
should be mostly to the anti-analog state which has all
quantum numbers except isospin the same. The ground state
of 65Ga has J* » 3/2“ while the 0.192 MeV state has
J11 ® 5/2" (19). By the Maripuu rules described in Chapter I 36
Figure 8 . Spectra in the Vicinity of the 1.90 MeV, 1.95
MeV, and 2.04 MeV Resonances. These resonances
were all placed on one diagram to show the
persistence of some of the peaks. The channel
number refers to the multichannel analyzer and
is proportional to gamma ray energy. In the
labels for important gamma rays the single
prime denotes a single-escape' peak while a
double prime denotes a double-escape peak. The
subscript indicates the energy of the final
state in the decay which produced the gamma ray. 160 64 Zn (p.r) er -125° 120 1.88 MeV. 1.96 MeV Xo" X.S7 Xo' 80 i { * t* * * • * 40 ■** » ;
0 1.90 MeV 1.98 MeV 120
% J 9 80 '0,19Z '0J92 '0,192 40 Wffcfr 0 1.92 MeV 2 .0 0 MeV 120
80 *» a * ,♦ *J * ** * 40
0 1.94 MeV 2 .0 2 MeV 120 X0' 80 40
0 I 1.96 MeV 2 .0 4 MeV Xk Xuk Xo v *X ct y» Tfioaf 120 X(,6T Xo' X0 fya i 'm b i I I ! ! 80
40 r m * * '''A».:»•. — HLvfSfh^S 0 882 982 1082 !I82 1282 1332 882 932 1082 1182 1282 1382 CHANNEL NUMBER 38 this analog to anti-analog transition should be weaker . than "allowed" transitions by a factor of. 20 or more since the parent state (^2^*2 = ^as ^2 “ ^2 “ 1/2. Figure 8 also shows the resonance of the gamma rays from the decay of the analog resonance excited at a> proton energy of 1.95 MeV. The curve of gamma ray yield vs. pro ton energy for this resonance is shown in Figure 9. Again the resonance position can be estimated from this curve.
This resonance is the analog of the state at Ex =» 0.054 MeV in ^ Z n and so has J v = 1/2"(17). The observed decay is to the ground state (J^ « 3/2") and the state at Ex « 1.67 MeV
(jir » 1/2") (18) in ^5Ga. Spins and parities would indicate that the state at 1.67-MeV is the anti-analog state. This is probably correct even though the branching to this state
(37.6%) is actually less than the branching to the ground state (62.4%). Again the parent state (^2^*2 “ Pl/2^ **as j 2 « <£2 "I/2* which by the Maripuu rules would indicate that only a weak transition to the anti-analog state is possible.
The total resonance strength of 0.609 eV shows that this is a very weak resonance in agreement with the above rule.
A resonance near a proton energy of 2.04 MeV can also be seen in Figure 8. An examination of Figure 10 shows that this resonance is at a proton energy near 2.04 MeV,
This resonance is the analog of the state at Ex 83 0.115 MeV
in **^Zn and has J11 « 3/2” . Although not as weak as the 39
Figure 9. Gamma Ray Yield Curve - 1.95 MeV Resonance
The gamma ray peak followed in this graph is
the one from the transition to the ground state. 40
200
o3 150
< CD
PROTON ENERGY (MeV)
• i> 41
Figure 10. Gamma Ray Yield Curve - 2.04 MeV Resonance.
The total net peaku counts for the gamma ray
from the transition to the 0.062 MeV state are
shown. 42
in
O _i 100 UJ >- <
< o
2.00 2.02 2.04 2.06 PROTON ENERGY (MeV) previous resonances the resonance strength of 1.28 eV shows that this resonance is still not very strong. Also the decay to the ground state in 6 ^Ga, which could qualify by spin and parity considerations as the anti-analog state/ is only 8.4% of the total. This is in agreement with the second Maripuu rule even though the condition for the first rule is met (j 2 *= I 2 + • Since the four excess neu trons in the 64Zn core are in the 2 P3 / 2 an<* ^^5 / 2 states, a partial cancellation is to be expected. The other gamma rays observed at this resonance (see Table 4) are also weak and do not enter into a comparison of experimental results with the Maripuu rules. They cannot be the result of transitions to anti-analog states since none of these states has a spin of 3/2.
The resonance observed near a proton energy of 2.95 MeV has a resonance strength of 6.74 eV and is the strongest resonance observed in this work. Figure 11 shows the gamma
ray spectrum in 10 keV steps over this resonance and Figure
12 shows the gamma yield vs. proton energy. From this lat
ter curve the resonance is estimated to be 2.95 MeV but
this value is likely to be much less accurate them those
for other resonances observed because of the strange
shape of the curve. The strongest transition in the decay
of this resonance (branching ratio 76.3%) is to the gg/ 2
state at Ex » 2.034 MeV in 6 5 Ga. A close examination of 44
Figure 11. Spectra in the Vicinity of the 2.95 MeV
Resonance. The primes on the gamma ray labels
denote single-escape and double-escape peaks
while subscripts indicate energies of final
states in the decays. PI ( X 10 ) 3 3 3 3 40 " GO £0 40 33 so -. '■ ■ 75 ■ 64 taT?i* t V ”V ) BIS SCO SCO BIS ) r,"™ - t + + v«^V $- a Z n ( p , / ) 6 5 G a NLMBER c f D u.Vv U. 4 ^V^<^A.w.Sv^ /> ^ v S wS. . A ^ < ^ 1^ V V k^JL £ £ % r2.04 + 318 SS 3 3 T i ' + r ^ v V llliS . V-s^^ ? v ^ ^ ^ s - V *XCT*V vf N y '654 2. MeV 2 .9 (2 1: ; W iiih 00 MeV 0 .0 3 .8 MeV 2.98 96 MeV 6 .9 2 94 MeV 4 .9 2 t iicp \ - - - - " y " y ;m y a l i; Figure 12. Gamma Ray Yield Curve - 2.95 MeV Resonance. The effect of the doubling of the strong 9 g/ 2 9g/2 t^nsition can be seen as a broadening at the base of the peak in this curve. GAMMA YIELD (COUNTS) 2.92 P R O T O N E N E R G Y ( M e V ) 64 2.94 Z (, ) (p,x Zn 2.96 2.98 p 47 this gamma ray reveals that it is a doublet. Figure 13 shows a series of diagrams of this peak at different proton energies. The doublet nature of the peak is quite evident and it can be seen that the two parts of the peak come up at different proton energies. This explains the strange shape of the yield curve and the reason for the uncertainty in the resonance position. Assuming a symmetric peak shape, which is seen to be valid from other Ge(Li) spectra, the peaks can be graphically separated. The result of this is shown in Figure 14, where it can be seen that the first member of the doublet reaches maximum height near Ep « 2.97 MeV while the second reaches maximum near Ep « 2.95 MeV. This splitting is probably due to a split ting of the resonance and is not observable in the other gamma transitions from this level because the gamma rays are very weak. The parent state for this resonance is the g9/2 fltate at Ex a 1.064 MeV in **®Zn. Since j ® t + 1/2 for this state a strong transition might be expected. However, the core is the same as before and some cancella tion is expected as a result of the original Maripuu rules. The later calculation by Maripuu, as discussed in Chapter I, shows, however, that a strong 9 g/ 2 ^ 9 g/ 2 transition can be explained by including more active particles in the calculation for transition strength. Again the other gamma transitions are weak and are to states which as a conse- 49 Figure 13. Gamma Peak - g9/ 2 + 9 9 / 2 Transition. The behavior of the doublet as the proton energy is varied through the resonance is shown. COUNTS - O C S 4 oo- 100 HNE NUMBER CHANNEL 2. The final analog resonance observed in 64zn is near a proton energy of 3.25 MeV. The resonance strength of 3.02 eV places this resonance somewhere between the strong res onance which has a strength =* 6.74 eV and the remainder of the resonances which have strengths on the order of 1 eV. The strongest transition then should be to the anti-analog state. The parent state for this resonance is the state at Ex = 1.370 MeV in *^Zn which is a <3 5 / 2 state with positive parity (18). The strongest transition is to the level at « 2.213 Ilev in (see spectra in Figure 15) which has been reported to be either a g If either one of these assignments is correct, the transi tion cannot be analog to anti-analog and the Maripuu rules do not apply. However, if the — assignment is made, the 2 transition could be through El radiation since there would be a parity change and LI « 1 (d * £) • This type of single particle transition is more probable than the one necessary 9+ if the — assignment is used (d -► g gives LI » 2 and with 2 no parity change, E2 radiation is indicated) • The fact that this transition is the strongest observed from this 5 — resonance, then, seems to favor the — assignment. The results of the ^*Zn(p, y ) experiment are tabulated 54 Figure 15. Spectra in the vicinity of the 3.25 MeV resonance in ^5 Ga. The primes on the gamma ray labels denote single-escape and double escape peaks while subscripts indicate energies of final states in the decays. 946 1046 1146 1246 1346 1446 1546 CHANNEL NUMBER 56 in Table 4. In addition to information which allows a test of the Maripuu rules as discussed in this chapter, branching ratios were computed for the decay of each resonance. These are also shown in Table 4. An angular distribution of the gamma rays from the 99/2 ** ^ 9 / 2 transition was taken and is shown in Figure 16. When this distribution was fit to the equation W W = IA„P„(^e) ft = 0 it was found that the best fit occurred for the following values of the coefficients: '7t = 0 ' -fa = 0.293 ±0.031 7r=0 > 7ff~-0.00&3± 0.0330 A theoretical calculation of these coefficients using the tables by Sharp, Kennedy, Sears, and Hoyle (20) yielded the following values for pure Ml radiation - ^ = 0.V80 , ^- = <5 while for pure E2 radiation the values were -£*■ = - 0 .3 3 0 , 4*-= -0.5t+5 n , r\o 64Zn(p, Y) Q - 3.943 He* Ep at « zn Parent States Pina! . States Branching C2J+1) I ey Resonance EX (2J+l)g t *x (2Jhl)c23 h Ratio(1) (ev) 1.90 0.0 S/2- 3.1 3 0.192 (5/2-) 3.89 3 5.62 74.5 0.0 (3/2") 1.07 1 5.81 25.5 0.713 1.9S 0.054 1/2' 0.71 1 0.0 (3/2") 1.07 1 5.87 62.4 * 1.67 1/2' 0.18 1 4.20 37.6 • 0.609 • . 2.04 0.115 3/2" 1.37 1 1.67 1/2“ 0.18 1 4.27 31.7 • 0.812 1/2- . 0.21 1 5.12 20.2 0.062 1/2“ 0.83 1 5.89 39.7 0.0 3/2 1.07 1 5.96 8.4 1.285 2.95 1.064 9/2* 7.8' 42.034 9/2* 4.05 4 4.859 76.3 0.812 1/2" .21 1 6.081 4.5 0.654 3/2“ .47 1 6.239 10.1 0.192 5/2“ 3.89 3 6.701 9.1 . 6.738 3.25 1.370 5/2* 1.5 2 2.927 5/2* .42 2 / 4.22 9.2 2.822 5/2 .23 2 4.32 11.5 2.213 9/2+r 5/2“ 0.72, 0.68 4, 3 4.92 58.8 0.654 3/2- .47 1 6.496 20.5 3.024 Table 4. Summary of the results of the 64Zn(p, y) experiment* ui 58 Figure 16. Angular distribution for the gamma ray produced in the £ 9 / 2 **■ ^ 9 / 2 transition in 65Ga. This distribution is consistent with a mixture of Ml and E2 radiation* The solid curve is a plot of the theoretically predicted distribu tion with the computed mixture. (see page 60) COUNTS UNDER PEAK l D E T E C T O R A N G L E ( D E G R E E S ) 0 9 60 Since neither type of radiation fits the data very well, a calculation using the equation \N(e) = W M1 (8) + 2.x Wa(9) +x2W£z(9) was made to determine the mixture of Ml and E2 radiation which would produce the observed distribution. In the above equation is an interference term which is also cal culated from the tables by Sharp, et al. while is the ratio of the intensities of the two radiations x 2 ~ l e z , i The value of the x was found to be -0.209 ± 0.020 Chapter IV Analysis of the 6 6 Zn(p, y) and 6 8 Zn(p, y) Reactions The resonances in 87Ga excited in the 8 8 zn(p, y) reac tion are much less distinct and much more difficult to iden tify than those described in Chapter III. The parent states for these resonances are the ground state and low-lying excited states in 6 7 Zn. A search was conducted for analogs of seven of these states, but a resonance vras observed in only four cases. The analog of the ®7Zn ground state was observed at a proton energy near 2.755 MeV and the analog of the 0.093 MeV Btate was observed at a proton energy near 2.83 MeV. Figure 17 shows a series of spectra near the 2.75 MeV resonance and Figure 18 shows a series of spectra near the 2.83 MeV res onance. The gamma ray yield as a function of proton energy near these two resonances is shown in Figure 19. The yield plotted is for the gamma ray produced in the transition to the 0.355 MeV level in 6 7 Ga. The curve of gamma ray yield shown in Figure 20 is for the ground state transition. The steps in the first curve indicate the presence of weak resonances near 2.73 MeV and 2.83 MeV. The large uncertain- 61 62 Figure 17. Spectra showing the resonance of the gamma rays in the ®^Zn(p, y) resonance at Ep = 2.76 MeV. The primes on the gamma ray labels denote single-escape and double-escape peaks while subscripts indicate energies of final states in the decays. 66 63 Zn (pty) 1200- 0v= 125 8 0 0 2.73 MeV Yq' ^0.826 ^0J67 Yq ^0,355 %J67 Y0 4 0 0 r o.355 0 - 2.75 MeV 4 0 0 0 2.76 MeV 4 0 0 0 2.77 MeV 4 0 0 0 2.79 MeV 4 0 0 / W S / g u 0 48 2148 2248 2348 2448 2548 CHANNEL NUMBER 64 Figure 18. Spectra shoving the resonance of the gamma rays in the 6 ^Zn(p,v) resonance at Ep= 2.83 MeV. The primes on the gamma ray labels denote single-escape and double-escape peaks while subscripts indicate energies of final states in the decays. COUNTS PER CHANNEL 400 400. 400 400 1 O O 8 0 8 18 28 38 48 2548 2448 2348 2148 2248 2048 O 0 0 0.355 0.165 70 0*355 '0J65 ' o '0 3 5 5 '0.165 '0.165 5 5 3 '0 o ' '0J65 0*355 70 0.165 0.355 A \ . ^ S V V v * * * 66 y// y// 0v = 125 CHANNEL Zn (p,/) * a v w v Y* ' / y y y y/ y' Jk Jk NUMBER ft A i w » w r0 2.85 MeV 2.87 MeV 2.83 MeV 2.79 MeV . 65 66 Figure 19. Yield curve for the gamma rays produced in the decay of the resonances near Ep = 2.76 MeV and Ep = 2.83 MeV in the reaction ®^Zn(p, y). These gamma rays are from the transition to the level at 0.355 MeV. GAMMA YIELD (COUNTS) 1000 1200 0 0 4 0 0 6 0 0 8 200 73 .7 2 75 .7 2 77 .7 2 PROTON ENERGY (MeV) ENERGY PROTON . 79 .7 2 2.81 83 .8 2 2 . 5 8 . 87 .8 2 -4 a\ 68 Figure 20. Yield curve for the gamma rays produced in the decay of the resonance near Ep « 2.76 MeV and Ep « 2.83 MeV in the reaction ®6 Zn(p, y ) • These gamma rays are from the transition to the ground state. GAMMA YIELD (COUNTS) 1000 1600 1400 1200 600 800 277 279 28 28 28 2J37 2.85 2.83 2.81 9 7 2 7 7 -2 5 7 2 3 7 2 , = 125° Zn (p,y) PROTON(MeV) ENERGY VO 0 * ty In the data, however, makes a precise determination of resonance position difficult for the 2.83 MeV resonance. The yield curve for the ground state transition shows no indication of a resonance at 2.83 MeV and the shape near 2.75 MeV is inconclusive. The gamma ray from this transi tion does not seem to resonate at either proton energy. From these curves it is apparent that the resonances are both weak and the gamma peaks are on top of other peaks which are probably from the decay of T-lower states in the vicinity of the resonances. These peaks, which shift with a change in proton energy, are approximately. 40 keV wide which corresponds to the target thickness. With a high density of T-lower states all having the same strength, this width of peaks and shifting of peak with proton energy is exactly what is expected. The gamma rays from the decay of a resonance which has a strength not much greater than these T-lower states would be expected to pro duce a distortion of the peaks and cause a difference of total counts in the peaks. They would not show up as resonating gamma rays in the usual way. Because of this condition, the data on total counts in each peak are proba bly not reliable enough for a computation of absolute res onance strengths so none was attempted. The 2.73 MeV resonance is an £5 / 2 state b o j 2 “ ^2 ” 1/2 and the Maripuu rules predict the observed weak transition. The resonance 71 at 2.85 MeV is a Pj./2 s^a^©# so again i*2 “ ^2 “ and the same condition exists. The analog of the 0.390 MeV state in ®7Zn was observed at a proton energy near 3.17 MeV (see spectra in Figure 21). The resonance is very weak and decays by a transition to the ground state of 67Ga only. A study of Figure 22 shows that the gamma ray corresponding to a transition to the ground state resonates. At the same timef Figure 23 shows that there is an inconclusive variation in the yield of the gamma ray corresponding to the transition to the state at 0.355 MeV. As in the previous resonances the resonating gamma-ray peak is embedded in a peak which has a width approximating the target thickness and which shifts in position as the proton energy changes. In this case a resonance strength was computed to be 3.00 eV but this value is likely to be much less reliable than those com puted for the 64zn(p, yj resonances. The thick target yield was assumed to be the difference between the value on resonance and the value on the plateau at 3.22 MeV (see Figure 20). The ground state in 67Ga appears to be the anti-analog state for this resonance. Both the resonance and the ground state are P 3 / 2 states with negative parity and this transition is the only one strong enough to be observed. The weakness of the transition is consistent with the Maripuu rules since the excess neutrons in the 72 Figure 21. Spectra showing the resonance of the gamma rays in the 6 6 Zn(p,Y) resonance at Ep*= 3.17 MeV. The primes on the gamma ray labels denote single-escape and double-escape peaks while subscripts indicate energies of final states in the decays. COUNTS PER CHANNNEL 0 0 4 0 0 6 200 200 0 M A * s V $ 200 08 18 28 38 48 2548 2448 2348 2248 2148 2048 0 0 0 1 ■ 1 ■ ■ j 1 0 ^yK^s>d^As/j * I* « # ^ # ^ V V y y^ y# y^ y# y« 0. 0, 0 ' 355 ' 165 ' 355 ' 165 '0 5 6 .1 '0 5 5 .3 0 ^ '0 5 6 .1 '0 5 5 ,3 '0 '0 5 6 ,1 '0 5 5 .3 '0 66 Zn ( p, / ) A . A CHANNEL . NUMBER k r»w » r J ♦’♦ 125° t , & V\*A /> v 3.20 MeV'3.20 3.17 MeV 3.17 3.18 MeV3.18 3.16 MeV3.16 2648 ^ -- 73 74 Figure 22. Yield curve for the gamma rays produced in the decay of the resonance at Ep = 3.17 MeV in the reaction *^Zn(p/ Y)• These gamma rays are from the transition to the ground state. GAMMA YIELD (COUNTS) 0 0 6 0 0 4 0 0 8 200 3.16 P R O T O N E N E R G Y ( M e V ) .8 20 3. 2 .2 3 0 .2 3 3.18 76 Figure 23. Yield curve for the gamma rays produced in the decay of the resonance at Ep = 3.17 HeV in the reaction 6 6 Zn(p, y)* These gamma rays are from the transition to the level at 0.355 MeV. GAMMA YIELD (COUNTS) 00 40 0 0 6 200 00 8 3.16 P R O T O N E N E R G Y ( M e V ) 3.18 3.20 3.22 77 78 gg Zn core are again expected to be in orbits 2 p 3 / 2 and If5 / 2 8 0 partial cancellation from core polarization is expected. The final resonance observed in the ^Zn(pr y ) reaction is near a proton energy of 3.36 MeV. This reso- 67 nance is the analog of the state at 0.602 MeV in Zn and is a g showing the only resonating gamma ray appears in Figure 24. The curve of gamma ray yield as a function of proton energy in Figure 25 shows that this resonance is rather strong and well-defined as a thick-target resonance. The resonance strength was computed to be 10.39 eV. The single decay of this resonance is to the gg/2 state at 1.196 MeV in ®^Ga which is clearly the anti-analog state. The explanation of the strength of this transition would be the same as for RA the distribution was taken for this gamma ray and the results analyzed to determine the coefficients in the equation wre) - £ A* P.(cos e) /1*0 The coefficients giving the best fit to experimental data were A. ~ A . ^ ^ *t£ = o > £± = -o.30s±o.izn = 0 f ■=* + 0. I£>0 * O.lbfc 79 Figure 24. Spectra showing the resonance of the gamma rays in the 6 ®Zn(p, y) resonance at Ep = 3.36 Mev. The primes on the gamma ray labels denote single-escape and double-escape peaks while subscripts indicate energies of final states in the decays. o 0 9 ro ° x CD cn P CH N M CO ax * j iD 1664 1764 1864 1964 2064 2164 CHANNEL NUMBER 81 Figure 25. Yield curve for the gamma rays produced in the decay of the resonance at Ep = 3.36 MeV in the reaction ^Zn(p/ y). These gamma rays are from the transition to the level at 1.196 Mev. 1800 1400 1000 6 0 0 200 3.34 3.36 3.38 PROTON ENERGY (MeV) 83 A theoretical calculation using the tables by Sharp, Ken nedy, Sears, and Hoyle (20) yielded the following coeffi cients for pure £ 2 radiation The A2 terms cam be seen to be the same within the stated error, but the A 4 terms differ considerably. The angular distribution of pure £2 radiation is shown in Figure 26 as a solid line and can be seen to not fit the data very well. Since the P 2 (cos 0) term for pure Ml radiation is of opposite sign to the observed P2 (cos 6 ) term it is not possible for this radiation to be Ml. When an attempt to find a mixture of £2 and Ml which would fit the observed data proved unsuccessful, the coefficients for M3 radiation were calculated as follows: 0.333 , = c.ozic. , -&■ = o.izi The angular distribution for this radiation is shorn as a dashed line in Figure 26 and can be seen to fit the data better than £ 2 radiation but the fit is still not very good. An attempt to find an £2 - M3 mixture which fit the data was also unsuccessful. The large uncertainty in the Legendre coefficients for the measured distribution and the small number of angles at which measurements were made undoubtedly are instrumental in preventing a more precise I 84 Figure 26. Angular distribution for the gamma ray produced in the g 9/2 * g 9/2 trans;*-t;‘-on *n This distribution is not consistent with a predominantly Ml radiation. The solid line is a plot of the angular distribution of pure E 2 radiation, while the dashed line shows the distribution for pure M3 radiation. COUNTS UNDER PEAK 00 40 600 800 L//. 0 D E T E C T O R A N G L E ( D E G R E E S ) 30 60 90 86 calculation of the type of radiation present. The only conclusion which seems to be safe is that the observed radiation does not contain a significant Ml contribution. In their paper explaining this transition in ^^Cuf Maripuu et al. work only with Ml radiation so it would appear that this observation is not yet totally explained. A tabulation of the results of the ^^Zn(pf y) work is given in Table 5. The experiment with ^®Zn was complicated by a high background count. For the higher energy resonances, where the ®®Zn(p, n) threshold was exceeded, the neutrons inter acting in the detector caused an even higher background. The search for resonances was stopped at a proton energy of 3.81 MeV because the neutron flux at the detector had become high enough to be damaging to the detector. A search was conducted for the analog of the ground state in ®^Zn-at a proton energy near 3.28 MeV, the analog of the 0.438 MeV state at a proton energy near 3.718 MeV, and the analog of the 0.531 MeV state at a proton energy near 3.811 MeV. No resonances were observed at any of these levels. The ground state is a Pi/ 2 level so the analog of this state also has i*2 B ^ 2 ** and on^Y weak transitions are expected by the Maripuu rules. The analog of the state at 0.531 MeV also is expected to be weak by the same rules 66 Zn(p, Y)67Ga Q = 5.270 67Zn Parent States ®7Ga Pinal States (2J+1) (Mev) (ev) * 9 J* 2 1 I Ex J* (2J+1) s I Ex ( J+ )s » 2.76 0 5/2“ 1 . 8 3 0.355 5/2" 3 8.03 2.85 0.093 1 /2 " 1 . 1 0 1 0.355 5/2“ 3 7.76 — 3.17 0.390 3/2" 1.03 1 0 . 0 3/2" 1 8.44 3.0 ± 1.0 3.36 0.602 9/2+ 8.4 4 1.196 9/2+ 4 7.43 10.4 ± 3.0 Table 5. Summary of the results of the ®®Zn(p, y) experiment. oo •j 88 since it is an £5 / 2 state- 0n the other hand, the analog of the state at 0.438, MeV is a 9 9 / 2 state and might be expected to have a strong transition to the 9 9 / 2 at I*98 69 MeV in Ga. Since no such transition was observed, it is evident that the Maripuu calculation concerning gg/2 ■*“ 99/2 transitions in ^ C u cannot be extended to nuclei with this many excess neutrons (i.e., higher isospins). It was deter mined that even with the rather large background a gamma peak containing as few as 50 counts could have been detected. Using y = 50 counts and the computed gamma ray energy in the equation for resonance strength, a value of 0.49 eV was found as an upper limit for the resonance strength of the 9 9 / 2 resonance. I Chapter V Conclusions and Error Analysis The results of this experiment are in general agree ment with the predictions of the Maripuu rules. In all case's where the parent state and hence the analog resonance have / = t - 1 / 2 r the gamma transitions are very weak. In some cases they were not observed at all. For those resonances with / = I + 1 /2 , core polarization apparently reduces the gamma transition strength except in the case of the g Maripuu rules since the active core nucleons in ®^Zn, ^Zn, and ^®Zn are expected to be in a (P3 / 2 ) 11 f5 / 2 configuration giving partial cancellation due to core polarization. The strong gg/ 2 ** 9 9 / 2 transitions observed in the ®*Zn(p, y) and ^ Z n ( p , y) reactions are violations of the Maripuu rules but are consistent with the results of the later calcula tions made by Maripuu et al. (14) on similar transitions in S^cu. The fact that the gamma rays from this transition in ®^Ga had an angular distribution not consistent with Ml radiation seems to indicate that more theoretical work is needed on the heavier nuclei. The absence of a 9 9 / 2 * 99/2 transition in ^ G a also points to this need. 89 Most of the resonance strengths computed in this work have not been previously reported. Resonance strengths for the gg/ 2 **" 9 g/ 2 transitions in ^5Ga and ®^Ga were, however, reported by Szentpetery and Szucs (21). Their value of g e 4.9 ± 1.0 eV for the °3Ga resonance agrees with the value reported here to within the accuracy stated. Their value 67 of 3.2 ± 0.6 eV for the Ga resonance, however, differs considerably from the value of 10.4 ± 3.0 eV computed in this work- There are two possible sources for this discrep ancy. First, Szentpetery and Szucs used a target which was approximately 2 keV thick while in this work the targets were 30-50 keV thick. The 30-50 keV targets can be classi fied as "thick” since the gamma ray yield curves show a range of ''■'20 keV proton energy where the yield is essen tially the same. These same curves indicate clearly that a target which is only 2 keV thick would be a "thin” target. A knowledge of the target thickness would be required for resonance strength calculations with these targets while for thick targets this information is not needed. (See Appendix B) It is not clear from the paper by Szentpetery and Szucs what technique was used for target thickness measurement and, therefore, an evaluation of their stated accuracy is not possible. Judging from the shape of the yield curves in this work it seems very unlikely that errors arising from the targets being too thin would be 91 large enough to account for the observed discrepancy. The second possible source of the discrepancy is the angular distribution of this gamma ray. Since it is not predominantly Ml radiation the P4 (cos 6 ) term in the angular distribution is not zero and the calculation for resonance strength made in this work was based on the assumption that only Pq and P2 terms were present. Since the measured value of the P 4 coefficient was small and had an uncertainty comparable in size to the coefficient itself, it was felt that a revised calculation of this resonance strength would not be useful in resolving the discrepancy. The errors in the computation of resonance strengths come from two major sources: 1. Error in the reported resonance strengths used in the efficiency calibration 2. Error in the number of counts in the gamma ray peak The error in the peak sum is computed in the same computer program used to find the sum. The calculation is based on the total number of counts in the peak and on the size of the background subtracted. The resonance strengths used in calibration were reported to be accurate to within 19%. This combined with an average error of 6 % on peak sums used gives a calibration accurate to within 25%. A second peak sum error is introduced into the calculation when resonance 92 strengths are computed to make these values accurate to only 30 to 35%. In calculating the branching ratios it is again neces sary to use the computed efficiency of the system. In this case, however, it is the relative efficiency which is im portant and this is more accurate. The error in resonance strength of the "standard" does not enter in here because whatever it is, it will be the same on all parts of the calibration curve. The shape of the curve is, therefore, not affected and only the peak-sum errors contribute to the branching ratio error. Since peak-sum errors enter in the calculation twice, the branching ratios are accurate to within the sum of two peak-sum errors. The branching ratios are accurate within 15 to 20% depending on the size of the background at the position of the peak. Appendix A Computation of Analog Resonance Energies The computation of the position of an isobaric analog resonance is based upon a simple concept. Since a neutron is replaced by a proton in going from a parent state nucleus to an analog state nucleus, the energy difference between the parent state and its analog is given by AE = Ac - (Bn - Bp ) Xn this equation Ac is the coulomb energy due to the charge on the proton, Bn is the binding energy of the neutron, and Bp is the binding energy of the proton. The values of the binding energies can be found in the Nuclear Data Tables but the values of Ac must be found by experiment or estimated by the equation(2 2 ) A,- -1.13 +1.44 ^ /3 where Z is the mean atomic number and A is the mass number. In this experiment the values used for Ac are those reported by Gaarde, Wilhjelm, and Jorgensen(23). The Q-values for the three reactions studied in this work were all positive and rather large. By knowing these values and AE from the first equation the proton energy necessary to excite the analog of the ground state in the 93 94 parent nucleus can be found from Ep * Q - AE This is, of course, a center-of-mass energy and must be converted to lab energy for comparison with actual experi mental results. The values of Ac, Bn , Bp , and Q along with the computed values of proton energy are shown in Table 6 . Target B E Ac n BP P 64 _ Zn 9.85° 7.99 3.95 1.9 66Zn 9.77 7,05 5.27 2.76 68Zn 9.64 6.50 6.62 3.28 6 . Summary of the results of the calculations for proton energies necessary to excite certain analog resonances. Ac is the Coulomb energy difference between the parent (target + neutron) system and the analog (target + proton) system. It is the measured value unless indicated as the calculated value by "c", in which case the formula Ac « -1.13 + 1.44 2/A1 / 3 was used. Bn and Bp are the separation energies for a neutron and proton in the target + neutron and target + proton systems, respectively. Ep is the laboratory proton bom barding energy at which the ground state analog resonance should occur. All energies are in MeV. Appendix B Efficiency Calibration and Resonance Strength Determination To determine resonance strengths it is necessary to relate this quantity to something which is measurable experimentally. In this work an equation relating resonance strength to gamma ray yield was used* The development of this equation follows closely a development by Gove(24). When a target is bombarded by a beam of particles with energy Eb , the gamma yield is given by where Y\ ** density of target gm probability that a particle in the beam has an energy between and Ej +■ JiEj w(f;. c probability that a particle with energy £% at surface of target has energy between E and E + d £ at depth X. Assuming that the energy distribution in the beam is inde pendent of the value of the mean energy and that the slowing 96 97 down mechanism for beam particles does not vary in the energy range of the resonance, equation A can be written £ AO OO J j 0"^) 9 dx,. (B) X-o fi-i» If this expression is integrated over X allowing £ -*»«£> r * J where K is -the stopping power of the target. Equation B then becomes 3 fa*., “>) = -g-Jsfa-e-)J a normalized function. The result is r° (D) = -g-\ er'(e') d e . — C3 A similar process where *£ is not allowed to approach re sults in the area under the resonance curve for a thin tar- _<=o get Y = rtt§o'(G)d£. 98 The target thickness in energy units is then = (G) The total cross section for a reaction can be written in more detail than in equation E as: 0- - 7 r . \ 1 J i'H )______I______j n r i (H) r is the total width of the resonance 17 is the width for formation Q is the width for decay J( is the spin of the resonance * is the spin of the bombarding particle Xc is the ground state spin of the target nucleus A is the center-of-mass wavelength of the bombarding particle ( Z T T X — X) Combining equations F and G the equation results. Combining this with the Breit-Wigner equation then gives Define £ = ~ and substitute equation G to get -yt ' ' * e / fr* (zj,+i)(2ic+0 C^Hr which simplifies to (zJl + l)££P = — oz(2l,+ (1 T l)i)*fry - 99 After substitution for /I and tf and conversion to the lab system, this becomes (2J.+ > ) ^ = *(**• + -f -f In this equation A is the mass number of the target nucleus M is the mass of the proton C. is the charge on the proton Q is the total charge bombarding the target during the run £ is the system efficiency is the total net count under the gamma peak on the step of the thick target yield curve The quantity is called the resonance strength of the resonance. To calibrate the system efficiency the final equation above was solved for £ and a reaction used for which the resonance strength was known. Since the other quantities in the equation are either constants or experimental para meters, the value of £ is easily found. Since £ is a func tion of gamma ray energy, several reactions must be chosen which give gamma rays over a spread of energies. In this case the 9.17 MeV and the 2.71 MeV gamma rays from the ^C(p, y ) resonance at Ep * 1.760 MeV were used along with the 4.23 MeV and 6.81 MeV gammas from the ^Al(p, y ) reso nance at Ep a 1.118 MeV. 100 To insure that the gamma yield being measured was representative of the total yield, the detector was placed at 125°, which is a zero for P2 (cos 0). Spins of initial and final states in each gamma transition ruled out the possibility that an angular distribution with terms higher than p2 (cos 6 ) could be present. In finding the total yield, the. yield as a function of 0 is integrated over 2 tt and in this process the P2 (cos 0) term integrates to zero. By placing the detector at a zero for the P2 (cos 0 ) term, this does not enter and the yield at that angle is proportional to the total yield. After finding efficiencies for several gamma ray energies a curve was plotted and efficiencies for the remainder of the experiment were taken from this curve. The stopping powers for the targets used were picked from a graph by Marion and Young (25) (see Figure 27). Since the target was a mixture of ^ C and 1 3 C, the stop ping power was computed using(23) where is the stopping power for 1 3 C, is the stopping power for *2 C, is the number of ^2C atoms per cubic centimeter, and is the number of 13C atoms per cubic centimeter. The resonance strength of 10.2 t 2.0 ev for the 2 ^Al(p, y) resonance was reported by Leslie et al.(27) and the branching ratios for the decay of this resonance were found by Lyons, et al.(17). The branching ratios for the Figure 27. Graph of the proton stopping power vs. the atomic number of the target material. Curves are shown for several different proton beam energies. STOPPING POWER FOR PROTONS (x I0~fr Prosser, et al.(16)* REFERENCES 1. E. Wigner, Phys. 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