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A STUDY OF THE GAMDW TELLER STRENGTH IN
40’42’44’4803 FROM THE (p.11) REACTION AT 119 Mev

BY

Janaki Narayanaswamy

A DISSERTAIION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1983

ABSTRACT
A STUDY OF THE GAMOW TELLER STRENGTH IN

40:42:44,48Ca FROM THE (p,n) REACTION AT 119 MeV

By

Janaki Narayanaswamy

The (Pm) reaction at 119.3 MeV has been employed to measure the

140,142,144 and “Ca. The experiment was carried

spin transfer strength in
out at the Indiana University Cyclotron Facility using the neutron time
of flight apparatus and time compensated scintillation detectors at a
target-to-detector distance of 131.5 meters. Analyses of the data by
several different methods indicate that a significant amount of 1+
strength is contained in what is conventionally taken as the background
in neutron energy spectra. This finding explains at best partially the
apparent quenching of the spin depdendent operator V0T when the data were
analyzed ignoring such a background. An earlier observation that the
16.8 MeV state in 11830 is wider than the parent state in “8 Ca at an
excitation of 2.52 Mev is confirmed by the present data. The 2.73 MeV

u
state in 88c is found to have an angular distribution corresponding to

L=O.

DEDICATED
TO
Seethalakshmi and Narayanaswamy

(My Parents)

ACKNOWLEDGMENTS

It is a pleasure to thank Professor Sam M. Austin for his guid-
ance. His patience and constructive criticisms have been indispensable
to the completion of this work. I have also benefited greatly from the
assistance provided by Professor Aaron Galonsky during data acquisition
and by Dr. Olaf Scholten during the final stages of the analysis.

I express my gratitude to the Department of Physics and Astronomy
of Michigan State University and the National Superconducting Cyclotron
Laboratory for financial support during my graduate program. The
faculty, staff and fellow students at the M.S.U. Cyclotron Laboratory
deserve special mention for their kindness. The hospitality extended
by the Indiana University Cyclotron Facility and the assistance provided
by Professor Charles D. Goodman and Dr. T.N. Taddeucci are gratefully
acknowledged. Thanks to R. Geetha, Shobha Prasad and Parul Vora for
making life in East Lansing more enjoyable. I am also most grateful
to Barbara Uacak and Patty Pirnie for their support during the difficult
time of thesis writing and to Ron Fox for helping me understand the
mysteries of the program SCOPEFIT. Special thanks to Shari Conroy for
the typing of this thesis.

Lastly, thanks to my parents for their love and support to a
daughter with unconventional ambitions, to Rukku and Raghu (my sister
and brother-in-law) for the countless pep talks, to my sister Hema for
her wishes and to my brother Kedarnath for repairing everything from

wristwatch to car and keeping me going.

iii

II.

III.

IV.

TABLE OF CONTENTS

List of Tables

List of Figures

List of Abbreviations
Introduction
Experimental Techniques
Data Acquisiton and Reduction
Data Analysis

Summary

Appendix A

Appendix B

Appendix C

Appendix D

List of References

iv

Page

vii

xi

17
31
68
86
9O
92
100
110

117

1.1

3.2

3.3

3.4

3.5a

3.5b

3.6
3.7
3.8
3.9

3.10

4.1

4.2

4.3

4.4

5.1

LIST OF TABLES

Relevant Operators for different probes
Target Information
Energy Band Centroid Shifts (in channels)

Normalization of Relative to Absolute Differential Cross
Sections (at 0°)

Computation of R as a function of assumed threshold energy

Dependence of Efficiency corrected peak areas on
threshold energies 7Li(p,n)7Be (g.s., 0.429 MeV)

ENeutron . 117.0 MeV

Dependence of efficiency corrected peak areas on
threshold energies 12C(p,n)12N (g.s.) ENeutronalloo'O MeV

Angular distributions for “°Ca(p,n)“°$c
Angular distributions for “2Ca(p,n)“23c
Angular distributions for I”‘Ca(p,n)"“Sc
Angular distributions for “BCa(p,n)“°Sc

Neutron energies (in MeV) below which TAC nonlinearity
is present in energy spectra

Optical Model parameters

I“'Ca(p,n)""$c. Contributions to 0° cross sections from
1+, 1 and 3+ states.

“8Ca(p,n)“BSc. Contributions to 0° cross sections from
1+, 1' and 3+ states

Comparison of 1- behavior from present data and background
falloff energies (from 0f 82)

Total GT strength from the present data (as percent of
minimum sum rule prediction)

V

Page

31
35

45

47

50

51

55
55
56
S7

58

72

74

83

87

D.l

D.2

D.3

D.5

LIST OF TABLES (continued)

Computation of total
background) for “20a

Computation of total
background) for l”‘Ca

Computation of total
background) for I”Ca

Computation of total

GT strength (with experimenter's
GT Strength (with Experimenter's
GT Strength (with Experimenter's

GT Strength for “Ca (with 1+

Strengths derived from DWBA analysis of data)

Computation of total

GT Strength for “30a (with 1+

Strength derived from DWBA analysis of data)

vi

Page
112

113

114

115

116

1.1

1.2

2.1

2.2

2.3

2.4

LIST OF FIGURES

Page

Graphs of K, defined in Eq. 1.7 and deduced from the 11
measured 0° (p,n) cross sections vs. <F2> and <ME>2.

The top graph contains only the pure Fermi transitions
while the lower graph contains the complete data set.
Error bars on K reflect uncertainties in measured

cross sections only. The transitions are labeled by
specifying the target nucleus with the excitation energy
in the final nucleus given in parentheses. The solid
curves represent the fits to 2 Mg data, the dashed
curves are the impulse approximation strengths, and the
dot-dashed curve the one-pion-exchange-potential
strength.

(Figure and caption from Goodman et al., (Go 80).)

The empirical quantity R(E ) for odd- and even-A 13
targets. The solid line represents the average value
R(Ep)/Ep=-(S4.9:t0.9 MeV)’1 determined from the even-A

target data for bombarding energies Ep_>_50 MeV.
(Figure and caption from Taddeucci et a1. (Ta 81).)

Floor plan of experimental areas showing locations of the 19
new pion spectrograph, beam swinger magnet and neutron
time-of-flight area.

(Figure and caption from IUCF Annual Report 1977-78.)

Magnet layout for beam swinger 21
(Figure from Goodman et al., (Go 79.)

This figure shows the geometrical parameters of time 23
compensation. B is the ratio of neutron velocity to

the velocity of light. n is the index of refraction of

the scintillator. tn is the transit time of the neutron

and tp is the transit time of the light (photon). L is

the length of the scintillator.

(Figure and caption from Goodman et al., (Go78b).)

(a) The curves show the fraction of forward emitted light 25
that has reached the phototube by time t, measured from

when the neutron crosses the plane through the front face

of the scintillator. The parameters used are: length of
scintillator=1 m, index of refraction= 1.6, phosphor

decay constant - 2.4 ns, neutron energy = 100 MeV. The

vii

2.4

2.5

2.6

2.7

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

(a continued) three curves are for scintillations at
the front, middle and back of the scintillator.

(b) This shows how time compensation is achieved by
tilting the scintillator. The calculation is the
same as for Fig. (a) except for the tilt.

(Figure and caption from Goodman et al., (Go 79).)

This shows the required tilt angle o, as a function
of neutron energy to achieve exact time compensation
for the axial light rays.

(Figure and caption from Goodman et al., (Go 78b).)

Block diagram of phase drift compensator.
(Figure and caption from Goodman et al., (Go 79).)

Block diagram of electronics as used for data taking
in the (p,n) experiment.
(Figure and caption from Goodman et al., (Go 78a).)

Arrangement of detectors in the 0° hut.

Time flight spectra for “0’“2’““

0°.

and “BCa (p,n) at

(top) Cosmic ray spectrum (data)
(bottom) Cosmic ray spectrum (average)

Time of flight spectrum for HCa(p,n)“Sc at 0°, with
cosmic ray contribution subtracted. Solid line indicates
foldover neutron background.

(a) Time of flight spectrum for 7Li(p,n)7Be.
(b) Time of flight spectrum for 12C(p,n)12N.

(a) Plots of log Y and log e vs. R(Th) in units of Compton
Edge. Note that these threshold values are only
nominal.

(b) Plot of R(Th) vs. E(Th) (in units of Compton Edge).
Solid line is the weighted average of the four values
and agrees with experimentally determined absolute
cross section ratios for (p,n) reaction on 7L1 and
12C for states shown in Figure 3.6(a) and 3.6(b), to
experimental uncertainties. The threshold values
shown are only nominal.

Energy spectra for “0’"2’““ and “8Ca(p,n)“°’“2’““ and “BBC.

Experimenter's backgrounds defined to fit peaks are
indicated by solid lines.

viii

Page
25

25

27

27

30

32

37

39
39

41

43

44

48

49

53

3.9

3.11

3.12

4.1

4.2

4.3

4.4

4.5

4.6
4.6

4.7

Angular distribution of 1+ state in “03c (dotted line).
Solid line shows an average of the 1+ angular distributions
derived from “2’““ and “88c.

(a) Angular distributions of observed states in l‘ZSc.

(b) Same as Figure 3.10(a).

“MS

(a) Angular distributions of observed states in c.

(b) Same as Figure 3.1l(a).
(a) Angular distributions of observed states in “88c.
(b) Same as Figure 3.12(a).

Schematic representation of the microscopic model used for
the background calculations in the figure 8F denotes the

Fenmi energy, E the nucleon separation energy, and Ep the

S
incident projectile energy. For the effective projectile
target nucleon interaction Veff the GBY interaction of

Love and Franey (Ref. 8) is used.
(Figure and caption from Osterfeld's work (0f 82).)

Zero degree spectra for the reactions “8Ca(p,n) (a) and
“°Ca(p,n) (b). The data (thick full line) are taken

from Refs. 13 and 14 (see text). The discrete lines are
calculated cross sections due to bound and quasibound
states. The arrow labeled with AL=-1 indicates the loca-
tion where the AL==1 resonance (0',l-,2-) would occur if
nuclear collectivity were included for these states. The
theoretical cross sections due to the GTR and IAS are not
plotted. The Optical parameters for the cross section
calculations have been taken from Ref. 20.

(Figure and caption from Osterfeld's work (0f 82).)

Comparison of measured and DWBA 79 predicted differential
cross sections for 1+ states in “2Ca(p,n)“28c and
“8Ca(p,n)“°Sc.

Plot of 1+, 1- and 3+ strengths vs. excitation energy in
HCa(p,n)“Sc at 0°.

Plot of 1+, 1- and 3+ strengths vs. excitation energy in
“8Ca(p,n)“BSc at 0°.

Application of Goodman's method in an idealized case.
continued

L#0 spectra at Glab=0.0 , for “2’““’“90a(p,n).

ix

Page
59

60
61
62
63
64
65

69

70

73

77

78

79
80

82

Page
5.1 Energy spectra for Blab=-0.0°. Present study. 88
5.2 High-resolution inelastic electron scattering spectra of 88
no “2 H ”Ca all measured at 8 -165° and E0 =39 MeV.

Magnetic dipole transitions are denoted by an arrow.
(Figure and caption from Steffen et al., (St 80).)

Appendix B Spectra (Efficiency Corrected and Energy Calibrated) 92-99

Appendix C.1 Relative detector efficiency versus neutron energy. 109
Threshold energies shown are electron energies.

DWBA

DWIA

GT

IAS

IUCF

N x Th

NTOF

PWBA

TAC

TOP

LIST OF ABBREVIATIONS
Distorted Wave Born Approximation
Distorted Wave Impulse Approximation
Fermi Transition or Operator
Gamow Teller Transition or Operator
Isobaric Analog State

Indiana University Cyclotron Facility
N times the zsth Compton edge

Neutron Time of Flight
Plane Wave Born Approximation
Time to amplitude converter

Time of Flight

I. Introduction

The discovery of the neutron in 1932 was fundamental to
the formulation of successful nuclear models. An underlying
assumption in all such models and verified experimentally is
that the two body nucleon-nucleon force possesses charge:sym-
metry and charge independence i.e., it is the same for p-p,
n-n, and p-n systems. In this picture, the proton and the
neutron are viewed as different manifestations of the same
fundamental entity, the nucleon. It is in the z axis pro-
jection of the isospin (tz) in iSOSpin space that the two
differ: the proton has tz==-l/2; for the neutron, tz==+l/2.
Then the nucleus can be viewed as an aggregate of nucleons,
whose intrinsic states are distributed among spin up or spin
down, and isospin up or isospin down donfigurations. But
recent experiments at intermediate energies have led to
speculation that one may have,to consider additional degrees
of freedom for the nucleon, for example, the A resonance (Os
79, Bo 81, Go 82, Ra 82, Ga 82). To be specific, this has
been brought about by an apparent quenching of the spin
dependent Operators observed in (p,p') (Ml strength) and
(p,n) (GT strength) reactions. Obviously, such a coupling
Of nucleon structure to nuclear structure is of fundamental

:hmportance to our picture of the nucleus. The goal of this

1

2

study is to locate the spin transfer strength from
40'42'44 and 48Ca, and to study the systematics of the
strength as a function of neutron excess. We employed the
(p,n) reaction on the calcium isotopes at a proton energy of
119 MeV. The following considerations will explain the par-
ticular usefulness of the (p,n) reaction in this context and
the relevance of the chosen bombarding energy.

The strength of the nucleon-nucleon interaction at
short range forces one to use an effective interaction, Veff’
in calculations of nuclear structure and reactions. This
interaction is assumed to be the sum of two body interactions
over all possible pairs of nucleons in the system. Many body
forces present in nuclei contribute less than 10% of the
binding energy (Be 72). Therefore, the nuclear Hamiltonian
can be written .

H = Z K.-+ Z V..

l i i<j 13 1.1

th nucleon,

h

Here Ki is the kinetic energy Operator for the i

th and jt

and Vij is the two body potential between the i
nucleons.

In practice, phenomenological effective potentials of
the form given in Eq. 1.2 are used to fit nucleon—nucleus or

nucleon-nucleon scattering data (Au 79);

V.. = Vcentral+Vtensor+vspin-orbit
1] 13 l] 1]
central _ + + + +
Vij - VO(£)-+VG(£)oi oj-+VT(£)Ti “j +
V + -+ + +
UToi OjTi Tj
tensor tensor tensor , .,
Vij (V (E) +Vt (3) Li Lj)Sij 1.2

3

Vspin-orbit = (VSO(£).1VSO(£);i.;j)£.§
Sij = Tensor operator 1.2 cont.

Simple shapes are assumed for the V's, often sums of Yukawas,
and the strengths of Vo(£), Vg(£), Vr(£)’ Vor(£) are deter-
mined from such fits.

Recent work on (p,n) reactions at intermediate energies
has broughtixalight a specific behavior of the effective
interaction that can be used to advantage (Go 80). The case
in question is the total Gamow-Teller strength, obtainable
directly from beta decay measurements only for a few N‘<Z
nuclei. In beta decay, a free or a bound neutron transforms
to a proton or vice versa. There are two components to the.
coupling of the nucleon to the weak field established by
this process: (a) The spin independent vector coupling or
Fermi B decay (F), and (b) The spin dependent axial vector
coupling or Gamowaeller B decay (GT). For a free neutron
the decay rate is expressed as (Go 81)

F1513: ciao: ' 1.3

where GV and Ga are the vector and axial vector coupling
constants. When a neutron is bound in a nucleus, its decay
rate is modified by the presence of the neighboring nucleons

and can be written

K ._ 2 2 2 2
ft - GV<F> -+Ga<GT> , 1.4

where

t - 2
B (F) : (F)

f 731:: 1<f111tfil1i>12

Bt(GT) =<GT>2= l l<fHZO tilli>l2
f ‘ ‘f—M k k k

|i>, |f> are the initial and final states and ti, okt: are
the spin and spin-iSOSpin operators that mediate the transi-
tions. The presence of other nucleons may block some
transitions because the single particle states into which
they must decay may already be occupied.

It is useful to define the reduced transition probabil-
ities B(F) and B(GT) such that B(F) =1 and B(GT) =3 for a
free neutron as is implied by Eq. 1.3. In these units, it
can be shown that the difference in beta decay strengths

for a nucleus with a neutron excess N-Z is given by

ll
U)
I
0')
1|

B(F) N-Z for a Fermi transition

B(GT)

ll
0')
I
(I)
ll

3(N-Z) for a GT transition

This model independent sum rule is derived in Appendix A.
Therefore, we can write
B(F) _>_N-Z and
B(GT) _>_3(N-z)
Thus, N-Z and 3(N-Z) are the minimum strengths one would
expect to find for Fermi and GT transitions respectively.
The equality holds when 88* is negligible.
It had been a puzzling observation that measured beta
decay rates were slow compared to simple model expectations.
The discovery of the isobaric analog state (IAS) in (p,n)

reactions contributed greatly to the understanding of this

phenomenon. The IAS happens to be nearly the projection of
the collective Fermi operator on the final nucleus and in
heavy nuclei the Coulomb displacement energy puts this state
out of the reach of beta decay, hence the slow rate. This
discovery further prompted postulation of the existence of

a giant GT resonance that would contain most of the GT
strength and would be located at an excitation energy near
and slightly above the IAS (Ik 63). In fact, if the nuclear
Hamiltonian were Spin independent, then the IAS and the GT
would be degenerate. But the spin dependent interaction
shifts the GT distribution. Obviously, the existence of
this giant GT resonance, out of the reach of beta decay for
N2>Z nuclei, had to be tested by some probe other than beta

decay. Table 1.1 lists the relevant operators for differ-

 

 

 

ent probes
Table 1.1
Relevant Operators for different probes
Transition O+-+O+ L==O 0++1+
S=0 s=l
+ + + ++ +
In XV ' . XV ° - .
(p ) . TIP T] ' OTop ojrp Tj
J 3
B decay Z I. (Fermi Z o.-r. (GT)
j J - J J
J
14* ( >7 7'
f :1 -I.G‘OT.I
l j'JP "‘3 3 J:

 

 

*
Ignoring current and small isoscalar parts of

the operator.

In the (p,n) reaction, the target nucleus gains one
more proton and loses a neutron. In this sense, the reac-
tion is similar to beta decay. Since the operators have the
same form in spin-isospin space one would expect strong
transitions in GT beta decay or M1 to be strong in (p,n)
reactions. This similarity suggests that the (p,n) reaction
can be used to mimic beta decays that are prohibited by
energy considerations and to determine GT strengths. But
one has to study first, nuclei with knowncxrmatrix elements
so as to understand the signature in the (p,n) reaction that
corresponds to beta decay strength and establish empirical
quantitative relationships between the two. More important-
ly, the beta decay conditions have to be simulated with the
(p,n) reaction as closely as possible (near zero momentum
transfer, for example) and quantitative corrections made for
deviations from these conditions. Then it is possible, in
principle, to extract beta decay information from the (p,n)
reaction in an almost model independent way (Go 80).

It was seen that the IAS, corresponding to superallowed
Fermi transitions stood out in (p,n) spectra. But the GT
transitions were not apparent in low energy (p,n) reactions.
The first evidence for the existence of GT giant resonances
came from 45 MeV (p,n) data taken at M.S.U. (Do 75). It
was soon apparent from intermediate energy proton beams (up
to 200 MeV) at IUCF that GT transitions dominate the 0°
(p,n) spectra at energies greater than about 100 MeV (Go 78).

This is a direct consequence of the relative behavior of VT

and VOT as a function of proton energy (Ta 81). These inter-
mediate energy (p,n) reaction studies led to the following
observations (Go 80).

The (p,n) reaction is mediated by isovector parts of
V. i.e., V

3p or
transfer) only low momentum components contribute appreciably

and VT in Eq. 1.4. At 0° (small momentum

to the cross section. Therefore, at 0°, the (p,n) reaction
favors states with significant allowed Fermi (L =0, S =0)
and GT (L==0, S:=l) matrix elements. At intermediate ener-
gies, strong transitions in (p,n) are direct; central parts
in Vjp dominate; for small q, noncentral parts can be
neglected. Also at 120 MeV, the impulse approximation has
some validity i.e., Véffw§the free nucleon-nucleon t matrix.
In the distorted wave approximation the cross section
for a reaction A(a,b)B is prOportional to the square of the
transition matrix element and can be written (Go 80)

d k
0 = ( 11 )2 f 1
35 2557 ET (2Ji+l)(2§p-+l)

 

2
i p] 1.5

Zlfxé-)*(£p)<f|§ Vjp(l‘-Pjp)li>x(+)(gp)d3r
where the x's are distorted waves generated in an appropriate
Optical potential; u and k denote the reduced mass and wave
number in the center of mass system respectively;

JP
the effective nucleon-nucleon interaction; knockout exchange

<f|Z Vjp(l-Pij)li> is the target matrix element, and V. is
J

is excluded by the term l--Pjp where Pjp is the permutation

operator. The inner sum is over all the nucleons in the

target; the outer sum is over the initial and final spin
projections of the projectile and the target.
Under the conditions observed for (p,n) reactions at

120 MeV, the 0° differential corss section can be written

k
do ~ u f D 2 D 2
d (00) _ (‘an ) E—i {NTIJT<F>] +NOTIJGT<GT>I I 1.6

where J,f and Jor are the magnitudes of the volume integrals
of the effective spin independent (Tj-Tp) and spin dependent
(Oj-Op Tj-Tp) isovector central terms in Vjp(l-Pjp), N3

and N21 are distortion factors defined to be the ratio of
the DWBA and PWBA cross sections; |<F>|2 and |<GT>|2 are the
squares of the Fermi and Gamow-Teller matrix elements given
by 1.4. Following Goodman et al., (Go 80) define for a pure

Fermi or GT transition,

k
__ do(0°) u 2 f 1)

Then from a plot of K vs. B(F) or B(GT) one can extract
empirically the corresponding interaction strengths, Jr and
JOT in Equation 1.6. Goodman et al., used the local t-matrix
interaction of Love et al., (LO 78) and computed the distor-
tion factor ND. They find that ND shows a smooth exponential
A dependence and is only moderately sensitive to the reac-
tion Q values and the model nuclear wave functions. By com-
paring the 0° (p,n) cross sections of the IAS and GT states
in the case of several nuclei to known F and GT beta decay

matrix elements, Goodman et al., find that there is a linear

correspondence between these two quantities and that

interaction strengths at Ep==120 MeV are 168 MeV-fm (spin
flip) and 89 MeV-fm (non spin flip). Figures 1.1a and l.lb
show the data and the fits from their work. This finding
demonstrates that the (p,n) reaction can serve as a precise
probe to measure GT strength for light and medium weight
nuclei.

Taddeucci et al., (Ta 81) define another convenient
empirical ratio
oGT(0°)/|<GT>[2KGT(E )

.E— 1.8

2
{R(E )} = o
p OF(0 )/1<F>TZKF(EP)

where OGT(O°) and OF(0°) are cross sections in the same
nucleus for a 1+ state with known Bf(GT) and the IAS with
B(F)==N-Z, respectively. In terms of the quantities in
Equation 1.6

J

 

 

~ or D D35
1.9
_ 2

It has been found from DWIA calculations that at intermedi-
ate energies the distortion factor ratio is approximately in-
dependent of energy and has the value 1.2 t0.l for GT and F~
transitions not widely separated in energy. The quantity
R(Ep) then represents roughly the ratio of interaction
strengths JCT/JT at momentum transfer q==0 but corrected

for small distortion effects. Taddeucci et al., considered
the variation of R with incident proton energy for several

odd and even mass nuclei and found that R<==Ep to a good

10

Figure 1.1. Graphs of K, defined in Eq. 1. 7 and2 deduced
from the measured 0° (p,n) cross sections vs <F>2 and
<ME>2. The top graph contains only the pure Fermi transi-
tions while the lower graph contains the complete data set.
Error bars on K reflect uncertainties in measured cross
sections only. The transitions are labeled by specifying
the target nucleus with the excitation energy in the final
nucleus given in parentheses. The solid curves represent
the fits to stg data, the dashed curves are the impulse
approximation strengths, and the dot- dashed curve the one-
pion-exchange-potential strength.

(Figure and caption from Goodman et al. (Go 80).

ll

 

 

 

 

 

  

 

 

 

 

 

 

 

 

AGE. .~>o<: «7.0. X. v.

I. _ _ _ _ _ _ .15 q _ _ 3m 3. «H _
.. . x. 1. ,m 1..
r. S .1 m 3.0....433s11l/ x W . .v
n . i / e
.m :mwhNom ’@ M
.. a 1m 4,...
e \
1 m 0 I flew. .YT
S 1... A» 6 12
m 2 _ :. in.
C \l . n... . . 11111 1.1 . ..
.. < . ,
ImM 2.30sz / I .O
T no Is 3362 1...;
Wan/u. 1 3.323111%”). 1...
1. d ... 1.14 A.W.Ovoan / “/
mF. ..m.om.<- (1.1»; .
III e bl. all .m. v0 \
Z 2 A n. I
a 3.9923 x Z
_ _ b _ b _ _ _ .
m w. 00 m M m m 8 6 4 2 . 00

(ME)2

Figure 1.1

12

approximation above Ep==60 MeV. Figures 1.2a and 1.2b show
the data that they used and the linear fit to the data. For
example, at 120 MeV, R =2.l9. This linear and model inde-
pendent relation can be used to compute GT strengths from
(p,n) reactions at 120 MeV with an accuracy only slightly
worse than that of the cross section measurement i.e., 20%.
One simply compares the IAS cross section with the l+ state
of interest and applies Equation 1.8. Note that such a deter-
mination is independent of calibration transitions, cross
section normalizations, and DWIA mass dependent extrapola-
tions. Hence, this method has a particular simplicity and
we use it exclusively.

Some measurements have already been made of GT strength

40,42 48

from (p,n) reactions on and Ca at 160 MeV, (Ga 81,An 80) ;.

but the current work is more complete and includes a 44Ca
target; it will serve as a parallel to the electron scatter-
ing studies of Steffen et al., (St 80). The measured B(GT)
is compared to the simple sum rule prediction to determine
the quenching of the spin dependent Operator or-. In recent
work on heavier nuclei, roughly 0.6::0.1 of the sum rule
strength was seen. This has been interpreted as evidence
for the coupling of the nucleon to the A isobar (T==Tz==3/2,
S =3/2) by several authors (Os 79, Go 82, Ra 82, Ga 82, Bo
82). There seems to be some evidence from pion inelastic
scattering also that such a coupling exists (Mo 82). Cal-
culations including this coupling to the spin-isospin

degrees of freedom of the nucleon suggest that roughly 65%

l3

 

 

 

‘ I
Even-A ,’

3»— s4
1 ' C i
r 1
b . u
I- 42 4
2L ‘ Co .4
A“). d
.1321 I
C 1- .1
D .
11- «:1
b c1
D d
1'. ‘1
-/ cl
I LL LLLLL4 1 LLI 111 A 1 1 J 4 LJL

 

 

 

 

 

1 I, ‘1

Odd-A , J

- 7L1 2

I ‘q

o 36 A

7 ..

-3c: .

.1
WW.

0 50 ED 50 ax: 233
5,, mm

Figure 1.2. The empirical quantity R(E )
for odd- and even-A targets. The solid
line represents the average value
R(Ep)/Ep = (54.9 e 0.9 MeV)‘1 determined

from the even-A target data for bombarding
energies Ep _>_50 MeV.

(Figure and caption from Taddeucci et a1.
(Ta 81).)

14

of the classical strength should fall in the nuclear excita—

208Pb (Ga 80). Sagawa used the constituent

tion region for
quark model to calculate the isobar-hole coupling matrix
element and finds that the combined effects of RPA correla-
tions and particle-hole coupling decrease the transition
strengths of M1 and GT states by about 35% (Sa 82). If
true, all the above observations point towards a significant
coupling of the nucleon structure to nuclear structure.
However, the work of Bertsch and Hamamoto, including

90Zr, indicates that the strong tensor

2p-2h states for
force shifts the strength to between 10 and 45 MeV excita-
tion (Be 82). Yet another approach to the problem of spin-
isospin excitations in terms of a unifying response function
by Ericson suggests that at low momentum, in addition to
creating a collective mode, the strong repulsive ph force,
also produces a quenching of the GT strength due to a
Lorentz-Lorentz effect similar to that of electromagnetism
(Br 82). Microsc0pic background calculations for (p,n)

40 and 48Ca at 160 MeV, carried out by Osterfeld

reactions on
imply that a significant part of the missing l+ strength is
contained in what is conventionally taken as an experimen-
ter's background and this accounts at least partly for the
larger values of the observed quenching of the spin depen-
dent Operators earlier deduced from (p,n) reactions (Of 82).
Thus the precise amount of quenching may bear importantly on

the question of the number of degrees of freedom in the

nuclear wave function. In the present work, an attempt has

15

been made to verify the last of the above hypotheses as
will be discussed in Chapter IV.

Finally, one notes that these results may have substan-
tial applications. The GT strength is a measure of the
degree to which nucleons are unpaired in the ground state of
a nucleus. The measured strength for 40Ca should therefore
be useful for an estimate of the same. The present study
also verifies a recent claim that the analog of the 10.3 MeV

state in48

Ca is significantly wider than the parent state
(An 80). The energy systematics seen in this study seem to
indicate what was already noted by Bertsch--i.e., one does
not expect pion condensation in nuclei (Be 81). The width
of the GT strength function is a necessary input in calcula-
tions of stellar nucleosynthesis. In the gross theory of 8
decay, Takahashi et al., use the mean energy of GT strength
to be degenerate with the IAS which is not quite right and
use a width of 10 MeV, much larger than seen in (p,n) reac-
tions (Tk 73). Redoing these calculations using the mean
energy and width of the GT strength values as suggested by
the current (p,n) reaction studies might improve our under-
standing of the r-process nucleosynthesis. Further, GT
matrix elements are of considerable importance in computing
weak decay rates in supernovae (Fu 80). We hope that the
current measurements will therefore, aid in calculations of
reaction rates in these stages of stellar evolution and

nucleosynthesis.

The organization of this thesis is as follows: Chapter

16

II contains a description of IUCF and the neutron time of
flight apparatus. Methods of data acquisition and reduction
are described in Chapter III. An analysis using DWBA 79 and
interpretation of our results are given in Chapter IV. A
summary of our findings is given in the concluding Chapter

V. The simple sum rule quoted earlier is derived in Appendix
A. Plots of energy calibrated spectra for all the four tar-
gets at the three angles measured (0°,6.3°,and ll.l°) are
shown in Appendix B. Neutron detector efficiencies are
listed in Appendix C. Appendix D contains Tables giving

the details of the computation of the GT strength.

II. Experimental Techniques

The electric charge neutrality of the neutron.doesxun;permit
conventhmuu.detection techniques, using magnetic spectrographs and
solid state detectors. Neutrons can only be detected by the charged
particle recoils, or the charged reaction products produced when they
scatter ffiwxn, or react with other nuclei. Although the energy signals
thus produced are not proportional to the neutron energy, the time of
emission of these signals in the detector relative to a fixed time
reference is proportional to the time of flight, which in turn, defines
the neutron velocity, and hence, the neutron energy. Thus, precise time
signals and long flight paths are required in high precision neutron
spectroscopy.

Quantitatively expressed, neutron energy E, neutron velocity v,

time of flight t, and the path length L are related as

 

 

2 u
2.1!. 3.1.
E Mnc (2 2+8 14'”)
C C
t = L/v (2.1)
2 A
~ 2 1 L 3 L
E'Mn°( 22+ 1111)
t c t c

where Mnc2 is the rest mass energy of the neutron.
In the nonrelativistic limit, energy resolution and time resoluticni are

therefore, related as

23/2 E3/2
; ___. ____. 2.2
A8 M1/2 L At ( )
‘n

17

18

Note that this is a lower limit on AB. The different factors
contributing to At are electronic, beam bunch width, scintillator
transit time, target energy loss and straggling, beam energy spread,
kinematic broadening, and intrinsic state width. One way to improve
energy resolution is to increase the flight path with a consequent loss
in count rate a: 13-2. Using large detectors can compensate partly for
count rate loss; but then, scintillator transit time causes a major loss
of time resolution unless one compensates for it by other means. At the
Indiana University Cyclotron Facility (IUCF) where the experiment was
carried out, typical proton pulse widths are 0.5 nsec. Using large
volume scintillators and a time compensation technique described later
in this chapter, Goodman et. al., have achieved subnanosecond resolution
for 100 MeV neutrons (Go 79). To get an estimate of the pathlength
involved, note from Equation 2.2 that for At-1 nsec, roughly a 115 meter
long flight path is required for an energy resolution of 300 Kev for 115
MeV neutrons. With these limitations, the major technical problems
associated with neutron spectroscopy are the need for (a) a beam swinger
(b) large detectors and (c) a stable stop signal.

(a) Beam Swinger: It is not very practical to move detectors
around the target to measure angular distributions, when the flight path
is long. This requires not only large space, but also very carefully
placed shielding along the flight path to insure that the detector sees
only neutrons from the target. It is easier to change the direction of
the incident beam on the target. The floor plan of the experimental
areas at IUCF are shown in Figure 2.1. The neutron station is located
at the northern end of the laboratory. The remoteness of this location

allows one to set up long flight paths with little inconvenience to and

l9

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20

from other sections of the laboratory. A major feature of the neutron
station is a beam swinger using three fixed magnets that enables one to
change the angle of incidence of the beam on the target; for a fixed
flight path, this is equivalent to changing the effective reaction
angle. Figure 2.2 illustrates the geometry. The first magnet bends the
beam away from its original path, the second magnet bends it back
towards the target. The pole faces of the second magnet are large
enough to accept a range of paths that impinge on the target at a range
of angles. The third magnet steers the beam into a dump. ‘With the use
of the third magnet, the beam dump can remain fixed, as the angle is
varied. Tins feature is particularly useful at high energies, when
massive shielding is required around the beam dump to keep the neutron
background low. It also makes possible Observations at 0°, where Lao
spin flip processes dominate.

In the NTOF system currently in use at Indiana, the angular range
on target Of incident protons is 260. The scattering angle 6 is
determined by the radii of curvature of the beam protons in the two
magnets, 91(6) and p2(e). Thus, to set the system for a given angle,
one sets the fields 82 and B1 to correspond to the magnetic rigidity of
the incident particle. The angle is then measured more precisely by
centering the beam on a motor driven slit that pivots around the target
position. The slit is used only when the beam is being focused and the
angle measured and is retracted during data runs to avoid neutron
background.owxn it. Since the scattering plane is horizontal one can
have multiple paths with all detectors at ground level. Currently, there

are three time of flight lines covering angular ranges of 0-260, 24-500,

21

A.Amn 00V ..Hm um :mEoooo Eouw Owsmflmv
.ummcw3m Emma Hem usoxma uocmmz

.N.N musmwm

 

 

 

 

 

 

 

22

and 145-710. The detectors are housed in huts that can be moved with a
fork lift and placed at the desired locations.

(b) Detectors: To get an idea of the size of the detectors needed
for our purpose, note that for a solid angle of 1rmn‘(typical for a
solid state detector of area 50 mm2 at a distance of 22 cm and
therefore, a comparable count rate assuming same efficiency of
detectnxn, a neutron detector at a distance of 100 meters from the
target has to have an area of 10 m2. A second consideration is that
neutron detectors are not 100% efficient. These two effects point in
the direction of large detectors. In a large scintillator (>10cm in any
dimension), there is some loss of time resolution because (i) the
measured time of detection of a neutron depends on the position at which
the scintillation event occurs; and (ii) the spatial distribution of the
light on the photocathode is different for scintillations occuring at
different points in the scintillator. The resulting loss of time
resolution can be reduced if one arranges to determine the position of
scintillation and applies a correction later. Alternately, a time
compensation technique can be used.

At IUCF, Goodman et. al., have employed a geometric approach to
tube compensation (Go 78a, Go 78b, 00 79). The detector axes are tilted
relative to the incident neutron direction such that the neutron and
photon transit times are independent of the position at which the
scintillation occurs. As can be seen from Figure 2.3, the time of
arrival of a photon at the phototube from a scintillation occuring at

coordinates x,y in the scintillator is

 

. . .214... 3.9.51-4 151mb
t(x,y,8,e) C0 + 0 cos 6 + c ( 8 cose) + c 8 (2'3)

23

.—

 

OINL°OWG 77 - 7035

 
  

V
\\

NEUTRON

 

xcoso

 

ysin¢
(Icos¢+ysin¢1 ' OIL-x1
'8. B: I- teas?

 

 

 

Fig. 2.3. This figure shows the geometrical param-
eters of time compensation. B is the ratio of
neutron velocity to the velocity of light. c is

the velocity of light. n is the index of refraction
of the scintillator. tn is the transit time of the
neutron and t is the transit time of the light
(photon). L Es the length of the scintillator.
(Figure and caption from Goodman etaal" (Go 78b).)

24

where to is the neutron time of flight up to the scintillator and other

variables are defined in the figure caption. What one would like to

achieve by time compensation is to make t nearly independent Of’ic and y

for a given neutron energy i.e., a given value of B. It is assumed that

the light is emitted isotropically. Light emitted with e>emax (limiting

angle for total internal reflection) is lost. For an index of
o

refraction n - 1.58, emax = 51 . The time equation then implies that

light from an instantaneous flash will arrive at the phototube over a
period from t(x,y,8,e - 0°) to t(x,y,B,6 - 51°). In a real
scintillator, the light is not emitted instantaneously; it follows an
exponential decay curve with a characteristic decay time which for
example, is 2.4 nsec for NE 102 scintillator. This is dominant ha
determining the light curve at En - 100 MeV. Note that the light
profiles illustrated in Figure 2.4a exhibit varying risetimes as well as
varying amplitudes, (due to random scattering angle in the neutron
reaction). Constant fraction timing can only compensate for variations
in amplitudes. A form of extrapolated zero timing is employed at IUCF
to compensate for varying risetimes.

The principle behind this method is as follows: The puLse shape of

the signal from the photocathode is found to have a parabolic shape near

the origin, represented by
A(t) . A ((t-t )/r)2 (2.4)
0 0

where t0 is the origin of the light pulse and both A arui T vary. 'The

0

objective is to determine t as marked in Figure 2.4b. Ikfidne two

0 9

25

 

 

 

 

 

 

TWNflE(ns1

(o)

  

TIME (as)

(b)

 

 

 

Figure 2.4

(a) The curves show the fraction of forward.
emitted light that has reached the phototube
by time t, measured from when the neutron
'crosses the plane through the front face
of the scintillator. The parameters used
are: length of scintillator - l m, index of
refraction - 1.6, phosphor decay constant -
2.4 ns, neutron energy - 100 MeV. The three
curves are for scintillations at the fkont,
middle and back of the scintillatOr.

(b) This shows how time compensation is achieved
by tilting the-scintillator. The calcula-
tion is the same as for Fig. (a) except for
the tilt. . -

(Figure and caption from Goodman et al. , ‘
(Go 79).)

26

amplitudes A and A

1 2, such that the corresponding times t and t

1 2
satisfy

t1 - to . t2 - t1 . (ta-t0) - (t1-t0) (2.5)

Set up two discriminators with thresholds at A1 and A2 to start two time

to amplitude converters (TACs) and measure (T-(t1-to)) and (T-(tZ-t )),

O
the stop time I being provided by the cyclotron rf to be described
later. Subtracting the output of the second TAC from that of the first

yields t -t ; with our choice of A and A

2 1 1 2, this is exactly the origin

of time. Thus, if Equation 2.4 is a valid approximation to the portion
of the pulses sensed by the discriminators, the required amplitude ratio
A2/A1 can be shown to be 14. Then the tilt angle should be chosen to
line up the the origin of the pulses and extrapolated zero timing should
be used with A2/A1 - 14. Figure 2.4b shows how tilting the detectors
lines up the origins of the pulses.

It can be seen that time compensation is exact for neutrons of a
particular energy only, because the tilt angle to accomplish it is
derived from B, the neutron velocity (Equation 2.3). Calculated tilt
angles vs. neutron energy for axial light rays are shown in Figure 2.5.
In an experimental set up with long flight paths, one is far from having
axial light rays; therefore, the tilt angle is determined by trial and
error. A known sharp line is obtained from a known target. On line
analysis gives the FWHM of this peak in the TOF spectrum. Tilt angle is
changed until the highest resolution is obtained. At IUCF, a triple
discriminator is used with levels 2 and 3 set fOr amplitudes A1 and A2

defined earlier. See Figure 2.7. Level 1 (the lowest threshold) .Ls set

as high as 1744 to 1/2 of the maximum neutron energy because the flight

27

 

BO

70

4O

30-

 

HLI ANGLE (no)

20—

10v—

 

 

I i 1 1 1 I i 1
0' 20 40 so so too 120 140 160 180 200
NEUTRON ENERGY (Mew

 

0

Figure 2.5. This shows the required
tilt angle O, as a function of neutron
energy to achieve exact time compensa-
tion for the axial light rays.

(Figure and caption from Goodman et al.,

 

 

 

 

 

 

 

 

 

(Go 78b).)
.‘ 013C11- mllt -
[1:3- ....... ...... .... .

 

 

“A: u "nu

SHIFTII

 

’ 4 >

m 5'” “st f—d 1111(qu

 

  

 

 

 

'cnuumn

 

 

w .

 

um 3mm.

 

 

Fig. 22.6 Block diagram of. phase drift compensator.

 

 

Figure and caption from Goodman et al- .(Go 79).

28

time of neutrons at that fraction of the energy becomes greater than the
separation of the beam pulses, and neutron spectra from adjacent bursts
would overlap if the threshold were set lower.

(0) RF Timing with phase drift compensation: A precise timing
signal for STOP input to the MOS can be derived from the cyclotron rf
signal" ‘The Indiana cyclotron is a three stage system consisting of an
ion source, a preaccelerator cyclotron and a main stage cyclotron.
Under normal operating conditions, there are 4 to 6 bunches per orbit in
the cyclotrons. Since the time separation between the bunches is too
small for TOF studies with long paths, one bunch per orbit is selected,
with the help of a pulse selector and a buncher located on the beam line
between the ion source and the first cyclotron. The beam is swept
across an aperture in a circle with a subharmonic of the cyclotron
frequency, f. One uses 3/4 f or 5/6 f to achieve 1 of A or 1 of 6
selection respectively. The reference time for the TOF system 1:: taken
from a phase coincidence between the f signal from the cyclotron master
oscillator and the subfrequency. If the magnetic fields on the
cyclotrons were stable, the proton transit time through the accelerator
system would be constant and the stop signal would be stable. In
practice, small phase drifts of the order of a few nanoseconds occur
between the accelerating voltage and the proton bunches and compensation
is necessary for good time resolution.

The phase compensation method devised by Goodman et al., is
illustrated in Figure 2.6. Protons elastically scattered from the
target are detected with a fast scintillation counter located along a

o

12 line with respect to the undeflected incident beam. The proton

signal is set to trigger a discriminator which generates a pulse with a

29

width of about 1/2 the rf period. This pulse opens the current gate of
a diode bridge. If the opening time is centered about the crossover
point cm? the rf sine wave, then the net charge passing through the gate
is zero. If there is a phase drift, this net charge is nonzero, being
positive or negative, depending on the direction Of’the drift. The
integrated output of the gate is a measure of the phase drift and is
used as an error signal into a phase shifter that shifts the phase of
the rf signal going to the stop pulse generator.

The standard electronics employed at IUCF by Goodman et. al., for
NTOF studies is shown in Figure 2.7. To obtain the highest resolution,
the tilt angle was varied to optimize the peak to valley ratio of the

barely resolved states in the 7Li(p,n)78e(g.s., 0.429 MeV) reaction.

Level 1 was set at nominally 10 times the Compton edge from 228Th.
Total charge was measured by split Faraday cups at the end of the third

magnet in the neutron station. The other details of data acquisition are

described in Chapter III.

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30

 

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III. Data Acquisition And Reduction
The experiment was carried out at the IUCF with a 119.3 MeV proton
beam. Beam energy was obtained from the calibration of tune beam

40,42,44 and “8C8, 711, and 12C) were

analysis system. The targets (
loaded on the ten position Geneva drive target ladder at the beam
swinger» Thais target drive was remotely controlled through the Sigma-2
cyclotron controls computer. The targets were protected from oxidizing
by the vacuum interlock of the target drive. The 00 flight path from
target to center of detector was 131.52 meters long. The cyclotron rf
was 28.72 MHz. With a 1 in 11 pulse selection, this corresponds to a

beam repetition period of 139.3 nsec. Target information is summarized

in Table 3.1. Four large volume plastic scintillators

Table 3.1 Target Information

 

 

Target Thickness Purity
(mg/cmz) (Percentagefl

“08a 29.2:0.3 99.965
l‘ZCa 30.5:0.5 93.60
”“Ca 28.5:0.S 98.68
“88a 28.5:0.5 97.30

7L1 A3.1:0.3 99.99

‘28 3u.9:o.5 99.99

 

 

 

and two anticoincidence paddles (to veto cosmic rays) were arranged ir1
the 00 hut as shown in Figure 3.1. The scintillators were coupled to 5"
phototubes with tapered light pipes at both ends. Another scimniillator
was housed in the 240 hut at a distance of 39.0 meters from the target,

and data were accumulated, but were not used in the analysis. A

31

32

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33

hardware threshold of nominally 23.8 MeV electron energy (10 times the
Compton edge of the 2.61 MeV gamma ray from 8 228Th source) was used.
If the detector had infinite resolution, then the Compton edge would be
seen as a sharp structure in the spectrum; the finite resolution of the
detector smears this edge with a Gaussian shape. Computations have been
carried to measure the position of the actual Compton edge relative to
the peak of this Gaussian distribution as a function of the resolution
(Ta 82, Ga 83). Ix.was found that the detector resolution was 25% at
the energy of interest. This yields the position of the Compton edge as
0.93 times the position of the half maximum point of the peak in the
spectrum. Additional software thresholds of nominally 17, 23, and 28
times the 228Th Compton edge were set within the IUCF data acquisition
program DERIVE. We refer to the spectra by these as labels. An off-
line analysis of the spectra from the 228Th source yielded values about
10% higher timui these corresponding to thresholds of 11.0, 18.7, 25.3,
30.8 times the 2'28Th Compton edge. In equivalent neutron (proton)
energy the thresholds were therefore at 32.6, 50.7, 65.9, and 78.4 MeV
respectively (An 79). The total incident charge, total number of events
witTUJl each detector, and total number of events vetoed were registered
by scalers. The time resolution achieved was 1.5 nsec, corresponding to
an energy resolution of 330 Kev, at the best.

7 12

The Li and C targets were used for purposes of cross section

normalization. These two targets were the first to be measured at 00;

the unresolved states in 7Li(p,n)78e(g.s.+0.429 MeV) were used to

determine the best tilt angle. Next, the calcium spectra were taken at
o . . . 7 . 12“ o
0 ; calibration runs with Li and u were repeated at the end of the 0

runs. Following this, background due to cosmic rays was measured for

34

about 211 minutes. Then measurements were made with the calcium targets
at 6.30 and 11.10. Beam current was maintained between 200 and 2400
namp.

1. Determination of centroid shifts for energy bands and choice of
threshold for analysis

Loss of time resolution results primarily from (a) variation in
risetimes of pulses and (b) variation in amplitudes of pulses. As
discussed in Chapter II, the method of extrapolated zero timing is used
to compensate for timing errors due to variation in risetimes of pulses.
The amplitude dependent 'time walk' was minimized by breaking the
observed range of pulse heights into bands defined by the threshold
settings and evaluating the necessary shifts using a standard peak. The
raw TOF data are in the form of 10211 channel spectra; there are 16 of
them-~four thresholds for each detector and four detectors. For
example, for detector 1, the TOE‘ spectra corresponding to the L1
thresholds are stored in arrays 1,5,9 and 13 with array 1 containing the
data for the lowest threshold and 13, that for the highest. First,
channel by channel difference spectra of these arrays i.e. 1-5, 5-9 and
9-13 are obtained. This is done for all the 00 runs. Then a sharp peak
is chosen in each target and its centroid found in each of the energy
bands 1-5, 5'9, 9-13 and array 13. The centroid shifts of the higher
bands relative to the lowest band 1-5 are determined. The results for
different targets are then averaged to obtain the final band shifts for
detector 1. The procedure is repeated for detectors 2, 3, and 4. Table
3.2 displays the results. Next the bands were added channel by channel
with appropriate shifts. Data from detectors 2, 3 and u were then added

to that of detector 1 with the necessary shifts. One thus obtains the

35

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36

final TOF spectra for all targets and all angles including the cosmic

uo,u2,uu and

ray run. Figure 3.2 shows the results for 00 runs for the
8Ca targets.

2. Cosmic ray and foldover neutron background contributions and
subtraction

Cosmic ray events were partially vetoed by the arrangement of the
anticoincidence paddles marked in Figure 3.1, but some background
remains. This can be seen from the cosmic ray spectrum measured between
the 0° and 60 runs. In the absence of any major transient phenomena
occuring on the Sun during our runs, it can be assumed that the diurnal
variation of the nuuni component of the cosmic ray background is
negligible (W1 76); therefore it is possible to correct for the
different counting times and subtract the cosmic ray background from the
TOP spectra.

The low counting rate for the cosmic ray background combined with
the brief mmnudng time (1uh1 seconds) resulted in relatively large
statistical uncertainties for all the thresholds except the lowest one.
In addition, examination of the cosmic ray spectra revealed that the TAC
had a nonlinear response for channels (290. To treat these effects, we
first obtained average counts by summing over every 50 channels. Figure
3.3 shows the cosmic ray spectrum for the lowest threshold, with the
open circles representing the averages over 50 channels. It can be seen
that the TAC is linear for channels >300. There are 500 channels in
this region which we define as the flat portion of the cosmic ray
spectrum. The weighted average of the flat portion was obtained hm“
each threshold. Next, the region of the spectrum between channels 100

and 250 was examined for the lowest threshold (11xTh case) and a

COUNTS PER CHANNEL '

37

MSU-83-226

 

 

2501. 4000 1
0 l 1 1 1
_ Co(p,n)Sc 42Co
Ep=|19.28 MeV
6LA&3=(31)°

400% THRESHOLD=18.7X

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r L

O L 1 4‘ W 1" I “T
8000- '
44Co

0 W1 1 1 1 1
48cc

3000- M V LA

(3 :i“iA‘—;fi 1 l 1 l
250 500 750

TIME OF FLIGHT (CHANNEL NUMBER)

Figure 3.2. Time of flight spectra for
uo,u2,uu a

nd “SCa (p,n) at 0°.

38

straight line approximation obtained. The two regions, channel >250 and
channel <250, were joined smoothly for the 11x case where the statistics
are good. The higher threshold spectra were obtained by scaling down
the 11x spectrum using as scale factor, the ratio of the flat portion of
the spectrum to that of the 1x case. Poor statistics made it impossible
to obtain reliable TAC nonlinearities directly from these spectra.
Figure 3.u shows the averaged cosmic ray spectrum for the lowest
threshold” These spectra were then time normalized and subtracted from
the TOP spectra for the different targets.

In neutron time of flight studies using a pulsed beam, there exists
the problem of slow neutrons from a certain beam burst and fast neutrons
from the next burst arriving at the detector at the same time. To
minimize this slow neutron background, the foldover neutron background”
one has to set the hardware threshold fairly high; in our case, this was
set at roughly 36.0 MeV neutron energy. The dynamic range of 120 MeV
neutrons at a distance of 130 meters for pulsed beam of period 139 nsec
is approximately 32.0 MeV. This means that to avoid the foldover
background completely one has to have the hardware threshold of at least
88 - (120-32) MeV. But this will reduce the count rate severelyu .As a
compromise, software thresholds between 50.0 and 80.0 MeV neutron energy
were set within the data acquisition program; the plan was to accumulate
all the data, and decide on a proper choice of threshold for analysis at
a later time. Offline analysis of the data revealed that the foldover
neutron background can be eliminated by extrapolating the TOP spectrum
from below the ground state to higher excitation energies and
subtracting it. This was done by examining the foldover neutron

u u
behavior in 60 and 110 spectra of the OCa(p,n) OSc reaction which has a

no
C)

COUNTS PER CHANNEL
(1)
O

O)
C)

20

 

MSU-83-228
I T T f 1 I I f 1 j T I T
COSMIC RAY SPECTRUM
THRESHOLD = II x

 

 

.L

 

__
«b—

l n I l l L l J
I r f I I i I l

AVERAGED COSMIC RAY SPECTRUM
THRESHOLD = le

 

 

.1 l J l 1 L 1 L L l 1 l L
200 400 600
TIME OF FLIGHT (CHANNEL NUMBER)
Figure 3.3 (top). Cosmic ray spectrum (data)

Figure 3.4 (bottom). Cosmic ray spectrum (average)

 

40

large negative 0 value and using this to guide the extrapolation in the
case of the other calcium targets. The 00 spectrum from uoCa(p,n)uOSc
which would have been ideal for this purpose had additional peaks
arising from a leakthrough beam burst and could not be used. The
foldover background thus obtained for the OO uoCa run was found to be
selfconsistent. Figure 3.5 shows 1mCa(p,n) spectra at 0°, with the
foldover background indicated. The errors accumulated by these
subtractions are discussed in section 7 of this chapter. The spectra
with the second lowest threshold (18.7x the 228m Compton edge) were
found to be the best compromise between poor statistics and minimum
foldover neutron background and were chosen for final analysis.

3. Deadtime Correction

The ADC is dead to incoming signals while it is processing a
previous event. This effect is significant at high count rates and has
to be taken into account when we calculate the differential cross
sections. In order to determine the ADC dead time, signals from the
proton monitor and the four detectors in the 00 hut were sent into a
sealer and also to the ADC. The ratio of the counts registered by the
ADC to the counts registered by the scaler is a measure of the live time
and is typically of the order of 80%. These fractional livetimes are
the correction factors to the Faraday cup readings and measure the
effective charge incident during the run.

11. Neutron detector efficiency and determination of absolute cross
sections.

In order to compute differential cross sections from the TOF

measurements, it is necessary to measure, or calculate reliably, the

detection efficiency of the neutron counters. The latter approach has

NUMBER OF COUNTS

41

MSU-83-227
10000.

 

t 44Co(p,n)44Sc
ED: II9.3 MeV
7soo- 9 '-' 0.00
THRESHOLD = 18.7 x

 

 

soon)-

 

 

2500 -

 

Tl

 

 

W

TOF (CHANNEL NUMBER)

Figure 3.5. Time of flight spectrum for HCa(p,n)“Sc
at 0°, with cosmic ray contribution subtracted. Solid
line indicates foldover neutron background.

 

 

 

 

42

been used by Rapaport et al., to predict the relative efficiency of the
neutron counters for detecting neutrons in the energy range 30 MeV to
200 MeV for different light thresholds (Ta 82). Basically the
program computes the probability that an incident neutron of a given
energy will induce in the scintillator material, nuclear reactions whose
charged products create more than a specified amount of light. Appendix
C shows the computed efficiencies for the neutron energy range of
interest.

The relative differential cross sections so derived have to be
normalized to absolute values. Two calibration runs were made at 00
with targets of 7Li and 120 and are shown in Figures 3.6a and 3.6b. The
absolute cross sections are known in the two cases by independent
means-"from angular distributions normalized to activation analysis
cross sections for 7Li(p,n)7Be(O.0 + 0.A29 MeV) and from
12C(p,p')12C(15.1 MeV) and arguments of isospin conservation. These
measurements have been made at Ep-120 MeV and reported elsewhere (Ta 82,
Ha 81, 01 79). Comparison of these relative and absolute cross sections
at 00 yields the cross section normalization constant; the relevant
numbers are listed in Table 3.3. Note that the absolute cross section
for the 1‘2C(p,n)12N(g.s.) reaction is only known to within 16% and the
7Li(p,n)7Be(g.s. + o.u29 MeV) cross section is known to within about 3%;
but the normalization constants derived from the two cases agreed to
within 6%. We took an arithmetic average of the two constants, 1vithout
weighting them by their errors.

The 7Li(p,n) and 12C(p,n) data can also be used to check the

relative efficiencies used in the analysis. Define

43

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EmeDZ JmZdeov 1.5;.

 

 

 

 

ooh cow OOH oo.
a11HaJIQwHildaai1nuflafluflnuflflnaMfiflflflflflflfifllflflflflflflfiflhfluflflfl
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mONImQIDmZ

44

 

 

 

 

 

 

 

 

 

 

 

 

300 T , 1 r , M§”‘83'2°.8
(0.0, I')
270- ..
240- I2C(p,n)'2N d
Sp: ”9.3 MEV
9=OO°
d 2“” Threshold =I8.7 x "
Z:
:2
< IBO- «
II
o
G:
LLJ ISOr .
Q.
m I
1— 1
z 1on- ; .
D 1
O 11
u .;
90H I n
I
BOr ‘
so 3 ! I a
l l l l L l
IOO 300 500 700

TOF (CHANNEL NUMBER)

Figure 3.6b. Time of flight spectrum for
12C(p'n)12N.

45

.29 x h.ma u paocmmucfi um omen mmwocmwowwmm «
.Nm m9 “mocmummwm An

.mm 69 .mn Ho "mmocmummmm Am

 

 

 

A.m.mv
1 .d
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:6:
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.Amnmymm\Aamwvmm a Aumxnsv Am>HumHmuv A>mz.
O ..mnmvae\oe A.Hmw.ce\oe «socmnOSOMmaonusmcm acnuommm

 

 

 

 

 

 

. A00 UMV QQOMUOGm mmOHU HQMUCGHQHMHQ QUDHOmQ/N

Cu m>wumHOm mo :ofiumNHHmeoz .m.m want

 

46

Peak Area (TOF)

T,Effectivex Ndx

Yield 5

 

rT,Effective a Faraday cup (total) x live time

Ndx

Target thickness in units of number/cm2

Y s Yield(7Li(p,n)7Be(g.s.+0.429 MeV))
Yield(12C(p,n)12N(g.s.))

Efficiency (117 MeV) (Th.)
Efficiency (100 MeV) (Th.)

 

6(Th.) E

5(Th.) 5 Threshold (in equivalent electron energy)

If the calculated efficiency had the correct energy dependence, then,

(a) Plots of log Y vs. B(Th) and log e(Th) vs. B(Th) should be
parallel curves;

(b) Plot of R(E(Th)) vs. B(Th) should be a constant, independent of
B(Th). The constant value - the ratio of experimentally determined
absolute cross sections, to within experimental uncertainties. As
indicated by Table 3.11 and Figures 3.7a and 3.7b, the relative
efficiencies do have the correct behavior. Yet another check on the
definition of the threshold and the corresponding efficiencies used in
the calculations is to look for the constancy of do/d0 with respect to
the threshold. For the nominal thresholds, there is a steady decrease

of the inferred cross sections for 7L1 and 12C, totalling 36%,as one

47

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2::
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48

 

 

 

 

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49

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czonm mosam> paozmmunu One .mmHuCHmuumoc: Hmucmeflwmmxm
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O_N-mm-Dms_

50

Table 3.5a

Dependence of efficiency corrected peak areas on
threshold energies

 

 

 

 

 

 

7L1(p,n)78e (g.s., 0.429 Mev) ENeutron‘=ll7‘° MeV

éThreshold Peak Efficiency A/e A/s
Area A e (A/e)10xTh

(0.9) leTh 0.2150 141884 1.00
(1.0) leTh 30505 0.2035 149902 1.00
(1.1) leTh 0.1922 158715 1.00
(1.15) leTh 0.1866 163478 1.00
(0.9) l7xTh 0.1508 123607 0.87
(1.0) 17xTh 18640 0.1370 136058 0.91
(1 1) lTxTh 0.1246 149599 ' 0.94
(1.15)17xTh1 0.1185 157337 0.96
(0.9) 23xTh 0.1106 96130 0.68
(1.0) 23xTh 10632 0.0930 114323‘ 0.76
(1.1) 23xTh 0.0776 137010 0.86
(1.15)23xTh 0.0696 152715 0.93
(0.9) 28xTh 0.0866 65485 0.46
(1.0) 28xTh ~ 5671 0.0600 94517 ”0.63
(1.1) 28xTh 0.0427 132810 0.84
(1.15) 28xTh 0.0347 163618 1.0009

 

 

 

 

 

 

 

 

51

Table 3.5b

Dependence of efficiency corrected peak areas on

threshold energies

 

 

 

 

 

 

 

 

 

 

12C(p,n)”N (g.s.) ENeutron==100.0 MeV
lThreshold Peak Efficiency A/e A/e
Area A e (A/€)10xTh

(0.9) leTh 0.2055 29188 1.00
(1.0) leTh 5999 0.1918 31277 1.00
(1.1) leTh 0.1801 33307 1.00
1.15 lOTh 0.1734 34595 1.00
(0.9) l7xTh 0.1358 23675 0.81
(1.0) 17xTh 3215 0.1185 27131 0.87
(1.1) l7xTh 0.1030 31229 0.94
1.15 l7xTh 0.0945 34021 0.98
(0.9) 23xTh 0.0857 17330 0.73
(1.0) 23xTh 1485 0.0660 22500 0.83
(1.1) 23xTh 0.0463 32080 1.03
(1'15)23XTh 0.0373 39812 1.15
(0.9) 28xTh 0.0477 11667 0.40
(1.0) 28xTh 557 0.0277 20108 0.64
(1.1) 28xTh 0.0194 28682 0.86
(1'15)28XTh 0.0148 37635 1.09

 

 

52

moves towards higher thresholds. A detailed analysis of the Compton
spectrum from the 228Th source revealed that the thresholds were, in
fact set about 10% higher than the nominal 10, 17, 23, and 28 times the
Compton edge; therefore, the thresholds were at 26.18, 44.51, 60.21, and
71.97 MeV equivalent electron energy. With this correction, the cross
sections do remain a constant to within 15% for all the thresholds.
(See Tables 3.5a and 3.5b). This was further verified with the calcium
target data. Tests (a) and (b) mentioned above worked as well as they
did because ratios were considered in each case; this shows the
insensitivity of the derived normalized cross sections to the precise
value of the threshold.

5. Neutron Energy Spectra

The TOF spectra (after subtracting the Cosmic ray and the foldover
neutron background) have been converted to neutron energy spectra with
the relative detector efficiency folded in, using the M.S.U program
TOFTOEN. The input data required are distance from target to detector,
detector efficiency as a function of neutron energy, proton beam
repetition period, TAC calibration in terms of nsec/channel, and the
centroid of one peak with known neutron energy. The neumwxienergy

calibration for the spectra shown in Figure 3.8 is

ENeutron(Mev) a (channel number + 2125)/25

Appendix C shows energy spectra for all calcium targets at the 3 angles

0.00, 6.30 and 11 .10 These spectra have been analyzed with the peak
fitting program SCOPEFIT, defining backgrounds as shown in Figure 3.8.

A reference peak was defined in each case based on a sharp peak in the

53

 

 

 

 

 

 

 

MSU-83-23I
4
4CRSO
2(
(D|flflaaiam~uzi§PEEhZl*$==-nn-_dm__¢__.dh__.__
4|
20- C0(p,n)Sc C0
Ep= II9.3 MeV

3>

Q) 9 =WDID°

:5 LAB

3;K)r

\

.0

s I

00

U 0 1 1 1 1
C3

1’ 44

blCN-
N

‘U

 

 

 

 

 

 

Figure 3.8. Energy Spectra for
and “3Ca(p,n)“°'“ '
Experimenter's backgrounds defined

 

  

 

 

     

105 110 115
ENEUTRON (MeV)

95 H30

40,42,44

““ and “88c.

peaks are indicated by solid lines.

to fit

54

high neutron energy end of the spectrum, peaks fitted and areas and
centroids obtained. See Tables 3.6, 3,7, 3.8 and 3.9. 1x;should be
noted that a constant time resolution does not yield a constant energy'
resolution; but the neutron energy range in the parts of the spectra
that were fitted with a given reference peak shape was small enough that
that peak width did not change by more than 9%. This has a negligible
effect on the derived centroid for the strong peaks which is known to +
40 Kev (i 1 channel). Relative differential cross sections were
converted to absolute values using the normalization constant derived by
the method outlined in Section 4 and are listed in Tables 3.6, 3.7, 3.8,
and 3.9. Angular distributions are plotted in Figures 3.9, 3.10a, 3.10b,

40,92.”“ and “80a respectively. The

3.11a, 3.11b and 3.12a, 3.12b for
TAC nonlinearity mentioned earlier is reflected N1 the energy spectra”
‘Table 3.10 shows theineutron energies at which this effect is starting
to influence the energy spectra

6. Calculation of the GT strength

The angular distributions were used to pick<out Lao transitions;
following an empirical method developed by Taddeucci et al., and
described in Chapter I, the 00 differential cross sections were used in
calculating the total GT strength in ”2’“ andL‘BCa and are compared to
the sum rule prediction of 8 (CT) > 3 (N~Z) (Ta 81). (See Appendix D).
It should be noted that the experimentally extracted strengths are
independent of the absolute cross section normalization.

The case Of l‘2Ca is an anomaly within our measurements. This has
been brought about by the fact that the target was contaminated with

oxygen and that the beam was apparently hitting the alwmnumitarget

4
frame during at.least part of the 00 run. The bump in the 2Ca(p,n)

SS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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58

Table 3.10. Neutron Energies (in MeV)
below which TAC nonlinearity is present
in the energy spectra

 

 

 

 

 

\. 6
Target x“ 0.0° 1 6.3° ll.l°
“°Ca 97.40 97.16 97.20
“2Ca 98.04 97.12 97.20
HCa 98.12 97.20 97.20
“°Ca 98.36 97.12 97.24,
1

 

 

 

dJ/dfl (mb/Sr)

59

 

       
 
  

 

 

 

MSU-BB-ZOI
'0-0_ 1 T I T _,
,_ 4OCO(D,O)4OSC ..
E E =119.3 MeV 7
L- p d
r- -I
L .
AVERAGE 1_=O/
_ DISTRIBUTION 3
FROM 42~44v4806(p.n1
(from IAS states)
(.0:— -_I
g ..
\i\ \ 2.73 MeV
.. \ \1/ -
\
\‘E
J l L I
0.2) 5 IO

Blob

Figure 3.9. Angular distribution of 1+ state in
“°Sc (dotted line). Solid line shows an average
of the l+ angular distributions derived from
“2,4“ and “88C-

60

 

 

 

 

 

MSU-83-202
42Co(p,n)425c 7
E =119.3 MeV 4
. ~ ‘ 10.28 MeV P
\ \
1- ‘ \ -
. . \\i~
L x1O
10.0 , .3
I: \ \ 0.6l MBV :
\
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P '\ \’ 4
D \ ‘i d
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9 \ . *4
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1- ‘ .1
16 I
\
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r ‘\
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l l
0.10 5 ‘0

Figure 3.10(a).

69Iob

Angular distributions

of observed states in “28c.

dU/dfl (mb/sr)

OJ

61

MSU-83-203

 

¢
I‘x

\

 

‘ ~ \ I.BO MeV

42Co (p, n) 423c

Ep =119.3 MeV 7

 

 

Figure 3.10(b).

.. \ _.
.- \ .1
. §-_~ -.
I— ‘ ‘ ~i .4
h 4
.. XIO.
)— -I
(L
_ T \ \ 3.43 MeV _
1— \ d
\
F \ fl
.- \ -I
{6
I— \ d
H \‘\‘ -
\
\
\i 1
)- d
I l
O 5 IO
Glob

Same as Figure 3.10(a).

 

62

MSU-BS-ZOS

44COIp,n)44Sc ‘

 

 

I- \ .1
\
\
I- \ d
‘L
\
\
\
\
Ioo- \ u.
I- \ .1
- ~§ 3
_. x10 3
,1 1'- 6-‘ 2.79 (1.4.5.) 7
b 1- \
Q ‘\ 7
g I- §\ 1
v \
d \
‘D >- \ -(
'B \
‘R \
‘ \
LOr- \ .—
: \f :
I .1
1*\
P -1
__ \
\ -(
\
I- '\ -I
\
\
\ ,—§
OJ 1 3-..-‘T l
O 5 IO

{Rob

Figure 3.ll(a). Angular distributions
of observed states in

““Sc.

63

MSU- 83-204

 

 

44CO(D, n) 445C

 

 

\ \ q
\
\ 0.67 MeV E = 119.3 MeV -
«\ “ P
.‘ -
x.\ \n\ 6
\
\ \
\.\ \R\- §\'\ 7
. .\ .
\
\ \ 977’NEV \ '\
IO \ \ 1/ \ \
' 3' \ \ ‘\ i -:
H \ \ ,/\'\ .
I 2‘ \ \ 3.12 MeV\§ :
f 7.31 MeV \ \§ _.
E7 4" \ \ -1
.o \ \
E h \\l.78 MeV \ "
V 1
<3 \ \
1E . \\~ \ l’,§ .q
‘o \i_..—-‘<\
\
0.“? \ -—I
- \ g
‘13 f 7
1L ‘\ 7
\ 12 82 M v 1‘
.. \ . e .
- \ q
\ .
F \ //T H
\ // x10
'- \ / .1
‘\f ‘,‘/
0.010 g '10
Blob

Figure 3.ll(b).

Same Figure 3.ll(a).

ch/dfl (mb/sr)

64

 

 

 

 

MSU-83-207

r T

148 ‘48
“3.0L CoIp,n) Sc —1
.. E =119.3 MeV '1
- “ P ‘
1- \ -‘
H ‘6‘\ . 4
. \\6.67 MeV (1.4.5.) ..
, \. .
1- §\ q
‘\
_ ‘x -
\
Ix \
\ \536 MeV
\\
‘\

1.0; \\ —-
_~‘ 7.8 MeV ~
~ ‘\ . ‘\ -
I- \ \ i‘ .- _ .- ..- .{ -I
_ \6 -

\

h— \\ "'
1— §\ ’ "‘

‘4 1
__ \ ..

‘\
\

\

1- \i ""
x10
1 I
0.10 5 ‘0
Blob
Figure 3.12(a). Angular distributions of

observed states in “88c.

dU/dfl. (mb/sr)

MSU-83-206

T T
i 48CoIp,n)"‘8Sc ..
\
‘I ~\ Ep =119.3 MeV
.. ‘\ ”.02 MeV 4

'\
'\
\
\\

40.0"" §\ "1
1- \ q
1’." \ 'I

~. \~ ‘
‘\ 2.52 MBV \ .1
\ \ \ -1
\\\ \Ԥ .1
‘ ‘ \ q
‘ \ \
x \ \
\ ‘ \\ .1
\ ‘-_§
\ \
\
- i
'0'" T‘\ -1
I- \ d
I" \ \ d
b \ d
, sf. 4
\ d
f 6 0.67 MeV fl} .
I‘ \ /
\ /
r- \ / “
\ /
\
.. \ ,’ .

 

 

 

 

0.1 1 1

 

Glob

Figure 3.12(b). Same as Figure 3.12(a

).

66

. 42 .
spectrum just below the ground state in So is at the correct energy

for the 27

Al(p,n) reaction. Therefore, the apparent measured GT
strength of roughly 82% of the sum rule prediction does not have much
reliability. The following reasoning might give a rough estimate of
what was actually seen from our run, excluding possible contributions
from oxygen and aluminum. Consider the high excitation regions of the
“2’“ and l‘8Sc spectra with no sharp resonances. The cross sections to
this part of the spectra can come from (a) valence neutrons, and
therefore, should scale roughly as the neutron excess in the target and
should be compared at the same excitation energy in the residual nuclei
and (b) valence neutrons from the “00a core, and therefore, should be
the same for all Ca isotopes, and should be compared at the same Q value
(same neutron energy). For the sake of simplicity, let us assume that

the knockout neutron background is independent of excitation energy in

the residual nucleus within the region of interest. Then we can write,

Height(Bkg) - C0 + (N-Z) x C1
.. . 1111 48
where to and C1 are constants to be determined. From the and So
cases, we can solve uniquely for CO and C1. Comparing the measured
background height to that predicted by the constants C and C for “23¢

O 1

would then provide us with a scale factor with which to reduce the
14
measured strength in 2Ca. For example, choose a neutron energy of

100.0 MeV; the measured heights of the backgrounds for the three cases

112,49 and ”880, are 1.83, 2.16, and 3.41 mb/sr, MeV respectivelY-

Solving for CO and C1 from the uu’HSCa data one gets

67

CO - 0.91 mb/sr, MeV, and C1 - 0.31 mb/sr, MeV;
Then the predicted height for 142Ca is 1.53; comparing this to the
measured value of 1.83 mb/sr MeV one gets the correction factor to be
0.83 in the knockout region. The measured GT strength of 82% should be
scaled by this factor to give a corrected strength of 68%.

One sees in the results for 44 and u8Ca the so called quenching of
the GT strength (40.5% and 51. % respectively of the sum rule
prediction) that has been seen in recent (p,n) reaction studies at
intermediate energies. Suggestions by Osterfeld that substantial 1+
strength may be hidden in the experimenter's background drawn to extract
the above cross sections was investigated in detail, and is discussed in
Chapter IV.

7. Error Analysis

There are two types Of errors affecting our
measurements--systematic and statistical. Sources of systematic error
include target thickness uncertainty (1 to 2%), current integrator error
(2%), and error in the normalization constant to convert relative
differential cross sections to absolute values (8.5%). Sources of
statistical errors are the uncertainties in the Monte Carlo calculations
of the relative efficiencies (1 to 3%), Cosmic ray and foldover neutron
background subtraction (0.1 to 3%), and background definition and peak
fitting (0.5 to 5%). By the nature of the method used to compute total
OT strength i.e., as a ratio to the IAS peak, the systematic errors do
not contribute, only the statistical errors are relevant. But the
absolute differential cross sections quoted here carry both the

statistical and the systematic errors, which were added in quadrature.

These were in the range of 8 to 19%, typically 10%.

IV. Data Analysis
In this chapter, some of the methods used to determine if there
really is a quenching of the GT strength in calcium isotopes are
discussed. It is appropriate to start with the question of whether the
experimenter's background contains substantial 1+ strength and the basis
for such a claim. Recently, Osterfeld performed microscopic background

”O’H8Ca at 160 MeV (0f 82). His

calculations for (p,n) reactions on
model assumptions were: (i) For (p,n) reactions at incident energies
>100 MeV, the reaction mechanism is direct, i.e., one step processes
dominate; (ii) The effective projectile-target nucleon interaction can
be represented by the free nucleon-nucleon t matrix, iHAe., by the G3!
interaction of Love and Franey (impulse approximation); (iii) The (p,n)
background is dominated by spin-flip transitions, i.e., 8:1, T-1; The
final nuclear states are assumed to be simple proton particle-neutron
hole states, including bound, quasi bound, and continuum states. The
cross sections were calculated with a DWBA code. This code includes
knockout exchange amplitudes exactly.

Figure 4.1 shows a schematic representathmicfi'the model. This
model reproduces 00 data for usCa (p,n)u8Sc in the continuum to within a
factor of 1.3. A striking prediction of these calculations is that the
continuum background drops to zero rather sharply at Q - -20 MeV, for
uaCa; a similar behavior is predicted for uOCa (p,n) at<Q==-25 MeV.
FigureINJZidlustrates this. This falling Off can be explained
qualitatively as follows: The incoming proton knocks out a neutron which
carries a major part of the energy leaving the proton with a small

amOLun; of kinetic energy (310 MeV). The combined effect Of the Coulomb

and centrifugal barriers keeps the low energy proton away from the

68

69

\‘4. Veff(otl) COOTIHUUH’I

E; \===E:::“E::jf==‘==== 1001

I
I

protons neutrons
FIG.4.ISchematic representation of the microscotzi:
model used for the background calculations. In the figure
6,- denotes the Fermi energy. £5 the nucleon separation en-
ergy. and E, the incident projectile energy. For the effective
projectile target nucleon interacxion V,“ the GJY interaCtion
of Love and Franey (Ref. 3) is used.

(Figure and caption from Osterfeld's work
(Of 82).)

{%\\2\\l\' NNN >‘.‘N~2\\V{\\

 

 

 

 

7O

 

  
 
     

 

 

 

3.— 1
1.3 -' (a)
Ca (p, n) ‘aSc
... i" f E:160 MeV 111.; 1
2‘“ : 69'“? 0' oius 11m
.‘5’, 10 L “-‘talttatw ‘
\ ‘--- talc. oxhqmtuxt 331 ‘1
2 [ --°~-eta.:atiu9rm 1' 7:1. I
- I inbfl'xtoc ' ‘
6° % S L j
'o g: ’ ~ . ‘
’ --.~::."—-"“ """"" 1’ ("‘50 T1} ....... Li”
D L’ 735.. L l 0.1 ‘3 ‘ ‘ L I
to - ‘ T *— ‘
LO LO (0) 1
I CaIp.nI Sc 1
6:160M9V
S .-

 

 

 

10
-Olp,nl IMeVl

FIG.4.2 Zero degree spectra for the reactions "Cam/t)
(a) and ”Ca(p.n) (b). The data (thick full line) are taken
from Refs. 13 and 14 (see text). The discrete lines are cal-
culated cross sections due. to bound and quasibound States.
The arrow labeled with AI -1 indicates the location where
the AL -1 resonance (0’. l’.2’) would occur if nuclear
oolleetivity were included for these states. The theoretical
cross sections due to the GTR and IAS are nor plotted. The
optical parameters for the cross-section calculations have
been taken from Ref. 20.

(Figure and caption from Osterfeld’s work
(Of 82).)

71

nuclear surface; this means that the proton wavefunction is small near
the nuclear surface and so are the transition rates to these states,
particularly when L .. O. The implication, then, is that most of the
background subtracted in the analysis of “8Ca(p,n) is in fact, GT
strength. Osterfeld finds that including this background raises the
fraction of the sum rule strength observed in this case from H31 to 51%.

Inspired by the above work, we have analyzed our data following a
method suggested by Rapaport (Ra 82). The energy spectra were used to
compute cross sections in 2 MeV bins from the ground state upwards,
peaks and background included. The angular distributions so derived,
were fitted with linear combinatins of DWBA cross sections to final
states 1+, 1-, and 3+. A least squares fitting routine was used to
minimize X2 for combinations of these final states, taken two at a time
and that pair which gave the least X2 was chosen to obtain the
corresponding spectroscopic strengths. The code used was DWBA 79, with
the free nucleon-nucleon matrix of Love and Franey; only «f5/2vf;}2

configurations were considered. Including 1rf caused negligible

vi"-1
7/2 7/2
Change in the angular distributions. Table ll.l lists the optical model
parameters used in computing the DWBA cross sections; Figure 14.3 shows
comparisons of measured and predicted DWBA cross sections for known

States in ”2 and “880. Tables 14.2 and ”.3 list the results of this type

Of analysis for “MB

Ca. A similar analysis was not carried out for
Ca because of contamination with oxygen and aluminum. As a rule, we
0- Li” ’48 T. + +
a ind that for Ca and Ca a mixture of l and 3 states represents the
+ ..
data at low excitations and a combination of 1 and 1 is required to

reproduce our data at higher excitations. It is interesting to note that

Osterfeld's prediction is borne out by the behavior of l- strength, as

72

Table 4.1

Optical Model Parameters+

 

 

RC: 1.25 fm
Vol. Real V: 9.73 MeV
r5 = 1444 fm
a0 = 0.52 fm
Vol. Imaginary W==13.73 MeV
r0 = 1.24 fm
a0 = 0.57 fm
80 Real VSO = 3.0 MeV
r50: 1.06 fm
aSO= 0.6 fm
SO Imaginary WSO==-l.00 MeV
r = 1.06 fm
Wso
a = 0.6 fm
Wso

 

 

1'Optical Model parameters provided
by N. Anantaraman (Ar 83) and
derived from p+53Ni data at 157 MeV.

See also Comparat et al.

(Co 74) .

73

 

 

 

 

 

MSU-83427l
r I
1 48Co(p, n)488c Ex=2.52 MeV
'0 2 42Co(p,n)42$c Ex=0.6l MeV
air- l g ..
I- \ \ \ fi
5 — x \ _.
- \ \ + d
.\
... . x‘ \ .
3’ ‘ 1
.LD _ ‘\ -
5: \
C3 ‘\
'U 1’ \
B \l
13
|() .~ )( '1:
- L .‘ x.“ 4;:
p \t -
_ -
\ fl
5'-' .‘axz‘: '-
- ‘\ a
\ 2
‘\
_ \. -
_ 0 Data \\ l
X DWBA '79 \\
I 1 l
(3 5 H3
6lob
Figure 4.3. Comparison of measured and DWBA 79 predicted

differential cross sections for 1+ states in “2Ca(p,n)“ZSc

and ҡCa(p,n)ҤSc.

'74

Table 4.2

HCa(p,n)""Sc
Contributions to 0° cross sections from
1*, 1' and 3+ states.

 

 

 

 

Ex(MeV) do/dQ (mb/sr)(0°)
1+ 1' 3+
1.0 6.401 - ' 0.208
3.0 8.757 - 0.256
5.0 7.298 - 0.377
7.0 4.024 - 0.321
“9.0 4.690 - 0.508
11.0 4.632 - 0.774
13.0 5.439 0.155 -
15.0 4.806 0.246 -
17.0 5.104 0.348 -
19.0 6.223 0.234 -
21.0 5.694 0.692 -

 

 

 

 

 

75

Table 4.3
Ca(p,n) Sc

Contributions to 0° cross sections from
1*, 1' and 3+ states.

 

 

 

 

Ex(MeV) + do/dQ‘(mb/sr) +
1 l 3

1.0 0.488 - .405
3.0 6.754 0.426 -

5.0 3.181 - .689
7.0 5.093 0.283 -
9.0 11.045 0.169 -
11.0 13.799 0.174 -
13.0 8.516 0.165 -
15.0 5.008 0.214 -
17.0 6.814 0.339 -
19.0 5.232 0.488 -
21.0 5.247 0.699 -

 

 

 

 

 

76

extracted from our data. The 1+, 1‘ and 3+ strengths from the best fits
are plotted vs. excitation energy in scandium and displayed in Figures
4.4 and 4.5 for A =- 44 and 48. One can also see that 1+ strength
extends to higher excitations than was previously thought.

Another way to extract 1+ strength from (p,n) spectra was recently’
suggested by Goodman and applied to the case of “20a(p,n) (Go 82). The
criterion for GT strength is that the angular distribution be that of L
- 0. The object is to subtract L40 contributions from the Co spectrum.
This is done by first subtracting the 00 spectrum from the 2.50 spectrum
scaled by the angular distribution for the L - 0 part so that the strong
GT peak subtracts out. The result is taken to be an approximation of
the La-O spectral shape as seen at 0°. This is then sealed by the cross
section ratio between the 2.50 and 00 spectra in the region of the L-1
1°esonance and is subtracted from the 00 spectrum to yield the L-O
.spectrum at 0°. It is instructive to apply the above method in-the
idealized case shown in Figure 4.6(a) to see its usefulness and check
the validity 6: the argument.

We see that the method would work well if only one Lao component,
say L-1, is important, and if there were no [.80 (1+) strength in the
region of the 1- resonance. These are implicit assumptions in Goodman's
method. If one used the ratio of cross sections in the Lai region to
Scale the so called L-O spectrum, and subtract it from the OO spectrum
to obtain a pure 1+ spectrum, then at least a part of the 1+ strength
Present in that region is subtracted out too. There is no reason for an
a priori assumption of no 1+ strength at high excitations. In fact, our
fits to the data (peak + background) through the observed range of

excitation indicate just the opposite. Therefore, we believe that

 

77

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79

 

 

 

 

 

 

MSU-83-212
(o) I+
9=0.0°
_ 8
A 'I+ 3;
2 9:
r-
(b)
8=2.5°
3. 1*
<2- |+ A
.. {5 Q
i L 7°"
(c) I"
k x (9=2.5°)
k=4/2=2
5. .
g l
5.
l" 3.
at
(d) "'
L’O SPECTRUM.
= kX(9=2.5°)-
g; (9=O°)
1i

 

 

Figure 4.6. Application of Goodman's
method in an idealized case.

80

MSU-83-243

(e)

I- "LfO" spectrum
rescalsd to match "1
of 6-6 ;* scale factor

7.5 7.5
25 L5H41'3”°

(2jfi

 

(f) _ "’

"Pure 1+" spectru-
(Goodman's) (Note

loss of 1* from high
excitation, as a

result of the assumption).

(413)

 

 

5.

*Including the l+ at high excitation as 1- leads to the wrong scale factnr
of 3.0; should be 7.5/1.5 - 5.0; making this correction leads to (e') and
(E').

 

(er) '- "Lia" rescaled
a I correctly.
:5
"F

(1")

“Pure 1+" spectrum

'4'

(413)

 

urn

 

,__

Figure 4.6 continued

 

81

Goodman's method is correct only up to the point where he obtains the
Lao spectrum. Therefore we used it to obtain the Lao spectra from the

42,44 and ”80a. These are shown in Figure 4.7. The

00 and 6.3° data for
small peaks in the region of the strong GT (1+) at low excitation arise
from the fact that we did not apply a correction for kinematic and
electronic shifts of the peak. A comparison can now be made of the 1-
behavior as derived from the methods of Rapaport and Goodman and an

estimate of the background falloff energy for 120 MeV protons on “2"“;

and l‘8Ca from Osterfeld's work at 160 MeV. As can be seen from Table
4.4., the agreement is not bad, considering the crudeness of our
procedure.

The 1+ cross sections at 0°, derived from our DWBA analysis (peak
and background included) were used to compute the total GT strength
again. We found that for M and ”Ca, 78% and 63% of the Sum rule
predictions were obtained respectively. Appendix 0 contains the Tables
listing the computations of the GT strength. Our analysis conforms with
Osterfeld's calculations; there is some 1‘F contribution from the
background; but one has to look elsewhere for at least part of the sum
F‘Ule strength. It should, however, be remembered that the decomposition
of the data into different final state angular momenta, with only 3
f‘Oicward angles is far from reliable. We therefore, believe that
additional data at somewhat larger angles would help resolve this
question unambiguously. One should also bear in mind the limitations of
uSing the code DWBA 79 which assumes that the final states are bound
While, in fact, they are not. Further, one does not have a check on the

Constancy of the angular distributions with excitation energy in the

1"esidual nucleus. Very often, DWBA predictions are not accurate because,

82

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84

for example, the effects of density dependence of the two body force

Verr are not very well understood.

There exists yet another way to extract GT strength in a
straightforward way from our data. Recall that the method outlined in
Chapter I and used to compute the GT strengths quoted in Chapter III
relies on normalizing the 1+ cross sections to that of the IAS;
therefore, it is very sensitive to the measured cross section for the

IAS. When there is an overlap of peaks near the IAS as in 44,48

errors are larger than if the IAS were isolated as in "2 Ca. Consider

Ca, the

now the measured GT strength from the 0.611 MeV peak in “280. Our
calculations give a value of 2.55 (using an experimenter's background)
while the matrix element obtained from B decay is 2.67 (Go 81).
Therefore one can normalize all the measured 1+ cross sections to the
0.611 MeV cross section in l‘ZSc, with a known strength. This way, we
can also extract BEx(GT) for the 2.73 MeV state in noSc. We carried out
such an analysis and obtained total GT strengths of 57.2% and 69.4% of

the minimum sum rule prediction for 44 and 1”3C

a, using an
experimenter's background. When one includes 1+ contributions from the
background as derived from the DWBA analysis, the total GT strengths are
110.7% and 82.9% of the sum rule prediction for 44 and “Ca. The major
limitation of this method is that it is sensitive to errors in
normalizations arising from charge and target thickness uncertainties
while the method of Taddeucci et al., is independent of such errors.
Note also that the difference between the 2 methods results partly from
42,44,481

the fact that the measured IAS cross sections for Ca do not

scale exactly with N-Z. Another reason the strength is larger when

85

normalized to 0.611 MeV state is that the extracted strength of 2.55 for
the state is scaled to 2.67 (obtained from 8 decay measurements).

The large GT strength for uuCa as indicated by the DWBA analysis is
presently not understood. Unfortunately, there are no previous (p,n)
measurements on this target at intermediate energies for us to compare
to. Evidently, this results from the persistence of considerable 1+
strength at high excitations (see Figures 4.5 and 4.6) for 1mCa, unlike
the case of uOCa. We are currently investigating this. In the uoCa
(p,n) data, there is a peak at 2.73 MeV, with L - 0 angular

distribution. Normalizing to 0.611 MeV gives a strength of B (GT) =

Ex

0.098 which compares well with the values of B x (GT) 0.15 5 0.04 and

E
0.13 5 0.04 at 159.34 and 200.0 MeV respectively reported by Taddeucci

et al., (Ta 82)

V. SUMMARY

The total GT strengths (percent of minimum sum rule prediction)
extracted from our data using the different methods outlined earlier are
shown below in Table 5.1. If one believes the fits obtained with the
DWBA 79 analysis, it would seem that substantial GT strength is
contained in the background and extends to higher excitations, as
proposed by Bertsch, et al., (Be 82). But one should be aware of the
ambiguities of these fits, as discussed in Chapter IV.

Our data for “00a indicate a GT strength of 0.098 from the peak at
Exza' 2.73 MeV. This compares with the values of 0.15 + 0.04 and 0.13 +
0.04 reported by Taddeucci et al.at rip-159.0 and 200 MeV respectively,
(Ta 81). Another finding from our data is that the 16.8 MeV state in
“880 is about 13% wider than the state at 2.52 MeV excitation. The
FWHM's in the TOF spectra for these states are 8.5 channels (Ex . 16.8
MeV) and 7.5 channels (Ex - 2.52 MeV); this observation was made earlier
by Anderson et al., (An 80).

Comparison of our data to the electron scattering studies of
Steffen et al., (St 80) indicated the following (see Figs. 5.1 and 5.2).

(a) The 2.73 MeV peak in ”03c has been identified on the analog
<0f the 10.32 MeV state in “00a (Ta 82); it has an angular distribution
corresponding to L - 0.

(b) More structure is seen in “23c than just the analog of the
11.2 MeV state in “ZCa, although it has not been isolated and identified
in our data.

(0) Electron scattering reveals practically no structure in uuCa,
While the (p,n) experiment indicates significant GT'strength in the
excitation range 10.8 to 14.5 MeV.

86

87

 

 

 

 

 

 

 

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I h.oaa m.mh I «.mm m.ov Mva
II I ll 0 .I. e mu
Amp mm 0 mm Na
oumum >02 oumum >0:
unmEowsmmoz Ham.o ou de ou acoEmemmwz Ham.o ou m<H ou
A:.mv Honuo mNMHmEHoz oNHHmeoz Ac.mv wonuo mafiHmEuoz oNflHmEuoz bomume
mfimmeC¢ an «mza oczoumxomm+xmom Unsoumxomm m.uoucmE«Hmmxm

 

 

 

 

 

 

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sumo ucomowm on» Eouw numcmuum Bu Hmuoe

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89

u
(d) The analog of the 10.3 MeV M1 state in 8Ca is seen clearly

. 4 . .
in 8Sc at Bx . 16.8 MeV; this seems to be the only strong resonance in

the range of excitation observed.

APPENDICES

APPENDIX A
Derivation of nonenergy weighted
sum rule of isovector (T-l) spin flip

and non-spin flip Operators

APPENDIX A

Derivation of non-energy weighted sum rule of isovector
(T=l) spin flip and non-spin flip Operators:

Consider

H57?

6 = t Fermi (non-spin flip)

w

k
0 = 2 0 t5 Gamow Teller (spin flip)
k -
The sum 2 is over the nucleons in the nucleus.
Define

S(B_-B+)= 21<f|6_11>|2
f

él<f|0+li>l2

A * A
X <f|0_|i> <f|0_|i>
f

A * A
- Z<flo+li> <f|0+|i>
f

z<i|0_T|f><f|0_|i>
f

- Z<i|0++lf><f|0+|i>
f

A + A ' ,
<i|0_‘0_li> - <i|0+T0J1>
It can be shown that for both Fermi and GT operations,

+ _ 7 _
0_ - 0+ and 0+ — 0_

9O

Then, S(B_ - 8+) = <110+0 - 0-0+ll>
= <1!EO+IO Jll>
For Fermi, [0+,0_]= 2 [tftf J
k,k'
SB--SB+=<1[ E Skk' 2t§l1>
k,k'
=2 2 t};
k
-2 l
- “2" (N‘Z) =N-Z
k k'
For GT, [0+,0 ]- E'Eokt+,0k,t_ ]

11>

 

 

APPENDIX B
SPECTRA
(EFFICIENCY CORRECTED AND

ENERGY CALIBRATED)

 

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APPENDIX C
MONTE CARLO CALCULATIONS OF

NEUTRON DETECTOR EFFICIENCIES (RELATIVE)

At each energy 32000 neutrons are incident on the detector. The
tabulated numbers are the percentage of neutrons detected at a given
bias. The bias is expressed in MeV of electron energy. The first
row contains results for biases of 0 to 9 MeV, the second row results

for biases of 10 to 19 MeV, etc.

100

mama.a m«s«.n omm=.m «:64.» “mag.” mama.~ zaaa.e
moeu.a Nana.a 2222.: «229.2 “222.2 om~n.o mmdq.a 2:24.: w:2~.m .efin.a
e~2=.= «022.2. nadn.u suma.u «-a.a on~a.a omwa.n 2522.. mama.» .Nnn.u c
n:na.a nonu.. «um=.a m«:=.u. n::a.a sesame Nays.a mama.m amm~.e mmms.n.
moms.a ance.: 3262.2. uses... ooma.n mum‘.n mzaq.a :Nmn.s aena.n .snma.m..
omoa.o noos.. 2292.; mama... 6824.: ooma.s m~=2.u mm22.m ~a=2.a mw«..a 9.
om««.n naad.a oa~«.a. o=~«.a -~«.a osm~.s ann4.~ msn2.e woma.m an22.a.r
no:«.a 2222.. m2m«.a ~mm«.a ~om~.a a~od.a “maq.m «mon.m N-2.a shud.mon
s«o«.a. mmo«.a 8222.9 n:o«.u. smm«.. una~.u a»sm.~ ~n2~.m am2~.a o-~.e p
--.a o~n~.. a~n~.a. n~:~.a. nu:~.a enm~.a acnu.a nno~.s m¢o~.a n~2~.a s
~m-.a Nze~.. omo~.u. smm~.a wean.» hoaa.a .soqn.n mama." ennn.m owsm.e
. w r . .a .... ... ..., m . 6
% .m<.mee¢2~ a. mazgammmmsu z_m awe—u 2.22
>m: nau.«. 229.: 2.2 >mx «92.2 ".m.m mzo.>uzm_o_duu 2(22.>2.
“use” embomhm: mzoehzuz ma 222222 -422—
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mmzuz_ .a.s a.a 6.9 u~.>.x c< pzmo_oz_

>6: oo.~”.oo.o~2 >mbmcm to 6:620:62 ooomm

101

mama.” mnuq.a «flu...
nmaa.s m:na.s amas.s ~51... :m.u.a un.a.m udaa.a ...... wmda.n “ram.a
ghsga.a omda.s hofia.s m~d=.a ma...a Noda.o mn...= amwn.n Jana.m .qu.o
mowe.s. «ow‘.m nana.a am...“ o:om.u :an.= ...... mfizn.n “33a.“ us:a.ao¢
ma:s.a mwma.n mmmm.a «oflm.= gang.» uneu.s. do...» omen.» hd~§.n .umn.saa
ohms.“ \mmsg.a anps.a mm...a ~mna.n -wn.e. rm»... maau.m mm...” mmad.sov
mma«.n adfiq.a «:d«.m as...a n-d.a mNNH.~ doufl.m :mma.n .mmn..m "mmd.ae.
mama.» o~:4.n mesa.» nunq.s onn«.a mm“... “mo... moa«.n «amd.a ~=~«.man
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a=-.n nmm~.a ~mnm.a. mm:~.a km:~.n ~«mm.~ -n«.a ”Non.“ m~o~.w aw“..o..
aon~.a m~m~.a :mm~.s‘ mna~.a .m.~.m «can.» we...» m:~n.s .mnq.m ad“...

mu m. A. m. .m b. m .N . o

om<~m omwu ch mitommmmmau z—m hmm_u mhuz

>w= mason. Ibo—z z—m >m: «macs nowox m1¢~>uzw~o~uuw 44mwmb4~

ombuwpwo mzamhauz no ummzzz 4<huh
«daonnnmdfi «mans: cum” hm.“

mammu

xx ramp—mam Asupuz— tooz<¢ x:

umwzumuo ze—~0u¢~o
qu>qx ~< FZuQ—uz~

u~:n.. a.. ..a...
muzuz_ 5.9 a.. «.5

>02 22 3.2: :35 t 283.2 83

102

.mmuao9

omuo.s

unsuoa.
Nmoooa.

smudge
umnaoa
cumuoa

mmwmon.

:so~.n
m

mat...

na~a.9

omamon
masses
:nadoa

osm«.a.

mnuaou

«nnw.a

mowmoa
&

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mason?

muanoa
mums-a
omsugu
«mhmos
Nosuoa
muzdoa
nwouon

omnmou.

m~m~..
m

masses
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unwaoa
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cos...

53:..u

mum...

osw~.a

ama~.a
d

>mz aaaodq thou;

>mz oo.~

s~na.u onsa.m ma.a.n
cnfim.a. msfio.a. 3m...»
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c~mn.a ozns.u. m~na.u
~«ma.o mama... -na.a
n.«.n :sdd.a a.~q.s
mc:«.u «mm... son«.e
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Newman
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cannon
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aowmnonomu

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mzuwam
nmowos
finance

1*

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smawe
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Chumcm. Q

E; F: a

zwm pmx_m~ who:
n.w.m uzo.»u:m_o_uuu 4.x:mhz_.

:w—oupwa wzompnur no mwmzzz a<hab

«wmzuz ouwa ww<4

(x za_b_momhz‘_h_z. :coz<a x.

gas...
a.“

HflOO.O- >wumcm mo mcouuamz OOONM

mumzqmou za_pou¢_a
u->~x b< ~2u:_uz_

103

was... was... swan.a..
.33..... can»... mnau.a. «was... «a...m «Nd... ”ma... ma...” mm...” mmdn.u 3
enac.u mca~.uaumo«a.u. oswn.a imam... anmn.u imam... ~m~n.a no~a.u dunmwwwv
smna.a_ mana.a nun..a :c:n.a Kn:».s moza.o. maau.a anmn.n:ixmmaqfizaquu.u.J
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kw .m An ”w m. .¢ .m .N _ o

.m<~m ommN oh mazommwmmoo zum hmmuu who:

>m: aau.«q zhouz zum >w: Nos-s nomom mZOq»ozu~ouuum 4amwmpzu

cmhomhwc mzomhamz as mumanz ...oh
ooeasmu~m mwmzaz a... hw.4

owned

.. za~__m°¢ 4._p~z~ zoaz<u ..
.Ngn... =.....ao.a .nrmz~meo zo~huu¢~s\\\\\\
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>0: oo.Nnfloo.moa xwumcm mo maouuamz coomm

ll.

104

, ...... ......m ...... ...... 52.... ...... ...... ...... .....~.M

........ ...... M2.... ”...... ....... ....... ...... ...... ...... 2......»

...... ”mm... .-m... ..N... ......_ «2.... ~50... ...... ...... w.......

~.m.... 2...... m...... 2..... ...... «...... 2..... ...... ...... ......pm

mm..... ...... ...... ...... «...... .....q. ...... ...... 2..... new.....

n2..... «...... ......_ ...... ..2.... ..2... “.2... ...... ...... ........

2...... N...... .m..... 2...... ...... ...... 2..... m..... ...... ......Qa

...... «mm... ...... ...... ~27... =.m~.. ...... .2.~.. ...... ......o.

...... ...N... ~2.~... ...... ...... ...... m2.... «2.... .22... ...... o
2.0 o W .w n v x. -... . , ...

...—m o..~ .. mozcmmumaco z_. .m2_u ...:

>mz ...... 2...: 2.. >mz «.... ".... wzo.».2u_u.... 4....»2_

aw... .u_om_uo “2.2.3.: .. mmmzzz 4....

......mu2 .umznz a... p.22

.. z._b_m.. 4....z~ :c.z<. ..

..2... ... ..2... .uc.z_m.o z.__u_2_o

mmzoz. ... .... ... u~.».x .2 pzaohoz.

>mz o... .oo.oo. ...mcm .o acouuamz co...

105

.5.....
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«.5..9
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madman

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no~599

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nw.aunr:~nnnuptlmmnfiwpl:55..ma. .
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P

 

mn-ou
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sumac:
acmqoa
nnmdou
aonwoa

2.....

w

>m= can... rhea:

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III-.--

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‘09.

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umuz—moo zonpUmc—o
u~.».x ~< hzwo_oz~

106

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unmcou.

onsaou
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m.

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u .... ....II‘oIIII'O'O(I‘|.Oll-I|"O

5...... ...... 2...... ...... ...... 2..... ......9.
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”w m N _ o

om<~m ommN ab maxemmwmmco z~m hmm—u who:
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capumpw: mzcmhzb: mo zmmzn: Jupop
amanwsoqu mwngz ogww hm<4

......

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>oz o... ...... ...... .0 .ao..=m2 co...

 

107

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manaos.
come-9
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finance.

v

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n.....

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ma....
n

«mange
noosoa
mousoa
933.9:

mnam-s.

newnoa
g

>uz ana.«q Iho~z

~n...u ...... .aN... «~59.» mm-.a ”......

may... ”ms... .31.}. cos... ~m:..s 5.. .m .

mmms.a Nam... 55.... m:a..a ms...» m5...w..

5am... mom... ~no..s 5a...» om5... 5e».....

~2~N.a n=n~.u 5:35.. som~.s e5.~.a ”.5... a

on»... :m:n... :non.a .05... .nmn.a 3....u ;
m 5 m 5 . .

.m<.n omm5.o. mazoamwmmoo z.m .mm.u ...z

2.9 >m; «a... u.w.m mzo.».z..o_mmu u<mmbpzm

nmm.~ cuhowpwo mzompamz no «muz;z ...g.

o.asn~aaw mamas: a... .m..

.. 2:...mom 4....2. xcez<a ..

.~:n.. ... a.=o.¢ um.z_m.u zc_.o.m_a

muzoz_ ... ..s ..a n5.».x .. .z.o_uz_

>o= oo.~u.oc.o5 .wumcu mo acouuamz oocmm

 

 

108

nausea
worsen
omoaon

3.5....
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m.

3

ngnom
mama-a
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mama's.
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m

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«mane?

m.

>mz mam... Ibo—1

 

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3333...}

mo...3 o.~a.u . «an... on»... N33... 5.33.3.3
.5m3.u. .3ma.a..3.m..3. n33... ...... «n5... .a5n.z§
5a.... au~..3 53w... 3cm... 333... 33m... um...woa
3.3.... nm3~.3. 3m.~.a 35u~.m 33n~.3 w~m~.. 3535.30,
...... 3333.3 5mon.s 3.33.. 333... 03.3.3 ......
w kw .¢ m N _ o
.m<_m 33m. 3. mazcummamou 2.3 .mc_u ...:
z_m 3m; m3... u.m.3 wzo.»uz._u_uuu ..33..2~
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3. :3_..mom 4._5_.. =aoz<m ..
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3.: 33.5 zz.m33..3o .mmmzm ma wzom.:.z uanmm
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wooo :uz mahowhmo 23mp3w2 Nafiumz to sea >0 tom“ bm town 3: o~zo mom ww—ozu~u_umm

.

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.Ammzucmv macamcmafia saw: HOumfidauaaum.umH:mcmuumm

109

0.2 MSU-83- 58!

 

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EFFICIENCY (RELATIVE)

0.05 -

    

 

 

  

 

0.0

 

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ENEUTRON (MW)

IZO

Figure C.l. Relative detector efficiency
versus neutron energy. Threshold energies
shown are electron energies.

 

 

 

APPENDIX D

CALCULATION OF GT STRENGTH

 

APPENDIX D

CALCULATION OF THE GT STRENGTH

Following the method prescribed by Taddeucci et al.,

and described in Chapter I (Ta 81), define

 

do (E )(0°) K
__ v; GT X l _ l r, F
B(GT) ~E 1.1+ dQ Xdc51,.(O°Yx(N 2” T27 fuq) XW
x T
R2(Ep=120 MeV) =4.71
i=(E /E )l°5
KGT Neutron,F Neutron,GT

The sum is over all l+ excitations, as obtained from
the measured angular distributions.
f(Aq) Ea.momentum transfer correction factor.
To compute f(Aq), calculate momentum transfers for all 1+
excitations of interest at 0° and for the IAS for e:=o to
10°; estimate 6' for the IAS that has the same momentum

transfer (Ag) as the excitation of interest at 0°; then

0
50 do ,
afi- IAS(9 )

 

 

f(Aq) =

For the sake of uniformity, we obtained angular distribution
for IAS by averaging over those for “2'““ and “88c. This
Curve,displayed on the top of Figure 3.9,was used in extrac-
ting 9'.

110

 

 

111

The computations are listed in Tables 0.1, D.2 and 0.3
for “2'““ and “8Ca for 1+ cross sections obtained from
defining an experimenter's background similar to those shown
in Figure 3.8. The l+ strengths derived by fitting our data
(peak + background) to predictions of DWBA cross sections
were also used to obtain GT strengths; this method was

an

applied to and “BCa only. The computations are shown 5

in Tables 0.4 and D.5.

 

 

 

 

 

112

 

 

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An

Ar

Au

Be

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Co

Do

Er

Fu

Ga.

Ga.

79

80

83

79

72

81
82
81
80

74

75

82

80

80

81

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