ABSTRACT

AN INVESTIGATION OF (p,d) REACTIONS
IN 1p SHELL NUCLEI

By Lorenz A. Kull

6 . 8

The energy levels of 5Li, L1, Be, 9B and 10

B

excited in the (p,d) reaction have been studied with a 33.6
MeV incident proton beam from the Michigan State University
sector focused, isochronous cyclotron. The differential
cross sections were measured for the strongly excited levels
using a solid state dE/dx counter telescope to detect the
deuterons. The angular distributions were also measured for

6

the elastic scattering of 33.6 MeV protons from Li, 7L1,

9Be and 10B. Optical model fits were made with a computer
code to this elastic proton data and to deuteron elastic
scattering data obtained from the literature in order to
extract optical parameters. These optical model parameters
were used in a computer code which performed distorted wave
Born approximation (DWBA) calculations for the (p,d)
reactions. The DWBA results were subsequently used to
extract spectrosc0pic factors for all the strongly excited
levels of the nuclei being studied.

Deuteron groups were detected corresponding to

strongly excited levels of 5Li at 0.0 and 16.6 meV excita-

6
tion and to strongly excited levels of Li at 0.0, 2.15,

Lorenz A. Kull

3.57 and 5.38 MeV excitation. The energy spectra show
deuteron groups corresponding to strongly excited levels of
8Be at 0.0, 3.1, 11.4, 16.95, 17.62, 18.18 and 19.21 MeV
excitation; a small deuteron yield was also observed
corresponding to 8Be excited levels at 16.6 and 19.15 MeV.
Deuteron groups were observed corresponding to strongly
excited levels of 9B at 0.0, 2.35, 7.1 and 11.75 MeV
excitation and to weakly excited 9B levels at 2.8 and 1A.6
MeV excitation. Deuteron groups were observed corresponding

to strongly excited levels of 10

B at 0.0, 0.72, 1.76, 2.15,
3.57, H.75, 5.18 and 6.04 MeV excitation; weakly excited
levels were noted at 6.57 and 7.5 MeV excitation.

The experimental spectroscopic factors were compared
with several different theoretical calculations for the.
reactions being studied. In particular, good agreement was
found between the data and an intermediate coupling model
of the 1p shell nuclei. 0n the basis of this general accord
between experiment and theory, spin assignments were made
for the observed 9B levels from the intermediate coupling
model predictions. Comparison of the experimental

loB excited states with results

spectroscopic factors for the
from other experiments show that spectroscopic factors
extracted by the present method do not depend significantly
othhe incident particle or its energy.

Angular distributions for all the strongly excited

levels observed, with the exception of the 8Be level at

Lorenz A. Kull

11.4 MeV (JTr = 4+), indicate the direct pickup of a.lp
shell neutron. Isotopic spin mixing in the higher excited
levels of 8Be and the possibility of 28-1d shell admixtures
in the ground state wave functions of the target nuclei

are discussed.

AN INVESTIGATION OF (p,d) REACTIONS
IN lp SHELL NUCLEI

By

.\ \U 3
x /

Lorenz AC’Kull

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics

1967

ACKNOWLEDGMENTS

I would like to express my gratitude to Dr. Edwin Kashy
for suggesting this work, for his continuing guidance during
the experiments, and for helpful discussions of the results.
I thank Dr. Morton M. Gordon for his intriguing introduction
to the field of nuclear physics.

Thanks go to Mr. Raymond Kozub, Mr. Phillip Plauger,
and Mr. Craig Barrows for their help in taking and analyzing
the data.

I acknowledge the financial assistance of the National
Science Foundation which provided partial support for the
experimental program. I also acknowledge financial support
from the National Aeronautics and Space Administration
Traineeship which I held for three years.

I want to express my deepest appreciation to my wife,
Joan, for helping with the typing and for her patience and

understanding during my graduate work.

I also want to thank all the Michigan State University
‘fiYclotron staff members who have made this work possible

Vfirth their untiring support of the nuclear eXperimental

pro gram .

ii

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . . . . . . 11

LIST OF TABLES . . . . . . . . . . . . . v

LIST OF FIGURES . . . . . . . . . . . . . vi

INTRODUCTION 0 O O O O O O I O O O O O O 1
Chapter

1. NUCLEAR THEORY . . . . . . . . . . 4

1.A. The Distorted Wave Born Approximation . 4

1.8. The Intermediate Coupling Model . . . l6

2.. EXPERIMENTAL APPARATUS . . . . . . . . 28

2.A. Cyclotron and Beam Handling Apparatus . 28

2.B. Faraday Cup and Current Integrator . . 29

2.C. Target Holder . . . . . . . . . 31

2.D. Beam Alignment . . . . . . . . 33

20E. DGtECtOI’S o o o a o o o o o o 314

2.F. Counter Telescope Assembly . . . . 36

2.0. Electronics . . . . . . . . . 37

2.H. Data Processing . . . . . . . . 42

2.1. Targets . . . . . . . . . . . 44

3. ESTIMATES OF UNCERTAINTIES . . . . . . 47

3.A. Beam Energy . . . . . . . . . 47

3.B. Target Monitor . . . . . . . . 49

3.C. Differential Cross Section . . . . 50

3.D. Energy Resolution . . . . . . . 52

4. EXPERIMENTAL RESULTS . . . . . . . . 55

4.A. 5L1 (p,d) 5Li . . . . . . . . . 55

“OB. 7L1 (p,d) 6L1 0 O O O C O O O C 61

4.0. 9Be (p,d) 88c . . . . . . . . . 64

140D. 10B (p’d) 98 o o o o o o o o 71

4.E. llB (p,d) lOB . . . . . . . . 81

iii

Chapter Page

5. DWBA ANALYSIS . . . . . . . . . . . 89
5.A. Elastic Scattering Measurements . . . 89
5.8. Optical Model Calculations . . . . 94
5.0. -DWBA Calculations . . . . . . . 96

6. SPECTROSCOPIC FACTORS . . . . . . . . 101
6.A. Experimental Spectroscopic Factors . . 101

6.B. Theoretical Spectroscopic Factors . . 102

6.0. Comparison of Results . . . . . . 104
CONCLUSIONS . . . . . . . . . . . . . . 118

BIBLIOGRAPHY . . . . . . . . . . . . . 126

iv

LIST OF TABLES

Energy level spacing for 6He states with LS
coupling . . . . . . . . . . . . . .

Energy level spacing for 6He states with 33
coupling . . . . . . . . . . . .. . .

Average energy of protons emerging from calibra-
tion block vs. their incident energy . . . .

Breakdown of the total uncertainty in the
differential cross section measurement . . . .

Experimental cross section ratios and+calcu1ated
isospin admigtures for the J1T = 1+, 24, and 3+
doublets Of Be 0 o o o o o ' on o o o o

9B excitation energies and widths for deuteron
groups measured in the reaction-10B(p,d)9B . .

Proton optical model parameters . . . . . .
Deuteron Optical model parameters A. . . . .

Average differences of spectroscopic factors from
mean values of the experimental data . . . .

Page

23

24

48

52

70

81
96
96-

112

Figure

1.

LIST OF FIGURES

6He Energy Level Spacing vs. Intermediate

Coupling Parameter, a/K . . . . . .
External Beam Geometry . . . . . .
Scattering Chamber and Counter Telescope
Block Diagram of Electronics . . . .
Mylar (p,d) Calibration Spectrum at 15°
6Li (p,d) 5Li Spectrum at 15° . . . .
6Li (p,d) 5L1 Spectra at 35° and 120° .
Energy Level Diagram of 5L1 . . .
6Li (p,d) 5Li Angular Distributions . .
7L1 (p,d) 6L1 Spectrum at 20° . . . .
7Li (p,d) 6Li Spectra at 40° and 110°

7L1 (p,d) 6L1 Angular Distributions . .

9Be (p,d) 88s Spectrum at 15° . . .

98e (p,d) 8Be Spectra at 600 and 110° .

Energy Level Diagram of 8Be . . . .

9Be (p,d) 8Be Angular Distributions . .
8

9Be (p,d) Be Angular Distributions

B (p,d) 9B Spectrum at 20° . . .

B (p,d) 9B Spectra at 40° and 90° . .
Energy Level Diagram of 9B . .

lOB (p,d) 9B Angular Distributions . .

vi

Page

26
30
32
43
53
56
57
58
60
62
63
65
66
67
69
72
73
74
75
76
79

Figure Page

23. 10B (p,d) 9B Angular Distributions . . . . . 80
24. 11B (p,d) 10B Spectrum at 20° . . . . . . . 82
25. 11B (p,d) llB Spectra at 40° and 120° . . . . 83
26. Energy Level Diagram of 10B . . . . . . . 84
27. 11B (p,d) 10B Angular Distributions . . . . . 87
28. 118 (p,d) 10B Angular Distributions . . . . .. 88
29. 6Li (p,p) 6L1 Angular Distribution . . . . .- 90

30. 7Li (p,p) 7L1 Angular Distribution . . . . . 91

31. 9Be (p,p) 9Be Angular Distribution . . . . . 92
32. 10B (p,p) 103 Angular Distribution . . . . . 93
33. Spectrosc0pic Factors for 7Li (p,d) 6L1 . . . 105
34. Spectroscopic Factors for 9Be (p,d) 8Be . . . 106
35. Spectroscopic Factors for 11B (p,d) lOB . . . 108

36. Comparison of Spectroscopic Factors for 10B States

from 1p Neutron Pickup Reactions . . . . . . 110

l

37. Spectroscopic Factors for 0B (p,d) 9B . . . . 114

11B (p,t) 98 Spectrum at 10° . . . . . . . 115

38.
39.

40. Lithium Drifted Detector and Mount . . . . . 124

11B (p,t) 9B Angular Distributions . . . . . 116

vii

INTRODUCTION

This thesis describes the results of (p,d) reactions

using 34 MeV protons with targets of 6L1, 7L1, 9Be, 10B,

and 11B [1,2]. The first successful attempt to measure
deuteron angular distributions for a variety of (p,d)
reactions was made by K. G. Standing in 1956 using 18 MeV
incident protons [3]. A clever and simple method was

used to detect the deuterons. NaI crystals were cut to a
thickness which Just stopped deuterons of a selected
energy. It can be shown that a deuteron at this critical
energy produces alarger pulse at the scintillation counter
output than any other deuteron or any proton. Thus, by
carefully selecting the crystal thickness, a deuteron
group correSponding to the ground state or a lower excited
state of the residual nucleus could be displayed on a
multichannel analyzer.

Previous studies of the (p,d) reactions with very
light nuclei have been made at Princeton University with
an incident proton energy of approximately 18 MeV in which
only the lower excited states of the residual nuclei could
be observed [4,5,6,7]. The same reactions were also
studied at the University of Minnesota using 40 MeV protons

[8,9],where a magnetic Spectrometer was used to measure

angular distributions out to 40° for most of the lower

excited states of the residual nuclei. Many other studies
of these reactions have been done at even lower proton
energies, most of which examined the properties of the
ground state and lower excited states of 5L1, 6L1, 8Be,
9B, and 10B [9]. The (p,d) reactions on these nuclei have
also been investigated with incident proton energies of
95 MeV and above [11,12,13]. The range of observable
excitation energy in the residual nuclei included all the
known strongly excited levels; however, the energy resolu—
tion did not permit the separation of closely spaced levels.
The purpose of this work was to use an incident proton
beam with sufficient energy to allow observation of all the

6 8Be, 9B, and 10

strongly excited levels in 5Li, Li, B,and
yet with a low enough energy to enable the use of solid
state radiation detectors with their desirable energy reso-
lution capabilities. An incident proton energy of about
34 MeV fulfilled both requirements. The intensity and
inherent energy resolution of the unanalyzed proton beam
available from the Michigan State University cyclotron at
this energy allowed angular distributions to be measured
out to an angle between 100° and 140°, depending on the
particular reaction being studied.

The data were analyzed to extract spectroscopic factors
using a method successfully applied to (p,d) reactions with
medium weight nuclei [14,15]. The experimental results

were then compared to the theoretical intermediate coupling

calculations in the 1p shell of Kurath [16], of Barker [17]

and of Balashov [18]. Special emphasis was placed on the
comparison of the data to Kurath's work which is a complete
model of the 1p shell for A = 5-16. The theoretical wave
functions have been tested with regard to predictions of
electromagnetic transition widths [19] and energy levels
[20]; this work provides a separate and different test of
this model's ability to predict experimentally verifiable

quantities over a wide range of nuclei.

CHAPTEva

NUCLEAR THEORY

1.A.‘ The Distorted Wave Born Approximation

 

The direct interaction is defined as one in which the
incident particle excites only one degree of freedom in the
target nucleus. The specific types of direct interactions
include knockout, inelastic scattering, stripping and pick-
up. The (p,d) direct interaction is a pickup reaction in
which the incident proton "plucks" a neutron from the target
nucleus without exciting any other degrees of freedom of
the target nucleus. The process can also be thought of as
the incident proton dropping off a neutron "hole" which then
interacts with the original target nucleus.

The direct interaction competes with the compound
nucleus interaction in producing the measured yield of reac-
tion products. The primary difference between these two
different reaction processes is the time involved for the
reaction to take place (At). The direct reaction has a At
roughly associated with the time it takes for the incident
particle to transit the nuclear volume («110'22 sec); the
compound nucleus reaction has a much longer At on the order
of 10'1“ sec LBllgFor the case of incident protons, the
compound process is dominant for very low incident energies

(<5 MeV), the compound and direct processes are approximately
4

equivalent at higher incident energies (5-15 MeV), and the
direct process is dominant for even higher incident energies
(>15 MeV). The exact dependence of the relative compound
and direct yields on incident projectile, incident energy,
and target is not known, although work has been directed
toward solving this problem for particular cases [22]. How-
ever, from this rough energy scale, this work at an inci—
dent proton energy of 34 MeV falls well inside the region
in which the direct process is predominant.

The best clue for a direct interaction process, which
the experimenter can look for, is an angular distribution
strongly peaked in the forward direction and oscillating
with increasing angle. The successful theoretical attempts
to describe the direct process all predict this diffraction
effect; the expression for the differential cross section
for the reaction A(a,b)B proceeding by a direct interaction
can be found in standard texts[23,24] and is given by

equations (1) and (2):

IQ

5'

d0" _, ”him; Kg. 2
(1) _...— - ---'5.'=~ _._. I
an (5273) K1 AV

(2) 7;,- = <v, X,H/\/,l$!’&>

mi(mf) = reduced mass in the incident (exit) channel.

ki(kf) = wave number in the incident (exit) channel.

vf = internal wave function of the final state nucleus.

x;-) = wave function for relative motion in the exit
channel with an optical potential between b and B.

W(+) = Coulomb wave of relative motion between a and A
plus outgoing Coulomb b waves from B.

Vf. = final interaction not included in the central
interaction of b with B.

A2 = sum over the unobserved quantum numbers in the

exit channel and an average over those in the
incident channel.

The equation (2) is an exact eXpression, however the

(+)

is not known. In order to perform the

(+)

exact form of W

calculation of (2), the function W is replaced by
(+) .

(xi Vi) where.

<+> z

xi wave function for relative motion in the
incident channel using an optical potential
as an approximation to the real interaction
between a and A.

vi = internal wave function of initial state nucleus.

This approximation is known as the distorted wave Born

approximation (DWBA).

d_0_
d0
eaquations (1) and (2) for the direct process A(d,p)B and

The approach taken here will be to calculate from

then use the principle of detailed balance to arrive at the

solution for %% for the inverse process, B(p,d)A. This
appears to be a somewhat round about way to arrive at the
answer. However,it was actually the procedure followed in
obtaining the DWBA results, since the Masefield computer
code, which was used to perform the calculation, originally
was written to solve the (d,p)0problem. .

The effects of the potentials involved in the reaction
A(d,p)B can all be located in the matrix element,‘Tfi.
Effects internal to all the nuclei are included in the nuclear
wave functions vf and v . Central interactions between in-

1
coming and outgoing particles with A and B are included in

(+) <-).

the distorted waves Xi and Xf Everything left over

is included in V (incident channel) and Vf (exit channel)

1
where
(3a) Vi = VpA + VnA
(p-proton; n-neutron)
= V
(30) V? pn + va

We assume VpA to be zero in (3b) and hence neglect
any non-central interaction of the outgoing proton with
the core, (A). Therefore only the neutron—proton inter—
action is left to couple the initial state to the final
state. We now rewrite (2) for the Specific case A(d,p)B

using the DWBA approximation.

an 7;. = (v. (?..a)><."’(R,,r>l\4<s>lm<mv. (a) x‘*’(mn>

The neutron is assumed to be captured into a shell
model orbit characterized by the orbital and total angular
momentum quantum numbers 2 and 3, respectively. Since the
shell model wave functions constitute a complete set of
orthonormal functions, we can expand VB in this set without

making any particular assumption about the nature of B.

:r
(5) VXXLE.) r; S: [V12 (i) X¢Mfuflm

We omit consideration of the intrinsic spin of the neutron
since it only complicates the calculation and doesn't add

1/2
anything to the results. 823 is the spectroscopic ampli-

tude. We can also write

(6) 5’»: (ZN 950.1?”38‘2 Gamma/1.) (77¢...
“hm

Now the assumption is made that the neutron goes into a

definite orbit (£,j) and the equation (5) can be written,
3' K a“ 2 ( >13;
8 " - - * - -

<7) v,.,,0..c.>- 9.. [Immxszfn .-.. ,.

We insert (6) and (7) into (4) and using the orthogonality

properties of the vi arrive at,

.. A *_ c—i' _ (+3, _ Pd?
(8) 7;, = S: C(JAMMN’Q $05601, @OWRWE 3mm . p

Consider the bracketed expression inside the integral in
equation (8). We will use the zero range approximation for

the deuteron wave function,

Y <3
(9) Q (for) = 3'". n, It.

2 2
where 251— = 2.33 MeV (binding energy of deuteron). The
np ,

meaning of this expression becomes clear if it is inserted

in the Schroedinger equation for the bound neutron.

(9.1:, mm = Ea

(10) 3m,

:27: [V2_ 31] ¢A " V"? W

But, 3' is the Green's function for the Operator (V2-y2),
i.e.
.8m,
1 63 - — J‘r‘-Y'
(ll) (vi—X)? - 477‘ (n r)
h

7

Substituting equations (9) and (11) into (10),

(12) «IE: (Er—3'— ;(r..-r,) =3 VMQUE)

‘anhf

10

With this choice of the deuteron wave function, we see that
the neutron-proton interaction is represented in the calcu-
lation by a Dirac delta function, the mathematical counter-
part of a zero range physical interaction. This is only a
simple approximation of the actual physical situation where
the interaction is of short, but finite range. The most
desirable feature of the approximation is that it makes the
calculation tractable. Some computer codes allow the inser-
tion of a potential function (Vnp) in place of the zero
range approximation (ZRA) and the problem of ascertaining
the effect of using the ZRA has been worked on [25,26,271-
Calculations made for medium and heavy weight nuclei show
little change in shape in the angular distribution, with

an overall increase in magnitude when the ZRA is used
instead of the finite range interaction. The effect is not
completely understood and is complicated by the fact that
the actual interaction (Vnp) is not known. The position
adopted in this work will be to use the ZRA, keeping in

mind its inherent limitations.

Inserting (12) into (8),

<- t (+1 _ _
< 3> T — 3" 15: flC(J/~Q’1"~'°Ws)]¢§°1§ 4.9x. (war
1 A- ”liéunw 1”

S

11

The expression (13) is then inserted into (1) and a

sum over the final magnetic substates yields a factor,

2J + l
EIET‘I— (from the Clebsch-Gordon coefficients); averaging

over the initial state produces a factor, 57——%—T—u Then

A

(Mend-Q: (Aflrw) ‘7': I?) 7%“ -MT "3’2 ’ $203 1816’:

where

351(— S Q? ( F) X610," F) Ximaai F.) AF

(14b) 6” an.
P

Let kd lie along the polar axis (the deuteron beam
points in the +2 direction). Then the Optical wave func-

tions (x) can be written (see equation 20).

{“005} = g 2 (5.17 fact») >326»
l a,

 

1 ,a «F row)! 3 (k R
( 5) X:3(?PIF) .- % £16?! I. £10917.) X7) (7. to)!

12

Now set
(16) ¢.: (F) . u,(r) WY?)

“where u2(r) is determined by using a potential well whose
depth and radius give the correct binding energy for the
neutron (Q-2.223 MeV). After inserting (15) and (16) into
the expression (140) for Btm’ the integration can be per—
formed over the angular coordinates with the aid of a

Clebsch-Gordon series [28]. The result is

 

 

(17) = .5: ‘firm 2 (31+!)Am71r2C6900b'0) X
in an”. K'KJ )A' 01-h)! 4‘ A
’ C(afum la'u’) R37" Pa (K'KJ)

(18) R”: =S£(Knr)£,(mr)ux(r)dr

The fA(Kr) in the integral expression (18) are ob-
tained.by fitting the elastic scattering data“ from p(B,B)p
and <d(A,A)d where the incident particle's energy is chosen
SOthat p and d have center of mass energies as close as

pOSSible to those encountered in the pickup reaction

 

 

*
This fitting was done using the computer code
AbaCus [29].

l3

B(p,d)A. The Schroedinger equation for the elastic scatter-

ing is given by

6V1+2ig U-K‘)Xm‘0 3 3.52. E

(19)

(Note: for simplicity, we are ignoring the Coulomb term.)

The solutions are of the form

(20a) x“) ’4}? Z/‘z £(Kr)y‘ (fly: (K)

3

X"’= £7: Z 12 500) 47") >507)

(20b) Kr, Qh
I

The (+) and (-) signs refer to the outgoing and incoming
*
boundary conditions, respectively. The fA(Kr) satisfy the

differential equation

(21) ("$1 + £1£1>+JU-K){(Kr) =0

where

<22) U: -.Va‘(r,R a.) we 99. Va. f0? 8/49“” (we? “I 39%,. 3‘07 R. an)

 

 

4- "outgoing wave"

-) amor- -
X‘ 4’ C 4' "incoming wave"

l4

. c.2135?"a
Here {6; R,Q) ’ ‘L' 3 X G

e"+l

The actual potential used includes a term (U0), the Coulomb
potential Of a uniformly charged sphere Of radius RAl/3
fermis. The potential also contains a "surface" absorption
term and a simple spin orbit dependence. The parameters Of
this Optical potential (U) are varied to obtain a calculated
elastic angular distribution which matches the data. These
parameters are then used in equation (3) tO numerically
evaluate the fi(Kr) for the integral expression (18).

Inserting equations (17) and (18) into (14a), we
obtain a calculable expression for the differential cross
section for the reaction A(d,p)B. This can now be related
in a very simple manner to the differential cross section
for the reaction B(p,d)A. The principle Of detailed balance
[30], which is a consequence Of the principle Of time

reversal, gives the following relation:

3’?!
(23) @(BWM) g—(M‘AMHEL K, (223));20'4)

Thus with (14a) this can be written

(2L1) ._. "U K: -J-— J:
fi§§E<fiB<fiJWA) Eggsfiy‘ —Tfi:.%%i:z;‘;uyq éififi [as

15

It should be noted that the distorted deuteron waves,
as calculated above, depend only on the position of the
center of mass of the deuteron, whereas the weak coupling
within the deuteron itself is likely to be sensitive to
deformations caused by interactions with the target nucleus.
This effect has not been taken into consideration in the
calculation for the particle transfer reaction.

It should also be noted that the distorted waves cal-
culated from an optical potential which reproduces the
elastic scattering become a worse approximation to the
actual outgoing deuteron waves as the residual nucleus is
left in states of increasing excitation energy. In
effect-we are assuming that the outgoing waves from the
residual nucleus' ground state are the same as those
from one of its excited states; or equivalently, the differ-
ent states Of the same nucleus are assumed to resemble one
another closely when considered as a scattering center. As
the increase in excitation energy allows more distortion of
the residual nucleus, the approximation gets worse. There
is also a practical problem with unobtainable optical param—

5

eters for the scattering from unstable nuclei (e.g. Li, 9B,

8Be). In these cases, the assumption must be made that the
unstable nucleus differs very little from its nearest stable
neighbor and then the Optical parameters for the stable
nucleus are used (e.g.6Li parameters for 5Li).

Other limitations which could affect the validity of

tkfiilflinal expression include the omission of the consideration

16

Of isospin in the Optical potential, non—local effects, and
inelastic effects. These have all been treated elsewhere
[31,32,33], but their effects on the calculations are not
completely understood. The philOSOphy adopted in this study
will be to attempt to obtain a reasonable fit to the data
with the simplest possible form of the theory, as has been
done in other similar (p,d) studies with different incident

energies and other target nuclei [14,15].

I.B. The Intermediate Coupling Model

The (33) coupling model has met with great success in
eXplaining the features of heavy nuclei [34]. In this model,
commonly referred to as the nuclear shell model, the spin orbit
interaction attempts to orient each individual nucleon's
spin (Si) relative to its orbital angular momentum (E1) to
form a total angular momentum (3,). The individual 3, then
interact to produce the 33 coupling scheme, a characteristic
set of energy levels for which various nuclear properties
may be calculated.

However, the nucleon-nucleon force may also attempt to
orient all of the individual nucleons' spins (Si) to form a
total spin (S) and their orbital angular momenta (Ii) to
form a total orbital angular momentum (f). The E and S
interact to produce the LS coupling scheme which is differ-
ent in general from the 33 scheme. LS coupling is commonly
referred to as Russell-Saunders coupling in atomic Spectro-
scopy; a field where this model has been very successfully

applied.

17

As mentioned previously, the 33 coupling model appears
to agree with eXperiment very well in the case of heavy nuclei,
but attempts to apply this model to the light 1p shell nuclei
have not met with similar success. Moreover, the LS coupling
scheme does not appear to fill all the gaps where the J] scheme
fails. This is not a surprising result since the 33 and LS
coupling schemes only mark the two extremes of a more general
theoretical model called intermediate coupling [35]. In this
model, the spin-orbit forces compete with the nucleon-nucleon
interactions, and produce a result which falls somewhere be-
tween the two extreme coupling schemes. If one were to plot
the relative amount of 33 to LS coupling as a function of the
mass number A, the 1p nuclei would be found occupying the
transition region between predominantly LS cOupling (very
light nuclei) and predominantly jj coupling (heavy nuclei)[36].
For this reason, the intermediate coupling calculations of
Kurath have been chosen to be compared with the experimental
results of this work [20]. The discussion of the intermedi-
ate coupling model which follows is not intended to be a com-
prehensive study, but only a brief survey Of the problem to
note some of its more important features.

Given a specific case Of n nucleons all in the 1p
shell, and using the basic physical laws Of conservation Of
angular momentum, indistinguishability of identical particles,
and the exclusion principle, it is possible to arrive at a
set Of allowed Jj or LS wave functions which can be used to

describe the ground state and excited states of the nucleus.

18

The energy level sequence and Spacing in which these states
fall depends On the interactions between the n 1p shell
nucleons. The phenomenological approach is taken in which
an attempt is made to represent these interactions in a
simple form which has empirical validity. We shall assume

a 2-body central interaction V(r ) between nucleons multi-

iJ

plied by a dimensionless exchange Operator, 013' In Rosen-
feld's book [37], it is suggested that the most satisfactory

version of O1 is

3

(la) 013 = 71 . T3 (0.1 + 0.23 31 . 3‘)

Here, T1 is the isotopic spin of the ith particle and 01
is its intrinsic spin. It can be shown [37] that the ex-

change Operator (0 ) can be approximated by an expression

iJ

involving only the spin and Space exchange Operators

(equation lb).

(lb) 013 = (O.93P—O.l3-O.26PQ + 0.46Q)

P and Q are the space exchange (Majorana) and spin exchange
(Bartlett) Operators, respectively and PO is the Heisenberg
operator. A simplified version Often used to make calcula-
tions more tractable and which approximates (1) closely in

effect is

(2) 013

II

0.8P + 0.2Q

P can be looked upon as roughly representing the saturation

effect in nuclear interactions and Q as an approximation to

19

the effect Of a tensor interaction [35]. The spin-orbit

interaction considered in this model is given by
(3) 22 01.2;“a
&

where the parameter a is different for each nucleon shell.

The approach taken here will be to determine the
energy level sequence and spacing for the allowed states of
a nucleus as a function of the parameters a and Vij’ the
result is then fitted to the experimentally Observed level
spacing and the magnitude of these parameters are fixed.
After they are known, the Hamiltonian can be constructed
and diagonalized and the wave functions for the levels
(determined. The wave functions can then be used to calcu-
lrite all the nuclear properties of the levels.

We consider now the relatively simple case Of 6He with
a ls shell filled with 2 neutrons and 2 protons which will
be: considered as an inert core. The states of 6He may then
be: characterized by a set of two nucleon LS wave functions
vfilich are made up from single particle wave functions with
the :following considerations. Given the space portions of
the 17wo single nucleon 1p shell wave functions,1pand ¢,
the Ibrinciple of indistinguishability (both 1p nucleons are

neutleons) requires the Space portion Of the two nucleon

wave function to be Of the form

(4) 1 (4 v2 r avg)

(2’

20

where ‘01 = ¢(f‘,) ¢l =¢(E)
9", =V<ra> ¢2 =¢<r‘,>

The spin portion of the two nucleon wave function can

similarly be written in terms of the single nucleon wave

functions oand 8*

°1°2
B182
(5)

% (a182 +8102)

2

The neutrons are fermions, therefore the Pauli prin-

ciple an... only a... completely antisymmetric functions:
’1’, = i- (‘6 «w Mac-ca.)
3K ‘75:(Vf¢1’¢~9{)o(.°(2

(6) I”. = #(WA'WAMA.
Y, = i (WA-Aviflactek)

 

—-\

’* a has quantum numbers S = 1/2, ms = 1/2 (Spin up)
and.Ei Ilas quantum numbers S = 1/2, mS = -1/2 (spin down).

21

Since only neutrons in the 1p shell are being considered, and
if the initial Hamiltonian (HO) contains the kinetic energy
and a central potential representing the interaction of the

lp neutrons with the core, the Vi are degenerate, i.e.

<7) Haj-6'52: 5;:1-8’

It can easily be seen that HO and OiJ”(equation 2)
commute and therefore have the same set of eigenfunctions,
however adding the nucleon-nucleon interaction between the
1p neutrons to the Hamiltonian will split-the degeneracy as
will be seen from the following arguments. Only the energy
differences between the LS wave functions are of interest
11ere so that in adding the interaction term 013 to the
Phamiltonian, integrals of the form

(8) aesmt‘WOA/fl

nnlst be evaluated. Consider the case for E2

1— L,S(W¢ ’fl ¢{>W(o(o¢,) \/,:(0.2P+oaa)(%¢§ fl'f'xdfi)

.1: [mamas {64% mm]
./6’[K~Lj

In atomic Spectroscopy the integral K is commonly

".

(9)

r"EIE‘EE’I-"l'edto as the exchange integral and the integral L as

the (Drxiinary integral. All the E1 can be expressed as a

22

linear combination of K and L so that the splitting of the
degeneracy can be expressed in terms Of the two parameters,

K and L. The fact that the E (i=l-4) will, in general, be

i
different is a reflection of the Pauli principle and the
antisymmetric construction Of the allowable wave functions.
The two parameters, K and L, are not completely

independent, but depend on the range of the nucleon-nucleon
interaction. This can be seen by considering two simple
cases. If the range of the interaction is very long with
respect to the spacial extent Of the nucleus so that the

potential is essentially constant out to the nuclear radius

= V), then L = V and K = 0. On the other hand,if Vl

(V12 2

is essentially Of zero range, (Vl2 = V6(rl -r2)), then

L = K = V. The actual case of a finite range interaction
must lie somewhere between these two extremes. Thus the
energy level spacing can be expressed in terms of a single

parameter K, where

(10) L-XK

and y is determined by estimating the range of the inter-
action in terms of the nuclear size. Since the splitting
now depends only'on the parameter K, it can be thought of

as a measure Of the strength of the LS coupling.*

 

*

K is less than zero; the Opposite Sign is used in
atomic spectrOSOOpy where the interaction between electrons
is repulsive instead of attractive as in the case here.

23

Returning to the case of 6He, the LS wave functions
which satisfy the conservation of angular momentum, the
principle of indistinguishability, and Pauli's exclusion

3 l *
o’ P2;,0’ D2. Using the range relation-
ship (equation 10) L=4K, the splitting of the degeneracy for

principle are 1S
the LScase has been worked out [38] and is given in Table 1.

TABLE 1. 6He energy level spacing with the nucleon-nucleon
potential in terms of the exchange integral parameter, K
(LS coupling).

 

 

State E E(L=4K) J

1D L—K 3K 2
2

3

P2,l’0 —L+3K -K 2,1,0

130 L+2K 6K 0

 

The Spin—orbit coupling term can now be introduced as a
perturbation which will split the degeneracy still present
in the 3P multiplet. It can be shown [35] that the spin-
Orbit interaction term (3) can be expressed as

Zara"; : ALMS

A;

i,
2

the energy level Spacing is Shown in Figure 1 by dashed lines.

where A = for the 1p shell. The effect of this term on

 

*The notation here is 2S+lLJ.

24

The two neutrons in the 1p shell Of 6He can also be
described by a set of 3] wave functions which satisfy the
same general conditions as those imposed on the LS set. The
allowed wave functions are given in Table 2 along with the
energy level spacing, assuming the only interaction to be
the Spin orbit term (equation 3).

TABLE 2.--6He energy level spacing with the Spin—orbit
interaction in terms Of the spin-orbit parameter a (33

 

 

coupling).
State J E
(p3/2)2* J=2,0 a
(93/2pl/2) J=2,l ‘a/2
(pl/2)2 J=O -2a

 

*The notation here is (AJ).

Note that the parameter a plays the same part in the J]
scheme that K plays in the LS scheme. Thus a can be thought
Of as a measure of the strength of the 33 coupling.

As would be expected, the same values of J are allowed
in both the LS and jj schemes since these are simply dif-
ferent representations Of the same states. This leads to
the assumption that each individual state (J) goes over
smoothly from LS coupling to 33 coupling. An equation
describing the Splitting between the states for each set of
allowed J's (2,1,0) is constructed as a function Of K and a

such that as K approaches zero, the roots are those calculated

25

fon;JJ,coupling, and as a approaches zero, the roots are
those.ca1culated for LS coupling with a spin orbit perturba-

tion. Thus we have for J = 2,

E2 - (2K + g) E + % Ka - 3K2 — g? = 0,
and for J = 1,

E = — K - g,
and finally for J = 0,

E2 — (5K—a) E — 6Ka - 6K2 —2a2 = 0

The.solution to these equations is plotted as a func—
tion,of a/K in Figure 1 which graphically portrays the
change in the energy level splitting as the coupling changes
from LS to 33, i.e. as a/K goes from zero to a very large
value. For this particular case, the relative position of
the first 3 levels Of 6He determined experimentally could
be used to fix the parameters a/K and K and the prediction
for the upper two levels used to test the theory against
experiment. Once the values of a/K and K are Obtained, the
energy matrix can be diagonalized and the actual wave func-
tions for the states determined so that other nuclear
prOperties of the theoretical levels can be calculated and

compared with experiment (19).

(LS) CO‘UPLING

-201-
- lo —
3 ””
E/K P2“ 1.

26

 

 

+20 .

Figure l.--6He energy level spacing vs.

.9...

(jj) COUPLING
(13.)2
Q
}%%kHfi%)
: : —40/k (a<0.k<0)
6 8 IO

 

intermediate

couple parameter, a/K.

27-

The above case of 6He is extremely simple and of little
practical use since only two levels Of 6He have been found
experimentally. The same is true for the T = 1 levels of
6Li for which the model also would apply. This case was
choSen simply to illustrate the more important considerations
in an intermediate coupling calculation. The method of cal-
culation used at the present time is far more sophisticated,
employing large computers and extensive search routines [39].
The inclusion of non-identical particles, such as in the
case of 6L1, introduces the concept of isotopic spin and
requires the extension of the Pauli exclusion principle to
preserve the total anti—symmetry Of the nucleon wave func-
tions. The additional symmetry considerations introduced by
the inclusion of isotopic spin can be said to have the same
kind Of effect as the addition of intrinsic spin,in that the
symmetries imposed on the wave function are reflected in the
level spacing. The inclusion Of more particles into the 1p
shell also complicates matters, but the basic ideas included

in this simple intermediate coupling model problem still

prevail.

CHAPTER 2
EXPERIMENTAL APPARATUS

2.A. Cyclotron and Beam Handling Apparatus

Negative hydrogen ions (H’) were accelerated by the
Michigan State University sector—focused, isochronous cyclo-
tron [40] to an energy of 33.6 MeV and a proton beam was
extracted by means of a 700 pg/cm2 aluminum stripping foil
[41]. This method of obtaining an external proton beam em—
ploys a thin metal foil placed at the radius at which the
beam is to be extracted from the machine. On passing through
the metal foil, the negative hydrogen ions are stripped Of
their two electrons and emerge as positively charged ions
(H+). The Lorentz force on the H+ ions is in the opposite
“direction from that on the H- ions so that the stripped beam
is deflected out of the cyclotron's magnetic field. The main
difficulty encountered was that,under certain conditions,
more than one turn of the internal beam may pass through the
stripping foil and hence two or more proton groups (each of
which is separated by m801uflfin energy) may be extracted.

The presence of more than one turn in the extracted beam was
detected by double peaking in the deuteron energy spectra, a
condition which prohibited taking useful data. .This situation

was corrected primarily by adjusting the internal beam
28

29

orientation (or turn structure) although a small amount of
beam from a second extracted turn could sometimes be prevented
from entering the scattering chamber by adjusting the param-
eters of the external beam handling apparatus.

The extracted proton beam travels down an evacuated
beam pipe through two quadrupole, vertical and horizontal
focusing magnets and a 20° bending magnet (see Fig. 2). The
strengths of the quadrupole fields are sufficient to focus
the beam at the collimating slit located near the entrance
to the 36 inch scattering chamber. Two small electromagnets,
referred to as "Kink" magnets, are used to provide small
vertical and horizontal deflection of the beam before it
enters the collimator. Just in front of the collimating slit
is a remotely controlled scintillating foil* which can be
moved into the beam line and viewed with a closed circuit TV
camera. The scintillator foil was used to initially locate
and focus the beam at approximately the point where it enters

the scattering chamber.

2.B. Faraday Cup and Current Integrator
Protons which pass through the target (at the geometric
center Of the scattering chamber) are collected in a Faraday
cup, insulated from ground, at the rear of the chamber (see
Fig. 2). Protonsstopping in the insulated cup build up

an integrated charge which can be measured to provide a

*
Pilot "B" scintillator, .010 inches thick from Pilot
Chemical, Watertown, Mass.

 

 

 

 

33 .6 MeV Protons

-.__-+-_-___

<-——- Movabie Slits
*—— Quad #l
*— Quad #2

i
(P‘— Bending Magnet
| \

20°.1 Y Kink Magnet #I
‘éKink Magnet #2
/' Remote Viewer

Collimator/ PM." Target
‘— 36 Scattering Chamber

+—- Movable Alignment Slits
‘—-_ Faraday Cup

Approximate Scale
iO'

L

#1
I '

Figure 2.--Externa1 Beam Geometry.

31

figure for the number Of protons incident on the target
during a run. The entrance to the Faraday cup is ~12 inches
back from the outer wall of the chamber; the diameter Of the
cup is 2 7/8 inches and the depth is 11 1/2 inches. Any
beam which can get through the collimating slit at the en-
trance tO the chamber falls within a circle 1 5/8 inches in
diameter at the entrance to the cup; thus, there is suffi-
cient allowance for the collection of protons undergoing
small angle Coulomb scattering in the target.

NO significant difference was noted in the collected
charge due to the loss of secondary electrons emitted inside
this deep cup in experiments performed at the laboratory
where permanent magnets were placed near the entrance Of the
cup to trap any escaping secondary electrons.

The beam current and integrated charge Of the Faraday
cup were measured using an Elcor model A3103 current indicator
and integrator. This instrument was checked to be accurate
to within 1% using both external and internal calibration

sources .

2.C. 'Target Holder

 

The target holder, positioned at the geometric center
of the scattering chamber, can hold up to three 2" x 1 1/4"
target frames and can be moved remotely in the vertical
direction to eXpose any of the three targets to the beam
(see Fig. 3). A standard target, such as a thin Mylar foil

With a large deuteron yield and a well known energy Spectrum

32

.oaoommaou sOpCSOO one penance wcfinmpmemII.m mhsmfim

I

:—
wi. <Um med—2 _xomn_n_<

wdooquwh mwbznoo

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m, IL . em.
n - n gnome Baum .mEExomadd
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24mm 5?
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_ /@/ \ ago >324“.

«022138 sink Os mozSfizm

’/
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/I_2m< me<>02 20
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maoza poems: to
”1.624 5:238 .o

33

was used in tuning the system or for taking energy calibra-
tion spectra and afterwards the target of interest was
positioned in the beam without disturbing the experimental
set-up or shutting Off the beam (see Fig. 6). The nominal
target size used was ml inch square which satisfies the
requirement that all beam which passes through the collima-
tor passes through the target area and is collected by the
Faraday cup. The beam Spot size on the target was about .12
inches wide and .25 inches high.

The target holder can be rotated through 360° and
positioned to an accuracy of t2°. This amounts to a small
uncertainty in target thickness of 11.2% at target angles of
~20°, but for the largest target angle used Of 45°, a sig-

nificant uncertainty of 3.5% is introduced.

2.D. Beam Alignment Procedure

The front and rear slits of the beam collimator were
aligned horizontally with the center Of the target frame
shaft (the geometric center Of the scattering chamber) using
an Optical telescope. The collimator was leveled and the
vertical height adjusted to that of the median plane Of the
cyclotron. In this way, a reference line was determined.
The center of the 20° bending magnet also lay along this
reference line. The movable counter arm was rotated until
the center of the arm was aligned with the center line to
determine the true 0 = 0° position. Finally, the adjustable

alignment slits between the rear of the scattering chamber

34

and the Faraday cup were aligned visually leaving an .12"
gap at the center line (see Fig. 3). The proton beam was
brought down the beam pipe and the cyclotron tuned until

the desired energy resolution was Obtained. The beam inten-
sity was then balanced on the adjustable alignment slits
with the downstream magnet array by measuring the current

on the slits; afterwards the slitswere moved out of the way

in order to collect all the beam in the Faraday cup.

2.B. Detectors

 

Solid state detectors were used in a AE-E counter
telescope configuration to identify and measure the energy
Of the incident deuterons. The AE counters were silicon sur-
face barrier detectors with thicknesses between 150 and 770
microns; they were manufactured commercially by ORTEC*.

The basic design Of these surface barrier detectors
consists Of a thin p-type layer on the surface Of a high
purity n-type wafer forming a p-n junction. ~Electrical con-
tact is made to the p-surface through a gold film ~150
Angstroms thick and to the n type surface through a non-
rectifying contact. Applying a bias voltage (Vb) to the
detector causes a depletion region ** to form Of depth (D)

where:

*ORTEC, Oak Ridge Technical Measurement Corporation.

**The depletion region is the region in which an
electric field (E) is present and where exact compensation
of the charge carriers exists.

35

(l) E = E (D-X) X = perpendicular distance
(microns) in the n-
type neterdai.measured
from the p-type surface.

(2) E - 4.2 x 10 (V ) p = n—type resistivity
MAX b/pn n in Ohm-cm
(3) D=O.5 Voan (for n-type silicon)

E is in volts/cm, D in microns of silicon, and Vb in volts.
The Operation Of the surface barrier detector is
analogous to that of an ionization chamber. Charged parti—
cles transiting the depletion region give up their energy by

creating electron hole pairs (~3.5 ev/pair); the electric
field present (E) separates the created charge carriers and
sweeps them out of the depletion region. The motion Of
these carriers induces a charge Q in the external circuit
which is proportional to the energy lost in the depletion
'region. An extensive treatment on the Operation Of these
detectors,including performance characteristics and noise
'figures,can be found in reference [42].

The E counters were lithium drifted silicon detectors
with a nominal thickness of ~3 millimeters. All of the
energy spectra presented in this work were taken with com-
mercially produced devices, however preliminary work was
done using lithium drifted counters which were fabricated
by the author. The operation Of these devices is similar to
that Of the surface barrier detectors. More details on their

Operation and construction can be found in Appendix I.

36

A 3 millimeter thick lithium drifted silicon detector
will completely stop 30 meV deuterons, SO that by selecting
AE counters with depletion depths between 150 and 770 microns,
31 to 34 MeV deuterons can be completely stopped in the AE—E
counter system. The minimum energy deuteron which can be
detected is ~6 MeV. This allows a minimum Of'2 MeV of the
incident deuteron's energy to be collected by the E counter

for particle identification purposes.

2.F. Counter Telescope Assembly

The counters were mounted in standard holders fitted to
a counter track. The track is accurately positioned on a
movable arm inside the scattering chamber so that the center
line Of the counters goes through the geometric center Of the
chamber. The remotely movable arm could be rotated to ~175°
on either side of the incident beam direction and the position
of the arm was read remotely to within an uncertainty of
30.4°. On the counter track, directly in front Of the AE
counter is a tantalum collimator, .060 inches thick (see
Fig. 3). This thickness will stop ~44 MeV.deuterons and ~34
MeV protons. The diameter of the collimator Opening is 0.152
inches which corresponds to an angle subtended by the counter
in-the scattering plane of 1 1° for the particular geometries
which were used. There is a second OOpper collimator, 1/4
inch thick with a 1/2 inch diameter Opening, placed 2 inches
in front Of the tantalum collimator (see Fig. 3). This
arrangement insures that the sensitive area of the counters

is-only exposed to charged particles originating from the

37

target area and not to those scattered from the beam colli-
mating slits.

The E counter is mounted in a c0pper holder which was
cooled to dry ice temperatures (~-78°C) by pumping cooled
alcohol through a piece Of OOpper tubing affixed to the top
of the mount. The alcohol is pumped from a source located
outside the scattering chamber through flexible plastic
tubing.“ Good charge collection was possible in the cooled
counters and the deuteron energy resolution Obtained was
100-130 KeV. In most cases, the cooling lowered a leakage
current of the order of microamps at room temperature by a

factor Of ~100.

2.G. Electronics

 

Signals from the E and AE counters are carried by cO-
axial cables** to TENNELEC model 100B charge sensitive, low
noise, preamplifiers which are located directly outside the
scattering chamber. The preamp outputs are routed to a
particle identification system [43]. A brief description
Of the system and its use in this experiment follows:

A beam of 34 MeV protons on a target (A) will produce

a large number Of reactions, A(p,x)B, where x refers to

_

a
Imperial-Eastman poly-flo tubing.

an
Two types Of cable are used:

(1) Sup. 6244 (capacitance/ft. = 9.3 pf, characteristic

impedance = 1259).

(2) RG-62 (capacitance/ft. = 13.5 pf, characteristic
impedance = 930).

38

protons, elastic or inelastically scattered, deuterons, tri-
tons, alpha-particles, etc. An energy pulse in the counters
could originate from any of these reaction products, since
there is no significant difference in the ionization produced
by a proton, deuteron, triton, etc. with the same energy E.
In this series of experiments, it was necessary to distin-
guish between deuteron energy pulses and energy pulses from
other particles. This is the underlying reason for detect-
ing a reaction product's total energy (E + AE) in two por—
tions, i.e. by a AE counter and an E counter.

The first two components of the Goulding system consist
of a set of matched amplifiers (see Fig. 4) which amplify
and shape the E and AE pulses. A coincidence between the E
and AE pulses is also required before either signal is
allowed to proceed further. A timing pulse, which refers to
the crossover Of the doubly differentiated AE pulse, is sent
to the mass generator, as well as a coincidence pulse which
insures that both the E and AE pulses are present.

The E and AE pulses from the matched amplifiers are
now sent to the particle identifier which:

(a) adds the E and AE pulses to produce a pulse

(E + AE) proportional to the total energy of
the detected particle.

(b) generates a pulse (P) whose amplitude is depend-

ent upon the mass and charge of the detected

particle.

39

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40

(0) contains the logic circuitry necessary to require
a coincidence between the (E + AE) output and
selected (P) pulses.
The Operation of the second function of the mass generator
(b) is based on the empirical range-energy relation (4) which
is obeyed by particles in the energy range, 10 to 100 MeV.
(4) R = a(M,Z)Eb R = particle range in absorber
(silicon)
a = constant depending on the
mass and charge Of the

particle

E = incident particle's energy

0‘
II

constant (~1.73)

Consider a particle (mass M, charge = Z) about to
enter the AE-E counter telescope with total energy (E + AE).
The range Of this particle (R1) in the counter medium

(silicon) is from (4),

(5) R1 = a(M,Z) (E + AE)b

After penetrating the AE counter, the particle has energy

(E) and its range in silicon is now given by (R2), where

[(6) R2 = a(M,Z)Eb

However,
b
1

(7) d = Rl-R2 = a(M,Z) [(E + AE)b — E

41

where d is the thickness of the AE counter. Equation (7)

can be rewritten,

d _ b
P.— a M,Z - (E + AE) - E

b

The quantity (P), which will be henceforth referred to as
the "mass" pulse, is characteristic of the type Of particle
being detected and its value establishes the identity of

the particle which produces the AE and E pulses. The heart
of the particle identifier is therefore a function generator
whose output is equal to the input (E + AE and E) raised

to a power of ~l.73.

The output pulses from the particle identifier
("mass",E + AE) are now displayed in a 2 dimensional mode
on a 4096 channel analyzer.* The "mass" pulses are also
routed through a single channel analyzer (SCA) whose output
is necessary to satisfy a coincidence requirement set for
the (E‘+ AE) pulses before they leave the particle identifier.
The window on the SCA is now closed until mass pulses corre-
sponding only to deuterons provide the coincidence required
for the (E’+ AE) signal and hence only those total energy
pulses corresponding to detected deuterons are fed to the
4096 channel analyzer. The analyzer is then set in a one-
dimensional mode with an input Of (E + AE) pulses from
detected deuterons; the Spectra displayed in Chapter 4 were

taken in this manner.

¥

5
Nuclear Data ND-160F 4096 channel analyzer.

42

Figure 5a is a one dimensional analyzer display Of the
"mass" pulse output from the particle identifier showing
peaks correSponding to protons, deuterons, and tritons;
Figure 5b is a similar Spectrum with the window set to allow
only deuteron pulses to get through. If Gaussian shapes are
assumed for the deuteron and proton peaks in Figure 5a, less
than 0.1% Of the deuteron pulses are excluded by setting
the gate and less than .0011 Of the proton pulses are in-
cluded in the deuteron peak. (These spectra were taken with
essentially no dead time on the analyzer.) The second
(lower) spike on the proton peak results from protons which

are not completely stopped in the E counter (dE/dx protons).

2.H. Data Processing,

Deuteron Spectra were taken in 1024channels and the in-
formation was punched out on paper tape. The paper tape was
then fed into an IBM tape-card converter and the card output
processed by a computer program, PLOT', which gives a linear
or semi-log plot Of the spectra and a channel listing. The
peaks were then stripped from the background by hand and the
actual cross sections determined by a computer program,
SIGMA.** Kinematics calculations, necessary for the deter-
mination of optimum detector depths and target thicknesses,
were Obtained from a computer program, 8-BALL,n which does

a relativistically correct kinematic calculation. Most of

 

a
PLOT was written by P. Plauger.

an
SIGMA and 8-BALL were written by L. Kull.

43

 

WITHOUT DEUTERON GATE

.—-—— deuterons

tritons

 

 

i I

WITH DEUTERON GATE

 

NUMBER OF COUNT S

 

 

 

 

1 1 1 4 1 1 1 1 1 1
I00 200 300 400 500 600 700 800 900 I000

CHANNEL NUMBER

 

Figure 5.--Mass spectrum with and without deuteron
gate.-

44

the computer programs were run on the Michigan State Univer-
sity CDC 3600 computer, however plots of the last few spectra
were Obtained from a revised version of PLOT running on the

MSU Cyclotron Laboratory's SDS SIGMA 7 computer.

2.1. Targets

 

The 6Li targets were made by rolling isotopically

enriched lithium (99.32% 6Li) between two precision ground
rolls to a thickness Of ~1.9 mg/cme. The lithium can be
reduced in thickness without tearing if care is taken to

keep the distance between the rollers set uniformly and the
spacing Of the rollers is reduced in steps Of .001 to .003
inches. During the rolling process, the target and rolls

are covered with a film of mineral Oil to prevent the lithium
'fkmmloxidizing during the rolling process. Before the target
is inserted in the scattering chamber, it is placed in a
kerosene bath in order tO remove the mineral Oil. The kero-
sene rapidly evaporates in the vacuum. The scattering
chamber itself is filled with an inert argon atmosphere
before inserting the target and again before the target is
removed from the chamber for the purpose of weighing it.

With these precautions, a typical Observed oxygen contamina-
tion was ~l.5%. The 7Li targets were similarly fabricated
from isotopically enriched lithium (99.993%7Li) with thick-

nesses Of ~2.3 mg/Cm2-

9 2

The Be target was a commercially rolled, 2.06 mg/cm

lO

foil of natural beryllium (100% 9Be). The B targets were

“5

purchased from the Nuclear Division of the Oak Ridge National
Laboratory. They were made by depositing a layer of boron
(92.15% 10B) on a glass slide using an electron gun. The
film of boron was fastened to a target frame and then
floated off the glass slide in water. This resulted in a
self supporting foil 158 ug/cm2 in thickness (calculated by
ORNL). The target thickness was remeasured using an alpha
particle thickness gauge with 5.u8 MeV particles obtained
from an 2ulAm source. Previously, the thickness gauge
measurements proved to be within 13% of the calculated value
for standard mylar targets. The result for the 10B target
was 165 ug/cm2; this is mu.2% from the ORNL value and hence
in good agreement with it, since the ORNL figure is probably
good to within 15%.

The 11B targets were made by using an electron gun to
deposit isotOpically enriched boron (98.05% 11B) on a carbon
backinngO ug/cm2 thick. The difference in Q value for the
reactions llB(p,d) and l2C(p,d) is ~7.2 MeV so that the car-
bon contamination does not interfere with the strongly
excited levels of 10B.

Natural boron targets were also made by making a sus-

ll

pension of finely ground natural boron (80.22% B and 19.78%

10B) in a solution of polystyrene (C6H CHCHZ) dissolved in

5
carbon tetrachloride (CClu). A few drops of the mixture are
placed between two glass slides to spread the liquid out.
When the CClu evaporates, a thin foil (1-2 mg/cmz) can be

peeled off. The ratio of the ground state differential

M6

cross sections for the llB(p,d)lOB and 10B(p,d)gB reactions
was obtained with the natural boron targets at several
angles; this ratio was used in conjunction with the differen-
tial cross section measured with the self—supporting lOB
target to obtain the absolute differential cross sections

for the llB(p,d) reaction. From these figures, the thick-
ness of the 11B deposited on the carbon backing was deter-

mined to be 53th ug/cmz.

CHAPTER 3

ESTIMATES OF UNCERTAINTIES

3.A. Beam Energy

 

The energy of the incident proton beam was determined
by the kinematic crossover method [44] and by an independent
range measurement. The crossover method is a technique in
which the angle is measured where protons inelastically
scattered from the 9.63 MeV state of 12C have the same energy
as those scattered from hydrogen. This angle uniquely de-
fines the incident energy of the proton beam. Measurements
were made on both sides of the beam line so as to cancel out
any asymmetries in the measurement. The protons scatterd
from a polystyrene target were detected at an average cross-
over angle of 33.910.2° which correSponds to an incident
proton energy of 33.4 t .3 MeV. The detected proton's
energy at this angle is m22.9 MeV and is easily stopped with
a combination of a 3mm lithium drifted silicon detector to-
gether with a 770 micron surface barrier detector.

The energy was also measured by observing the protons
elastically scattered from a 12C target after they have
passed through a precision ground aluminum block of thick—
ness 1,165.4 t .3 mg/cm2. The protons passing through the

'block are detected by a silicon surface barrier counter.
47'

48

Table 3 shows the average energy of the protons which were
through the block as a function of the energy at which they

enter it.

TABLE 3. Average energy (EAVG) of protons emerging from the
energy calibration block as a function of the energy at which
they enter (BIN).

 

 

 

EIN (MeV) EAVG (MeV)
30.130 0.0
30.180 1.0
30.290 2.0
30.435 3.0
Notice that there is a magnification, AEAVG/AE = M28
IN

in the range AB = 1-3 MeV. This system yields a sensitive

AVG
measure of the incident energy since any small change in the
incident energy (GEIN) is reflected as a measured change
GEAVG = MonIN. ‘Measurements were made on both sides of the
incident beam to eliminate asymmetries in the measurement.
Once an angle vs. AEIN in curve has been determined, refer-
ence to kinematic calculations for the reaction 12C(p,p)
yields the proton beam energy. The result for the method
was Ep = 33.6_i_.2 MeV. This method was then used as a

rapid check on the incident energy for subsequent runs; the

results for the incident energy always fell within 200 keV

49

of the above value. As can be seen, results from both

methods agree to within their respective experimental errors.

l

3.B. Target Monitor

A cylindrically shaped cesium iodide crystal, 0.5
inches long and 0.25 inches in diameter, was mounted on a
photomultiplier tube and placed at a fixed orientation
relative to the incident beam, usually at 135° relative to
the incident beam direction on the opposite side of the
beam line from the movable AE-E detectors as shown in
Figure 2. The pulses from protons elastically scattered
from the target were selected out with a single channel
analyzer and scaled. The ratio (R) was recorded for each
run where,

_ Q
M cos 0

:U
I

T

Q = charge collected in Faraday cup (coul.).

(l) M

number of elastically scattered protons detected
by monitor.

9T: target angle (this term accounts for increased
target thickness due to a change in the angle
of the target).
Significant changes in R between runs can reflect the follow-
ing experimental problems:
(1) a change in the target thickness due to the wander-
ing of the beam spot over a non-uniform target.

(2) a malfunction of the target rotation mechanism.

50

(3) a malfunction in the charge integrator or the
presence of an obstacle in front of the Faraday
cup.

(4) destruction of a portion of the target.

In short, this additional counter monitors the performance
of the target and charge collection devices. Typical figures

7

from the experiment, Li(p,d)6Li, are given below.

10

R (measured) = (.962 x 10- ) i3.2%

Considering the uncertainty in the target angle (CT), the
accuracy of the charge integration circuitry, and the
statistical uncertainty in M, the calculated uncertainties
are:

uncertainty for forward angles = 12.1%

uncertainty for backward angles = 33.7%
The importance of using the monitor is realized if the ratio
R is calculated and compared after every run to provide the
experimenter with an up-to-date measure of the state of the

target and charge integrator system.

3.C. Differential Cross Section
The differential cross section (g% (0)) for A(p,d)B

is defined [45] for solid targets by the expression (2).

 

()3 2’2." = m r (“z")
2 00169) MTa/R

51

Z
3‘
(D
"S
(D
:3
II

d no. of counts in the deuteron group corresponding
to the state, B.

N6 = no. of protons incident on the target.
T = no. of target atoms/cm2

d9 = solid angle subtended by the detector.

This expression can be expressed in terms of directly

measurable variables with the result (3),

-7 mR‘q “fr (”7)
.. 9' 0 z 5"
<3) fimpzfl 6)” Q”

where R = distance from target to detector (in).

0..
II

diameter of detector collimator (in).
a = gm. mol. wt.of target (gm/mole)

target angle (see Fig. 2)

”*3?

= collected charge in Faraday cup (microcoulombs)

target thickness (mg/cmz).

.<
II

A list of the estimated uncertainties for those
quantities for which the uncertainty is.: 1.0% is given in
Table 4.

The uncertainty in the detector angle must also be con-

sidered, but its effect on the uncertainty in the cross

section depends on the value of %e(%%). For angular dis-
tributions with steep slopes, such as the forward angles

of the 9

Be ground state distribution; this correction is as
large as flag for relatively flat distributions, the cor-

rection is negligible.

52

TABLE 4.—-Estimated uncertainties in parameters related to
the measurement of the differential cross section. Two

values representing the extremes are given when the uncer—
tainty varies considerably between particular eXperiments.

 

 

Quantity Uncertainty

nd 3.2%

R2 1.3%

cos 6t 2.2% (30°); 3.5% (45°)
Q . 1.0%

d2 1.3%

Y 2% (9Be); 7% (118)

 

The estimate for the total uncertainty in do/ml falls
between 16% to 19% for the individual experiments. These
figures do not include contributions from the uncertainty in
separating the deuteron peak from the background. In general,
however, the differential cross sections measured at forward
angles with little background and small target angles have
an uncertainty of i6% to8%, whereas in the backward angle
measurements the uncertainty due to peak stripping is sig-
nificant and the measurements of the differential cross

section are accurate to within 1 7% to 12%.

3.D. Energy Resolution

 

The deuteron energy resolution varied between 100 keV
(mylar calibration spectrum, see Fig. 6) to 160 keV (11B)

with typical figures of 120 keV. Main contributions to

53

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505: ”13:11 $023.30..
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08.

 

 

54

this figure come from electronic noise, incident beam reso-
lution, target thickness, and detector resolution. Elec-
tronic noise for the entire system from the counters to

the E +AE output was m70 keV. Assuming single turn extrac-
tion and less than 60 phase width, the best estimates of
the cyclotron designers place the energy resolution of the
34 MeV proton beam at m35 keV. The target thickness intro—
duces a spread in the energy of the outgoing deuterons of
m55 to 75 keV depending on the particular target in use.
Since the proton beam cannot be magnetically analyzed at
the present time, no accurate figure can be obtained for the
detector resolution, but the combined effect of detector
resolution plus incident beam resolution introduced an

energy spread on the order of 75 keV.

CHAPTER 4
EXPERIMENTAL RESULTS

4.A. 6Li (p,d)SLi

Figures 7 and 8 show deuteron energy spectra taken
at lab angles of 15°, 35°, and 120° which show deuteron
groups corresponding to the ground state (JTT = 3/2—) and
16.60 MeV state (JTT = 3/2+) of 5Li. The location of the
broad ground state of 5Li (I = 1.3 - 1.4 MeV) just above
the a + p separation energy (Fig. 9) is an inducement to
use a simple cluster model [46] description of the state,
consisting of an alpha particle coupled to a proton with
orbital angular momentum 2 = 1. Possible spin and parity
assignments for this configuration are 3/2- and 1/2—. A
very broad 1/2- level (I = 3—5 MeV) has been reported at
an excitation energy of 5 to 10 MeV [10]. A deuteron group
corresponding to this level has not been identified in the
energy spectra, but because of its large width, it may be
impossible to isolate it from the background due to three
body breakup. It is also possible that a significant frac-
tion of the yield of this 1/2‘ level lies below 5 MeV
emcitation energy, and that the deuterons corresponding to

thiss state have been included in the tail of the ground

Statie peak.
55

56

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sh ooupooon mam50H>mpo a scam soapsnfianOO m modaoca has xwoo mumpm

 

 

 

 

 

 

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57

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mum—2:2 4mzz<Io

 

 

 

 

 

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000.

'13N NVHO / SiNnOO

58

 

/ l6.6 3 +
/////§;;;;§§§7//‘2 / _3 H, 2 + d

 

 

 

 

 

j? 28.8 MeV
V///////////,3/2'/
/////////////,-/,
4He+p_
°Li+p- d

 

Figure 9.--Energg level d%agram of 5Li. Only the states

observed in the gLi (p, d) Li reaction are shown and the

excitation energies listed are those measured in this
.reaction.

59

No other levels have been reported [6] below the rela—
tively narrow (F = 360 keV) 16.6 MeV state which lies just
3

above the He + d separation energy as shown in Fig. 9.
There, in a situation analogous to that of the ground state,
a simple cluster model description consisting of a 3He
nucleus coupled to a deuteron with Q = 0 seems appropriate
for this state. The above configuration allows JTr values

of 3/2+ and 1/2 +.

The 16.6 MeV level of 5Li(J1T = 3/2+) was strongly
excited in this reaction and a search was made in the
vicinity of this peak in order to detect the presence of the
l/2+ member of the doublet. Various incident proton energies
were tried between 30 and 40 MeV, as this was the experimen-
tally obtainable range of energies where the available
phase space for competing three body breakup was calculated
to be smallest [47]. No evidence was found that would locate
the excitation energy of the 1/2+ level. There was also no
indication that a (3/2+, 5/2+) state previously reported at
20 MeV excitation is excited in this reaction [48].

Figure 10 shows a comparison of the angular distribu—
tions for the reaction 6Li(p,d)5Li (g.s.) calculated using
the distorted wave Born approximation assuming the neutron
was picked up from the ls, lp, and 1d shells (orbital angular
momenta in = 0,1 and 2, respectively). In the same figure
it can be seen that the experimental angular distribution

5

for the ground state of Li shows a characteristic shape for

transfer of a neutron from the 1p shell (in = l) by a direct

60

 

IOO
50 ' . .
r- Ep = 33.6 MeV
-_,$ ' /'---\ I Ground State I'd/2'
m: X i I6.SO MOV State
it. \ \' J" W
.I \‘ \\
IO b/ \fi \. .
: ._ ‘\ \_\ ------—- ls pickup
: g \_ ---- lp pickup
5 - \\. \ ----- Id pickup
- . \I \
A 2 \ \ \
h i \ i \
W b ', \\ \ .\
\ x I\ \.
a '1 \\ I \.
é - /'° \\ \' \\
b 6 a \ \\ \ \.
\ \
6L0 g \\ ! \
I "" 1 \\ \
: Q‘\u \‘ \\
: ' \ \‘!\l \x
5 - \
- E ;K\h/ar \ \\r/J\\l
- \\\ \§ /!
~ ‘\ \'

‘2 i \

 

 

' l I I J l I l I I I I l l l I
IO 20 30 4O 50 SO 70 BO 90 IOO IIO I20 ISO I4OI50

ecumeg)

 

Figure 10.--6Li(p,d)5Li angular distributions. The error

bars shown only represent the uncertainty due to statis-

tics and the solid lines are drawn to guide the eye. The

dashed line shows the DWBA fit to the ground state differ—
tialwcross section.

61

reaction mechanism (Fig. 10). For Q values in the range

0 to -20 MeV, the angular distribution has a first peak in
the neighborhood of 10° (center of mass angle) for the pick-
up of a lp shell neutron from a target with A = 6 to 11.
Angular distributions for the same cases involving the
pickup of a ls neutron or a 1d neutron have a first peak

at 0° and approximately 20° respectively. The angular dis-
tribution for the 16.6 MeV state could not be obtained for
lab angles greater than 35° because the deuteron peak could
not be distinguished from a strong background due to three
body breakup. This state is excited by the pickup of a ls
neutron from 6L1 but, due to the small amount of data,
little can be said concerning the shape of the angular

distribution.

4.B. 7Li(p,d)°Li

 

Four deuteron groups were observed in the energy

7Li (p,d)6Li reaction corresponding to

spectra from the
states of 6Li at 0.0, 2.15, 3.57 and 5.38 MeV excitation
energy (Figs. 11 and 12). A small peak corresponding to

the ground state of 15

0 indicates the presence of a small

amount of‘oxygen contamination on the target (less than

1.5%). No evidence for any other strongly excited states

was found up to 18 MeV of excitation energy for 6L1.

Deuteron groups corresponding to the positive parity states
6

of Li at 4.57 and 6.0 MeV were not observed; hoWever,

these states are broad and if weakly excited the peaks

62

em.a - oo use

0001

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COUNTS / CHANNEL

I000

750

500

250

I000

750

500

250

63

 

 

 

 

 

 

 

 

 

 

 

 

'Li(p.d)'Li ’«3
Ep '33.6 MeV ‘35 I:
F- :1 3a .1
9“. 840" “’i '3
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CHANNEL NUMBER

Figure 12.4-7Li(p,d)6Li spectra at 40° and 110°.

64

would be difficult to extract from the background. The
shapes of the angular distributions for the 0.0, 2.15, 3.57
and 5.38 MeV states are characteristic of in = l pickup

(see Fig. 13). This fixes the relative parity between the
initial and final state [49], in particular, this assigns

a positive parity to the 5.38 MeV level. A positive parity
fits in with the tentative T = l isospin assignment [10] for
this state and places it in the isospin multiplet of which

6He(JTr = (2)+) is a member.

1.80 MeV state of
It is interesting to note that the slopes of the first

peak of the angular distributions for the T = 0 states at

0.0 and 2.15 MeV are much steeper than those of the lowest

T = 1 states at 3.57 and 5.38 MeV. This may have some

implication concerning the isotopic Spin dependence of the

reaction mechanism.

4.C. 9Be(p,d)8Be

 

The energy spectra from the reaction 9Be(p,d)8Be
(see Figs. 14 and 15) show deuteron groups corresponding
to strongly excited levels of 8Be at 0.0, 3.1, 11.4,
16.95, 17.62, 18.18 and 19.21 MeV. A very small yield was
observed for excited states of 8Be at 16.6 and 19.15 MeV.
The first three levels of 8Be can be understood, at least
qualitatively, by a cluster model of two alpha particles

+ and 4+ (Fig. 16)

excited into the rotational sequence 0+, 2
[50]. Measurements of the differential cross section for

the 11.4 MeV state (J1T = 4+) were made from 40° to 140° in

65

 

 

'O‘E‘N'N. 7 _.
: \ Li(p.d)6Li
i ‘\ E. = 33.6 MeV

14— \N\\ 1

\ \\ ,1\ GROUND STATE

'\ J'= 1* T=o
L\ \ \ ‘/'/‘

...../\,
:2 J
,/

E . . .
s \ \ \1/
.o .51 \\ \ ‘ ~~~~~~~~~ 2.15 MeV STATE ‘
E Z '\ .11;/' J ' = 3* T= 0
.313 \1/
Vi“ , 3.57 MeV STATE
.1. i\ \*”’*\ J'=O+ Tel _
; \I \ /./
s \\’/I
__ \f/I\ I

I

5.38 MeV STATE

1} I

r\*\. J'=( 1*T=1 -
\\$_%/{

IIIIIli

 

 

1

V

l

V

e L l l 1 l l l l l l l

10 's'o - 5'0'76'9'0111'0' 1:310
ecu (deg)

Figure l3.--7Li(p,d) Li angular distributions. The
DWBA fit to the ground state differential cross sec-
tion is shown by a dashed line.

 

15'o 17'o

66

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67

 

 

 

 

 

 

 

’Be(p,d)'Be
E,=33.6Mev
0....‘60’
15
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250

CHANNEL

500

NUMBER

 

750 IOOO

Figure lS.--9Be(p,d)8Be deuteron spectra at 60° degrees.

Ehe broad peak corresponding to the 11.4 MeV level of

Be can be clearly seen at back angles where its yield
is comparable to that of the narrower levels.

68

the lab with a large uncertainty due to the width of the
state (Pm? MeV) [10] and a high background. The data show
little structure in this range, the average value of the
cross section falling between 0.02 and 0.05 mb/sr-MeV at the
resonance. The angular distribution does not exhibit the
forward peaking characteristic of a direct reaction, since
the peak could not be seen at angles less than 35° (see Figs.
1“ and 15). This leads to the conclusion that this state
is excited principally by a compound nucleus mechanism and
_not by a direct process in which some lf admixture in the
ground state of 98e contributes to the cross section [13].
The next set of known levels of 8Be appear in the

7 7Be + n separation energies

region of the Li + p and
(Fig. 16). Previous experimental evidence has established
the fact that isospin mixing is present within each of the
three doublets (J1T = 2+, 1+ and 3+) in this region of exci-
tation energy [51,52,53,54,55]. Wave functions for these
doublet states have been calculated by mixing intermediate
coupling shell model wave functions of pure isospin with a
.charge dependent interaction [15]. The mixing coefficients
were obtained by fitting existing experimental data and
are given in Table 5. The ratio of spectroscopic factors
5(16.6)/S(l6.95) calculated using this model is l/HS [l7],

Vfllereas the ratio obtained eXperimentally is less than

1/20.

69

 

 

 

 

 

H75“ ~
CALCULATED
I-SPIN 4 50/.< ‘
MIXTURES
_46%< -—
J/ 30.2 MeV

 

 

’ '/ ‘ 2*6‘

 

980+p-d

 

0* o ‘flfl‘H!

 

 

The levels drawn

Figure l6.--Energy level diagram of Be.
h dashed lines are those weakly excited in the Be

in wi
(Pfli)§Be reaction while those drawn in with the solid lines
co1"1"'ESpond to strongly excited levels. Also shown are the

iSOSIXIn admixtures which have been calculated for the J1T
2+, 1+ and 3+ doublets (17).

70

TABLE .5.—-Experimental cross section ratios and isospin ad-
mixtures calculated by Barker [17] for the J7T = 1*, 2+ and 3+

 

 

doublets.
Ratio of Ratio of Isospin admixturesa
Doublet cross cross sec- (amplitude squared)

sections tions as calculated by

(34 MeV) (ulMeV) [51] Barker [17]
(16.6)/(16.9) <1/2o 1/25 u5%
(l7.6)/(18.2) 2.6 3.5 6%
(19.1)/(19.2) <l/20 17%

 

a50% admixture represents a doublet with maximal
isospin mixing and 0% a doublet with states of pure iSOSpin.

Some indication of the amount of isospin mixing within
the doublets can be obtained if the single particle cluster
model is used to describe the states [51]. In this case,
the (p,d) reaction will excite only one member of the
doublet if the pair is maximally mixed in isospin (50%).
Conversely, if the members of the doublet are states of
pure isospin (T = 0 or 1), both states should be observed
by the (p,d) reaction with the same yield. Table 5 shows
the data to be in general agreement with this simple model.
The experimentally measured widths for the 16.95 and 19.21
MeV deuteron groups of 103 i 15 keV and 208 t30 keV, respec-
tively, are in agreement with the previously obtained values
[10] of 83 t 10 keV and 190 keV insuring that only one of

the states in these doublets is strongly excited. The

71

experimentally obtained cross section ratios for these doub-
lets are in agreement with those obtained at Ep = U0 MeV [56].
The angular distributions for all strongly excited
states of 8Be (except for the above mentioned 4+ state)
exhibit the characteristic shape for in = l pickup (Figs. 17
and 18). The differential cross section measurements for
these states are in reasonable agreement with those obtained
for Ep = 36 MeV [59]. The relative flattening of the dif-
ferential cross sections as the excitation energy of the
state increases is a Q value effect and was reproduced in

the DWBA calculations.

u.D. lOB(p,d)9B

 

The deuteron energy spectra from the reaction
loB(p,d)9B are shown in Figures 19 and 20. Deuteron groups
were observed corresponding to strongly excited levels of
9B at 0.0, 2.33, 7.1, and 11.75 MeV and small deuteron
yields were noted correSponding to weakly excited levels at
2.8 and 1M.6 MeV. The very broad, weakly excited level

9

observed with a B excitation energy (EX) of 14.6 MeV may
correspond to the level observed at EX = 1U.9 MeV in the
same reaction using 156 MeV protons [57]. With the higher
incident proton energy, however, the 14.9 MeV level was
observed to be strongly excited with a cross section com-
parable to that of ground state at forward angles, whereas

the 3“ MeV data show the lu.6 MeV level to have a cross

section ml/lO that of the ground state at forward angles.

72

 

IIIIII
lJLLJJ

I
1

IR gBe (p,d) 8Be
_ *\ Ep= 33.6 MeV

I

\ K

Q
' .— \\I 1
- i‘x -.
: \K ‘
.. \i. -
- \ Ground State ..

1 r f \“ -:
~03; I \ {\il’.’ >1 2
‘\‘ : \és- {/4 j
13 - k \\i // -
E5 L \i ‘. ./L -
v \I ‘\\ S.
{DICB L ‘\\ x, -
“U '0 {.1 x

IIII

\ 310 MeV State
J'= 2+

. IfirWnr
\m
w/
FOO/m
.L
J
I

 

 

 

\ u
i i
_ \, \, . .
\ _ \\_J/4‘4
| —- I . .—
E \’/!‘{\ ‘ :
: !\ I695 MeV State 1
L ’\ J'= 2” -
- ! ged~§ -
\./' ~
_ i \\I l/yr§~1
\i/I -‘
I I I I I I I I I I I ‘I I I I I I I
O 20 40 60 80 IOO IZO I40 ISO |80
ecu(deg)

Figure l7.—-9Be(p,d) Be angular d stributions for the

0.0, 3.1 and 16.95 MeV states of Be. The DWBA fit to

the ground state differential cross section is shown
with a dashed line.

73

 

 

 

d_a'
d3 (mb/SIr)

 

I I I I

 

 

F \ I 9' I I I I I8 I I _i
: .\ E, = 33.6 MeV :
' ! t’§\ l7.62 MeV State ‘
\+/ \! '7 +
\ J = I
E- \! i‘\ I ‘2
" ’ *\ . /. ‘
;\! ,
/I\; \,/
3 . _
: \ l8.l8 MeV State“:
I. \I/¥\§ J7: I... :
\t -
\Isfxi {
\?\1“i-3-i,// d
I
_ 73x _
: I \ I9.2l MeV State?
- 7 - + _
: 1"é‘hq J -‘3 Z
- \, , ..
'- I\§__,§’I\I\I i / -
\i
I I I I l I l I ~I I I I I l I
20 40 so so IOO l20 I40 I60 l80

90M(deg) '

Figure 18.--9Be(p,d)8Be angular distr butions for the

17.62, 18.18 and 19.21 MeV states of

Be.

74

 

 

 

 

 

 

 

 

  

 

  

 

 

 

 

 

  

 

 

 

. . O
I I I o
12
(tr/El) .
_th (H) a. mono-am «09.x ‘
. 3' ,
(9m!) plows-m 9+!19h—. f.
.2/9 (sea) a. _ ‘ A .j
- j
ISDISOI“ ’3 8
" (era) 90"__’"7e.5'."~.
(tt't) so. ‘
(SI‘Z) Son—'- _1
st:
. (19'c)9¢.——.- .'
/ l )9 .-
3 1. ( 1. . (fl) o..—-
at 1—1 1’
(9.98.9) 331—— l.
.1“.
.‘
I“°)3||——- _
(E I '9'26'9‘) so.
" (2n. suns 1 g --
- ) ( . . .' . ID
(00mm. *.
'I”:
(9|‘9) o..—.—-=<::‘
(9'...) a. 1 wk:
. .3.
.?:‘"
v5.5
"93.
ti o
.. -".!'~,.""|O
{-3 N
> “‘3
u 1
m 2
. O
V N
d n II
V II I
m a j
2 m 0
l I I O
8 8 0 o
0
IO N _

'IBNNVH 0 / smnoo

NUMBER

CHANNEL

grees. Deuteron groups can be seen

~l%) contaminants.

um at 20 de

160(

d)9B spectr
B(~8%) and

1

due to 1

Figure 19.-lOB(p

75

.oom cam 00: pm mauoodm mmAu.qvmodlt.om mpswflm

mmmEDZ Buzz/‘10

000. 03. 000 On. N O

 

 

 

 

 

 

 

  

. ... -.., ............. 5...... . . . o
.. . . I... z
, .w .1
.11
86
t 1 w. .. oo.
1 m
1 . u
. mm
93
96 6 Com H m
t m m . a L 08
( m >05 w mm u m
C.
mm AU Q vmo.
1%.; tfiafiawaxhrfit.,aurxxamtftfix o
_ 1
m 1 1 on.
1 hm... m m... m...
.H 1.... - w w
I 1. l.\ . l
1 m. m... 00.
1
. 1
.L
1 m
r 9.. ..
0 00¢ u 0 CON
m a
M >34 0 mm u w
mm Cu .Q vmo.

 

 

 

'IBNNVHO / SiNfiOD

76

 

l4.
7%??ng 135127}

 

 

 

 

{1% 4%! y 30-6
%V ‘/ Md!

 

 

 

 

 

 

 

5LJ+a 233
BBe+p
eats/K
IOB+p-d

 

 

Figure 21.--Energy level diagram of 9B. Weakly excited
levels are drawn in with dashed lines; strongly excited
levels are drawn in with solid lines. The very weakly
excited positive parity 9B level at ~2.8 MeV excitation

is not shown.

77

A level at 9.7 MeV also reported to be strongly excited in
the 156 MeV work was not observed to be excited in the 34
MeV data [57].

Two positive parity 9

B states at excitation energies
of 1.5 MeV (J" = 1/2+) and 2.83 MeV (J" = 3/2+, 5/2+) [10]
are of special interest, since their presence in the spectra
could denote the first evidence of 2s-1d shell admixtures
in the ground state wave functions of stable nuclei with
A i 10. No evidence was found for the excitation of the
1.5 MeV level which correSponds to the 1.67 MeV level of
9Be(J" = 1/2+), however results from the lOB(p,d)gB reaction
using 11 MeV protons show a level at 1.7 MeV very weakly
excited by a compound nucleus mechanism [58]. The present
34 MeV data do not rule out, on the basis of a statistical
argument, the possibility of the same degree of excitation.
A small deuteron group (EX = 2.8 MeV) with a differ-
ential cross section of approximately 120 ub/sr was observed
at about 30° (center of mass angle), but it was difficult
to follow over an extended range of angle because of the
masking effect of levels arising from a 11B impurity in the
target (see Fig. 19). At 60°, the deuteron group corre-
sponding to the 2.8 MeV level was not masked by the deuteron
groups arising from the 11B impurities, but was not observed.
This could signify a rapidly decreasing cross section
typical of a direct reaction process and therefore Open the
possibility for an observable 2s-ld shell admixture in the

ground state wave function of 10B. The evidence, however,

78

is scanty at best and the only definite conclusion one can
draw is that any 2s-1d admixture in the 10B ground state is
very small.

A single strong deuteron group was observed corre-
sponding to an excitation energy of 11.75 MeV in 9B. There
are two previously reported states at 11.62 MeV (J" = ?)
and at 12.06 MeV excitation (JTr = 1/2‘, 3/2‘) [10] allowing
two possible explanations for the data: (1) the 12.06 MeV
state has JTr = 1/2' and cannot be excited by a direct
reaction process due to angular momentum selection rules.

In this case the single observed level has a measured exci-
tation energy of 11.75 i .1 MeV as compared with a previously
determined energy of~1l.62 : .1 MeV [10]. (2) the 12.06 MeV
level has JW 8 3/2- and is weakly excited in the reaction
causing the centroid of the doublet peak to be

shifted up in excitation energy from the strongly excited
level at 11.62 MeV to the observed value of 11.75 MeV. The
first explanation seems to be the more likely one, since the
deuteron group shows no sign of a doublet structure over a
wide range of angle and the observed width of 800 i 150 keV
is close to the previously reported width for the 11.62

MeV level of 700 i 100 keV [10].

Strongly excited levels of 98 at 0.0, 2.33, 7.1, and
11.75 MeV excitation all have angular distributions with
Shapes characteristic of neutron orbital angular momentum

transfer in = 1 (see Figs. 22 and 23) and the parity of

79

 

10.0

 

 

 

 

 

I I I I I IIOI I I I 9I I I I I r I
: f B (p,d) B I;
-' . Ep = 33.6 MeV -
_ :\k- 0 SHORT a tnNTQ,
,.\:~\\ E, = 37 MeV
10 ___ a} - ----- DWBA CALC. 1
— \.\\ :
2L /(\ \k I
1: _ I \ \‘k-a' GROUND STATE ..
Q — K "\ J'= 3/2‘ ..
E KM . \ 1\
v LO L— ’\l\ \\ l\! 1
8'8 fi kg“ 2.35 MeV STATE 3
‘!- J‘s-5'72" 3
_ "r. ,
t— \’ .—
w, \1
L0 :—/II\‘ -:
C I 1 1
: 7.1 MeV STATE 3
- L’I\I .1'= 7/2' ~
_ I I“; -.
OJ 1 1 1 1 1 1 1 1 1 1- 1 1 1 .1 1 1 1
O 20 40 60 80 IOO |20 I40 I60 ISO

ecu (deg)

Figure 22.---10B(p,d)9B angul r distributions for the 0.0,.

2-35, and 7.1 MeV states of B. The DWBA fit to the ground

Stéite differential cross section is shown with a dashed
line.

80

.Hm>mH >mz mw.HH on» now QSMAU pmzp mm madam meow on»
zaopmefixonaqm mm: mucfioa mama Hm>ma.>oz m.qa on» nwdonnp asapo mafia Umnmmv one
.mmpmpm >mz w.:a vcm m~.HH on» you mCOHpannpmHU amaswcw mmA©.QVmOHII.mm mpswfim

2.53 5m

 

 

0m. 0m. 0! ON. 00. om om 0v ON 0 .
A A A A A A A A A T A A A A A A A _o
A-N\mvuhA..
.. “.55 >22 we. w -
lim/ .A 1
I \m /x x 1 p p
H m/m\m /W/ M a/MKM‘A: H U D
W .ANRAuuA, A/A/A .m 0.. w
MES >22 m5: 0.
A w
1 (K .. U1.“
1 . a 1
H >22 m mm u m .1.
T .Q 1
m mefiw Aflfiv vvmmwnv— U
A A _A A r A F A A A A A A A A r A 1 0.0.

 

 

 

81

these levels is negative. Poor statistics for the lu.6
MeV level data do not allow the definite assignment of the
picked up neutron's orbital angular momentum, however the
dashed curve in Figure 23 is approximately the same shape
as that observed for the ll.75 state and shows that an zn = l
assignment is a reasonable possibility for this state. The
angular momentum assignments for these states have been made
on the basis of the measured spectroscopic factors for

these levels and will be discussed in Chapter 6. Table 6

is a list of the measured excitation energies and line

widths for the observed levels of 98.

TABLE 6.--Measured 9B excitation energies and widths for
deuteron groups observed in the reaction 10B(p,d)9B.

m

 

Excitation energy (MeV) Width (MeV)
0.0 NO
2.35 1 .02
7.1 ‘1 .2 1.95 i .2
11.75 i .1 0.850 i .050
111.6 i .2 1.35 i .2

 

u.E. 118(p.d)1os

 

The deuteron energy spectra from the llB(p,d)lOB
reaction (see Figs. 24 and 25) show deuteron groups cor—

responding to strongly excited levels of 10B with excita—

tion energies of 0.0, 0.72, 1.76, 2.15, 3.57, “.75, 5.18,
and 6.0M MeV; levels of 98 with excitation energies of
6.57 and 7.5 MeV were observed. The deuteron group cor-

responding to a 10B excitation energy of 5.18 MeV could

82

.m>onm comm Edmuomam QHH_
wcoppm on» CH chuHSmop .mconmn cognac mEo\w: om1 am no woodpoaw>m mHH mo Nao\m:
am no Umpmfimcoo powpwu one .mmmhwmo om pm Eduuomam commusmo moHAw.avaHII.zm mmswfim

mwmzaz JMZZ<IU

 

   
  

 

 

 

 

 

 

 

 

 

 

 

000. on» 000 com 00
b
1 . . . . . . ... .evfiNNVAWvV.’ .Hnu: N.~.\r¥c...fi..o.n \J- .\ ......4 . .. 01%....1.‘ ul .1 1 a
. . I I 1 o. 1. ... .Io .... I . . 2. I:
‘ J fl . xi .4 .<......x ....<..,..1...¢.1u....%1....... . ... A
, A
n . A A
8 , _
1 . . _ _ A A
m. 1 1 1 1 1 1
1 . m. %m _ m Q m.« m
a .m,+ a m w M m
A 1 _ .... .
‘ A w 1w. w m m m w
. _ _ .1 _ u A A ( ( ( ( (
1 1 1 1 m 1 1 1 1
1T % nwnw co m%% aw aw 1100.
m, H a m... .mm m m...
L 1. .l c. [I .O C.
R m m H mm w U.
I 0 I .6 I‘m. KIA... .6
o o o o z I 6
0’- a
( + +
.c. 9
m. 9
A _
a Z
00 00
A U .u
[
11 A 1oo~
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.10
fl m<A
A1 oON u 0
31 . a
..m >22 awn" m
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A A A com

WBNNVHO / SanOQ

83

 

 

"8‘ 9.0)..8

23 on 111

 

 

 

 

       

33. on I
«Snell
......NAFI

:35... II

3b.? ADE
3.6 Ami III
30.0.00.
2.9.900.

 

56.0.0: I

Ep - 33.6 MeV
e... - 40°

 

 

 

200

m o

e“. - 120°

 

 

 

 

 

15225.8 \ 95500

I000

750

CHANNEL NUMBER

Figure 2S.-—llB(p,d)lOB deuteron spectra at “0° and 120°.

 

8H

IOB

 

 

 

 

 

 

 

 

 

 

 

 

+ +
{ 1.1.5. §JAGAZA pAL'iIlLQI.
7.47 (24)
9
361-9. .612: ........ z-
{5.92.6.3 2*,O;Z
{5.l7,5.l8 2+,I,1*, //
1 30.8
6 _ 4.77 (22 I0 /( M V
Ll+a 9
3.591 2*J)
2Ll5 |+,o
|.74 0*.l
(17I7 . P30
B’JD
9.23l
ll
10 + B-d
Figure 26.--Energy level diagram of B. Weakly excited
levels are drawn in with dashed lines; strongly excited
levels are drawn in with solid lines. Brackets indicate

groups

of levels which could not be resolved experimentally.

85

103 [10] at 5.16 MeV (J" = 2+)

correspond to known levels of
5.18 MeV (J1T = 1+) and 5.11 MeV (JTr = 2—) excitation. The
5.11 MeV level should only be weakly excited, since it can
only be excited in the direct reaction process by pickup of
a 2s-ld shell neutron. The 5.16 and 5.18 MeV levels can
both be excited by a direct reaction mechanism and deuteron
groups from the two could not be separated with the 160 keV
energy resolution obtained in this eXperiment.

The deuteron group corresponding to 6.0“ MeV excita-
tion energy in 10B could correSpond to previously observed
levels at 5.92 MeV (J"T = 2*), 6.0M MeV (J11 = u+), and 6.13
MeV (JTT = ?) excitation [10]. The level at 6.0M MeV cannot
be excited by a direct reaction process due to angular
momentum selection rules, hence principal contributions to
this group are from the 5.92 MeV and 6.13 MeV levels.

No evidence was found for the excitation of negative
parity states at 7.0 MeV (JTr = 1’), 7.8 MeV (JTr = l“), and
8.1 MeV (JTr = 2‘) excitation [10] which might denote con-
figuration admixtures from the 25-1d shell in the ground
state wave function of 11B. However, as mentioned pre-
viously, deuterons corresponding to the 5.11 MeV state
(J" = 2-) of lOB could not be resolved.fimm1strongly ex—
cited positive parity levels,nor could two negative parity
states in the 7.5 MeV region of excitation. One can
therefore state that there is no direct evidence for sizable

23-ld admixtures in the ground state wave function of 11B.

86

The angular distributions for the 10B levels at 0.0,
0.72, 1.76, 2.15, 3.57, and ”.75 MeV excitation have shapes
characteristic of the direct pickup of a 1p neutron (see
Figs. 27 and 28). The deuteron groups corresponding to 1013
excitation energies of 5.18 MeV and 6.0“ MeV have similarly
shaped angular distributions. This indicates that contri—
butions to the 5.18 MeV group from the 5.11 MeV level
(JTr = 2-) are indeed small as previously conjectured, and
that if the 6.0“ MeV group contains contributions from the
6.13 MeV level (J1T unknown), the parity of this level is

positive.

87

 

 

 

 

.- I I T I I III I I I I '3 I T I I I I
B ( p.d) B
I0.0 E- {'9’ E9: 33.6 MeV -E
; --- DWBA CALC. j
P {\{\i !"\'\\\ .1
\ \R§\
'~°“' 5 VA.\ GROUND STATE ‘5
g \ J' = 3’ :
1 “~\- -
'- i‘!‘ “x‘ 'I
A 1- % \\\ J
3: 1- % §i‘I-i—i 4
en 1\ \1 ~\
3 f “\i -----
1.0 \ \§ 0.72 MeV STATE 1
E \I 7 _ + "l
v I- \% \\ J ' I :
bl c: L 1
-e 'o - 1k, \N -
_ \ ‘1 1 .
\ \i"”\
'0 1 I\ 1.76 MeV STATE
- r t = + -:
: \¥4_h1 i a o :
.. \ I _,
- {/4 s
_ \I/H\ I/ A
\* 1
r
1 1s—1
3 2.15 MeV STATE 7-
I J'= 1* I
l l l l l l l l l I l l 1 I l l l
O 20 4O 60 80 ' IOO IZO I40 I60 ISO.
em (deg)
Figure 27.-—llB(p,d)lOB angular distributions-for the

0.0, 0.72, 1.76, and 2.15 MeV states of 103. Thev
DWBA fit to the ground state differential cross section
is shown with a dashed line.

88

 

”B(p,d)mB

LO _— 'T.

1.,\ E,=33.6 MeV 3

- {\I‘I'Ij} A

0.1 :_ \HPI\§ 3.57 31w 2STATE q

: \ I

t \l -

\IrI-fixi 4.75 MeV STATE -

'5 °-' .- ‘I J = (2) -:

(n : Pr}\1 I

\ \V \

'3 { 1~ {\ikN

bl 13 ~ \ -

'0 13

1.0 _. \{VLKN 5.l8 MeV STATE -;
R (5.|7+5.l8 - .1'=2‘,1*):

I\\ ‘

 

 

 

! Q J
\i/
LO :- a
I I\ j
- I -
A I 6.04 MeV STATE A
- \H‘I (5.92+6.I3 - .1 =2‘,?)*
A \I—‘I‘I\, A
' Ir!
./
OJ 1 1 1 1 1 1 1 1 1 1 1 1\ 1 1 1 1
o 20 40 so so - ICC 120 140 160 130
11 109”, (deg)
Figure 28.-- B(p,d) B angular distributions for

the 3.57, 4.75, 5.17 + 5.18, and 5.92 + 6.13 states
of 10B.

CHAPTER 5
DWBA ANALYSIS

5.A. Elastic Scattering Measurements

Angular distributions for the elastic scattering of
protons from targets of 6L1, 7Li, 9Be, and 10B were measured
from 12° to 130° in the lab (see Figs. 29, 30, 31, 32). The
experimental set up was similar to that described for the
(p,d) reaction measurements, except that the counter tele-
scope was replaced by a cylindrically shaped cesium iodide
crystal, 0.5 inches long and 0.25 inches in diameter,
mounted on a photomultiplier tube. A copper collimator with
a thickness equivalent to the range of ~50 MeV protons with
a .125 inch diameter opening was placed in front of the
crystal. The size of the crystal was kept as small as pos—
sible to minimize background contributions from neutrons
and gamma rays. Pulses from the photomultiplier tube were
amplified by a Landis preamp and then routed to an ORTEC
amplifier for shaping and further amplification; the out-
put was displayed on a 256 channel analyzer. The overall
proton energy resolution obtained for these measurements
was ~500 keV.

In the case of 7Li(p,p), the proton groups correspond—

ing to the ground state and 0.48 MeV excited state of 7Li
89

90

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91

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see .sOAuseAApmAe sesamse_AAAoemeAAAm11.om msswAm

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n

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9“

could not be resolved. Angular distributions had been
measured for both states at an incident proton energy (Ep)
of 25 MeV [60] and the same relative yields were assumed
in computing the differential cross section for the ground
state of 7Li at an incident proton energy of 34 MeV. This
amounted to an average correction of 2% at forward angles
and between 15% and 25% at backward angles.

Similarly, proton groups from the ground state and
0.72 MeV excited state of 10B could not be resolved. Data
taken from the same reaction at incident proton energies
of 19 MeV [61] and 185 MeV [62] show the cross section of
the 0.72 MeV state to be approximately 1% to 2% as large as
that of the ground state, so that this small correction to
the ground state cross section was ignored. The contribu-
tion to the differential cross section from an ~8% llB
impurity in the target was also not considered. This is
not a serious omission, assuming that the 10B and 11B
angular distributions do not differ appreciably in shape
and magnitude. This is a rather good assumption in the

case of the 6Li-7

Li pair where the magnitudes differ by
~33% and the shapes are very similar. The accuracy of the

absolute differential cross sections is 6% to 9%.

5.8. Optical Model Calculations

 

The Abacus computer code [29] calculates the angular
distribution for particles scattered from an optical poten-

tial of the form

95
(1) U U-V§(r,Rq&)1.74%5013994-1:IKrR)

-RA%
C1

 

Here 5032,01): 8.3—; 5 X:

and U0 is the Coulomb potential from a uniformly charged
sphere of radius RAl/3 fermis. The code can be used to ob-
tain agreement between the calculation and the experimental
angular distribution; the method used employs a least
squares criterion and allows any number of chosen parameters
to be varied to arrive at a best fit to the data. The
"best" fit is decided upon on the basis of a chi-squared
calculation in the program itself and visual inspection of
the overall fit to the experimental data. The optical model
calculation representing the best fits for the elastic
scattering of protons from 6L1, 7Li, 9Be, and 10'B are shown
in Figures 29, 30, 31, and 32. The parameters used to
obtain these fits are given in Table 7.

The deuteron Optical parameters were obtained in a
similar manner by fitting data from the elastic scattering
9

of deuterons from Be at an incident deuteron energy (Ed)

of 27.7 MeV [63] and from 7Li at Ed = 28 MeV [64]. The best
fit optical parameters obtained are given in Table 8; no
spin orbit term was included in the optical potential and
the imaginary diffuseness (al) was set equal to the real

diffuseness (aR). Deuteron optical parameters for the

96

boron calculations were obtained from the literature [65]

and are given below.* In this case, a volume absorption

term is used in the imaginary portion of the potential.

TABLE 7.--Proton optical model parameters.

 

Target V(MeV) W(MeV) VSO(MeV) B(f)

3R

(f) aI(f)

 

 

 

 

Li uu.56 6.92 7.38 1.124 .578 .685
7L1 A6.u5 6.39 7.18 1.187 .u78 .727
9Be 48.92 6.uu 6.30 1.139 .613 .616
103 53.99 6.22 6.31 1.097 .5u8 .611
TABLE 8.-—Deuteron optical model parameters.

Target V(MeV) W(MeV) R(f) aR(f)
7 a

Li 79.u5 11.23 1.09A .769

9Be 7u.03 11.67 1.239 .736

 

.aData renormalized by 0.85.

5.C. DWBA Calculations

 

Distorted wave Born approximation calculations (see

Chapter 1) were carried out using the Masefield computer

code on the CDC 3600 computer. The calculation has been

 

*Deuteron optical parameters for lOB(d,d) E
V = 83.5 MeV, W = 14.94 MeV, R = 1.33 f, a

a
I

1.6 MeV

= 2
0.65 f.

97

checked and found to agree exactly with identical calcula-
tions performed with the DWBA code, JULIE [66], when no
spin orbit term was included in the proton optical potential;
there was a slight difference between the shapes of the
angular distributions from 0° to 5° and for angles 1 80°
when a spin orbit term was included in the potential.
There is no apparent explanation for this difference, how-
ever it does not affect the general features of the calcue
lated angular distribution and most important, does not
affect the extraction of the spectroscopic factors.
The DWBA analysis was carried out with parameters for
the picked up neutron of an = 0.65 f and Rn = 1.25 Al/3 f.
No spin orbit term was included in the neutron potential.
The DWBA calculations lead to an interesting result,
in that it was impossible to get a reasonable fit to the
(p,d) angular distribution data using the optical parameters
in Tables 7 and 8. ‘However, if the imaginary well of the
deuteron optical potential (Wd) is increased by a factor of
three in the case of 9Be(p,d)8Be and a factor of four in
the cases of the lithium and boron (p,d) reactions reasonable fits
are obtained in all cases (Figs. 10, 13, 17, 22, 27). A
20% variation of any of the other parameters would not pro-
duce similar results. The same situation was encountered
in applying a DWBA analysis to the data from uHe(p,d)3He
with'Ep = 31 MeV [67].

98

This anomalously large value of W may be a consequence

d
of using the optical model potential to describe the inter-
action of the scattered deuteron with a relatively small
number of nucleons which comprise the scattering nucleus.

It may also be due to the fact that in the optical model,
the deuteron is treated as a point particle, whereas the
weak coupling within the deuteron itself is likely to be
sensitive to deformations caused by interactions with the
target nucleus. No similar effect was noted, however, when
optical parameters obtained from elastic scattering were
used in DWBA calculations of the (p,d) reaction with heavier
nuclei [1“]. Thus it appears that the first possibility

may be the more relevant of the two.

The same effect was encountered by Siemsson [68] in
attempting to fit data from (d,p) reactions with 1p shell
nuclei. The incident deuteron energy was m2OMeV. Reason-
able fits to the data were obtained by using a cutoff
radius in the DWBA calculations [33]. It was found, how-
ever, that the amplitude of the first peak of the differ—
ential cross section varied as a function of the cutoff
radius. Roughly, the amplitude of the first peak of the
differential cross section had two maxima, the first maximum
appeared at a cutoff radius of 0 fermis and the second at
a cutoff radius of 3 to 5 fermis. The variation in the
Cross section peakwas approximately 3 to l. Cutoff radii

corresponding to the second maximum were used in the

99

subsequent DWBA calculations in which reasonable fits to the
data were obtained.

Thus, it appears that a large increase in the strength
of the imaginary deuteron well depth and the use of a cut-
off radius both have a similar effect on the DWBA calcula-
tion. As opposed to using a rather arbitrary cutoff,
increasing the deuteron well depth varied the amplitude of
the first peak of the differential cross section by less
than 15% in all cases except that of loB(p,d) 9B, where the
change was of the order of 20%.

The concern about the behavior of the amplitude of the
differential cross section's first peak arises because the
spectroscopic factor is assumed to be directly proportional
to the ratio of the maxima of the DWBA and experimental
distributions' first peaks. If the parameters of the DWBA
calculation are varied in order to produce theoretical
results which bear a reasonable resemblance (in shape) to
the experimental data, the effect of these variations on
the amplitude of angular distribution's first peak must be
considered in deciding Just how meaningful the extracted
spectroscopic factors are.

In summary, neither method of obtaining reasonable
fits tO'the data eXplains the reason for the anomalous
behavior of the DWBA in the case of light nuclei. The
effect is large and reproducible, and it has been observed

in the case of (d,p) and (p,d) reactions at several

100

different bombarding energies. It deserves further study
in that it points out weaknesses in the DWBA calculations
which are especially emphasized in the case of light

nuclei.

CHAPTER 6
SPECTROSCOPIC FACTORS

6.A. Experimental Spectroscopic Factors

 

The experimental spectroscopic factor SA+B for the
transition A(p,d)B, which proceeds by a direct pickup of

lp3/2 and 1p1/2 neutrons, was calculated from the expression

S = OEXP
A+B 1.60M

DWBA

OM is the magnitude of the differential cross section at

the angle for which it has its characteristic in = 1 maximum.
The DWBA result, which uses the zero range approximation,

is multiplied by a factor of 1.6 to make it approximately
equivalent to a calculation using the effective range

theory [69, 70].

This method of extracting the spectroscopic factor
is based on the assumption that the experimental angular
distribution and the DWBA have the same shape and differ
in magnitude by a constant factor, i.e., the spectroscOpic
factor. Thus, the magnitudes of the integrated or total
DWBA and experimental cross sections also differ by the
same spectrosc0pic factor. In practice, the DWBA calcula—

tion does have a shape similar to that of the experimental
lOl

102

distribution, with the difference between the two shapes
appreciable for angles 390°. The disagreement between theory
and experiment at backward angles results in part from
physical effects not included in the DWBA formalism.

The difference between the integrated cross sections
is essentially determined by the values of the angular dis-
tributions at forward angles because of the characteristic
forward peaking of the direct reaction angular distributions,
and is not significantly affected by their detailed behavior
at backward angles. For example, in the case of 7Li(p,d)6Li
the contribution to the integrated cross section from 90°
to 180° is m“%. Assuming that the shapes of the DWBA and
experimental distribution match quite well at forward angles,
determining the spectroscopic factor from the relative peak
heights of the characteristic 2 = l maxima is equivalent to
determining the spectroscopic factor from the relative
magnitude of the integrated cross sections. Spectroscopic
factors can be extracted using this method in cases where
the integrated cross section cannot be obtained directly
because of experimental difficulties encountered in measur-

ing the angular distribution at baCkward angles.

6.B. Theoretical Spectroscopic Factors

 

The theoretical spectroscopic factors were obtained for
the transition A(p,d)B from the coefficients of fractional

parentage, B , calculated by Kurath using the intermediate

13

l03

coupling model for lp shell nuclei [16]. The theoretical

spectroscopic factor S is given by

A+B

Z 2

1— — — I I 2
SA+B(2n—l gn— 3/2,1/2) — n(T 1/2 MT l/2‘T MT) 98 B13

1/2,3/2
l

n is the number of nucleons in the lp shell of A and (I) is

a Clebsch Gordon coefficient with T', M' and T,M the

T T
isotopic spin and its projection for the final state and
initial state respectively. As calculated above, the
Spectroscopic factors relate to states with pure isospin.
Other sets of spectroscopic factors for the reactions

loB, 10B(p,d)9B were obtained from

7Li(p,d)6Li and llB(p,d)
the shell model calculation of Barker [17] and the inter-
mediate coupling calculations of Balashov [18], respectively.
Theoretical and experimental relative spectroscopic
factors were obtained by normalizing the sum of the spec-
troscopic factors for each reaction to one. Considering
the difficulty in extracting meaningful absolute spectro-
scopic factors from the DWBA comparison to the data, the
relative spectrosCOpic factor was calculated to provide a
better look at the relative amount of overlap between the
target nucleus' ground state wave function and wave func-

tions of the residual nucleus' different excited states

plus a lp shell neutron.

104

6.C. Comparison of Results

 

The agreement between theory and eXperiment for
7Li(p,d)6Li is good (see Fig. 33). The experimental
spectroscopic factors of zero for the 4.57 and 6.0 MeV
states could be due to the difficulty in extracting the
small deuteron yields, corresponding to these broad
states, from the background.

Figure 34a shows the large discrepancy between theory

8Be JTr = 2+

and experimental spectroscopic factors for the
doublet at 16.6 and 16.9 MeV and also for the JTr = 3+
doublet at 19.1 and 19.2 MeV. This disagreement could
result from the fact that the experimental spectrOSCOpic
factors have been extracted using a DWBA calculation with
deuteron potential parameters obtained from the elastic

9

scattering of deuterons from the ground state of Be, whereas

the nucleus is actually left in‘a state 17 to 19 MeV in
excitation above the ground state of 88e. The effect of
this approximation on the extraction of the spectroscopic
factor is not known, but it should be noted that the same
large discrepancies are not present in the results for the
J“ = 1* doublet at 18 MeV excitation. The last observation
fits in with another possible explanation for the observed
disagreement. The theoretical calculations assume the
states to be pure in isotopic spin, whereas previous eXperi-
ments have shown considerable iSOSpin mixing to be present
within the J1r = 2+ and‘3+ doublets. If two states of pure

isospin are mixed to produce two new final states of

105

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106

  

 

 

 

 

 

 

 

159.2540
9 8
_4qb E36(l1“j) E36
--A-- Experiment
.3..- Q —‘— Theory (Kurath)
I\
.2.-
A
0: ,’
E 4‘ ’
< IH- I
u, I
g I
§ ,, 1, 1 » 1 1 1 7“? 1
V, .1 0 2* 2* 2* 1* 1* (3) 3*
gsgmvioc 3.1 16.63 l6.95 17.62 16.16 19.05 19.21
8
a.
U)
E: Fu1354b
g .4" 9Be(p,d) 8Be with I-spin mixing
52‘
.3--
.2--
A
I--
W’ l’ l 1 I I l r“
.1 0* 2* 2* 2* 1* 1* (3) ‘ 3*
E,(Mcv10.0 3.1 16.63 l6.95 17.62 16.16 19.05 19.21

Figure 34.--Comparison of theoretic 1 and egperimental
relative spectros00pic factors for- Be(p,d) Be. Good
agreement‘ is obtained except for the JTr = 2+ and 3+
doublets. vathe sum of the theoretical spectroscopic
factors within these doublets in 34a is fixed, but the
ratio of strengths is adjusted to best fit the experi-
mental data, the Figure 34b is obtained. This is equi-

valent to mixing states with definite isospin within the
dnnhlptg

107

indefinite isospin, the ratio of Spectroscopic factors for
the isospin mixed pair will be different, in general, from
that originally found for the‘pair with pure isospin. How-
ever, the sum of the spectroscopic factors for each pair is
the same for both cases. Assuming, therefore, that the
eXperimental results only represent a mixing of the
theoretical iSOSpin pure states, there should be agreement
between theoretical and eXperimental sums of spectroscopic
factors for each doublet. The sum of the experimental
Spectroscopic factors for the J" = 2+ and 3+ doublets is

.32 and .19, respectively, whereas the sum of the theoretical
spectroscopic factors for the same J" = 2+ and 3+ doublets
is .33 and .11, respectively. This same approach was also
used in obtaining Figure 3Ub. Here the ratio of spectro-
300pic factors within the J1T = 2... and 3+ doublets has been
adjusted to give better agreement with eXperiment, while the
sum of spectroscopic factors within the doublets is the same
as that in Figure 3Ma. Thus, good agreement with theory for
the 98e(p,d)BBe experiment can be obtained, assuming that
the isospin mixing with the J" = 2+ and 3+ doublets is the
cause of the major differences observed.

Relatively good agreement is obtained between the
theoretical calculations of Kurath and experimentally ob-
tained spectroscopic factors for the llB(p,d)lOB reaction
(see Fig. 35). Somewhat poorer agreement is obtained with
the calculations of Balaskov; in particular, there is a

marked difference between the calculated and experimental

108

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109

spectroscopic factors for the 0.72 MeV and 2.15 MeV levels
of 10B. Balaskov's calculations also do not include a
spectroscopic factor for the JTr a 2+ level at ”.75 MeV.

Both Balaskov and Kurath predict a weakly excited
level (JTr = 3+) around 5-6 MeV excitation in 108. There
are three known levels in the region 6.5 - 7.0 MeV excita-
tion in 10B with unknown spins and parities [10]. None
were observed to be excited by the (p,d) reaction, however,
the deuteron yield may have been very small and lost in the
background.

'The spectroscopic factor for the deuteron group
observed at a 10B excitation energy of 6.04 MeV was calcu-
lated assuming only a JTr = 2+ state contributed to the
deuteron yield, when, as mentioned previously, the energy
resolution could not have separated contributions from
previously observed levels of 10B at 5.92 MeV (J" = 2+)
and at 6.13 MeV (J" = ?) [10]. A comparison of the eXperi-
mental result with the calculation of Kurath indicates that

the 10

B 5.92 MeV level is the main contributor to the
observed deuteron group.

Spectroscopic factors have now been extracted for the
llB(p,d)lOB reaction at incident proton energies of 18.9
MeV [7], 155 MeV [57], and 33.6 MeV; they have also been
extracted for the llB(d,t)lOB reaction at an incident
deuteron energy of 21.6 MeV [65]. The results are shown in

Figure 36, where the spectr0600pic factors for the ground

state transition have been normalized to one. The

llO

 

 

 

 

1.6
Spectroscopic Factors for '°B States from I p Neutron
1.6 Pickup Reactions
:1 (d,t) 21.6 MeV
x (p.d116.9Mev
1.4 A (p,d)l55.0MeV
0 (p.d) 33.6 MeV
'2 0 Theory (Kurath)
§
8
“ 1.0 0
0
.a A
O
3 0.6
2
3 0
a a
"’ 0.6 .
A
8
0.4 ‘3
D
‘ O .
(12 3 2 x
D
g 3
'°6 0.0 0.72 1.74 2.15 3.56 4.77 5.16
Excitation
. Energy

Figure 36.--A.comparison of experimentally obtained spectros-
' 00pic factors for 10B states.

lll

experimental spectr0500pic factors for the deuteron group
corresponding to a 10B excitation energy of 5.16 MeV have
been extracted assuming that only the 5.16 MeV level of
10B (J1T = 2+) contributes to the yield. In all cases,
however, the energy resolution was not good enough to
separate out contributions to the observed deuteron yield
from the 5.18 MeV level of lOB (JTI = 1+). Contributions

to the observed deuteron group from both levels were
assumed in the calculation shown in Figure 35. The experi-
10

mental spectroscopic factor for the 5.16 MeV level of B

extracted from the Ep = 155 MeV work also contains contri-

10B (J" = 2*); the two

butions from the “.77 MeV level of
levels could not be resolved with this high incident proton
energy.

The spectroscopic factor for the 2.15 MeV level of
10B obtained from the work at Ep = 18.9 MeV appears likely
to be in error, as its value is significantly different
from a closely grouped series of results from (p,d) experi—
ments performed over a wide range of energies, Kurath's
theoretical calculations, and a (d,t) experiment (see
Fig. 30). It was on the basis of the work done at Ep =
18.9 MeV that a previous investigation proposed an isotopic
spin dependence in the (p,d) and (d,t) reactions which
would account for significant differences in the observed
spectroscopic factors for the 10B 2.15 MeV level [65];

the present work does not support these contentions.

112

With the above data point ignored, a mean spectroscopic

factor was calculated from the experimental data for each

loB level; the results are shown in Table 9.

TABLE 9.——Average differences of Spectroscopic factors from
mean values of the experimental data.

 

Spectroscopic Factors from: Average Difference
from Mean Values

 

(p,d) reactions 15%
(d,t) reactions 18%
theoretical calculation (Kurath) 20%

 

From these results, the following general conclusions

appear to be valid:

1. Spectroscopic factors obtained over a wide
range of incident energies agree to within
15% - 20%.

2. Spectroscopic factors obtained from 'the (d,t)
reaction are not significantly different from
those obtained with (p,d) reactions.

3. Kurath's calculations agree with the experimental
spectroscopic factors to within m 20%.

4. A reasonable absolute error for the Spectroscopic
factors obtained in this work falls somewhere in

the region of 15% e 20%.

113

Experimental and theoretical spectroscopic factors for
the reaction lOB(p,d)9B are shown in Figure 37. The 98
levels at 4.“ MeV and 5.7 MeV have been predicted theoreti-
cally by both Kurath and Balaskov, but have not been
observed experimentally. The predictedyeilds are small,
however, and the peaks may have been lost in the high back-
ground.

The 96 levels at 0.0, 2.35, 7.1, and 11.75 MeV all
have been determined to have negative parity (see Chapter A),
while the 9B level at 1H.Ol MeV has been tentatively iden-
tified as having negative parity. Assuming the experimental
spectroscopic factors agree with theoretical calculations
to within ~20%, the Spins for the observed levels were
assigned by comparing the theoretical and experimental re-
sults (see Fig. 37).

Additional evidence to support these assignments was
obtained from triton energy spectra for the reaction
llB(p,t)9B. These Spectra were taken with the same llB
targets used in the llB(p,d)loB reaction work and the
particle identification system adjusted to detect tritons
(see Fig. 38). The Shapes of the angular distributions
shown in Figure 39 can be explained with the following
simple model for the (p,t) reaction. When the incident

proton picks up two neutrons as a pair from 10

B, they must
be in the Singlet state with a total Spin, S = 0 and the
orbital angular momentum of the pair must be even

(L = 0, 2, A . . .) from symmetry considerations. Using

114

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Ep= 33.6 MeV

lljll

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l
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-
q

GROUND STATE

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b
'O
.' 1. - 2 \ !\i ‘
isi/I\I .-
" 2.33 MeV STATE -
.1": 5/2'
(1| 1 1 1 1 1 1 1 1 1
o 20 40 60 60 100

ecu‘deg)

Figure 39.--11B(p,t)9B angular distribgtions for the ground
state and 2.33 MeV excited state of B.

117

this simple picture, the ground state angular distribution
for llB(p,t)9B has a characteristic shape for the pickup of
a dineutron with orbital angular momentum L = 0. This

means the ground state of SB can only have the assignment

J" = 3/2-, in agreement with the 10B(p,d)9B work. The
angular distribution for the 2.33 MeV state has a character-
istic shape for the pickup of a dineutron with L = 2
allowing for Spin and parity assignments of J“ = 7/2',

5/2‘, 3/2-, and 1/2—. These values do not contradict the
previous Jn'c’5/2- assignment for this state. It should
also be noted that the assignments for the levels at 0.0,
2.35, and 7.1 MeV coincide with the spin assignments for
isobaric analogue levels of 9Be at 0.0, 2.H3, and 6.66 MeV
excitation [10]. There is therefore a Significant amount

of supplementary evidence to support the spin and parity
assignments which were made on the basis of agreement between

eXperimental and theoretical Spectroscopic factors.

CHAPTER 7
CONCLUSIONS

The experimental results of this thesis Show that
Kurath's intermediate coupling model of 1p shell nuclei
correctly describes the actual physical Situation. The
only case where the theoretical calculations of Kurath and
the experimental data were not in reasonable agreement was
that of the J" = 2+ and 3+ doublets of 8Be, however, the
observed differences were eXplained by the inclusion off
isotopic spin mixing in the wave functions for these doublet
states. In fact, considering the otherwise good agreement
obtained between theory and experiment, the discrepancies
noted in the 9Be(p,d)BBe reaction illustrate in a very con-
cise manner that the 8Be 2+ and 3+ states contain admixtures
of T = O and T = 1.

0n the basis of the intermediate coupling model's
ability to predict spectroscopic factors to within ~*20%,
Spin assignments were made for the observed negative parity

9

levels of B by comparing the experimental data with the
model predictions. The same general agreement between
theory and experiment was observed for these states of
previously undefined Spin as was observed for states of

known spin in other lp Shell nuclei.
118

119

Thus, this systematic study of the effectiveness of the
intermediate coupling model in the 1p Shell has provided a
basis for extending our knowledge of the 1p shell nuclei
by helping to establish a reliable framework into which new
experimental facts can be fitted. It should be emphasized
that the present work only tests one aspect of the model,
i.e. its ability to predict spectroscopic factors. Other
checks have been made to test the model's ability to predict
energy levels [20] and electromagnetic transition widths
[19]. These studies have revealed a failure of the model to
reproduce collective effects, a weakness which is not re-
flected in the extracted spectroscopic factors.

The direct comparison of the results of this work with
results from neutron pickup reactions performed at different
energies and with different incident particles Shows that
the spectroscopic factors can be measured to within an un-
certainty of approximately 120%; an estimate generally held
among workers in the field, but one for which there was
little firsthand evidence. More important, the spectro-
scopic factors do not appear to depend Significantly on the
incident particle or its energy; this gives some assurance
that the experimental Spectroscopic factors obtained here
do yield a reasonable measure of the overlap of the target
and residual nuclear wave functions.

No evidence was found for any 2s-ld Shell admixtures

7

in the ground state wave functions of 6Li, Li and 9Be; no

Significant admixtures from this shell were found in the

120

ground state wave functions of 10B and 11B. The strongly

5

excited 16.6 MeV state of Li is the only case where neutron

pickup from the ls Shell was observed with any appreciable
yield. The 11.“ MeV state of 8B6 (JTr = 4+) appears to be

excited by a compound nucleus mechanism and not because of

9Be ground state wave function [13].

From this study, therefore, the ground states of 6Li, 7

10B and 11B appear to consist of tightly bound Is

any lf admixture in the
Li,
93e,
cores, the remaining nucleons residing in the lp Shell with

no sizable admixtures from other Shells.

APPENDIX I
LITHIUM DRIFTED SILICON DETECTORS

The method used to fabricate lithium drifted Silicon
detectors was similar to that described by Goulding [71].
Wafers from 2 to H mm thick were cut from p-type Silicon
(typically with a resistivity of ~100 ohm-cm). The crystal
faces were lapped with #95 A1203 grit and #1000 silicon
carbide grain to smooth the surfaces and remove saw marks.
One surface was then coated with a lithium-mineral oil
suspension and the wafer heated in an oven for 8-12 minutes
at ~350° C in an argon atmosphere. In this process, the
lithium donor ions diffuse into the surface of the p-type
silicon forming a p-n junction.

After cooling, the wafer's sides were etched in an

HF-HNO solution to rid them of impurities and the junction

3
tested for diode characteristics. The etching was repeated
until the leakage current was of the order of microamps
with no Junction breakdown evident for a reverse bias of
several hundred volts. At this point in the fabrication
process, typical surface resistances were 200-300 0 for the

lithium n-side of the wafer and m100 K9 for the p—side of

the wafer.

121

122

If a reverse bias is now placed across the junction,
the lithium donor atoms diffuse or "drift" into the p—type
silicon. At equilibrium, they compensate the effect of
the acceptor distribution, causing the region to react like
an "intrinsic" or pure material, so that an electric field
applied across the region will cause very little current
to flow (on the order of .01 - .1 u amps). The "drifting"
apparatus consisted of a hot plate kept at a temperature of
80°— 11100 C to which the wafer was affixed. A reverse bias
on the order of 500 volts was placed across the junction
resulting in a drift power (energy dissipated in the crystal)
of 0.5 to 2.0 watts depending on the particular crystal and
the amount of time Spent in the drift. The width of the

intrinsic region (W) is roughly given by [A],

(1) w = /2uEVt (cm)

V = drift voltage
“L: mobility of Li ions (cm2/volt sec.)
t = time (sec.)

The mobility of the lithium ions (uL) depends on the
detailed characteristics of the silicon material used
(impurity content, defect concentration, etc.) and varies
directly with the drift temperature. Typical lengths of
drift time for depletion depths of ~3mm were 2 1/2 - 3

weeks. If at any time during the drift process the leakage

current grew so large that only a small drift voltage (V)

123

could be used in order to stay within a crystal power dis-
sipation of 2 watts, the wafer was removed from the apparatus
and its sides etched in the HF-HNO3 solution to clean off

any accumulated surface impurities. It was then replaced

in the apparatus and the drift process resumed.

The procedure for checking the depth of the depletion .‘
region consisted of placing the wafer in a CuSOu solution, “B
to which a few drops of HF had been added, so that the n-
face of the crystal remained dry. When placed in sunlight
or strong artificial light, copper will plate out only on Q
the intrinsic region and hence the depth may be readily
determined.

When the desired depletion depth was obtained, the
crystal was cut into a Shape similar to that Shown in
Figure 40. The surfaces were lapped and then cleaned by
etching. ‘Gold was plated on the upper and lower surfaces
for electrical contacts and the finished detector placed
in a mount similar to that Shown in Figure 40. The design
of the detector minimizes the sensitive region of the
detector and hence minimizes the background due to neutrons
and gamma rays. The detector encapsulation protects the
surfaces of the crystal from accumulation of pump oil and
other impurities and makes the detector easy to handle.

Detectors could be made in this way with depletion
depths of about 3 mm. and produced deuteron energy spectra

4 with an overall energy resolution of 100—150 keV. They

1le

QTHIUM DRIFTEQ SILICON DETECTOR

-Region used for particle detection
Particles enter from opposite side
I—Lithium n-side

 

 

 

 

T
W= depletion depth
I .1 (~3mm)
’ -t o'o
Gold plating P ype 61 Icon
for electrical / .
contacts ‘ """ Electrical lead for —'

 

 

  

 

 

I positive bias

Holes for plastic
fastening screws

 

Copper spring 8——-
electrical contact

Plastic holder»
for detector

 

Copper front-—' 0
plate (grounded)

 

Detected particles
enter through I/4
mil mylar window

 

' DETECTOR MOUNT ‘

Figure u0.--Lithium drifted detector and mount.

125

were, however, difficult to produce and their lifetime
short (one week or less). The reason for this short
useful life was probably due to imperfect sealing of the
encapsulation and not to radiation damage. Commercially
purchased detectors with Similar initial characteristics,
but with more sophisticated packaging, had lifetimes of

1 1/2 to 2 months with approximately 100 hrs/week of

.actual use with proton beam currents of 1—100 nanoamps.

 

1.

2.

10.

11.

12.

13.

14.
15.
l6.
17.
18.

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