ABSTRACT
INELASTIC PROTON SCATTERING

16

FROM 0 AT BOMBARDING ENERGIES

FROM 2H.6 T0 ”0.1 MeV

by Douglas Bayer

Proton inelastic scattering from 16O has been measured
at bombarding energies 2M.6, 29.8, 33.5, 36.6, and ”0.1 MeV.
Angular distributions have been obtained from 10° to 100°
for the doublet of states at 6.05 MeV (0+) and 6.13 MeV
(3‘) and the doublet of states at 5.92 MeV (2+) and 7.12
MeV (1-). The cross sections for exciting these four states
have been analyzed using realistic nucleon-nucleon forces.
The nuclear structure information necessary to construct
form factors suitable for DWM calculations was obtained by
fitting the available inelastic electron scattering data.
The long range part of the Kallio-Kolltveit interaction
provided an adequate description of the magnitude of the
cross sections. The shapes of the calculated differential
were insensitive to the interaction used, with all inter—
actions adequate to describe observed shapes. A macro-
scopic collective model analysis of the data was also

undertaken. The deformations were found to exhibit little

Bayer

energy dependence from 29.8 to no.1 MeV and were in good

agreement with electromagnetic transition data.

INELASTIC PROTON SCATTERING

16

FROM 0 AT BOMBARDING ENERGIES

PROM 2H.6 T0 ”0.1 MeV

by
C '3

Douglas'Bayer

.I
V-

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics

1970

ACKNOWLEDGMENTS

I would like to thank Dr. W. Benenson for suggesting
this experiment as a thesis topic and Dr. Edwin Kashy for
his advise and assistance in developing the experimental
techniques used in aquiring the data.

Ivan Proctor provided invaluable assistance both as
a cyclotron Operator and a consultant in solving the elec-
tronic and mechanical problems which arose during the long
hours of the individual runs.

I would also like to express my appreciation to Dr.
W. Kelly for his suggestions and guidance during the writing
of this thesis.

I wish to express my appreciation to Harold Hilbert
and N. Mercer for responding so gallantly to my repeated
calls for assistance.

I acknowledge the financial support of the National
Science Foundation and Michigan State University throughout
my graduate work.

Finally, I wish to express my deepest appreciation to
my wife, Maria. She has courageously endured my explana-
tions of problems related to computer programming, data
acquisition, and theoretical analysis, none of which she

understood.

ii

 

 

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TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

l.

2.

INTRODUCTION

EXPERIMENTAL PROCEDURE

2

2

2.

2.

.l

.2

8

9

Cyclotron and Beam Transport
Spectrograph

Detectors

Monitor

Targets

Setup Procedure

Electronics and Particle Identification
Data Reduction

Error Analysis

EXPERIMENTAL RESULTS

3.

1

The 6.05 MeV State
The 6.13 MeV State
The 6.92 MeV State

The 7.12 MeV State

NUCLEAR THEORY

DWBA Formalism

Form Factors

Collective Model Form Factors
Microscopic Form Factors

Optical Parameters

iii

Page

vi

12
12
15
17
2a
25
28
28
31
3a
37
I40
1+1
41
us
as

1+7

iv

5. COMPARISON OF DATA TO THEORY

5.

5.

l

2

Collective Model

Microscopic Model

Comparison of Microscopic Fits to the Data
The 6.13 MeV State

The 6.92 MeV State

The 7.12 MeV State

6. SUMMARY OF RESULTS AND CONCLUSIONS

6

.l

6.2

Results

Conclusions

APPENDIX A

APPENDIX

B

LIST OF REFERENCES

Page
52

52
52
59
an
68
68
78
78
79
80

91

97

LIST OF TABLES

Page
Summary of Errors 27
Optical Parameters 50
Deformation Parameters BL Extracted from Collective
Model Fits at Five Bombarding Energies 56
Values of V O in MeV Obtained from the Microscopic
Calculationg using the Yukawa Interaction 72

 

 

go

no

LIST OF FIGURES

Experimental Area of the M.S.U. Cyclotron
Laboratory

The Wedge Increases the Separation of Particles

from Dl at the Plate Holder to D2 at Detector

A Typical Position Spectrum for the .3 mm Thick
Detector with a 15° Wedge

A Typical Position Spectrum from the .12 mm
Thick Detector Without a Wedge

A Typical Monitor Spectrum from the 5 mm Sili-
con Surface Barrier Detector

A Cross Section Drawing of Rotating Target
Holder (Ma 68)

Counter Efficiency Versus Plate Height

Block Diagram of Electronics When Routing Was
Used

Flow Chart of SETUP Mode Interrupt Routing
Flow Chart of RUN Mode Interrupt Routing
Center of Mass Cross Section Plotted as a
Function of Scattering Angle for the 6.05 MeV
State

Center of Mass Cross Section Plotted as a

.+

Function of Q = |ki - kflfor the 6.05 MeV State
Center of Mass Cross Section Plotted as a
Function of Scattering Angle for the 6.13 MeV
State

Center of Mass Cro 3 Section Plotted as a Func—
tion of Q = |ki - kfl for the 6.13 MeV State

Center of Mass Cross Section Plotted as a Func-
tion of Scattering Angle for the 6.92 MeV State

Center of Mass Cross Section Plotted as a Func-
tion of Q = |ki — kfl for the 6.92 MeV State

vi

Page

10

ll

13

I”

16

19
22

23

29

32

33

35

36

.10

.11

.12

.13

.1”

vii

Center of Mass Cross Section Plotted as a
Function of Scattering Angle for the 7.12 MeV
State

Center of Mas§ Cro§s Section Plotted as a Func-
tion of Q = |ki - kfl for the 7.12 MeV State

DWM Calculations for the 6.13 MeV State
DWM Calculations for the 6.12 MeV State
DWM Calculations for the 7.12 MeV State

Electron Scattering Form Factor Using the
Transition Density Extracted from the Least
Squares Fit

Electron Scattering Form Factor Using the
Transition Density Extracted from the Least
Squares Fit

DWM Microscopic Calculations for the 6.05 MeV
State Using a If Range Yukawa Interaction

DWM Microscopic Calculations for the 6.05 MeV
State Using the Long Range Part of the K-K
Interaction

The Form Factor for the 6.05 MeV State With-
out Including Exchange

DWM Calculations for the 6.13 MeV State Using
a If Yukawa Interaction

DWM Calculations for the 6.13 MeV State Using
the Long Range Part of the K-K Interaction

DWM Calculations for the 6.13 MeV State Using
the K-B Interaction

Electron Scattering Form Factor Using the
Transition Density Extracted from the Least
Squares Fit

DWM Calculations for the 6.92 MeV State Using
a lf Range Yukawa Interaction

DWM Calculations for the 6.92 MeV State Using
the Long Range Part of the K—K Interaction

Page

38

39
53
5M

55

58

60

61

62

63

65

66

67

69

70

71

viii

Electron Scattering Form Factor Calculated
from the Transition Density Extracted from the
Least Squares Fit

DWM Calculations for the 7.12 MeV State Using
a If Range Yukawa Interaction

DWM Calculations for the 7.12 MeV State Using
the Long Range Part of the K-K Interaction

DWM Calculations for the 7.12 MeV State Using
the Long Range Part of the K-K Interaction

Page

7”

75

76

77

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1. INTRODUCTION

This experiment investigates the first four excited

l60(p,p')160* reaction. Differential

states in 160 via the
cross sections for J1T = 0+ state at 6.05 MeV, J1T = 3- state
at 6.13 MeV, JTr = 2+ state at 6.92 MeV, and JTr = 1' state at
7.12 MeV, were measured at five bombarding energies from
29.6 to 90.1 MeV.

The measurements were made using the M.S.U. double
focusing split-pole magnetic spectrograph. The spectrograph
has the facility to compensate for the effects of kinematic
broadening. This permits measurements subtending angles
as large as 2° in the reaction plane without sacrificing
energy resolution. Recent developments in the fabrication
of silicon surface barrier position sensitive detectors,
which provide position resolution of up to 0.5 mm and
permit count rates in excess of 50,000 counts per second,
enabled the strongly excited 3— state and the weakly
excited 0+ state to be taken simultaneously using an on
line computer.

Theoretical interest, particularly in the 0+ state at
6.05 MeV, provided the motivation for this experiment. In
order to construct an even parity state using a harmonic
<Dscillator potential, one has to excite at least two quanta
(If energy. Calculations using such excitations produce

. . . . +
Ikevels which overestimate the p081tion of the 0 by more

than 20 MeV.

 

 

system.
band St
at 6.92
using t‘
to repr

not lcwt

U1

7‘:
‘ I

energy t

 

 

Inelastic alpha scattering from 12C performed by

Carter et al (Ca 6%) at 10 to 19 MeV identified the 9+

160

at 10.36 MeV and the 6+ at 15.2 MeV in the compound
system. He identified these states as part of a rotational
band starting with the o+ at 6.05 MeV and including the 2+
at 6.92 MeV. Brink and Nash (Na 63) and Borysowicz (Bo 6H),
using the SU3 symmetry scheme of Elliott (El 58), were able
to reproduce the level separation within the band, but could
not lower the 0+ state relative to the ground state.

Brown and Green (Br 66), noting that the configuration
energy of a up - uh state was lower than that of a 2p - 2h
state for a deformed nucleus, used the SU3 symmetry group
to construct wave functions which were in agreement with
electromagnetic transition rate data.

e')16

Recent 16O(e, 0* data by Bergstrom et al (Be 70)

provide a direct measure of the nuclear structure of the
0+, 3-, 2+ and 1. states. This structure information,
along with the appropriate multipole of the nucleon-
nucleus interaction, define the distorted wave method (DWM)
form factor. This provides a test of the nuclear structure
in an independent experiment.

The negative parity states have been investigated by
Gillet and Vinh Mau (Ci 6”) who constructed wave functions
by promoting one particle from the lpl/2 orbit to the sd
shell. In this work the cross sections predicted by these

wave functions were compared with those derived from the

electron scattering data.

 

 

is

contp

Re C

The nucleon-nucleus force, being independent of the
nuclear structure, can be varied in the calculations. In
this work a variety of effective interactions have been
investigated. These investigations indicate that the shape
of the calculated differential cross section is not par-
ticularly sensitive to the details of the interaction.

A collective model analysis was also undertaken.

The deformations were found to be in agreement with elec-
tromagnetic transition rate data.

The energy dependence of the differential cross
sections was found to be monotonic from 29.8 to 90.1 MeV.
The data at 29.6 showed indications of strong compound
contributions. The agreement between the calculations and

the data, in general, improved with energy.

lib! Nul‘ ‘ "

 

 

 

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2. EXPERIMENTAL PROCEDURES

In order to measure differential cross sections for
inelastic proton scattering, one must have a proton beam
of well defined energy, a detection system which permits
unambiguous identification of the quantities being measured
and an analysis procedure which accounts for all known
sources of systematic and random error.

In this chapter the apparatus and procedures involved
in measuring the cross sections are discussed and the

error analysis is presented.
2.1 Cyclotron and Beam Transport

The proton beam was accelerated in the Michigan State
University sector focused cyclotron (B1 66) and extracted
with 100% efficiency via an electrostatic deflector and
magnetic channel. The transport system (Ma 67), illustrated
schematically in Figure 2.1, focused the extracted beam on
slits 81 and 83. Bending magnets M3 and M9 each bend the
beam 95° providing energy dispersion of .03% mm. The beam
energy was determined from nuclear magnetic resonance
probes placed in the central fields of M3 and M9. Bending
magnet M5 was used to deflect the beam 95° into the spectro-

graph beam line.

 

 

 

 

 

 

 

 

 

   

 

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//////// , of the M.S.U. Cyclotron Labor-
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'2.2 Spectrograph

All data were taken using the M.S.U. split pole,
double focusing magnetic spectrograph. A .368" x .372"
slit, subtending 1.202 millisterradians, was used to define
the solid angle. The spectrograph was chosen because it
provided a way to eliminate the effects of kinematic
broadening, allowing a large solid angle without loss of
resolution. Furthermore, the problems of pile-up and dead
time due to the large forward angle cross section of the
elastic peak were circumvented by keeping the elastic peak
off the detector.

The kinematic variation of particle energy with angle
moves the position of the focal plane in closer to the
target. Particles scattered into the high angle side of
the entrance slit are less energetic, and thus less rigid,
than the axial ray, while particles scattered into the low
angle side of the slit are more energetic and thus more
rigid. These rays will cross somewhat more quickly after
deflection in the spectrograph than will particles of the
same energy following the same three defined trajectories.
A linear approximation to the displacement of the focal
plane presented by Enge (En 67), was computed by the pro-
.gram "SPECTKINE" (Tr 70) which computed the NMR frequency
required to place the axial ray at a specified effective
radius of curvature p as well as the displacement of the

plate holder from the first order focal plane.

1.. l
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he X3

2.3 Detectors

At bombarding energies of 29.8 and 33.98 MeV, two
Nuclear Triode Silicon surface barrier position sensitive
detectors were placed on the spectrograph plate holder with
appropriate separation to simultaneously observe the
6.05 - 6.13 MeV doublet on one counter and the 6.92 - 7.115
MeV doublet on the other. The two detectors were of
dimensions 30 x 10 x .3 and 30 x 11 x .12 millimeters re-
spectively. At 29.6, 36.6 and 90.07 MeV the second detec-
tor was unavailable requiring the states to be measured
separately.

The position sensitive detectors provide two signals,
the E signal, proportional to the energy deposited by the
particles in passing through the counter and the XE signal,
proportional to the product of the energy loss and the
position. In order to get optimum position resolution,
the XE signal is divided by the E signal, which eliminates
the effects of straggling. The E signal also provides a
measure of Zz/M, where Z and M are the particles charge and
mass respectively. This information can be used to dis-
tinguish between reaction products of the same magnetic
rigidity.

The noise associated with the XE signal proved to be
the limiting factor in position resolution of high energy
protons. This noise is produced by a relatively small

resistance of lBKO in parallel with the large capacitance of

3e Ce:

q

t

 

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the detector. Attempts to decrease one of these components
leads to an increase in the other, implying the necessity
of a large XE signal. The amount of energy lost in the
detector by 23 to 39 MeV protons did not provide a suffi-
ciently large signal to enable us to resolve the 80 KeV
doublet, even though the particles pass through the
detector at 95°, making its effective thickness 925 microns.
To increase the effective thickness of the detector as

well as the effective dispersion of the spectrograph, a
wedge of 15° was inserted between the plate holder and the
counter. The effective detector thickness is thereby
increased by l/cos(¢ + 95), where ¢ is the angle of in-
clination, which increases the energy loss by 50% for a

15° wedge. The effective dispersion of the spectrograph

is increased by a factor of

l
l - tan¢

 

or about 39% for a 15° wedge. With the wedge, the 6.05 -6.13
MeV doublet was separated at all energies to better than

full width at half maximum (FWHM) of the 6.05 MeV peak at

90 MeV and was cOmpletely separated at all lower energies.
The effects of the wedge are illustrated in Figure 2.2.
Typical position spectra for the two counters are illustrated

in Figures.2.3 and 2.9.

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Figure 2.2 The wedge increases
the separation of particles from
D at the plate holder to D2 at
detector.

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Figure 2.3 A typical position
spectrum for the .3 mm thick
detector with a 15° wedge.

 

 

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sassv‘zm‘zs's 29:90 19:90 OAHUNBZ os'tad‘dMSISBOO ms

 

 

 

 

 

 

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Figure 2.9 A typical position
spectrum from the .12 mm thick
detector without a wedge.

 

 

2.9 M:

A

monitor

c p:er

PPO‘COI‘L

 

 

EPO‘ind

' +-

2.5 '3

12
2.9 Monitor

A 5 mm silicon surface barrier detector was used to
monitor the oxygen elastic peak. The detector was placed
at 90° at 29.8 and 33.98 MeV where the proton range was
less than the detector thickness. At 36.6 and 90 MeV the
detector was placed at 150° and an absorber of 10 mil
copper was placed in front of the collimator to lower the
proton energy. In all cases the oxygen and carbon ground
states were completely resolved. At 29.6 MeV a Na I(Tl)
scintillation crystal mounted on the face of a photo-
multiplier was used. In this case the carbon and oxygen
ground states were UnreSOlved. In Figure 2.5 a typical

monitor spectrum is shown.
2.5 Targets

Commercially available .25 Had; Mylar containing
approximately 300 ug/cm2 of oxygen was used. Mylar,
whose composition is C10(H20)u provides an excellent
target to investigate the low lying states in 16O. The
relatively high oxygen content along with the absence of
heavy elements provided an almost background-free energy
spectrum at all angles. The hydrogen peak serves as
calibration point for measuring the angle. The only
problem encountered with Mylar was that the heat of the

beam melted the target. This effect was minimized by

positioning the center of the target 3/8" above the beam

 

 

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'60 6.3.

C3
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Figure 2.5 A typical monitor
spectrum from the 5 mm sili-
con surface barrier detector

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15

and rotating it about its center at about 600 rpm. An
electric motor magnetically coupled, through a vacuum seal,
to a shaft which extended down to the target kept the tar-
get rotating at a constant speed. The frequency of rota-
tion could be varied from about 50 to 1600 rpm with a
Variac. This method allowed the target to withstand a
constant beam current of 120 nanoamps for twelve hours with

only 10 to 20 percent decrease in the target thickness.
2.6 Setup Procedure

The cyclotron beam was threaded through the beam
transport system, energy analyzed and deflected into the
spectrograph beam line. The beam was focused to a small
point and positioned over the center of the scattering
chamber. A television camera focused on a quartz scin-
tillator allowed direct observation of the position and
size of the beam spot. A piece of wire, mounted vertically
on the scintillator defined the center of the scattering
chamber.

The target holder was removed, the monitor counter
and target rotator mounted, and the spectrograph set to
20°.. The amplifier gain on the monitor counter was ad-
justed and the single channel analyzer window set.
Inelastic protons from the 6.13 MeV state of 160 were swept

across the position sensitive counter to determine the

counter efficiency and resolution as a function of position

 

 

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16

COUNTER EFFICEE‘NCY VERSES
PLATE HElGHT

B=5mm.

 

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._1/.( B_' 1 . .

 

l I l
3.0 , 3.2 3.4 3.6 3.8
PLATE HEIGHT (ENCHES)

Figure 2.7 B is height of beam
spot at the detector.

17

on the counter. The magnetic field at which the best reso-
lution was obtained was used to find the effective radius
of curvature p. The plateheight was then varied to deter-
mine the vertical detector efficiency and the image size

of the beam spot at the detector. The beam spot was
typically four millimeters high at the counter. Figure 2.7

shows a typical vertical efficiency curve.
2.7 Electronics and Particle Identification

The XE and E signals were amplified by separate ORTEC
109A preamplifiers which were placed on top of the spec-
trograph. The amplified signals were transmitted out to
the data room where the XE signal was input to a Tennelec
TC 200 amplifier which had 0.8 usec differentiation and
integration time constants. The E signal was fed into an
ORTEC model 951 spectroscopy amplifier with all shaping
times set at 0.5 usec. The resultingprompt bipolar E
pulse was then input to a single channel analyzer which
was used strictly as a lower level discriminator while the
delayed monopolar pulse was input to an ORTEC 992 linear
_gate stretcher. The bipolar output of the TC 200 was de-
layed and fed into a second ORTEC 992 linear gate stretcher.
Both signals were enabled by the logic pulse from the single
channel analyzer. The output signals of the linear gates
“were rectangular in shape, one usec wide and were adjusted

so that their leading edges were within 100 nanosecOnds of

18

each other. These pulses were then input to two Northern
Scientific 13-bit, 50 megacycle analog to digital converters
run in coincidence mode. When two detectors were used,
separate amplifier systems were used for each detector.

The signals from the linear gates were multiplexed together
with two summing amplifiers. The logic pulses from the two
single channel analyzers were fed into two of the seven
inputs on the routine box associated with the ADC's. The
routing bits were ORed into the upper three bits of the
sixteen bit general purpose interface register. The thirteen
bits from the ADC conversion were put into the lower bit
positions. Block diagrams of the electronic configuration
are shown in Figure 2.8.

The monitor signals were amplified by an ORTEC 109A
preamplifier and an ORTEC 951 spectrosc0py amplifier. The
bipolar pulse was fed into a single channel analyzer
which was set to output a pulse only for the oxygen elastic
peak. The output of the single channel analyzer was fed
into a scalar and a live—time clock input on the ADC's.

The ungated monOpolar pulses were fed into one of the four
1029 channel subgroups of the Nuclear Data ND—160 9096 multi-
channel analyzer.

The data acquisition task TOOTSIE, operating under the
JANUS (Ko 68) time sharing supervisor, was used to process
the data as it was presented to the Sigma 7 computer.

TOOTSIE was designed to process all types of two and three

19

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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20

parameter data requiring some form of event identification
taken by the users of the Michigan State University cyclotron.
A variety of options provide for various calculations to

be performed on the data before being stored. Only the
XE/E routine, which was used in this project, will be de-
scribed here. A complete list of the available data
acquisition routines is given in Appendix B.

The program operates in two modes, SETUP and RUN. In
SETUP mode the E signal is stored as a function of the
quotient XE/E in a 69 x 69, 69 x 256, or 128 x 128 two
dimensional array. The data are displayed on a TEKTRONIX
611 storage sc0pe, appearing as a series of bands across
the screen. Polynomial fits, generated by accepting a
series of points with a movable cross, define the lower
and upper bound for each band.

When routing is used, bands for each detector are
set independently. A total of fourteen bands can be gen-
erated. 3

Service routines provide the facility to punch, print
or store the contents of the 2D analyzer on a permanent
disk file. Analysis routines provide a display of the mass
spectrum by summing channels horizontally, as well as low
resolution position spectra by summing channels vertically
between the bands. A three dimensional isometric display

provides an overview of the data.

21

When all bands have been set, the program is switched
into RUN mode via a teletype command. Tables of 256 points
per fit are generated and stored for each detector. Events
are then checked against the tables corresponding to the
detector indicated by the routing bits and the appropriate
channel of the spectrum in which the match was found is
incremented. The spectra ranged from 512 to 8192 channels.
Figure 2.9 is a flow chart of the SETUP mode routine and
Figure 2.10 is a flow chart of the RUN mode routine.

In order to assess the overall quality of the data, a
routine computes the centroid, area, full width at half
maximum and ratio of peak area to monitor counter for up
to fifty peaks in two spectra which can be displayed
simultaneously on the storage scope.

With the resolution of a 128 x 128 multichannel
analyzer, irregularities in the charge collection efficiency
of the counter could be seen as dips in the energy bands.
Particles falling on these dips would produce distorted
peak shapes.

The use of digital gates provides a great deal of
. flexibility in identification logic. A procedure often
_ used to increase the peak to valley ratio is to embed one
band within another. The inner band is very close to the
. data while the outer band is set to assure that no counts
are lost due to electronic gain shifts or changes in pulse

height as a function of scattering angle.

.22
SET UP MODE

 

    

INTERRUPT

READ
AND RESET
ADCS

I

 

I

INCREMENT
CHANNEL
ZERO

I

 

 

 

 

 

 

 

 

X I I6384 X XE/E
E-EAS

 

I

x-umsfl

 

 

 

 

I-XUE

I

Figure 2.9 Flow chart of SETUP
mode interrupt routine.

 

 

RUN MODE

INTERRUPT
0 CW5

READ

       

<19

 

  
   
 

 

 

  

 

 

 

AND RESET DATA“)

INCREMENT

CHANNEL STACK INDEX
ZERO

 

 

 

 

 

 

 

 

 

INCREMENT
LOST CHANNEL
COUNTER

 

 

 

 

 

 

X- 2048¥XEIE SIGNAL TASK ‘

7
I

X-ROUTING BTS

I

 

 

 

 

 

 

 

 

 

 

 

N IS WMBER OF
BANDS Fm DETECTOR I

J-NII)

 

 

 

 

 

 

 

 

OFFSET IS INDEX ,9,”
To FIRST amoron ’ orFsETm
DETECTOR l

L

r

 

 

 
   
 

Low IS LWER “Low"

FIT 0F BAND

   

NO

 

+V
K-K+256
J'J-I

 

 

IIX+K¥8

 

 

 

 

 

 

 

 

Figure 2.10 Flow chart of RUN
mode interrupt routine.

29

The computer, when used as a particle identifiergpermits
simultaneous acquisition of more than one reaction fragment

from more than one detector with a minimum of electronics.
2.8 Data Reduction

At all beam energies except 90 MeV,the 6.05 and 6.13
MeV states were completely resolved. The peak areas and
centroids were extracted with the data reduction task MOD7
(Ba 70), operating under the JANUS time—sharing supervisor.
The data are displayed on a TEKTRONIX 611 storage scope.
The user communicates with the code through 32 sense
switches.

To ascertain the background under a peak, regions on
both sides of the peak are selected with a movable cross
and fit with a polynomial of up to ninth order. The left
and right peak limits are selected with the cross and the
area is computed by subtracting the sum of the background
from the sum of the data points.

At 90 MeV, the peaks were resolved to FWHM of the
comparatively weak 6.05 MeV state, leaving approximately
12% of its area unresolved from the 6.13 MeV peak. To
extract this area two Gaussian peaks with exponential tails
were fit to the data determining the relative strength of
the two peaks in the overlapping region. Typical X2/N

values were between 1.1 and 1.9.

25

The cross sections were calculated relative to the

monitor with the formula:

Oexp = N (Cp - Bp) / (Cm - Em)

C is the total counts in the inelastic peak, Cm is
the total counts in the oxygen elastic peak of the monitor
counter spectrum, Bp and Bm are the respective backgrounds
and N is a normalization obtained by requiring the oxygen
elastic cross section measured in the spectrograph agree

with those of Snelgrove (Sn 68) and Cameron (Ca 67).

2.9 Error Analysis

Two main factors contribute to errors in the measured

cross sections:

1) Statistical fluctuations

2) Normalization errors

To estimate the error due to statistical fluctuations,
a Gaussian distribution was used to approximate the
Poisson distribution. The standard deviation in the counts
in a peak for which a Gaussian distribution is valid is
given by /E , where c is the total number of counts in the
peak including background. The monitor counter and inelastic
scattering statistical errors were added in quadrature since

they are independent errors.

26

As a result of the normalization procedure, three
errors have to be considered. Since the normalization was
determined by forcing the elastic cross section to agree
with that measured by Snelgrove and Cameron at 60°, any
error assignment must include the experimental errors
which they assigned. This error was of the order of one
to three percent. The error in the scattering angle at
which the normalization was extracted was estimated to be
0.l°. To estimate the resulting normalization error, the
derivative of the cross section at this angle was evaluated
indicating an error of 0.5%. The large solid angle sub—
tended by the spectrograph weights the scattering angle by
the cross section. This displacement was of the order of
0.01°. These three errors were added in quadrature.

An additional error was introduced at several energies
due to a bombarding energy mismatch. Linear interpolation
of the cross section was used to correct for this. The
energy never deviated by more than 600 KeV from that of
Cameron (Ca 67) requiring a correction of 8% to the cross
section. The error in this procedure was estimated to be
0.5%. This error was added linearly to the other errors.
Table 2.1 summarizes the error contributions for a typical
point on the angular distribution of the 6.13 MeV state at

86.65 MeV.

Table 2.1

A)

B)

C)
D)

E)

27

Statistical Error

1) Inelastic peak

2) Monitor peak
Normalization Error

1) Cameron Experimental

2) Angle error at 60°
Added in Quadrature
Interpolation Error

Total Error Added Linearly

3. EXPERIMENTAL RESULTS

The angular distributions for the first four excited

160 were measured at five energies from 29.6 to

states in
90.06 MeV. Experimental errors were estimated to be less
than 5% at bombarding energies less than 90 MeV. At 90 MeV,
the errors were somewhat larger due to the previously dis-

cussed resolution problems and somewhat larger normalization

errors. Figures 3.1 - 3.8 show these angular distributions.
3.1 The 6.05 MeV State

The angular distribution for the JTr = 0+ state at 6.052
MeV of excitation shown in Figure 3.1 is strongly forward
peaked at energies above 29.6 MeV. A second maximum at 35°
_grows monotonically with energy. The minimum at 60° becomes
less distinct as does the third maximum at 80°.

The most striking feature of the angular distributions
is the rather drastic change in shape between 29.6 and 29.8
MeV. The shape measured at 29.6 MeV is essentially the same
as that of Crawley (Cr 65) at 17.5 MeV, indicating that the
shape does not change appreciably at lower energies.

In order to view the data from a different perspective,
the center of mass cross sections are plotted as functions
(If momentum transferred to the nucleus in Figure 3.2. By
displaying the data in this way, the dependence of the shape

Of the differential cross section on the energy of the incident

28

£9

 

'60 (RR) Ex=6.05 Ep=24.6 TO 40.!
- ‘Jtl=:c)+

_
I I I [an

 

—rTTHIIl ¢
0
o

 

’ . . ' o . o
. ° 00 o ‘4().IIVIQ\/
o
O
o
o
A O. O 9 o O O
s. ‘ .
U) ‘80 . 36.6 MeV
‘\ . o
D o
E I o . . . 0 ° 0 .
~—a o
' 0
C3 ' . 33.5 MeV
32» o
.8 '. . ' .
o o

I: .

I: o EESIIB IV“3\/

_. . O o O O 9 O . .

_ o

o o o. 0
OJ ‘

24.6 MeV

I |lliirq
Q

 

(3")l.L11 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 L 1 I 1 1 1

 

 

20 4-0 60 80 I00 I20

9cm (deg)

Figure 3.1 Center of mass cross
section plotted as a function of
scattering-angle.

‘5

III

\rrjnng? WWII!

(Ia/d5). (mb/sr)
ES 8

O.I

0.0I

.30

 

 

J9

ICI)_\’\TIITT

 

I6
0 (P,P’) Ex=6.05

.J“=o+

Ep=24s TO 40.1

 

O . o
. 0 9 40.' MeV
O o O O

2‘ 0
E9. 0 O . O O 36.6 MeV
P .h' 89 o
L___ ' . , . .
_ 0 o o o

. , . 33.5 MeV

. o

.. . O O o .
E
t ' . 29.8 MeV
I. O . O O o . o O O
b o o o.
_ o O O
E . 24.6 MeV
E
J l I I I 1 I 1 I4 1 1 1 I 1 I l 1_1I 1

0.5 LO II.5 2.0

O (F I
Figure 3.2 Center of mass cross

sectiqn plotted as a function of

Q : Iki ‘ k I

f

 

 

31

particle is removed. This allows one to qualitatively inves-
tigate the "directness" of the interaction. On the basis of a
simple plane wave theory of direct reactions (Bu 57), the cross
sections are functions of q. If this picture is valid, one
would expect the shape to be nearly the same at all bombarding
energies. Since this is the case for the bombarding energies
above 29.6 MeV, one is confident that the theory applied there
is valid. However, the differential cross section measured at
29.6 MeV is in serious disagreement with the others. One
possible explanation put forward by Cameron (Ca 67) is that

the reaction at this energy proceeds through states in 17F, and
thus is a compound nuclear phenomenon. A second explanation
(Au 70) is that the 0+ state is being excited through an inter-
mediate state which is strongly excited by inelastic scattering
(presumably the 6.13 MeV state). If either of these processes
have strong contributions to the cross section, the analysis

within the framework of a direct reaction theory is subject

to question.
3.2 The 6.13 MeV State

The angular distribution for the J1T = 3- state is plotted
as a function of center of mass scattering angle in Figure 3.3
and as a function of momentum transfer in Figure 3.9. These
angular distributions Vary smoothly with angle and Show
little structure. The maximum of the angular distribution
occurs at approximately 95° in the center of mass. The

magnitude of the angular distribution decreases monotonically

 

dim/d5). (mb/sr)

Jot

 

IO

A

IO

["dLITIIHW V TIIIUW

ID

A

LO

9

V I IIIUI
.
o

I IIIIIIIT V I IIIIIII

[j I IIIIII

 

O.I

J“=3

'60 (P,P’) E..=6.I3 Ep=24.s TO 40.:

MeV ‘

o o ’
. O
o
o
o
o
00.... . ‘
o . o
‘ ° 40.I
o
o 0’ .. . . o . o o O o
‘ .366 MeV
o
o
. 0 ° ° 9'0 o
0 ° 0 O
. 33.5 MeV
o
o
' o29.8MeV
o
o

' 0, .24.6 MeV

O

IIIIIIIIIIIIIIIIIILIJLIIIII

 

 

20 4O 60 80 I00 I20
QCM (deg)

Figure 3.3 Center of mass cross
section plotted as a function of
scattering angle.

dm’dQ (mb/s r)

33

 

'601P,P') Ex=6.l3 Ep=24.6 TO 40.1 .1“=3'

 

 

'0 E- 0 0 ° . -_-_-:
E . ' ’ , E
1. ..
4%, . _
0
I0 LE:- .. 0 ° 0 . . o -'_.:
r: . ° _ , 3
4:, ’ , , 40.| MeV
h 0
"D E_ 0 ’° 00 o . . . 0 O 0 -E
C .0 O O :
‘37, . o 36.6 MeV
.. . .1
Io 23" o o o o . o . . '1;
5 °' ' ‘ . 33.5 MeV 2
<2? , -«
O
_I-_—- o o 9 1
mg”... ' 29.8MeV :
_ o I
E o ‘0. i
1.0 =- . 24.6 MeV 4.-
E :1
" "I
1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1

O.I

 

0.5 I.O I.5 . 2.0
0 IF")

Figure 3.9 Center of mass cross
section plotted as a function of

Q" Iki‘kfI

34

with energy, and the shape as illustrated in the momentum
transfer plots, does not change.

The relative strength of the 6.13 to 6.05 MeV state
ranges from a minimum of 7:1 at 11° where the 6.05 MeV state
is at its maximum, to 60:1 at the maximum of the 6.13 MeV
state. These ratios confirm the assumption of Austin et al
(Au 70), that the contribution of the 6.05 MeV state could
be neglected in evaluation of the angular distribution of the

6.13 MeV state.

 

The sum of the 6.05 and 6.13 MeV angular distributions
in the present work were compared with the cross sections for
the unresolved doublet measured by Austin. The agreement was
found to be very good at 2u.6, 36.6 and H0 MeV. At 29.8 and
33.5 the agreement was good from 30° to 110°, however the
Austin cross sections fall off much more rapidly between 30°

and 20° than the present measurements, being 30% lower at 22°.
3.3 The 6.92 MeV State

The differential cross section of this state at the
lower energies decreases rapidly from 10° to 20°, level off,
then drop an order of magnitude between ”0° and 65°. The
second maximum is considerable weaker than was observed by
Crawley (Cr 65) at 17.5 MeV. The energy dependence of the
cross section of this state exhibits a monotonic decrease in
the forward angles with no apparent change in the shape

beyond 0.6f_l.

Cid/d0. (mb/sr)

\33’

'60 (P,P’) Ex=6.92

5 .

h-
C:
_ o O ’
I: 0
P
1
ICE;-
, o
t:
L. O o
L...’ . o O.
O
I:
>
O

5

 

E- o
E
I: O Q
..o’ 0 "" ° 0
’ O
‘.

0

IO '
O
00 0
O

J— ... O.
> O

O

'0... ‘
I;
L.-
L.
C o , 10
O

__ O

'0

.0
WWW—{fin

 

GCMIdeg)

Ep=24s TO 40.1 .1“'=2+

. 40.l MeV
' . 36.6 MeV

. 33.5 MeV

O

. 29.8 MeV

. 24.6 MeV

O

11I111I111I111I111I111I

20 4O 60 80

IOO IZO

Figure 3.5 Center of mass cross
section plotted as a function of

scattering angle.

 

IO

331

dcr/dQ. (mb/sr)

5

LO

0.!

.36

 

'50 (P,P') Ex=6.92. E

 

l IHHIIl

 

p
\rfl=:22+

= 24.6 TO 40.|

' . . 40.l MeV

O O
.0 O O O. O O
O
0
l0 5- '

: O

r— . O .

h’ o

1... ’ 3 O O o

L— O

4%, o

I o

:—

5” .

._ 9 o O O

_ O
o

:- ‘

E o , o o

r—

L.—

1 1 1 1 I l 1 1 1 I 1 1 1 1

I

O
O

' . 36.6 MeV

O

O

' , 33.5 MeV

‘ . 29.8 MeV

24.6 MeV

1111|1

 

0.5 1.0
Q (F")

l.5 2.0

Figure 3.6 Center of mass cross
section plotted as a function of

Q: Iki‘kfI

 

37

3.u The 7.12 MeV State

The differential cross section of the JTr = 1" state at
7.12 MeV rises rapidly from 10° to 20°, levels off, then
exhibits a weak, broad second maximum between u5° and 65°.
The energy dependence appears to be smooth, with the second
maximum growing slightly stronger with energy. Beyond 65°
the angular distributions drop off slowly. The shape ob—
served agrees with that of Crawley (Cr 65) at 17.5 MeV. In
the E = 29.8 MeV measurement electronic difficulties re-
sulted in the loss of the angular distribution for this state.
The analysis is not seriously affected due to the slow,

smooth variation with energy of this state.

38

 

 

I6 , ' , .-
0(P,PI Ex=7.ll5 15:24.6 TO 401 J“=I
I0 I..— .3
= a
y— -1
I- -I
V . ‘
'0 =3". ' ' . ’ . '-:-
<§> ’ o .
RIO-E- . o . O o. O O o . . 40.| BAG" -:
L- »— . 9 Z
(.0 (F o 2
B > ° .
E _- oo. . 0 _-
CS I0 ET? . ‘ o , o 36.6 MGV '73
3?; : ' '3
i: 4‘ o '—
3 > 33.5 MeV
ICI— —
LO" ' o . . 24.6 MeV—
O.I IIILIIIIIIIIIIIIJIIIIII

 

20 4O 60 50 I00 I20
QCMIdeg)

Figure 3.7 Center of mass cross
section plotted as a function of
scattering angle.

 

37

 

l6
0 IP,P') Ex=7.|2 Ep=24.6 TO 40.1

1":1

10r— ' ‘ ‘ . , 40.! MeV

 

o
' o
-<>, ' o
0
IO— . O O . . O O o . O
' ' . 36.6 MeV
<39 0 o
O O 00 9 O O . O o O
IC)E'.° ' o . o
I . 33.5 MeV
<45 . O O . o .
I _ I . O O O .

' 24.6 MeV

05 1.0 1.5 2.0
Q (Fa)

Figure 3.8 Center of mass cross

section plotted as a function of
->

Q: Iki'kfI

 

1+. NUCLEAR THEORY

A direct reaction is defined as one which excites only
one degree of freedom in the target nucleus (Au 61). Proton
inelastic scattering at the energies considered is assumed
to be a one step process. The interaction involves only
the projectile and one nucleon, providing a direct measure of
various components of the nuclear force. Since only one
nucleon is affected by the interaction, the cross section
will be dominated by a direct overlap between the initial
and final states. Provided that the correct form of the
operator which causes the transition is available, the
(p,p') results can be a powerful tool for investigating the
structure of the initial and final wave functions.

The calculations were all carried out within the frame-
work of the distorted wave method (D.W.M.). In this approx-
imation the scattering process is pictured as a transition
between elastic scattering states. The distorted waves
used for the entrance and exit channel, derived in the optical
model approximation, cannot be expressed in simple analytical
forms, hence the computer code "TAMURA" was used in all
calculations except a few test cases which were run with
"JULIE" for comparison. Extensive discussions of DWM have
been presented by Tobocman (To 61) and Satchler (Sa 6”). The
most important features of the theory and the approximations

employed are discussed in the following sections.

'40

”1

4.1 DWBA Formalism

It can be shown (Sa 6”) that the cross section for the

inelastic scattering process A(a,b)B is given by

 

93 = “a 2 1 EE- 2 IT | 2 (1).
d9 2th? 2 2JA+1) ka MA MB DW
mm
a b

where “a is the reduced mass of the projectile, JA is the spin

of the target, and T is the transition amplitude given by

DW

(- t (+) + + + +
TDw = 5iYXt’ ) (Kb,§b> <bB|V|aA> xa (ka,r)dradrb (2)

The x(k,r) are the distorted waves describing motion in
the entrance and exit channels. The remaining factor,
<bB|V|aA>, refered to as the nuclear form factor, is the
matrix element of the interaction V taken over internal states
of the colliding pair: It is a function of ra and rb and
plays the role of the effective interaction which induces
the transition between the initial and final elastic

scattering states.
4.2 Form Factors

In order to isolate the radial dependence, the inter-

action V is expanded in a multipole series

1 z <->J‘“ vT
LSJu

+ , A
LSJ,u (r’XA)TLSJ,-u (r,§a) (3)

H2

where xa’XA represent the internal coordinates of a and A

respectively. In this expansion we have assumed that %a = F

in (2). The spin angle tensor T is defined by

LSJ,u

T

LSJ,u

= z <LSm,u-mIJu>iLYDn(r)SS “_m (Qa) (u)
m 3

By construction V is a spherical tensor of rank J.
’ LSJ,u
Inserting the expansion for V into the nuclear form factor

we have (Sa 66)

.-L T

b

<bB|V|aA> = Z l GLSJ (r) YL; (r)(-)Sa-ma'
TLSJ
x <SaSb ma, —mb|S ma - mb>
x <JA J MA, MB - MAIJB MB><LSm, ma - mbIJMB - MA>
x <TA T TA, TB - TAITB TB><ta T Tb, TB - TAIta TA>

where the nuclear quantum numbers have been specified in
detail in an obvious notation. The transfered angular mo-

mentum Z, S, and 3 are defined by the vector relations

A B,3=§a-~§,t=3-§.

The radial form factors G(r) are expressed in terms
of reduced matrix elements of the various multipoles of the

interaction (3),

(5)

H3

0

(r) = /2sa+1 <JBTBIIVLOL

(r,xA)IIJATA > (6)

where S = T = 0.
Since different values of T contribute coherently to
the cross section, it is convenient to take all contributing

values together by defining (Sa 66)

_ T
GLSJ (r) ' é GLSJ (r)<TATTA’ TB ‘ TAITBTB>
x <taTTb, TB - TAItaTa> (7)

The radial form factors contain all the physics of the
inelastic scattering problem. The remainder of this dis-
cussion will be concerned with these quantities for the

specific models used in the theoretical calculations.
u.3 Collective Model Form Factor

In the collective model the interaction V is derived
from a non—spherical potential well which depends only on
the distance from the nuclear surface. The derivation of
the form factor is given elsewhere (Ba 62). The explicit
form used in the present calculations is (Sa 66)

1/2 1/3 b
0 _ 28.411 6% fix 1 - _L
BL a R

G - ————— L+l
LOL R r

2L+l

W
l/3 W D d
rIA I a; f(xI) - u 53 3;; f(xD){} (8)

+ i

 

uu

 

 

where
X.
el .
f(xi) = x. , l = R, I, D
l+e l
x = (r - r Al/3) / a i = R I D
i i i’ ’ ’
A L
_ Z ZA aR Rc
b — -u.32
L V r A173
R R
RC = 1.25 A1/3 fermi

The parameters VR, W, WD, rR, rI, aR, and aI were obtained
from the optical potentials of Cameron (Ca 67) and Snelgrove
(Sn 68). The deformation parameter BL was determined by
normalizing the theoretical cross sections to the data.

The reduced electromagnetic transition probability
B(EL) can be related to the deformation parameter by

(Fe 70)

B(EL; 0+L) = <Ti_-1Z-1- RE” BL)2 (9)

where a uniform charge distribution has been assumed.

The B(BL) are then related to the partial transition

widths for gamma transitions by (Pr 62)

.., 8“ . (Ev 2L+l
r = -— B(EL) (10)
L LGZL+1HI>7 “C

 

where BY is the energy of the emitted gamma ray. Care must

be taken in comparison of the deformation extracted from the

 

45

inelastic scattering to that extracted from gamma transition
rates. The radius R0 is dependent on the model chosen for
the nuclear charge distribution. Gruhn (Gr 69) has shown
that the deformations are extremely model dependent.

B(EL)'s differing by as much as factors of four were found

for different models.
”.0 Microscopic Form Factors

The radial form factor can be separated into two parts

by introducing the transition density (Fe 70)

LSJ,T (

F r1) /2(2T+1) <TA T MA, MTB-MTAITB MTB>

x <l/2T T T - T |1/2 T >
a b a

b)

X

N (F I ) T
<J I];l 5 lira TLSJ(i)T (i)llJ

l

BTB ATA >

I’

(11)

The radial form factor G now becomes (Fe 70)

_ LSJ,T “ 2
GLSJ (r) - Z 4rSTL (r,rl) F (rl)rl dr1 (12)

T

where the multipole coefficientlngL (r,rl) is related to

T .
VLSJ,p (r,xA) of equation (3) by
VT (*1-zw ( )T (A)
LSJ,u r’XA ‘ i STL r’ri LSJ,u XA Oi

 

'46

This form of the form factor provides an important
separation of the nuclear structure part contained in

FLSJ,T

from the interaction contained in‘U‘S"TL (r,rl).
Within the framework of the Born approximation, the
electron scattering form factor can be written in terms of

the same transition density as the proton scattering (Fe 70)

IF( )I2 - —1 2JB+l 2| ” ' ( r): LOL T 2 2 '(qa )2

q ‘ 2 2 2J +1 Io 3L q F ’ (r)r dr| e ———E—
z A L T 2

(13)

where jL(qr) is the spherical Bessel function.
If harmonic oscillator wave functions are used for the
single particle wave functions, the transition density can

be written (Fe 70)

LSJ T gb LSJ N+3 N -02r2 (1n)
F ’ (r) = CN 0 r e
N=N
a.
where N = (l + l') .
3. mln
Nb = (1 + 1' + 2n + 2n' - n)
max

and where a is the harmonic oscillator strength parameter,
1, l' and n, n' are the quantum numbers of the contributing
luarmonic oscillator wave functions Unl’ Un'l' .

The quantities CkSJ are sums of products of Clebsch-
Gorflan coefficients and coefficients of fractional parentage.
Since the shell model configurations for the 6.05 and 6.92

MeV states of 16O are quite complicated, the coefficients

 

117

LSJ
N

functions. Instead a least squares fit of equation (13)

C were not constructed from the available nuclear wave

to the available electron scattering data was used to de-

LSJ
N

Three forms of the radial dependence of the interaction

termine the C

were used in the calculations. The Kallio-Kolltveit (K-K)

(Ka 6”) interaction

V = 0 r a 1.025 f

the Yakawa interaction with a l f range,

 

and the Kuo-Brown (K-B) (Ku 66) interaction derived from the

long range part of the Hamada-Johnston (Ha 62) potential.
M.5 Optical Parameters

Two sets of optical potentials spanning the energy
region of this experiment were available. The potentials

of Cameron were of the form
I

V(r) = VC(r) - VR f(xR) - iW f(xI) - iWl e

+ (VSO + 1W

 

H8

2
— t
where VC - 22 e /r r 3 RC
_ . 2 2
- ZZ e 3 _ £__ r < R
ZRC R 2 C
C
X:1 -1
and f(xi) = (l + e ) i = R, I, I', SO
l/3
xi = (r - ri A )/ai = R, I, I', 80

where ri are the radius parameters and ai are diffuseness

1".

parameters. These parameters are listed in Table ”.1.

This potential contains a Gaussian surface imaginary

U-

term while the DWM codes assume a derivative Woods-Saxon 1
form:

x
D).1 ; x = (r - rI Al/3)/aD

d
”W a;— (1+e D

D D

It was assumed that the derivative of the Woods-Saxon po-
tential had the same strength and width at half maximum as
the Gaussian potential; thus W1 = WD; and aD = 0.072aI.
These potentials were used in most of the calculations be-
cause the fits were made to data at bombarding energies
closest to those of this experiment.

The other optical potentials were those of Snelgrove

(Sn 68) which were of the form

d
S - UWD Egg) f(XI)

2
h l d .+
" Vso (m c) s a; “W (I 0’

V(r) = V - VR f(xR) - i(W

C

 

1+9

where VC(r) and f(x) are as defined above. The fits obtained
with these parameters were within 10% of those obtained with
Cameron's, hence were used mainly as a consistancy check

throughout this work.

ins

50

Table ”.1 Optical Parameters

Optical parameters of Cameron (Ca 67)

E V W W V

p R D 80
(MeV) (MeV) (MeV) (MeV)
23.“ ”7.25 0.0 7.06 ”.09
2U.5 ”M.SI 0.0 6.83 5.Ul
27.3 H8.u3 0.0 7.28 5.63
30.1 ”7.50 0.0 8.35 6.82
3H.1 ”7.02 2.31 6.52 6.UH
36.8 ”6.37 0.28 8.55 7.98
39.7 ”6.58 2.25 7.65 7.32
”3.1 ”H.67 3.15 6.32 6.20

The geometrical parameters are:

rR = 1.1M2 F PI = 1.268 F r80 = 1.11” F
aR = 0.726 F aI = 0.676 F aSO = 0.585 F
aD = 0.H63 P rc = 1.25 F

Snelgrove average optical parameters are (Sn 68)

VR W WD V

SO
(MeV) (MeV) (MeV) (MeV)

“6.8 0.80 6.20 7.0

Table ”.1 cont.

51

The geometrical parameters are:

rR - r80 = 1.12

aR = aSO = 0.60

1.35 F

0.”8 F

I‘

1.15 F

5. COMPARISON OF DATA TO THEORY

5.1 Collective Model

The calculations for the 3- state at 6.13 MeV, shown in
Figure 5.1, exhibit the correct phase and general shape, but
do not agree in detail with the data. At all energies the
fits tend to fall off more rapidly than the data between
50° and 100°. A shoulder predicted by the theory from 85°
to 110° is not observed.

The calculations for-the 2+ state at 6.92 MeV were also
in general agreement with the data. The slope of the forward
angle differential cross section was too large at all ener-
gies, but was better at higher bombarding energies. The
calculations reproduced the position and relative magnitude
of the second maximum but tended to drop off more sharply
than the data.

The calculations for the 1- state at 7.12 MeV displayed
much more structure than the data. The first and second
minimum as well as the second and third maximum predicted by

the theory were not observed.

5.2 Microscopic Model

The coefficients C§SJ of equation (1”) were determined

for all states by a least squares fit of the electron scat-
tering form factor defined by equation (13) to the data of

Bergstrom et a1 (Be 70) and Crannel (Cr 66). For the 7.12'

52

IBOIP.P‘I
15 COLLECTIVE

A A ~A_A;..

IO‘

10

A— A A—AAAAA

10I

’dCT/dfl (mb/sr)'

A

4

IF

 

 

53

EX28.13 EP=29.8 3E-It
“DEL

40"

38.6

33.5

2 948

2 4.5

 

JW.5:

CENTER OF

L l L ._J l L L L
“If. ' ' '807' r 780. IOEI. I20. '0'
mass SCRTTERING ENGLE X10

Figure 5.1 DWM calculations for
the 6.13 MeV state. Normaliza-

tions were extracted from the
integrated cross sections.

5”

IEOtP.P‘I Exas.92 EP:2”.S 21+:
10‘ COLLECTIVE MODEL

6.

4OJ

3 6.6

33.5

29.8

 

24.6

 

I.

4 . . . k. L. l . . . I L_. . l L . . l L . l ;;4
U. " ' '20. TI 5'10. ' I I60. T 5 F8075 ITOU. ' ' I20. 0
CENTER OF mass SCHTTERING HNGLE X10

Figure 5.2 DWM calculations for
the 6.92 MeV state. Normaliza—

tions were extracted from the
integrated cross sections.

dry/(IS). (mb/sr)

55

 

   
 

 

'60(P.P’) Ex=7.l|5 Ep=24.6 TO 401 .1"=1"
COLLECTIVE MODEL
“3 E‘ a
d: -
IO § —§
4?: ..
IOE‘ “:5-
‘12 40.1 MeV J
10 E". “g
f; 36.6 MeV _
I 2' 33.5 MeV 31
3
: 24.6 MeV ..
1 1 11 I 11 1 11,1 11 1 11 I 11 1 I1 1 1| 1
O.I O 20 40 60 80 I00 I20

 

 

Ocmweg)

Figure 5.3 DWM calculations
for the 7.12 MeV state. Nor-
malizations were extracted
from the integrated cross

sections.

56

.A90 Hmv 009009 .m.z.9 9Q0H0>9SU0 9E90m 099 £993 :099SA999090 0m90£0 E90990:

m0955000 0909909099 0990cw0EO99o090 5099 U090099X0 0903 0909905909090

.090905090m 9009990 90 0900 9:0909990 mcwms >0 00:09 >0c0a090090

039 £993 0939090000 :9 00000 090990 90099099090 0:9 090 009050 09099m

«mmoo.o
£mm.o

«mm.o

Ho.owom.o
Ho.oumm.o
mo.onm.o

>02
H.o:

Ho.ouom.o
Ho.ouow.o
mo.onm.o

>02
m.mm

Ho.oflom.o
Ho.oumm.o
mo.oflmm.o

>02
m.mm

Ho.oumm.o
:o.oflkm.o

>02
m.mm

Ho.oumm.o 99.9
Ho.oHs~.o No.0

mo.ouoo.o m9.o

>02 >02
0.3m >m90¢m
00990990xm

.009m9090 wcflv90naon

0>9w 90 0999 H0005 0>99o0aaoo 5099 0090099x0 40 0909080909 00990590900

H.m 09n0h

57

LSJ
N

of Gillet and Vinh Mau (Gi 6”). Since these wave functions

MeV state, the C were constructed from the wave functions
for the 6.13 MeV state were used by Austin et a1 (Au 70),
these calculations were not repeated.

The inelastic electron scattering data illustrated in
Figure 5.” for the 6.13 MeV state covers the entire range of
momentum transfers spanned by proton inelastic scattering,
providing a good test of this method.

LSJ,T

The explicit transition densities F obtained from

the fitting procedure were:

POOO’O = (1.47 03 - .922 05 r2) e'o‘2P2

F303’0 = (-0.537 cur + 1.89 06r3 - 0.111 a8r5) e_a2r2
F202’0 = (-1.41 05r2 + .900 670”) 6"”‘21”2

F101’0 = (3.87 cur - 1.57 cars) e-02r2

The chi-square searches were undertaken with the h0pe

that the coefficients C would converge to values which re-

N
flect the shell model configurations from which the states
are to be constructed. This was not found to be the case.
The coefficients of the terms in the transition density were
not uniquely determined by the fitting procedure. A wide
range of parameters were found to give approximately the
same values of X2. One finds that the more parameters one

allows to enter into the expansion, the better the fit that

is obtained.

(FtOIIooQ

x10 -3

7.00

A
r

A
V

r

1.01

A
f

0.01

A
7' r~ 7

:IT

 

L__ . . L I

58

ISOIE.E‘I EX-6.13 FIT TO ELECTRON SCHTTERING 0819

9
0(3)! -0.Ill

,XTNMO.

II

. . . L .
r ' ' 1:6 ** '* r 2.0 T
o (1/F1

Figure 5.” Electron scattering
form factor using the transition
density extracted from the least
squares fit.

 

IIII)... {in (1111.; .

 

 

 

59

On the basis of this experience, no structure infor-
mation can be extracted from the fits. The expansion in
terms of harmonic oscillator wave functions is to be viewed
as a convenient form because it provides coefficients which

can be input directly into available form factor codes.
5.3 Comparison of Microscopic Fits to the Data

The calculations for the first excited 0+ state at
6.05 MeV were very poor at lower energies but improved
significantly as the energy increased. This improvement was
due to a slight increase in the structure exhibited by the
calculations and a rather large decrease in the structure
of the experimental angular distribution.

The rather large discrepancy at forward angles is par-
ticularly disappointing because the electron scattering data
shown in Figure 5.5 covered the corresponding momentum transfer
range. The underestimate of the second maximum is not a
serious problem for two reasons: first because the electron
scattering data did not exist for the corresponding momentum
transfers requiring extrapolation of the transition density.
Secondly, the shape of the angular distribution in this region
is very sensitive to the point at which the form factor
crosses zero (Figure 5.8). By forcing the form factor to
cross zero 0.” fermi closer to nuclear center, the second
maximum could be reproduced at all energies.

Inclusion of the exchange contribution increased the

forward angle cross section by approximately a factor of 2.5

 

(FtOIIch

60

IEOIE.E‘I EX=6.052 FIT T0 ELECTRON SCRTTERINB DHTH

01
o
O
r‘ A. " 4" v r

Ul
O
c:
r—T 6—

.1
7'

C(2I=-.92299 ‘

0 XZ/N=O.73

 

 

 

 

Figure 5.5 Electron scattering
form factor using the transition
density extracted from the least
squares fit.

 

Cid/d5). (mb/sr)

K
'00 :7
r

[.0 -

O.I

0.0I

6!

t. J

 

 

 

I 7r 111ml V "

 

 

I60 (P,P') Ex=603 Ep=24.6 TO 401
' 1J"=O*

YUKAWA FORCE
TRANSITION DENSITY FROM ELECTRON
SCATTERING DATA

40.I MeV

36.6Mev

 

 

33.5 MeV
E. 298 MeV
I: 24.6MeV
a 1 1 1 I 1 L 1 I L 1 L I I 1 1 I 1 1 1 I 1 I I I 1 1 1
20 4O 6O 80 I00 I20
OCM(deg)

Figure 5.6 DWM microscopic calcu-
lations using a If range Yukawa
interaction. The strengths were

extracted from the integrated
cross sections.

 

("Ia/0'0 (mb/sr)

62

 

.0

0.0l

'60(1=,P') Ex=6.05 Ep=246 T0 401 .1"=0“
K-1< FORCE 111011 OUT EXCHANGE

fTRANSITION DENSITY FROM ELECTRON
ESCATTERING DATA

 

  
 

 

 

 

40.1 MeV E
36.6 MeV _:
g:
:3— 33.5 MeV .1
E
E- 129.8 MeV -;
" ‘ 24.6Mev I
1.111I111I111I111I11LI11LI111
O 2.0 40 6.0 80 I00 IZO
€%M(deg)

Figure 5.7 DWM microscopic
calculations using the long
range part of the K—K inter-
action.

FORM FRCTOR

 

 

63

 

 

x10 0 FORHFQCTCR FOR U(+) STHTE WITH K'K FORCE
TRHHSITIOH DENSITY FRO“ ELECTRON SCHTTERING BETH
0: II'
.1
1
-50 ‘1' *
1L
11
'10. ‘b
.1
'15: ‘1'
I1
I II
1
-20, .1.
1L I1.
-25. ‘-
L A 4’ ‘ I ‘ ‘ - L . . 1
OT . . 72:0 . 7 ”HI I T150
1110 U

R (FERHI)

Figure 5.8 The form factor for

the 6.05 MeV state without in-
cluding exchange.

6”

and the total cross section by a factor of 3. The second
maximum between 60° and 80° was enhanced slightly.

The fits obtained using the K-B and K-K force were
identical in shape with the K-B being approximately 28%
smaller.

The Yukawa potential was also very similar in shape to
that of the K-K and K-B, but slightly less forward peaked and
thus in somewhat better agreement with the data. The strength

of the effective interaction was extracted by normalizing

 

the integrated cross section of the DWM calculation to that
of the data. The meaning of this strength is somewhat
clouded by the quality of the fit. These strengths are pre-

sented in Table 5.2.
5.” The 6.13 MeV State

The calculations with the K-K, K-B, and Yukawa forces
with the exchange contribution included, were all very
similar. The K—K and K-B interactions predicted identical
shapes with the K-B force about 35% smaller in magnitude.

The Yukawa fell off slightly more rapidly with angle, thus
providing the best fit.

The calculated cross sections reproduced the data out
to about 50°. From 50° to 70° the calculations with the
exchange contribution included overestimated the cross
section. This overestimate reached approximately ”5% by 70°.

Calculations neglecting the exchange contribution, when

(ICC/0.9. (mb/sr)

IO

IO

.11-.44..a

5

1 1* IN!” "1 IIWTTUF“

I.O

O.I *F

65'

 

‘q T1711”

 

I T [WWI

 

I6 11 ..
O (P,P') Ex=6.l3 Ep=24.6 TO 40.I J =3
YUKAVM FORCE ‘4“! ITH EXCHANGE

TRANSITION DENSITY FROM ELECTRON
SCATTERING DATA

 

' . 29.8 MeV

/\ A 3 . 24.6 MeV
. ‘:T77:“\\\~

 

1 1 1 I I 1 1 I 1 1 I I 1 1 1 I l 1 1 I 1 1 1 I 1 I 1

 

20 4O 60 8'0 I00 I20
0 (deg)

Figure 5.9 DWM calculations
using a If Yukawa interaction.
The strengths were extracted
from the integrated cross
sections.

 

 

66

15019.9-1 Ex-s.13 Ep.2u.s T0 «0.1 41911-31-4
.K-K FORCE HITH EXCHRNGE
go TRHNSITION DENSITY FROH ELECTRON scaTTERINC 08TH

 

 

 

1r
:1 . ’ ' .
l1
1
10:."
3
n
d
l
{I 400'
101,
1
’1: 36.6
:0
\ I
4:
E “’1’
V 1.
i 33.5
C: r
‘2
g 29.8
1011 . . - .
II - - . ‘ o O
1 ,
0 ' " 2406
' ”Ir -
1; _
o
a
1+
1n
0 2 0 q 0 6 O 8 O o O O a
CENTER OF nass SCHTTERING HNCLE X10

Figure 5.10 DWM calculations
using the long range part of
the K-K interaction.

67

 

 

 

 

.P'I EX-B.13 EP-Zq.6 T0 “0.1 JIPII-St-I
. ~a FORCE HITH ExCHRROE .
.09 TRHNSITION DENSITY FROM ELECTRON SCHTTERING ORTa
Ra
4CL1

t .

10
~Q
.13
E5
V 36.6
g
\x u)
t)
It: :53C5

O
'0 5 o " O .- O 2908
o . ’ - o O
' '* . 2&6
14) -
OJ“ 2'. III- 6'. 8|. 0'. 21,
CEN.=R OF Mass schTERTNO HNGLE X10 0

Figure 5.11 DWM calculations
using the K—B interaction.

68

normalized to the data at u0°, underestimate the data by
approximately 20% from 50 to 75°. This implies that the
approximate method for including exchange tends to exag-
gerate its affect in this region.

Beyond 75° all calculations overestimate the cross
section. This overestimate is attributed to the fact that
the electron scattering data in the corresponding momentum
transfer region did not resolve the 2+ and 1- states from

the 3‘. The transition density extracted from the fits

1'

1‘

includes contributions from these states and is expected to

overestimate the 3- cross section.
5.5 The 6.92 MeV State

The Yukawa and K-K interactions, as in the case of the
6.13 and 6.05 MeV states gave very similar fits. Both forces
overestimate the forward angle cross section and reach their
first minima and maxima about 10° early. The exchange con-
tribution again overestimates the large angle cross sections.
These calculations are illustrated in Figure 5.13 and 5.1”.
Figure 5.12 shows the fit to the electron scattering data.

The strengths extracted for the Yukawa interaction are

listed in Table 5.2.
5.6 The 7.115 MeV State

The electron scattering data for this state, as is

evidenced by the fit in Figure 5.15 did not cover a

(H0 I I-MQ

 

69

 

EX26.92 FIT TD ELECTRON SCRTTERINB DRTR
LIB
I 2/1\1-1 4
1‘ I X " ‘
3.0‘
205‘
2.0‘
iOS‘
I
1
100‘
0.5‘
I
0.0‘
' ngv a :7 e I- t : :7 * 1, e—4—
0. 3.5 1.0 1.5

0 (HF)

Figure 5.12 Electron scattering
form factor using the transition

density extracted from the least
squares fit.

70

 

'60(P,P')_Ex=6.92 Ep=24.6 To 40.1 .1"=2+
YUKAWA FORCE WITH EXCHANGE
TRANSITION DENSITY FROM

. ELECTRON SCATTERING DATA

 

,-/\- n‘ *

 

a: 40.! MeV
Q A, \ ,\ :- - ! r
n
:3,
36.6 MeV
‘5
D
'0

. 33. 5 M 8V

29.8 MeV

 

 

24.6 1’3 OV

A A A 1 A A A l A A A l A A 9 A A A l A A

L L 1l11uI 1‘1 1 1Lu1I J 1 111111l 1 1 1111111 I L1141IlI

L L lJILul

 

 

20 4O 60 80 I00 IZO
OCM(deg)

Figure 5.13 DWM calculations
using a 1f range Yukawa inter-
action. The strengths were ex-
tracted from the integrated
cross sections.

(If/33.513 (mb/sr)

5

~

A

Rf’“”rfiT

as A
Tfivmmmq

5

N

5

”WTWW

<1 335
II
POI:-
E nfinn
t 25.01
I
I. 1.5 2.4.6 3

q L
C'-

71

 

'60(P.P’) Ex=C.°~2 Ep=24.e TO 40.1 .1"=2*
K-K FORCE mm EXCHARCE
TRARs1T1C-1 DENSITY Fro

ELEC RON OCATTEREE‘JO DATA

 

III

   
   

If

‘TTW

,7_1 L1,I 11 1 I1 1 1I 1 11 I 11,1 In 1 1I 1 1
3

o 20 4O eon o zoo 120
I681? {32'

ff)

.fi‘s
{T

"AEJ

Figure 5.1M DWM calculations
using the long range part of
the K-K interaction.

 

 

‘II'

72
Table 5.2

Values of VOO in MeV obtained from the microscopic

calculations using the Yukawa interaction.

State
Energy 2H.6 29.8 33.6 36.6 40.1
MeV MeV MeV MeV MeV MeV

6.05 35.0:2.5 37.0:2.6 32.0:2.2 32.0:l.6 33.0:1.6
6.13 66.0:5.0 59.0:3.0 66.0:3.0 59.0:3.0 59.0:3.0
6.92 48.0:3.O us.o:2.o 46.0:2.0 47.0:2.O 45.012.O

7.12 26.8:l.5 ---- 21.6:l.l 21.6:l.l 21.6:l.l

Errors listed are the statistical errors added in
quadrature with the fluctuations found by using different

optical parameters.

73

sufficiently large range of momentum transfers to adequately
define the overall normalization of the transition density.

The calculations using the K—K force with this transi-
tion density overestimated the cross section by a factor of
5. The experimental shape, as expected, was not reproduced
for momentum transfers larger than those covered by the
electron scattering data.

The transition density constructed from the wave functions
of Gillet and Vinh Mau did a good job in reproducing the
angular distribution out to 80° with the K-K force being
slightly better than the Yukawa. Beyond 80° the fits fall off
much more rapidly than the data.

The strength of the Yukawa interaction was extracted as
before. In this case both the (LSJ) = (101) and (111) terms
were summed and thus the strength of V00 and Vlo are included.
The contribution of the spin flip term is of the order of 2%,
permitting the extracted strength to be identified as V00.

The values are listed in Table 5.2.

(F(0II-¢§2

 

74

 

lgfltEaE'I EX=7.12 FIT T0 ELECTRON SCSTTEKING 09TH
no -3 CI: 1 3=’I.FEI.3253
q 0‘_ C(23=.&de3
.1 1w? .5
is //?h::E<)o
I
{I
3.0“
11
TI
1
2'0‘b %
(I
9
1
I O
1.0.. .
«I I",
a
0.0"-
hJ——+—4——+—a——J ., :4 t : 3 ,_ t t; . J L44 : ‘ L
0.0 6.3 1.0 3.: 2.0
10 3

OtI/FI

Figure 5.15 Electron scatterin

form factor calculated from the
transition density extracted
from the least squares fit.

dJ/dfl (mb/sr)

H3“

10

 

 

75

IBUIP.P‘I EX:7.12 EP=24.8 T0 ”0.1
YUKBHH FORCE WITH EXQBRHSE
TRRNSITION DENSITY qufi BILLET END VINH flfiU

4 I_. _. . I I ,_1 _4
’20. T'7 740. r r '80. 7 'TBU. r '
CENTER OF H955 SCHTTERING RNGLE

j j
r“ r

Figure 5.16 DWM calculations
using a 1f range Yukawa inter-
action. The strengths were ex-
tracted from the integrated
cross sections.

4 I l l A j l

100. '

JIPllslt-I

 

Q. (mb/sr)

d

U]

‘ IV?)
(I. I w
.4

7b

 

“50113 P’) Ex=7.12 Ep=24e To 40.1 .1"=I"
K K FORCE 1511 H EXCHANGE FITsx o 2

TRANSITION DENSITY Fem ELECTRON
SCATTER'YG DATA '

IO

IO

 

' ITIITHI “VA—r I [[1111

. I.

I0

IO

 

T T I—I—TII]

   
   

33. 5 MO

'9
‘I

 

O.I JILIIILIIQIILIIIIILIIILILII

20 4C 60 Co 100 120
I

Figure 5.17 DWM calculations
using the long range part of
the K-K interaction.

m3

\Jcnm (Cflg

24.6 MeV

 

IO

.4;

" V Y T'Y'V‘r‘

‘v-

 

10-

'fl
9"”-

{Hart i 1&1

'1 L‘s-11:3

11 1'13... 111.1211. .1", r." '1 111.111 1
AK. 4. . s “Owl “0 J 5 '4'.
l“ . 1 .;

ME! I I l P" ' P .l

‘3 {141... 14.7.-;_£T ,1

 

14CL!

33:5

 

, L n ' L 4 n 2 n n 1 ' n. l
r r, r_ v r Y’AP. r 1 1'9". r r .1 r....
‘\-' O "“10 Du. h.-‘\.'o ‘UJO ‘\-o
.. .- 1101‘ U
1111111 -_-- .4- . .43.. ~-:~- 711111.15 (11111:: 1:: 11.11..
1 1'_ o 2....451..U 60 Was-ah:

ure 5.18 DVH calcula

the
-K

tion
long range art of

interaction.

6. SUMMARY OF RESULTS AND CONCLUSIONS

6.1 Results

The deformation parameters,B, extracted from the col-
lective model are tabulated in Table 5.1. These values ex-
hibit no energy dependence from 30 to #0 MeV. The large
differences at 24.6 MeV are attributed to the difficulty in
fitting the elastic scattering for the exit channel. The
deformations extracted from the partial transition width data
of Alexander and Allen (Al 65) for the 6.13 MeV state to
ground state transition and of Evers et al (Ev 68) for the
6.92 and 7.12 MeV states to ground state transitions are
compared to the present values. The radius of an equivalent

uniform charge distribution (El 61), R : 1.35 Al/3

, was used.
The agreement is very good for the 6.13 and 6.92 MeV states.
The 7.12 MeV state is expected to show poor agreement because
the isospin selection rules prohibit electromagnetic dipole
transitions in N = Z nuclei (Tr 52). Since the shape of the
differential cross section calculated using collective model
were in poor agreement with the data, the deformation ex-
tracted for this state is of questionable value.

The strengths of the central part of the real Yukawa
interaction are tabulated in Table 5.2. The validity of

these strengths for the 6.05 and 6.92 MeV states is ques—

tionable due to the poor overall fits.

78

79

The three interactions used in these calculations pro-
vide the same shapes for the angular distributions. The
magnitude of the K-K was in good agreement with the data
while the K—B was about 30% low. The Yukawa, when normalized
to the data was almost indistinguishable from the K-K. On
the basis of overall magnitude, this study indicates that the
K-K interaction provides the best description. No conclu-

sion, however, can be drawn from the predicted shapes.
6.2 Conclusions

From the analysis of the data presented, it appears
that the transition density obtained from electron inelastic
scattering provides a description of the nuclear structure
adequate for calculating cross sections with realistic
nucleon — nucleon interactions. The success in reproducing
the general features of the angular distribution of the 3-
with the K-K interaction encourages further development of
this approach where good electron scattering data are avail-
able. One can now require the electron scattering form
factors to predict the proton inelastic scattering, elimi-

nating ambiguities which might otherwise occur.

 

 

APPENDIX A

16

Tabulation of 16O(p,p') 0* Differential Cross Sections

The following pages contain listings of the laboratory
and center of mass differential cross sections with the
corresponding statistical and total errors for the inelastic

16

scattering of protons by O. A discussion of the errors

is found in Chapter 2.

80

160(P1P')166

EP8 24063 EX! 6005

81

CO”. ANGLE SIGMA C0M0 LAB ANGLE SIGMA LAB

(Ma/SR)
307686-01
30809E-01
30426E-01
30456E-01
3.354E-01
3'2C1E'01
3.2585-01
2.998E-o1
208488-01
2'383E'01
10539E-01
10029E-01
101015-01
10449E-01
104465-01
103425-01
101115-01
506815-02

(MB/SR)
9.893E-01
7.981E-o1
506115-01
#03155-01
302455-01
20730E-01
107245-01
102185-01
90944E-02
l'OOEE-Ol
102195-01
103995-01
101065-01
5’292E-02

‘ (DEG) (MB/SR) (DEG)
10.64 3.2696-01 9090
looco 303195'01 14090
21036 209935'01 19090.
28084 30039E'01 26090
36029 20985E'01 33090
42065 20867E'01 39090
47092 20992E'01 44090
53018 20733E'01 49090
58040 206235'01 54090
63061 202185-01 .9090
71087 1.460E-c1 67.90
80°05 909515'02 75090
90017 10092E'01 85090

100.16 1.476E-01 95090

110002 10511E'01 105090

113092 104165‘01 109090

119075 101905'01 115990

129036 602365'02 125090

165(PIP')168.
EP‘ 29081 EX' 6'05
c.m. ANGLE SIGMA c.M. LAB ANGLE SIGMA LAB
(DEG) (MB/SR) (DEG)
11.69 80615E’O1 10090
15097 60966E'01 14090
21032 409155’01 19090
26066 30798E‘01 2Q09O
34011 20880E'01 31090
39041 204405'01 36090
46080 10558E'01 #3090
51.00 10109E'01 47090
55019 901215.02 51°90
63051 90346E’02 59090
71077 10158E'01 67090
79095 1035#E'01 75090
88005 10092E'01 83090
10#001 50442E‘02 99090
113082 309fi6E'02 109090

3'7“3£-02

STAT. ERRBR TBTAL ERRBR

b?

.0 0‘00 0 o. o o. o
WLNHWUUTOC)HLflUHJ\JV

wcouwrunJm(oumrun)m’~

STAT- ERRaR TBIAL ERRGR

(Z)
'1.7
201
105
207
209
300
303
309
305
300
303
206
209
401
401

(X)
400
306

g
.

(fl#n¢#r¢4>#WF#P¢LU#W#4?w
IULHGHUC)\Hfl\J#CDODmLUUTm(O

(Z)

mcnrwn4>¢nctn¢up0rwruu3m
mmowmmmormHmmtw

C.M.

C0M0

165(P1911168

EP‘ 33048
ANGLE SIGMA C0M0
(DEG) (MB/SR)

9054 605135'01
11068 é'OIEE-Ol
15096 406545'01
21031 30876E'01
24051 30333E'O1
28077 30273E'01
23077 20963E‘01
31096 209845'01
37026 20539E'01
42055 1095CE'01
47082 1'“OBE'01
53036 1I057E'Ol
58.28 7.5575-02
63047 EOEQIE'OE
68064 90235E'OP
76085 100365'01
84098 90455E'02
94033 70434E’02
Q3096 40543E'02

163(tUt”)165

EP: 35055
AVGLE SIGMA C0M0
(DEG) (MB/SR)
10061 4-7325'01
15095 3'817E'01
15095 306995'01
2103C 3'1935'01
21030 3’175E'01
28076 20765E'O1
31095 208525'01
37025 20406E‘01
42053 1'774E'01
47080 1'244E'O1
53004 90h55E'02
63045 50704E'02
73075 60503E'02
83094 60661E'02
94000 607885'09
99098 6'071E'02

118061

109955'0?

FX3

.0-

LA?

6005

A\3LE
(DEG

3090
10'93
14090
19090
32090
26093
26090
29090
34090
39090
44090
49.90
54090
59090
64090
72-90
30090
39090
99090

EX: 6'05

LA?

ANGLE
(DEG)

9093
14090
1QOSC
19993
19993
26090
29093
34090
39090
44090
49090
59090
69093
79090
89090

(t‘ (3
330,0

114090

sxswA

82

LAB
(rs/SQ)
70423E-O1
50324E-01
404185-01
3.79SE-o1
3.705E-o1
3.354E-o1
303665-01
20845t-01
20169E-Ol
105515-01
I'ISSE-Ql
8.1828-02
80833E-02
90788E-02
1-0465-31
906475-02
7-4165-02
40420t-02

SIGMA LAB

(MB/SR)
504226-01
40363E-01
402285-01
306435-01
3.6175-01
30128E-O1
302155-01
20694E-O1
109725-01
10372E-01
1°O335-01
7.1335-02
603115-02
60812h-“2
60766E-02
S0966E-32

1o7‘QE-02

‘¢u}waUJN(JRJwFUhJN<¢fi1N

~0or-cnwwm0ro<>uruznwn»

STAT. ERRBQ TaIAL ERROR

(Z)
108
207
20k
208
20#
304
207
209
300
303
300
303
304
303
305
307
507

UL¢4rML#UJ¢LQ$WJUJNCHQHUnJ¢
ooooooooooooooooo
C)0CD\U‘CDQHOC)N‘QUHHP.\HOP‘

(z)

«»4>:.¢¢u¢¢r¢4>¢99¢wu$wu¢rw
OOOOCCOCOCCCOOOO
\nmu1wcn:~»uuumn00vv~ooc>w-

163(P1P')163

EP= “3'37 X: 6°CS_

C0M0 ANGLE SICVA CoV, LAB
(DES) (VB/SR) (3E3)
10°60 3'2165'01 9093
21029 30356E’Cl 19090
31093 207955‘01 29090
37023 20193E'01 34090
42052 105455-01 39090
53032 70705E'02 49090
58-24 6-aaoE-ce 54-90
63043 600335'02 59090
73073 50175E-02 69090
78083 4058fii‘02 74090
83091 “OISIE'CZ 79090
91097 40689E'02 87090
108083 20929E'02 104090

160(P191)169

EP= 24063 EX3 6913

C0M. ANGLE SIGMA C0M0 LAg ANGLE
(DEG) (HS/SR) (DEG)
10054 70185E+00 9090
16000 70525E+OO 14090
21036 8013OE+03 19090
28084 80361E+CO 86090
36029 30301E+03 33090
42065 908765+OO 39-90
47093 906BEE+OO 44090
53018 90215E+OO 49090
580#1 50449€+OO 54093
63061 703385+OO 59090
71088 507825+OO' 67090
80006 40250E+OO 75990
90018 2097OE+OO 85090
100017 '2027QE+OO 95090
110033 108935+OO 105090
113093 10704E+OQ 109090
119076 106BSE+OC 115093
129037 809O3E'01 135090

83

ANGLE SIG%A LAB

(MG/SR)
50973E-01
308195-01
30093E-Ol
204505-01
10720E'01
69945E-02
604235-08
50419E-02
40744E-C2
(+0275E-02
4970lE-02
808165-02

SIGMA LAB

(MB/SR)
80285E+OO
80657E+OO
903135+OO
10OCSE+01
1-049E+01
10103E+01
10066€+01
100115+01
901765+OO
708335+00
60098E+OO
4039SE+00
20993E+00
2023EE+OO
108115+00
10614E+OO
10519E+OO
801925-01

STAT. ERRSQ TOTAL ERROR

(Z)
109
204
202
200
303
301
305
303
303
4.0
303
309
504

STAT- ERRBR TBIAL ERPSQ

(z)
005
005
005
O04
005

005'

005
004
005
005
005
005
007
007
008
100
009
100

(X)
6'5
609
606
603
707
703
706
704
70“
802
704
800
905

(X)
201
201

runnmrun1mwannvn0m
0.0.0.0....
.pn3¢rowua\DHWUh*O

C0M0

C0".

ANGLE
(DEG)
11069
15098
21032
26065
34011
39041
46030
51001
55019
63052
71078
79096
88006

104002
113083

ANGLE
(DEG)

9'54
11068
15096
21031
24051
23077
28077
31096
37027
42055
47082
53006
58028
63048
68065
76085
84098
94003

103-97

E?

S

EP

8

.163(P,P')163

= 99081

IGVA COM0

(Ma/SR)
50597E+OC
50889E+Oc
50447E+OO
70373E+CQ
803325+CO
900555+OO
90254E+OQ
8.771E+oo
80157E+OQ
5088OE+OO
3-836E+03
20#31E+OO
10624E+OO
100315+OO
70954E'01

EX=

5'13
LAP AKSLE
(DEG)
10090
14-93
19090
24090
31090
36090
43.90
47090
51090
59090
67090
75090
83090
99090
109090

1AH(D,D')1A5

= 33048

IONA CoM.

(M3/SQ)
4-757E+OO
5024ZE+OO
60026E+00
60984E+OC
704385+OO
80396E+OO
709785+OO

80465E+OO'

9OIQIE+OO
90534E+OO
90157E+OQ
80963E+OQ
609SOE+OQ
50371E+OC
40074E+00
ZOSOOE+OO
10617E+CO
10074E+OO
70025E'01

Fx:

6013

LAB ANGLE

(DEG)

80’9C
89093
99990

8”

SIGWA LAQ

(MB/SR)
604235+CO
607495+QQ
703616+oo
89379E+Qo
90447E+OO
10OISE+01
10024E+01
90638E+OO
80894E+OO
60307E+OO
4°O4OE+OO
20512E+OO
106#5E+OO
90735E-01
70545E-01

SIGMA 9A8

(MR/SR)
504725+OO
600115+OO
écsasa+oo
79952E+OO
30515E+00
§OSC7E+OO
9.034E+oo
9°552E+00
1P0?Ot+01
190615+01
190105+01
9OOQEE+OO
70526E+OO
So755£+03
#03185+QC
2.601E+oo
1&6505+CO
10071t+00
60833E-01

STAT. ERRfiR TSIAL ERRO?

(%)
007
0'7
00%
006
O05
005
004
004
004
O0#
006
006
O07
009
009

STAT. ERRGR TBIAL ERROR

N

naraoc3c30<3c>o<3c>o<3c>ocac:o-»F~
oc3xsonnunwuatcucwnaacch¢wnme

4N
v

RHVTthwwahnHwar¢nHDF-mfvr~
OOOOOOOOOOOCOOO
Ht‘C)m\O\JVCD030C)HWQRJH

(X)
207
200
203
107
109
107
203
109
107
105
106
105
105

’105

106
106
108
200
200

85
1623(Pjp' )1’.“

SP: 36056 X= 6013

m

c.M. ANGLE 31$”A C.M. LAP ANGLE SIGMA LAB STAT. ERRa? TeIAL ERRB?

(Dag) (”B/SR) (000) (”4/SR) (Z) ‘2’
10.51 3.811E+cg 9.9g 40368£+00 0.5 202
15096 40913€+03 14090 50499E+QQ 007 205
15096 4.759E+CQ 10.99 504415+00 006 203
21033 50939E+OQ 19093 606515+QO 006 20“
21.33 50939E+03 19093 50765E+Qo 005 202
28076 70335E+OC 3609C 80299E+OO 006 205
31095 70733E+QQ 29090 807IBE+00 005 203
37025 50877E+00 34090 90943E+OO 005 202
42.53 9°148E+co 39093 100165+01 004 201
47050 E0793E+OQ “#090 90701E+CO 004 200
53004 705535+OO 49090 80254E+CO 003 108
63045 40579£+OQ 59090 409CSE+OO 004 108
73076 E0555E+CO 69093 20677E+OO 005 108
83.90 10451E+oo 79.90 10484E+oo 007 109
94030 80983E'01 89090 80958E-01 009 201
99098 60864E-01 95090 60743E-01 103 202
118062 20662E'01 114093 20#99L-01 104 205

169(P:P')168

EP= #0007 EX: 6013

C0M0 ANGLE SIGMA COM0 LAR ANGLE SIGMA LAB

srAro ERRBR TQIAL ERRGR

(DES) (MB/SR) (050) (MB/SR) (2) (x)
10.60 4.234E+00 9.90 0.849E+oo 006 508
21029 600135+oo 19.90 60844E+OO 006 5.8
31094 70854E+00 29090 808495000 004 50%
37-24 70984E+OO 34.90 80937E+OO 0.3 5.2
42052 .808035+OO 39090 90788E+OO 004 506
53.02 6.7426+oo 49.90 70364E+OO 003 501
58084 40981E+00 54090 503885+OO 004 501
630#3 30823E+oo 59090 4009BE+00 000 500
73.73 10971E+00 69090 200645.00 005 500
78084 10423E+OO 7409C 10473E+CO ' 007 502
83.92 10099E+00 79090 10123E+OO 006 500
91098' 80275E-01 87090 80297E—01 0.9 5.3
108.34 2.4255-01 104-93 2.332E-0 109 601

EP= 24063 EX= 6'92
C0M0 ANGLE SIGMA C0N0 LA? ANGLE SIGMA EAB STATo [RRBR TBTAL ERRBR
(DES) (MB/SQ) (DEG) (M3/SQ) (%) (%)
10.66 3.#OIE+OO 9.90 3.934E+CO 0.9 2.5
16033 30229E+OO 14090 30725E+OO 006 201
21.40 300025+00 19.90 3-450E+00 100 207
28089 20831E+OO 26090 3023QE+OO 009 204
42072 30696E+OO 39090 30019t+00 009 205
#8030 2.273E+CO 44093 20522E+OO 103 205
58050 1.442€+00 50.90 10569E+00 106 302
63070 1.030E+oo 59090 10113E+oo 1.5 2.9
71097 70503E'01 67090 709285-01 200 305
80.16 609075'01 75090 701475-01 109 303
90028 70451E'01 8509C 705135-01 107 300
100027 708335‘01 9509C 706845-01 201 305
110.12 60998E-01 105.90 606885-01 2.0 3.0
160(P2P')168
Er= 5:001 tx= 6092
C0M0 ANGLE SIGMA C0M0 LAB ANGLE SIGMA EAB STAT. ERRBR TBTAL ERROR
(DEG) (MB/SR) (DEG) (MB/SR) (%) 1%)
11071 30587E+OO 10090 40129E+OO 008 202
16000 301645+OO 14090 30635E+OO 100 204
21035 E0948E+OO 19090 3037QE+OO 006 109
26069 30083E+OO 24090 30518E+OO 009 203
34015 30O7IE+OO 31090 304695+OO 009 202
39046 20925E+OO 36090 302805+OO 009 202
46055 20149E+OO 43-90 203825+OO 009 201
5100& 1063lE+OO 4709C 107955+OO 100 203
55025 10EIQE+OO 51090 10326E+00 009 202
.63059 503546’01 59090 50749E-01 103 204
71085 409155'01 67090 591825-01 106 208
80003 502095-01 75090 50385E-01 103 205
88013 50286E‘01 83090 50354E-01 103 205
104009 40057E-01 99.90 3.9035-01 105 206
113.90 30382E'01 09090 30205E-01 104 2.5

169(P1P')163

86

163(P0P')163

EP= 33048 EX= 0309?

87

ANGLE SIGMA C0M. 1A3 AstE 516%; 1A9 . 5 R3? TBTAL ERR
(DEG) (MB/SR) (SEQ) (va/SQ) (z) (z)
9055 301355+03 8090 30635§+GO 109 209
11069 30334E+CQ 19090 30832E+CQ 009 2'1
15098 30329E+oj 14093 3'317E+CO 1.1 2.5
21.33 3.941E+oo 19.93 3.933£+Co 006 108
24053 305252+OO 22090 40016E+CO 008 200
26067 30653E+OO 20.99 40159E000 103 207
31099 30614E+OC 29090 400355+OO 008 200
37030 30231E+OQ 34093 306955+OO 007 109
42.59 206266+oo 99.9: 20927E+oo 006 107
47087 103325+OO 44090 20024E+OO 008 109
53.11 1.163€+09 49090 10270E+00 009 109
53034 60823E'01 54090 703975-01 101 201
63053 40923E'01 59-9 502815-01 102 201
68073 40829E'Cl 64093 501235-01 104 204
76091 5.1958-01 72.99 5.499E-o1 1.2 2.2
94.10 40115E-o1 89.93 40104E-o1 1.5 205
104003 20527E'01 90090 2°457E-01 107 207
159<D:D'>149
EP= 36066 Ex: 6092
ANGLE SIGMA C.M. LAB ANGLE SIGMA 1A3 ERRSQ TBTAL ERRBR
(DES) (MB/SR) (DEG) (M9/39) %) " 1%)
10052 20957E+OO 9090 30407E+OO 09 205
15097 Booa7€+oo 10.90 3.466E+oo .9” 206
15097 20955E+CQ 14090 30384E+00 09 206
21032 3012QE+00 19090 305645+OO 09 206
26.65 30479i+ce 34.90 30951E+oo .9 2.7
‘31098 3063BE+00 29090 40103E+OO' 08 205
37028 30172E+00 34090 305585000 09 206
42057 2337SE+OO 39090 2064SE+OO 00 206
47.84 105103000 40.90 10778E+Oo 209
53008 90304E'01 49093 10OISE+OO 209
63050 40537E'01 59090 408645-01 3'“
73.31 4.3925-01 6909C 406035-01 309
84000 4'033E'01 7909C “01136-01 205 308
9#006 209255-01 89090 _2.917E-01 205 308
100004 20227E-ct 95.93 2.18gE-o1 3.4 4.6
108092 1.5095-01 130-9: 10513E-01 301 4.3
118067 90124E-08 110.90 aossaE-oa 408 809

C0M0

C0M0

169(PID')169

5P: 40.07
AVGLE SIGMA C0M0
(DEG) (”fl/SR)
10061 30150E+QQ
21031 30325E+OQ
31096 306015+OQ
42055 20339£+OO
53036 70491E'01
58023 4041QE-01
63047 305346'01
73078 30750E'01
78089 30333E'01
83097 20976E-01
92003 202355-01
99001 10635E'Ol

108039

SP:

10064E-01

Ex:

e~92_

LA? AmELE
(DES)
9090
19090
29090
39090
49090
54090
59090
69090
74090
79093
87093
94090

104090

159(P1P')169

24063

ANGLE SIGMA C03.

(DES)
10066
16004
21040
28090
42070
48002
58092
63072
72000
30019
90031

100030~
110015

(MB/SR)
10033E+OO
10707E+00
20286E+09
2052€E+OO
2025SE+00
10983E+OO
10426E+00
10293E+oo
101365+OO
90661E'Ol
80712E-01
700426-01
60053E-o1

EX=

7'12

LA? ANGLE
(DEG)
9090
14090
19090
36090
39090
44090
510090
59090
67090
75090
85090
95090

105090

88

40063E+OO
20491E+OO
R.191E-o1
7.77SE'O1
308415-01
309296-01
30518E-o1
30044E-01
202416—01
106116-01
1.0226001

SIGMA LAB

(MB/SR)
10251E+OO
1°97lE+OO
20629E+OO
90887E+OO
20527E+oo
200915+OO
1'5525+OO
103925+OO
102005+OO
IOOOOE+OO
8'732E-O1
509095-01
597885-01

107

'UFUUJNTUHDN
0 o. 000. o
®\DC)N£UVHU

R TQTAL ERRBQ
(Z)
506

50

on
C

C
mruu>own4rxunruquru

‘Q‘JVCFO‘OCfiO‘OWfi

STAT0 59939 TBIAL ERRBR

1%)
107
009
102
009
100
101
106
103
107
106
105
202
202

(Z)

wwunJunnnJunnrun)mchu
010. .00. 01.. 000’ .
<>00m0*wwnn)unfiu1m10n)

89
163(P1P!)168

59: 33-48 EX: 7-12

C.M. ANGLE SIGMA C.V. LA9 ANGLE SIGMA LAB STAT~ £8898 TSTAL EQQOR
(DEG) (HQ/SR) (955) (ma/SR) (z) (z)
9.55 7.4322-01 ' 8.93 BosaaE-Ol 2.9 4'1
11.70 9.719e-01 13-93 1o117E+oo 106 2'7
15.98 10276E+CO 14-90 1.464E+oo 108 3-0
21034 10524E+CO 19099 1'742E+OO 0'9 2'0
24.54 1-512E+OO 22.99 1.723E+oo 1-2 3-4
25.52 1-458E+CC 24.93 1~659E+Oo 2-0 3-3
32.00 1.407E+oo 29-90 10592E+OO 103 3°“
37.31 1-374E+oo 34.90 1.543E+oo 1oz 2-3
42.51 1.3qss+oo 39-93 1-500E+oo 0.9 109
47.88 1.341E+oo 44-90 .104835+OO 100 2'0
53.13 1.277E+co 49-90 1-399E+oo 008 1-9
52.35 1.1355+oo 54-90 1-231E+oo 0.9 1-9
63.55 1.0125+oo 59.90 1008éE+OO 008 1-8
53.72 8.9455-01 64990 9.491E-01 loo 2-0
75.93 7.7815-01 72.90 801015-01 loo 2-0
94.11 4.993E-o1 89-90 409805-01 104 3'“

104.35 3.0165-01 99.90 2.932E-01 1-6 2'5
163(P,P')IEB
HP: 36066 EX! 701’}.

C0M0 ANGLE SIGMA C0”: LAg ANGLE SIGMA 9A3 STATo ERROR TBTAL ERQflR
(Des) (Ma/SR) (DEG) (MR/Sq) (x) ‘ (2)
10062 608585-01 9.90 708785-01 1.9 3.3'
15097 IOOOéE+OO 1409C 10152E+OO 106 301
15097 90743E'01 14090 10116E+OO 106 300
21032 10103E+OO 19-90 102SSE+OO 1.5 3.0
26.66 1.081E+oo 24.33 1.229E+OO 1.7 3.2
31098 1'153E+OO E9090 103C3E+OO 105 300
37029 1'157E+OO 34090 1°298E+OO 106 301
42.53 1'852E+oo 39.90 1.394€+oo 1.4 2.9
47.85 1.234€+oo 44.99 1-363E+oo 1.5 3.0
53010 102115+OO “9090 10336E+00 103 207
63.51 1-019E+oo 59.90 1-093E+oo 1.4 2.8
73032 70115E'01 69090 7'453E-01 200 30#
84031 50417E'01 79090 50541E-01 202 305
94'37 3’729E'01 89093 307195-01 203 305

100.35 2.957e-01 95.90 2-915E-01 2.9 #.2
108.93 106355'01 104.99 1-5135-01 3.3 4.4
118068 901425'03 114093 805735-32 505 605

Cflrgg

ANGLE
(0E3)
10051
21-31
31097
42.56
53-07
58029
63.49
73979
78090
83098
92034
99002

1C8090

16?(P:P‘)16?

EP= 40-07

SIGMA C99.

(MB/SR)
700533'01
1009DE+OO
1914EE+CC
1039CE+OO
19173E+OO
909SCE'01
501185'01

50613E'Ol,

408465'01
4°OO7E'01
30248E'Ol
E0204E’01
102515-01

E¥= 7-t1.

LAB ANGLE

fir‘f‘
i1f_\3

9099
19-90
29990
39090
49090
54090
59090
59090
74090
79090
87090
94090

104090

90

SIGMA LAB

(ME/SR)
SolCeE-Ol
1°243E+OO
192895+OO
10547E+OO
1~233E+oo
1'079E+OO
8-7COE-Ol
5-8815-01
500185-01
40C99E-01
3'256E-01
20171E-01
152025-01

STAT. ERRSR TSTAL ERRBQ

(Z)
105
102
103
100
102
101
1.5
106
109
109

7204.

206
302

(x)

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O. O O O O O O. O .0

APPENDIX B

In this appendix a description of the nine different
data acquisition routines available in TOOTSIE will be
given.

The datum consists of two or three lB—bit numbers in
coincidence, labeled X, Y, and Z, presented to the XDS
Sigma 7 computer through the general purpose interface.

Each event causes an interrupt to occur. The interrupt
routine must completely process one event before the computer
will accept another. The ADCs, however, can begin processing
a second event as soon as the interrupt routine reads and
resets them, providing considerable overlap in conversion

and processing time.

Each interrupt routine operates in two modes. In SETUP
mode data are stored in a two dimensional matrix, allowing
nonlinear bands to be selected with polynomial fits defining
the lower and upper boundaries of each band. In RUN mode
events are compared against tables generated from the fits
which define the bands. A spectrum of counts verses channel
number is accumulated for each band in the tables.

The interrupt routines can be divided into two classes
determined by the identification criterion required in RUN
mode. The first class of routines requires only that the
function F(X,Y) fall within one of the bands defined in

SETUP mode. The second class of routines require each event

91

92

to satisfy two identification criteria. The function F(X,Y)
must lie within a band and G(X,Z) must lie within a band
corresponding to the band in which F(X,Y) was found.

Four of the five routines in the first class differ
only by the calculation F(X,Y), performed on the data before
it is stored in the matrix and before identification. These
routines provide options such as simultaneous magnetic tape
recording of the raw data and eight way fan out with routing
bits.

The routines are:

l) EDELTAE:
For this routine F(X,Y) = Y, and the matrix
elements in SETUP mode are DATA(F(X,Y),X). In
RUN mode F(X,Y) is compared against the tables
of bands to identify an event and spectra of
counts versus X are accumulated. One use of
this routine is in two counter telescope ex-
periments in which energy lost in a thin AE
counter is plotted as a function total energy.

2) E*DELTAE
This routine differs from EDELTAE only by the
definition F(X,Y) = X*Y. This routine is
primarily intended for two counter telescope
experiments. The product of AE and total
energy plotted as a function of total energy
is a straight band. This simplifies the pro-

cess of drawing bands.

93

3) E*T**2
This routine also differs from the EDELTAE
routine by the definition of P(X,Y) =

X*(Y-Y0)**2/N + Y1, where Y N, and Y1 are

0’
input from the teletype. This routine is used
in charged particle time of flight experiments.
The function F(X,Y) is directly proportional
to the mass of the detected particles.

H) XE/E
This routine defines F(X,Y) = N*X/Y, where N
is a normalization factor determined by the
number of channels in each spectrum. In SETUP
mode the matrix elements are DATA(Y,F(X,Y)).

In RUN mode Y is checked against the tables of
bands and spectra of counts verses FCX,Y) are
acquired. This routine, as discussed in the
text, is used with position sensitive detectors
in the Spectrograph.

5) LIGHT
This routine requires three parameters. In
SETUP mode the matrix elements are labeled
DATACFCX,Y),X), where F(X,Y) = Y, and the Z
datum is ignored. In Run mode F(X,Y) is
checked against the tables and spectra of

counts versus Z are generated. This routine

9a

is used for neutron time of flight data. The
X and Y signals are used to separate neutrons
from gamma rays while the Z signal is flight
time.

The four routines in the second classification differ
only in the calculations performed on the data before being
stored. These routines also provide options such as simul-
taneous magnetic tape recording of the raw data.

The operation of these routines in SETUP mode is somewhat
more complicated than in the previous routines. Two indepen-
dent sets of bands, corresponding to F(X,Y) and G(X,Z) must
be defined and a correspondence between them established. To
define the bands for classification of events, the matrix
DATA(F(X,Y),X) is stored, ignoring the Z datum. A teletpye
command switches over to storing elements DATA(G(X,Z),X),
disregarding Y datum. Lists of bands to check in the tables
for G(X,Z) for each band in the F(X,Y) tables are entered
via the teletype.

In RUN mode the function F(X,Y) is checked against the
table of bands until a match if found. The bands in the
G(X,Z) tables which correspond to the appropriate band are
then checked. If a match is found, the appropriate channel
in the counts versus X spectrum corresponding to the band

in the G(X,Z) tables is incremented.

95

The functions F and G for the four routines are
given by:

l) EDELTAESEDELTAE:
F(X,Y) = Y; G(X,Z) = Z
This routine has been used in life time
measurements when more than one decay chan-
nel was Open. A two counter telescope de-
tector arrangement was used to identify the
decay product and a time signal was used to
determine when the event occurred.

2) E*DELTAE8E*DELTAE:
F(X,Y) = Y; G(X,Z) = X*Z
This routine has been used in three counter
telescope, redundant identification experi-
ments. An event must have the correct AB in
both transmission counters. This reduces the
number of accidental events and thus increases
the peak to valley ratio.

3) E*T**28EDELTAE:
F(X,Y) = X*(Y-Y0)**2/N + Y1

Y0, N, Y are input on the teletype.

l
G(X,Z) = Z
This routine is also used for redundant iden-

tification. In this case, an event must have

the correct mass and 22/m to be counted.

96

H) E*T**28E*DELTAE:

F(X,Y) X*(Y-YO)**2/N + Y

1

G(X,Z) Z
This routine is also intended for redundant
identification using flight time and AE infor-

mation.

A more complete description of these routines and the
operation of TOOTSIE is given in Michigan State University

Cyclotron Computer Report Number 13.

LIST OF REFERENCES

A1

Au

Au

Ba

Ba

Ba

Be

B1

B1

Bo

Br

Bu

Ca

Ca

Cr

Cr

65

61

70

7O

70

62

70

59

66

6M

66

57

67

61+

66

65

98

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Da

Da

E1

E1

En

Ev

Gi

Gr

Ha

Ka

Ko

Ku

Ma

Ma

Na

Pe

Pr

68

58

58

61

67

68

an

69

62

6”

68

66

67

68

63

70

62

99

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W.W. Daehnick (1969)

A.S. Davydov and G.E. Filippov, Nuclear Phys. 8
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J.P. Elliot, Proc. Roy. Soc. A245 (1958) 128

L.R.B. Elton, Nuclear Sizes, (Oxford University
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H.A. Enge and J.B. Spencer, Split Pole Magnetic
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D. Evers, G. Flugge, J. Morgenstern, T.W. Retz-
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T.T.S. Kuo and G.E. Brown, Nucl. Phys. 5 (1966)
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G.H. Mackenzie, E. Kashy, M.M. Gordon, and H.G.
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D.M. Brink and G.E. Nash, Nucl. Phys. 5g (1963) 608

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M.A. Preston, "Physics of the Nucleus", Addison-
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Sa

Sa

Sn

To

Tr

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66

68
61

70

52

100

G.R. Satchler, Nucl. Phys. 55 (1964) 1

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G.E. Trentelman, Private Communication

L.E.H. Trainor, Phy. Rev. §§.(1952) 962

47

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8
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