ABSTRACT

INELASTIC PROTON SCATTERING AT “0 MeV

FROM THE EVEN NICKEL ISOTOPES

By

Kenneth M. Thompson

A study of inelastic scattering from the even nickel
isotOpes has been done using U0 MeV protons from the
Michigan State University sector focused cyclotron. Angular
distributions from about 15° to 90° were obtained for each
nucleus in 5° steps using Ge(Li) charged particle detectors.
The best energy resolution achieved was 45 keV. All of
the resulting angular distributions are presented in both a
tabular and a graphical form.

A high precision goniometer was designed and con-
structed to facilitate the use of Ge(Li) detectors. The
details of the construction of this apparatus are given.
Also described in detail are the procedures used in the
calibrations of the remotely operated detector support and
target positioning mechanisms.

The experimental angular distributions for all of the
observed states were compared with calculated distributions
using a collective model distorted wave theory. From these

comparisons values for the nuclear deformation parameters,

Kenneth M. Thompson

BL, were obtained. The resulting nuclear deformations,
BL R0, were used to calculate the vibrational model
parameters and the reduced transition probabilities. The
deformations were also compared to results from other
experiments. The fractional depletion of an energy weighted
sum rule and a sum rule based on the shell-model were also
calculated for each state. The dependence of the reduced
transition probabilities and sum rule limits on the model
used for the nuclear charge density was also examined. The
results of these calculations for a uniform charge density
with r0 = 1.2OF and r0 = 1.31F are given along with those
for a Fermi distribution with r0 = l.lOF and a = 0.566F.
These are tabulated for all of the observed states.
Comparisons of the calculated quantities were made
with results of experimental studies of electromagnetic
transitions in the nickel isotopes. There were also com-
parisons made with the results of calculations using
strongly admixed spherical shell model configurations done
by N. Auerbach and a modified Tamm-Dancoff approximation

done by Ram Raj et al.

INELASTIC PROTON SCATTERING AT 40 MeV

FROM THE EVEN NICKEL ISOTOPES
By

Kenneth M. Thompson

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics

1969

557737

73293;?

ACKNOWLEDGMENTS

I am greatly indebted to Dr. Charles Gruhn for his
guidance, encouragement, and assistance throughout my
graduate work and particularly during the work for this
thesis.

I am also grateful to Dr. Barry Preedom for his
assistance in the understanding and the implimentation of
the techniques of the distorted wave analysis needed for
this work. I also acknowledge the many helpful discussions
with the professional staff of the Michigan State University
Cyclotron Laboratory.

Thanks go to many who aided in the design and con-
struction of the goniometer used in this experiment—-to
Dr. William Johnson, Robert deForest and the staff of the
electronics shop for their help in the design and constuc-
tion of the electrical and electronics systems; to Norval
Mercer, the staff of the mechanical shop, Gunther Stork,
David Rozof, and the members of the technical staff for
their help in the design, construction, and assembly of
the mechanical systems; and to Andrew Kaye for his help
in procurring the necessary raw materials.

I am also grateful to my fellow graduate students

for their helpful discussions throughout this work but

ii

especially to Carl Maggiore, Tom Kuo, Larry Samuelson,
and Bill Seidler for their assistance during the data
acquisition for this experiment. Also the aid of the
computer personnel is acknowledged as is their provision
of the software which established a time sharing computer
system which greatly facilitated the analysis of the data.

I also acknowledge the financial support of the
research program at MSU provided by the National Science
Foundation and the personal support from the NSF during
the work for this thesis.

A very special thanks go to Mom and Dad for their

support and encouragement during my graduate studies.

iii

ACKNOWLEDGMENTS

LIST OF TABLES.

LIST OF FIGURES

Chapter

TABLE OF CONTENTS

I. INTRODUCTION.

II. HIGH PRECISION GONIOMETER . . . . .

[\J [\JNN

[\J NNMMN NNN

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43' UUUQUUUOUU NNN

bErm

CLOUD?

Design Features .
The Ge(Li) Detector Package.
List of Included Features

Goniometer Construction and
Operation.

Goniometer Drive . .
Local Electrical System
Remote Control Panel

Calibration of the Goniometer
Main Arm Angle Calibration
Target Angle. . . .
Target Height .
Concentricity Checks

Installation.

III. EXPERIMENTAL PROCEDURES

3.

:AFJH

WWWUUUUWUU WWW
4‘: U0 NNNN H

1

0235

0..

(DUB)

Cyclotron and Beam Transport
System. . . . . . . . . .
Cyclotron.

Beam Transport System. .
Alignment of the Beam into the
Target Chamber .

Faraday Cup and Current Integrator

Set up of the Goniometer.
Target Chamber . . . .
Targets . .
Detectors.

Electronics
Data Acquisition

iv

Page
ii
vii
ix

Chapter

IV. DATA ANALYSIS

V. DI

APPENDICES

I. De

Experimental Analysis.

Computer Programs Used .

.l Peakstrip . . . . . . .

.2 Reltomon .

.3 Foiltarcal.

.M Sigtote. .

Lab Angle Calibration.

Elastic Cross Sections . .

Normalization of the Data to

Obtain Absolute Cross Sections.
Dead Time .
Ratios of the Monitor Counts to
the Integrated Current. .
Method of Normalization

HFJFHAFJFHJFJH

HJ‘DQJCLQ: CLO- DJOU‘DDEDEDEDW
NFJ

Corrections

U‘l-EUO

Final Results. .
Inelastic Angular Distributions
Excitation Energies . .

Theroetical Analysis . . . .
DWBA Theory .

Vibrational Model Parameters and
Reduced Transition Probabilities
Sum Rules. . . . .
Optical Model Parameters.

DWBA Calculations . . .
Extraction of Deformation
Parameters, BL

ranR)+#FJFJFH4 FH4
0'51)

JrJrJz-J: 4:222: 4:41-4:22: 4:4:- .z:-.::-.I:-J:J:-4:-J:J:-J:-
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SCUSSION OF THE RESULTS

5.1 Comparisons with Other
Experiments . . . . .

5.2 Comparison with Theory . . . .

5.3 Conclusions .

tails of the Construction and Operation

of the Goniometer

II. Calculations of the Angles in Reference I

Used for the Main Arm Calibrations.

III. Compounding of the Errors in the Points for

the Main Arm Reference Angles

Page
69

69
7o
70
7o
71
72
73
75

76
76

76
77

8O
81
82

88
88

95
98
99
102
10“
117
120
126
128

133

136

216

218

APPENDICES Page
IV. Experimental Data . . . . . . . . . 227
IV.l Tabulated Angular Distributions
IV.2 Plotted Angular Distributions
IV.3 Tabulated Nuclear Deformations
IV.“ Tabulation of Quantities
Calculated from the Nuclear
Deformation in IV.3
REFERENCES . 28A

vi

2.

2.

2

3.

A
L;

“.3

L;
A
A
A

L;

A.

.5

1
.1

.2

.u

.5

.6

.7

.8

9

.10

LIST OF

The reference I angles
errors. 0 O O O

TABLES

and estimated standard

Summary of the results of the calibration
of the main arm. . . . . . . . .

Summary of the results of the calibration
of the target angle . . . . .
Summary of the results

of the calibration
of the target height . . .

Summary of the results of the concentricity

checks. . . . . . . . . . .

The self-supporting foil targets used
58

for 60Ni

for 62Ni

Excitation energies for Ni . .

Excitation energies
Excitation energies
Excitation energies for 6“Ni

Average optical potential parameters used.
Optical potential strength parameters used

JTr assignments for states in 58N1 and the
excitation energies and L-values used in
this experiment. . . . . . . .

JTr assignments for states in 60Ni and the
excitation energies and L-values used in
this experiment. . . . . .

J1T assignments for states in 62NI and the
excitation energies and L-values used in
this experiment. . . . . . .

JTr assignments for states in 6“Ni and the
excitation energies and L-values used in
this experiment. . . . . .

vii

Page

31

38

41

an

145
57
84

85

86

87

100

102

105

106

107

108

Table

“.11

5.1
5.2

5.3

5.“

5.5

5.6

5.7

5.8

509

5.10

III.1

III.2

III.3

III.L;

Estimated upper limites for the 6 for the

second 2+ states .L
Tentative L assignments.

Nuclear deformations for 58Ni and comparison
with experiments representative of other
reactions. . . . . . . .

Nuclear deformations for 60Ni and comparison
with experiments representative of other
reactions. . . . . . . .

Nuclear deformations for 62Ni and comparison
with experiments representative of other
reactions. . . . . . . . . . .

Nuclear deformations for 6”Ni and comparison
with experiments representative of other
reactions. . . . . . .

Comparisons of reduced transition probabili-
ties, B(EL; 0+L), in units of F2L. .

Experimental surface tension parameters,
CL(MeV) . . . . . . . . .

Experimental mass transport parameters,
DL/h2, in units of (Mev-l) .

Experimental and theoretical results for
B(E2)'s in the nickel isotopes.

Experimental and theoretical results for
B(E2)'s for the nickel isotopes. The
effective charge assumed in the theoretical
calculations was 1.35e

Estimated standard errors for the primary
angles in reference I for the main arm
due to errors in the linear measurements

Estimated standard errors for the primary
points in reference I due to the error in
the central, 9OO angle . .

Total estimated standard errors in the
primary points in reference I

Total estimated standard errors in the
secondary points in reference I . .

viii

Page

116
119

121

122

123

123

12“

125

126

127

129

223

225

225

226

Figure

2.1

3.1

3.2

3.3

3.“

3.5

3.6

3.7

“

.1

LIST OF FIGURES

Vertical cryostat Ge(Li) detector package
Goniometer drive unit

Local control box . . . . . .
Remote control panel

Floor plan of the geometry for the primary
points in reference I . . . .

Floor plan of the geometry used in the 900
transfer of the primary angles of
reference I. . . . . . . . .

Experimental area of the Michigan State
University Cyclotron Laboratory . .

Block diagram of the electronics used with
the Ge(Li) detectors. . . . . . .

Block diagram of the electronics used with
the monitor counter . . . . .

58Ni(p,p')58Ni spectrum at eLAB = 29.“0 for
Ep = “0 MeV. . . . . . . . . . .

6ONi(p,p')6ONi spectrum at SLAB = 57.80 for
Ep = “0 MeV. . . . . . . . . . .

62Ni(p,p')62Ni spectrum at eLAB = “7.80 for
Ep = “0 MeV. . . . . . . . . . .

61ANi(p,p')6uNi spectrum at eLAB = “7.80 for
Ep = “0 MeV. . . . . . . . . .

Comparisons of the experimental, elastic
scattering results and the theoretical
calculations using the optical potential
parameters given in Tables “.5 and “.6

ix

Page

1“
20

21

26

30

52

6O

62

65

66

67

68

103

Figure Page

“.2 Comparisons of the experimental inelastic
scattering results and the theore ical
DWBA calculations for states in 5 Ni with
known J1T assignments. . . . . . . . . 110

“.3 Comparisons of the experimental inelastic
scattering results and the theore ical
DWBA calculations for states in 5 Ni with
known J1T assignments. . . . . . . . . 111

“.“ Comparisons of the experimental inelastic
scattering results and the theorgBical
DWBA calculations for states in Ni with
known J7T assignments. . . . . . 112

“.5 Comparisons of the experimental inelastic
scattering results and the theor tical
DWBA calculations for states in 2Ni with
known J" assignments. . . . . . . . . 113

“.6 Comparisons of the experimental inelastic
scattering results and the theorgfiical
DWBA calculations for states in Ni with
known J" assignments. . . . . . . 11“

I.1 Schematic of the structure of the main arm
used to calculate the location of the point
(A) at which the brace meets the main arm. . 139

1.2 Results of the calculations and measurements
of the vertical deflections in the main arm
under a load of 100 lbs. . . . . . . . 1“1

1.3 Section view of the “:1 gear train for the
main arm drive. . . . . . . . . . . 1“7

I.“ Plot of the speed factor, XS, versus angular
velocity, RPM . . . . . . . . . . . 157

1.5 Section view of central column . . . . . . 173

I.6 Section view of the target chamber and sliding
vacuum seal. . . . . . . . . . . . 180

I.7 Remote control panel . . . . . . . . . 195

11.1 Schematic of the geometry used to calculate
the angular position of the primary points
of reference I used in the calibrations of
the main arm . . . . . . . . . . . 217

CHAPTER I

INTRODUCTION

In recent years there have been many studies done in
the 2p3/2, 1f5/2, 2pl/2 region of the periodic table. Of

particular interest in this thesis is the work that has been

done on the stable even nickel isotopes 58Ni, 6ONi, 62Ni,

and6uNi. Fricke et al. (Fr 67b)*, for example, have used

elastically scattered protons and their measured polariza-

tion to establish the Optical model potentials for 58Ni and

60Ni at “0 MeV. Fricke et al. have also studied the inelas-

tic scattering and the inelastic asymmetries of “0 MeV
protons from the highly excited first 2+ and 3" states in
58Ni and 60Ni (Fr 67c). There have also been a number of
other studies involving these targets: for example (a, d')
on 58Ni and 60Ni (Ja 67) (In 68), (d,d') on58Ni, 6ON
62Ni (Jo 69), and (e,e') on 58Ni, 6ONi (Cr 61) and on 58Ni,
60 62

Ni, Ni (Du 67). In most of these experiments the

1.

emphasis was placed on the strongly excited states.
In addition to these experiments theoretical calcula-

tions of the excited levels and reduced transition

 

*

The references are specified by the first two letters
of the primary author's surname followed by the year of
publication. These are listed alphabetically at the end of
the thesis.

probabilities have been made for these isotopes. N.
Auerbach has, for example, described the nickel isotopes

in terms of strongly admixed spherical shell-model neutron
configurations (Au 67). Raj et_al, have also done calcula-
tions for the even nickel isotopes using a modified Tamm—
Dancoff approximation (Ra 67).

As pointed out by Glendenning and Veneroni (G1 66) the
proton is a useful probe of the micros00pic structure of the
nucleus. They calculate the (p,p') angular distributions
of the low lying levels of the nickel isotopes using a
microscopic description of the excitations. Comparison of
results of the present work with these calculations are not
given in this thesis, but these comparisons are expected
to be made in the near future.

The nature of these experiments and theoretical calcu-
lations revealed the need to do a systematic study. The
study which was done for this thesis, therefore, involved
the examination of inelastically scattered, “0 MeV protons
from the even nickel isotOpes. For such a study to render
information to test the microscopic interpretations,
angular distributions were needed for the weakly excited
states as well as for the strong, collective states.

In order to obtain these distributions a detection
system was needed which had good resolution and which would

minimize the background contributions.

A Ge(Li) charged particle detector was selected
for this experiment. In order to facilitate the use of
this detector system, a "spider" geometry scattering rig
was designed and constructed. The details of the design
and construction of this goniometer, i.e., angular measur-
ing device, are given in Chapter II and Appendix I.

The collective model distorted wave theory (Ba 62)
(Sa 6“) was used in the analysis of the angular distribu-
tions obtained in this experiment. This type of analysis
has developed into a widely accepted method and therefore
provides results which can be readily compared or repro-
duced if necessary. The optical model parameters used in
the calculations were obtained from Fricke gt_al.

(Fr 67b). The analysis of the present data yielded

deformation parameters, 8 for the observed states.

L’
There is evidence that the low lying excited levels
of the nickel isotopes are vibrational in character (La 6“)
(Bo 67a). For this reason the vibrational parameters
associated with the observed states were calculated.
Recent studies of electron scattering from the
nickel isotopes (Du 67) (Cr 61) yielded values for the
reduced transition probabilities for various states;
therefore, the B(EL)'s were also calculated for the pre-

sent experiment to allow comparisons with those earlier

experiments as well as with several theoretical estimates.

Using the comparisons between the results of this
experiment and other experimental and theoretical studies
it was possible to draw some conclusions concerning the
extraction of model dependent parameters from the experi-
mental data and the consistancy of several theoretical

approaches.

CHAPTER II

HIGH PRECISION GONIOMETER

Before the data for this thesis was acquired, the
instrumentation needed for obtaining angular distributions
of charged particles using Ge(Li) detectors was designed
and built. The form of construction used in the final
system is a "spider" geometry similar to that used by
others (He68a) (Ca67). This consists of detector position-
ing elements outside of a central vacuum chamber with the
detectors viewing the targets through a sliding vacuum
seal. The alternative vacuum pot configuration, in contrast,
consists of a vacuum chamber containing the detection
instruments and targets. This vacuum pot design, however,
was less compatible with our experimental requirements.
Since the fundamental purpose of this instrument is to
measure the angular positions of detectors, it is called

a goniometer.

2.1 Design Features

 

This device was built to facilitate charged particle,
nuclear reaction studies in the energy range of 20-75 MeV.
In particular the design was guided by the experimental

requirements of inelastic proton scattering and 3He

induced reactions. Among the proposed experiments, there
were many which needed to use Ge(Li) charged particle detec-
tors because of their energy resolving capabilities. Such
detectors have been successfully fabricated at Michigan
State University Cyclotron Laboratory (MSUCL) by a group
supervised by C. R. Gruhn (Gr 68). They have been shown to
be capable of giving energy resolution of 22 keV FWHM for “0
MeV protons (Gr 68a). Several types of packages were tried
by this group for maintaining these detectors at liquid
nitrogen (LN2) temperatures in a vacuum environment. A
package similar to the vertical cryostat design of Chasman
(Ch 65) was found to be most convenient, and, therefore,

the final design of the goniometer was made to be compatible
with such a package.

The final configuration of this device is the result
of compromising on several points. The results of a number
of experiments representative of a variety of reactions were
examined. The largest fractional change in the differential
cross sections corresponding to an angular variation of 0.010
was estimated in each case. A maximum fractional change of
2% was defined as being acceptable. This required an
angular precision of at least 0.020 in the majority of
cases examined.

In order to obtain high angular precision as well
as to allow for flexibility in the use of this device, the
final design incorporated a “ foot radius detector support

called the main arm. This arm can be remotely positioned

with an accuracy of i0.02° relative to a reference direc-
tion. Implementing a support capable of holding a vertical
cryostat, detector package at this radius inside a vacuum
pot scattering chamber would necessitate a very large

vacuum system. The chamber would be prohibitive in cost,
and the necessary evacuation times along with the difficulty
of reaching the interior points would make this approach
unacceptable. The spider geometry, on the other hand,
avoids these problems since the detector positioning ele-
ments are located outside of a small, central, target vacuum
chamber.

2.1.a The Ge(Li) Detector
Package--Figure 2.1

 

The Ge(Li) charged particle detector configurations
which have been used at MSUCL have been discussed elsewhere
(Gr 68)(Gr 68a). The detector package which was found to
be most convenient to use is a vertical cryostat design.

The final goniometer design facilitates the use of this

type of package. The final configuration does not, however,
prevent the use of other choices of detectors or detector
packages.

The Ge(Li) detector needs to be kept constantly in a
vacuum and at temperatures near the boiling point of LN2,
77°K. This vertical cryostat design contains an isolated,

copper cold finger which is put into LN2 and is in thermal

contact with the detector. The vacuum is maintained inside

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M

 

 

 

 

 

 

2.1 Vertical cryostat Ge (Li) detector package.

the enclosure by a cryopumping agent. The portion of the
package containing the cold finger and cryopump can be
inserted into the neck of a standard, 25 liter, LN2 dewar
permitting the storage of the system for up to 2 weeks with-
out refilling.

The detector mount connected to the cold finger con—
tains the collimator which defines the solid angle of the
detector system. The package cap which encloses this mount
contains an entrance port for the scattered particles. The
exact details of this port and of the coupling used
between this package and the target chamber depend on the
requirements of the experiment. Several possible configura—
tions are described here.

The package itself may contain a thin foil window.
This window must be opaque and be able to sustain atmospheric
pressures. It must, however, produce a minimum energy
straggling contribution in the scattered particles. Win-
dows that have proven successful in covering holes up to
3/8 inch in diameter are 1/10 mil Havar*and l/“ mil,
aluminized mylar. The staggling contributions have been
calculated for “0 MeV protons to be about 9 keV and 3 keV
respectively. The calculations use a computer program,
TARGET,by J. J. Kolata. This program incorporates calcula-
tions of the VaVilov distribution of the energy of the
transmitted particles. These windows have been glued to

the aluminum cap using Eastman 910 adhesive.

 

*Hamilton Watch Company, Lancaster, Pennsylvania.

10

The package can be coupled to the foil window of the
target chamber (see Appendix I) by using an evacuated tube
with a thin foil window on each end. One of these addi-
tional windows can be eliminated by coupling the tube
directly to the cap through an O—ring seal. A second window
can be eliminated by permanently coupling the tube to the
cap and removing the window on the cap itself.

The KF-20 Leybold vacuum fitting shown in Figure 2.1
is attached to the cap through an O-ring seal. This fitting
allows the convenient implementation of the second arrange-
ment described above. It also provides a means of coupling
the detector to the target chamber through a pipe attached
to the sliding seal. The window on the cap can also be
eliminated by connecting a ball valve, for example, to this
fitting. This allows the detector to view the target
through the sliding seal in a windowless geometry providing

the ultimate conditions for high resolution experiments.

2.1.b. List of Included Features

 

In addition to the aspects described above there are
additional features included in this goniometer which add
to its versatility and convenience. The following list
enumerates these features as well as those presented above
and those of general interest. These are described in

detail in section 2.2 and Appendix I.

10.

11.

11

An adjustable stand which permits adjustment of
both the vertical and horizontal position, and
the levelness.

A remotely movable “—foot radius detector
support, the main arm,capable of holding a
vertical cryostat for Ge(Li) detectors and the
associated LN2 dewar,or a maximum of 100 lbs at
“ feet.

A precision of :0.02° in positioning the main
arm.

A manually positioned secondary arm that can be
positioned to :0.1° and can support a maximum

of 50 lbs at 2 feet.

A central, target vacuum chamber compatible with
a sliding vacuum seal or with a thin foil window.
A target transfer and hold look.

A target height positioning system with a pre-
cision of :1 mil.

An automatic target selection system for three
targets. I

A vernier dial readout for the main arm position
capable of being read through a television
system to 0.005°.

A target rotating system with a precision of
i0.3°.

A local control of all functions.

12

12. Independent, remote digital readouts for the
main arm, target angle, and target height
positions.

13. A remote, graphic readout system which indicates
the relative angular positions of the detector

supports, the target, and the incident beam.

2.2 Goniometer Construction
and Operation

 

 

In order to provide a system which was to be easily
modified, the goniometer was designed for a modular con-
struction. The mechanical as well as the electrical
assemblies are composed of individual, easily removed sec—
tions. This design philos0phy permits modifications to be
easily incorporated into the total system to satisfy the
requirements of a specific experiment.

This goniometer is comprised of three basic units
joined by one multiconductor cable and by “8-pin connectors.
These units are a semi—portable goniometer drive and two
control and power supply assemblies, one at the local
station and one at the remote. These can be interconnected
in either a retracted or an extended configuration allowing
for the system to be easily moved from one location to

another and to be conveniently tested.

l3

2.2.a Goniometer Drive

The goniometer drive assembly is shown in Figure 2.2.
This includes three remotely controlled drive systems which
position the target and the “ foot radius main arm. These
systems are rigidly fastened to an adjustable steel and
aluminum base (Figure 2.2A). The four threaded steel legs
allow the goniometer to be adjusted so that the main arm is
located between 3 and 12 inches below the scattering plane.
These also permit alignment such that the main arm remains
in a level plane during a complete revolution with its center
of rotation intersecting the incident beam line. An X-Y
stage is also incorporated to allow for a maximum of 1 inch
of adjustment in the horizontal plane.

There are two rotating elements in this system which
are used to locate detectors with respect to the beam direc-
tion (Figure 2.20). First there is the “ foot radius,
remotely positioned, main arm. This element has a dual
beam, counter balanced construction capable of supporting
a maximum of 100 lbs at a radius of “ feet. The dual beam
design allows the vertical cryostat, Ge(Li) detector package
along with its LN2 dewar to be securely supported between
the minimum and maximum radial positions.

This arm is driven by a Slo—Syn, 881800-1005,
bifilar stepping motor which is operated in both an AC
synchronous mode with a speed of 72 RPM and in a DC

stepping mode with 200 steps/revolution at a speed of 20

1“

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chz I o .sfimmu snow Ema cfimz L m .ommm I < "was: o>Hno mmpoEOHcow m.m

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fig

  
 

 

IIIIIIIIIIIIIV
2<mn

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steps/sec. The motor is connected to the main arm through
a “:1 gear train (see Figure 2.28) and a 90:1 worm gear.
This worm gear mechanism is a Bridgeport, 15 inch, rotary
mill table. The resulting rotational velocities of the
arm are 72°/min with the motor running in the AC mode and
6°/min for DC Operation.

This table is a precision device and precautions were
taken to prevent overloading the gears which it contained.
To permit the use of the maximum load described above, it
was necessary to construct an arm which allowed for a small
flex when the angular position of the element was changed.
The details of these considerations are given in Appendix I.

The angular position of the main arm is indicated by
a vernier scale with a least count of 0.0050 and a remote
digital readout with a least count of 0.02°. The digital
counter is driven by a pair of synchro motors which is con-
nected directly to the Slo-Syn motor shaft.

The second detector positioning element is a 3/“ inch
thick aluminum arm located just above the main arm. This
manually positioned element has a radius of about 2 feet,
and is designed to support maximum loads of about 50 lbs.
The angular position is indicated relative to the main arm
by a vernier scale with a least count of 0.l°.

The drive mechanisms for the target angle and target
height are located below the rotary table. Both of these

utilize a worm gear driven by a dual speed motor system.

16

The position of the target is indicated on two remote
digital readouts each of which is driven by a pair of
synchro motors which is in turn connected to the drive
motor shaft. The least count on the angle readout is
0.02° while the height is 0.2 mil. The gear train used

in changing the angular position of the target results in
an angular velocity of “32°/min in the fast mode and 36°/min
in the slow mode. The target height can be varied at a
Speed of 1.80 or 0.072 inches/minute. Below the target
drive elements are located five microswitches which are
activated by a cam on the end of the target shaft. Two of
these switches define the target height limits of travel
while the remaining define the predetermined positions for
three targets in the target holder.

Located just above the arms of the goniometer is the
target vacuum chamber (Figure 2.2D), containing a 6 inch
high target ladder. The exact configuration of this chamber
depends on the experimental needs. These determine, for
example, what type of monitor port is incorporated and
its position. Also, the experiment dictates the type of
beam entrance and exit ports used and the type of coupling
needed between the detector and the target vacuum chamber.

The target chamber was designed to be easily modified
by providing a replaceable section in the median plane.

The first section constructed is 8 inches in diameter and

17

has two fixed monitor ports at —“5° and -135°, a slot for
the scattered particles from -l5° to 170°, and a single
beam port. There is an O-ring seal around the outside of
the slot which permits the use of a sliding vacuum seal
as well as a thin foil window.

The sliding seal is similar to others (Fe 66) (Bo 67)
and was designed to be used with Ge(Li) detectors in a
windowless geometry. The seal strap is made of 10 mil
stainless steel and is rotated using only the scattered
beam port to transfer the torque between the main arm and
the strap. The lubrication of this seal which provides a
satisfactory operation is Dow Corning, high vacuum,
silicone grease. A mixture of vacuum grease and oil with
molydenum disulfide powder was also tried but was rejected
because it was less convenient to use.

A thin foil window of 1/2 mil Kapton* has also been
successfully used in place of the sliding seal on this
chamber. Both of these designs are used with an external
beam dump located beyond the goniometer. As a result the
particle beam must pass through either the foil window or
the steel strap. In the latter case serious background
radiation is produced and is, therefore, a limitation to the
usefulness of this design.

In order to remove this limitation of the 8 inch

chamber a 16 inch diameter section was fabricated with the

 

*
E. I. DuPont de Nemours, Wilmington, Delaware.

18

following features: It includes a sliding seal with a
similar construction as the first, and extends from 8° to
110°. This still allows the angular distributions to be
obtained, however, from 8° to 172° accomplished by rotating
the chamber 180°. It also includes a windowless beam exit
port as well as an entrance port, along with two monitor
slots with removable thin foil windows of Kapton.

A target transfer and hold lock (Figure 2.2E) is con-
nected to the top of the target chamber through a standard,
“ inch, Marman vacuum coupling. This lock consists of two
vacuum valves and a small chamber containing a transfer
mechanism. This assembly can be used to insert a target
into the central chamber without breaking the chamber vacuum
or, if necessary, without exposing the target to the atmo-
Sphere.

The detector carriage is shown in Figure 2.2F. The

detector packages and the LN dewar are held by this support

2
between the dual beams of the main arm. The radial position
of the detector is fixed securely when the detector mount

is tightened and the carriage is pinned to the main arm
with l/“ inch, steel dowels. In addition to the single
detector mount shown here, a dual mount has been made for
holding two detectors side by side. The LN2 dewar used

with this latter system has a pot life of about 10 hours.

l9

2.2.b. Local Electrical System

The local electrical system includes a portable con-
trol box connected to a power supply by 30 feet of multicon-
ductor cable. The power supply along with the control
relays are completely enclosed in a steel cabinet isolating
the contact noise of the relays. The control box shown in
Figure 2.3 contains all of the functions found on the
remote control panel except an automatic angle increment
feature of the main arm which is described below. In addi-
tion to these controls, however, there is a main arm limit,
override switch permitting the detector to be driven through
zero degrees if necessary. This feature was incorporated
only into the local control trying to minimize the possi-
bility of an accident and not worrying about the slight
inconvenience it might create. The mobility of this local
control box greatly facilitates the alignment of the gonio-

meter on the beam line.

2.2.c. Remote Control Panel

 

The remote control panel is shown in Figure 2.“. The
controls on the panel are placed in three verticle groupings.
The right hand section contains the cOntrols and digital
counter for the target angle. In the center is located the
target height controls and counter. The three buttons
located in a horizontal row are used for the automatic
positioning of three targets in the target chamber. Any one

of the targets may be selected by merely pushing the

20

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2.“ Remote control panel.

22

corresponding button. In addition to this automatic
feature there is a manual mode which permits, for example,
a target uniformity scan.

The last group of controls on the left is for the
main arm. The digital counter used for this readout is a
dual bank type* which indicates the scattering angle of
the detected particles increasing in either direction from
0°. At the bottom of this group is located a predetermined,
electromagnetic, digital counter. This counter is used to
select the number of steps--0.01°/step--that the main arm
is to be moved. In a typical experiment, for example, it
is not uncommon to measure an angular distribution in equal
angular steps. In such a case the size of the step is set
on the preset counter and the motion is automatically com—
pleted when the run button is activated.

This remote control panel also contains a graphic
display which shows the relative angular positions of the
incident beam, the main arm, the target, and the manually
positioned arm. This display is in the lower portion of
the panel and is coupled to the digital readout system for
both the main arm and target by a pair of small synchro

motors.

 

*
Durant Manufacturing Company, Milwaukee, Wisconsin.

23

2.3 Calibration of the Goniometer

 

The calibration of the goniometer involved the measure-
ment of the various quantities which could affect the
accuracy of the readout since they are the most direct
source of uncertainty in the position of the various ele-
ments. There are other aSpects, however, which affect the
actual positions of the elements. These may include the
concentricities of the rotating elements and the levelness
of rotation of the main arm. The levelness is a control-
able quantity and depends primarily on the care which is
taken during the installation of the goniometer. To check
the accuracy with which the readouts can indicate the true
position of the corresponding element, it is necessary to
be able to measure the position of the element independent
of the goniometer and with a greater precision than that of
the readout system being tested. This independent system
of measurement is referred to as the reference in the follow-
ing sections. To obtain a figure of merit for a readout
system, comparisons were made between the reference measure—
ment and the value assigned by the readout. From these
comparisons, figures can be obtained which show how well
the device can be repositioned to a fixed location, how
accurately the element can be positioned at a location,
and what size of backlash is involved in the entire system

when the drive is reversed.

2“

2.3.a. Main Arm Angle Calibration
‘2.3.a.l. Construction of the
"ReferencestGeometrics

One reference (reference I) used for calibrating
the main arm was a set of points set up about a center
point in a large open area. The area above the roof of the
shielding at MSUCL offered a large, unobstructed area about
132 feet long and 75 feet wide. The shielding roof made
of two layers of 18 inch thick, prestressed, solid concrete
beams provided a stable base for the calibration measure-
ments.

Two surveying instruments were used in the setup of
this reference, a K.& E jig transit with a 30X sc0pe,(TR #1),
and a K & E surveying transit,(TR #2), each of which was
mounted on an X—Y adjustable stage. TR #1 contained a front
surface mirror at the end of its horizontal axis of rotation.
This mirror was used to set the two transits such that the
lines of sight were perpendicular.

The surface of the mirror on TR #1 was adjusted to be
perpendicular to the horizontal axis of rotation. This was
done by observing with TR #2 some object that was reflected
in the mirror from a distance of about 30 feet. The mirror
was adjusted to keep the reflected image fixed in the field
of view of TR #2 while the scope on TR #1 was rotated about

its horizontal axis.

25

To obtain an idea as to what effect the levelness of
the transit had on the measurements, the following check was
made. The transit scope was leveled and a surveying target*
was sighted at about 30 feet. The scope was then tilted
from level to produce a shift of about 30 mils of the cross
hair on the target corresponding to a shift of about 0.005°.
During all of the steps used in this calibration, however,
the level was repeatedly checked,and the bubble was kept to
within 0.03 inch of perfect alignment. Therefore, the
errors due to the levelness of the transit were kept to
better than 6 mils in 30 feet or 0.001 degree.

Performing a similar test on the level of TR #2 gave
the results of 0.003 degree per division on the level. This
scope was also kept to within a small fraction of a division
of being level throughout the measurements, and, therefore,
this also contributed a negligible uncertainty.

According to the specifications of TR #1, the straight-
ness of the line of sight from 8 inches to 100 feet is 1
mil. The specs on TR #2 are unknown but they could be 30
times worse and still contribute a negligibly small error.

The reference points at 0, 90, 180 and 270 degrees——
points A C B D in Figure 2.5--were set up first. The 0°
and 180° points were located by simply placing two survey—
ing targets on the opposite walls along the larger dimen-

sion of the room. TR #1 was set approximately midway

 

*
Keuffel and Esser Company, Hoboken, New Jersey.

26

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27

between these points, leveled, and adjusted such that the
two targets could be sighted on the cross hair in the sc0pe
by only rotating the scope on its horizontal axis.

The scope was then rotated about its horizontal axis
so that the floor beneath it could be viewed through a hole
in the transit mount. The sc0pe was then rotated about its
vertical axis and adjusted about its horizontal axis until
the spot beneath the cross hair remained fixed in the field
of view. A target was placed on the floor at the center
of the cross hairs and formed the center of the reference,
point 0.

TR #2 was placed about 2“ feet from the mirror on TR
#1, which sighted along the AB line (see Figure 2.5). A
sharp pointer was placed about 8 feet in front of TR #2.

TR #2 and the pointer were adjusted so that the center of
the reference, the pointer, the image of the pointer in the
mirror, and the internal cross hair in TR #2, were all
coplanar. When this was accomplished, the pointer lay on

a line through the center and perpendicular to line AB.

The scope of TR #2 was rotated about the horizontal axis

to determine the positions of targets C and D.

TR #1, still located over the center, was used to
place two points, E and F (Figure 2.5), on the floor.
These points were located on the two perpendicular lines
at a distance of about 32 feet from the center. A 100
foot,Lufkin, chrome-clad, steel measuring tape was used

for the linear measurements.

28

The two targets were located on the two lines in the
following way. First, TR #1 was aligned on the line of
interest. It was then sighted towards the floor at a point
about 32 feet from the center. A target was stuck to the
floor at this point, but since the line of sight made a
small angle with the floor, there was a problem in aligning
the target accurately. To provide a more accurate align-
ment, a second target was used. The targets have a fine
line at the center of each side and intersecting the edge.
By placing this target vertically over the target on the
floor such that the fine line at the edge is aligned with
the center point of the target on the floor, the target on
the floor could be accurately adjusted so that its center
was on the line of sight.

Next the edge of the measuring tape was placed over
the center point, and the same edge was placed over the
point located on the line. The tape was held taut, and a
sharp pin was used to punch a very small hole in the target
surface at an appropriate distance and also on the proper
line. The distance OF was 33.500 feet, and OE was 32.000
feet.

TR #2 was lined up so that it could sight along the
line between points E and F. The same technique used above
was incorporated here to lay out points on the hypotenuse
of the 90 degree triangle at distances in multiples of

7.000 feet from point F.

29

Now TR #1 could be used to transfer this first set
of points into the quadrant between points B and C. TR #2
and the sharp pointer were set up as shown in Figure 2.6.
TR #2 was aligned to sight along the line between the point
on the hypotenuse and the center. TR #1 was then adjusted
so that the cross hair of TR #2, the pointer, and the
reflected image of the pointer in the mirror were colinear.
TR #1 was then used to place a target along its line of
sight on a conveniently accessible, stable spot at a dis—
tance of about 30 feet from the center. This point is
then located 90 degrees from the associated point on the
hypotenuse.

The reference angles that resulted from the above pro-
cedure are shown in Table 2.1. The details of the calcula—
tions used to determine these angles are given in Appendix
II. Also shown are the standard error associated with each
point as determined in Appendix III.

A second reference (reference II) was used for small
angles from 0° to “°. This consisted of the Lufkin scale
fastened to the vall at point A, Figure 2.5. This scale was
located at a distance of 71.576 feet from the center. The
typical distance that was measured on this tape was 1.50
inches corresponding to 10 steps of the drive system at
0.01°/step. This gave an angle and a standard error

(Appendix III) of

0.1000 i 0.0010

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31

TABLE 2.l.--The reference I angles and estimated standard

 

errors .
0.0000 i 0.0010 0.000° : 0.001°
+9.6u9o : 0.007o —6.155° I 0.005°
+22.u7u° : 0.007o ~18.7l7° : 0.005°
+38.379° i 0.0060 -3“.“20° : 0.00“°
+55.580° : 0.005° —5l.62l° i 0.0030
+71.283° : 0.005O -67.525° : 0.003°
+83.8uu° : 0.005° -80.35l° : 0.002o
+90.000° : 0.00“° —90.000° : 0.00“o
+99.6u9° : 0.002o -96.155° : 0.005°
+112.u7u° i 0.0030 —108.717° : 0.005°
+128.379° : 0.003o -l2“.“20° : 0.005°
+1“5.580° : 0.00“° -l“1.62l° : 0.006o
+161.283° : 0.005° -157.525° i 0.0070
+173 8uu° : 0.005° 470.351o : 0.007o
+180.000° i 0.0010 -l80.000° : 0.001°

 

With the reference determined, TR #1 was replaced
with the goniometer at the center. The goniometer had to
be placed so that its axis of rotation was on center and
such that the main arm rotated in a level plane.

Having made checks of concentricity of the rotating
elements (section 2.3.d) it was felt that the center of
the target shaft, Figure I.“s, and the center of the
target screw, Figure I.“z, would determine the axis of
rotation of the goniometer. To locate this axis, TR #1
was set up on line CD and TR #2 on line AB so that each
could view two 90° brass points, one located over each
end of the axis. The goniometer was then placed on center
to within 1/2 inch by the use of a specially built dolly.

The four legs were then used to raise the goniometer to an

appropriate height.

32

At this point the main arm could be leveled approxi-
mately by adjustment of the four legs. Then, by using
the adjustable X-Y base of the goniometer and the leg
adjustments the two pointers located on the axis of rota-
tion were simultaneously brought into coincidence with a
vertical line, determined by TR #1 and TR #2, at the center
of the reference.

TR #1 was then adjusted to be level at a height such
that the cross hair was coincident with the top surface of
the main arm at the point where it is fastened to the
central column. The bolts in the main arm were loosened
and both main arm beams were adjusted so that the tOp sur—
face, over the entire length was level to i 2 mils during
a rotation of 360°.

The 6 bolts which hold the beams to the upper section
of the central column were now securely tightened. The arm
was rechecked for any changes. It was noticed that when
the braces for the main arm were tightened the ends of the
beams on the detector support side of the arm were drawn
together. This was found to be caused by a slight twist in
the brackets on the lower column section to which the braces
were bolted. To prevent this problem, shim stock was
placed between the brace and the bracket. All the bolts
on the main arm were then tightened and the levelness of

the arm was again verified.

33

With the goniometer arm leveled and the axis of
rotation in the center, the X-Y base could be tightened.
As the bolts in this base were secured, the main arm was
viewed to see if there were any shifts, but there were
none.

TR #2, mounted on an X-Y stage, was now fastened to
the end of the main arm. A counterbalance of 25 pounds of
lead was also put on the arm. The arm was viewed by TR #1
to verify that it had not moved. TR #2 was adjusted to be
level and to be on line AB of the reference. This assured
that the transit line of sight was through the axis of
rotation of the goniometer. TR #1 was readjusted on line
CD and was used to monitor that the goniometer remained on

center during the calibration.

2.3.a.2. Calibration Procedures

There are two quantities which were used as a measure
of the accuracy of the readout system of the goniometer--
the RMS deviation, 6, and the backlash. In each case the
positions of the elements as indicated by the reference
were compared with the corresponding positions as indicated
by the goniometer readout system. The 6 is defined by the

equation

2 1/2
6 = ((XG — XS) /N)

where XG is the position of the element as read on the

goniometer readout system, X is the position as read on the

S

3“

reference system, and N is the number of measurements.
There are two different values of 6, one for each direction
of motion; therefore, care must be taken not to include
backlash effects in this value. For this reason the 6

that is considered includes only those measurements in
which the system is driven in a fixed direction from a
starting location which was initialized in that same direc-
tion.

The backlash of the drive systems is found by the
following method. During the calibration runs, the drive
system of interest is stopped at specific (set) locations
as indicated either by the reference or by the digital
readout system. This is done at each location a number of
times for both directions of motion. The backlash at each
of these points is then defined in terms of the deviations
of the results of the measurements obtained from the non-
set readout system of the set location for the element
approaching that point in both directions. The backlash of
the readout system is then defined as the RMS of the devia-
tions found for all of the set points.

When considering the actual case of the goniometer,
one is concerned with a third quantity, the reproducibility
of a position. This reproducibility is a measure of how
well a position can be reset when the same number is set on
the digital readout. To obtain this figure, the reference

values were averaged for each specific location of the

35

element treating each direction of travel independently.
The uncertainties in the reproducibility at the specific
location is then defined in terms of the deviations from
this mean value.

There are several different operating conditions
under which the main arm had to be checked. These include
stepping through large angles, stepping through small
angles, operating under a light load, and operating near
a maximum load. Since there are two methods which can be
used to read the position of the main arm (which are
independent of each other), the local vernier scale and the
remote digital counter, it was necessary to calibrate both.

The scope which was placed on the main arm was used
to sight the reference points. All calibrations were made
with respect to the 0 degree reference point. When the
arm was rotated in the positive, CW, direction from this
point the scope was positioned to view the target in the
"backward" direction over the axis of the goniometer.

When in the negative, CCW, direction, however, the SCOpe
was rotated about its horizontal axis, and the targets
were viewed in the "forward" direction.

The arm was, in general, driven in a fast mode until
it neared the reference point of interest. Then the drive
was switched into the stepping mode, and the arm was
slowly rotated until the cross hair in the scope coincided

with the target point.

36

When the checks were made for large angle stepping,
the arm was set exactly on 0 degrees. The drive was then
set to automatically step the arm in 90 degree increments
through 360 degrees.

For the measurements of the small angle stepping, the
arm was positioned so that the cross hair in the scope was
located on a convenient starting point on the tape on the
wall. The arm was then automatically stepped through “
degrees in 0.1 degree increments.

When the arm was run in a loaded configuration an
additional 50 lbs was placed at about 3 feet from the
center with 75 lbs as the counterweight.
2.3.a.2.a. Total Errors in the

Comparisons with the Reference
Measurements

 

 

The errors which needed to be accounted for in the
total errors arise from the centering of the goniometer
on the center of the reference, the alignment of the line
of sight of TR #2 across the axis of rotation, the sighting
of the target with the scope, and the total surveying
errors in the reference points themselves.
1) Centering errors
a) Scope setup lines AB and CD 0.0008°
b) Goniometer centering 0.0008°

2) TR #2 alignment on line AB 0.0008°

37

3) Alignment of cross hairs and target
(Includes finite motor step size)

a) Reference I 0.0008°
b) Reference 11 0.002°
“) Errors in standard points
a) Reference I (Table 2.1) 0.001°-0.007°
b) Reference 11 (Appendix IIIB)
The total errors involved in the comparison of the
goniometer position to the reference points is the sum in
quadrature of (l, 2, 3, “) above.

The total errors in the measurements range from

i0.002° to i0.007O

These results of the total errors are 3 to 10 times
smaller than the errors that are expected in the ganiometer
(0.02°). This verifies that the references that were con—
structed to test the main arm readout systems had sufficient
accuracy.

2.3.a.2.b. Results of the
Calibrations

 

 

1) Large angle stepping.--This check showed that

 

after stepping through 360 degrees, the arm returned to the
same point to within the accuracy of the sighting (0.0008°).
This verified that the stepping motor had not lost or

gained any steps in the 72,000 necessary for one revolu-

tion in this one check.

38

2) 5 and backlash results and conclusions.--The

 

results of the calibrations of the main arm readout systems
are shown below in Table 2.2. Included here are the RMS
deviations measured, the number of measurements which go
into the RMS determination, N, and the maximum deviation,

MAX, observed during the measurements.

TABLE 2.2.-—Summary of the results of the calibration of the

 

main arm.

Digital system deviation, 6: RMS MAX N
1) No load 0.012° 0.02“0 77
2) Load 0.011° 0.02“° 15

Vernier system deviations, 6:

1) No load 0.008° 0.018° 77
2) Load 0.009° 0.020° 15

Total deviations, 6, for

load and no load discounting

backlash effects:

1) Digital 0.015° 0.038° l“9
2) Vernier 0.019° 0.050° l“9

Backlash:

1) Digital 0.020° 0.062° “2
2) Vernier 0.027° 0.060° “2

 

These figures show that the main arm can be positioned
to better than 0.05° even when certain precautions, such as
avoiding backlash, have been neglected. When the necessary

precautions are observed, however, angular measurements with

39

an accuracy of 0.02° are shown to be obtainable with this
goniometer.

A fact that was noted in the test involving
reference I was that the deviations were largely random in
nature. This shows that there are no large systematic
errors. During the small angle increment tests, however,
there did appear a small systematic effect of about 0.01°
in a 1.0 degree cycle in the digital readout, but none
appeared in the vernier. This indicates a nonlinearity in
the digital readout system, which probably accounts for a
large part of the errors in the main arm readout. This

error could possibly be corrected.

2.3.b. Target Angle

2.3.b.l. The Reference Used and
the Calibration Procedures

 

The reference which was used for the target angle was
the main arm itself. This reference has been shown in sec—
tion 2.3.a. to have a precision of better than i0.05°,
which is about “ times better than the expected accuracy of
the target drive.

A front surfaced mirror was placed into the target
ladder. A fine hair was placed in an open frame and was
attached to the main arm. The target ladder height was
adjusted, and a transit was placed in such a position so

that the hair could be viewed by the scope in the mirror.

“0

The target ladder was set at a position such that
the corresponding position of the main arm was 0.00°. The
target angle digital counter was set for 90.0° at this
location. From this initial position the target was
rotated to locations between 20° and 160° in 10° steps as
indicated by the digital readout of the target position.
At each location the main arm was rotated until the hair
located on it could be viewed on the scope cross hair.

The angular variation of the main arm with respect to its
initial position was twice the angular change which was
read in the digital readout for the target angle with
respect to its 90°, initial position. By comparing the
readings of both readouts, an error for the target angle
could be determined.

This procedure was used with the target drive Operat—
ing in the slow mode and in a combined fast + slow mode.
Tests were also made, after raising or lowering the target
ladder, to determine the effect of the vertical motion on
the angular position and to determine how well the target
angle could be reset to an initial value after a vertical
motion.

The error introduced into these measurements by the
method of comparison was negligible because of the factor
of two resulting from the use of the mirror. Since this
error and the error of the standard itself were small com-
pared to the expected error of the target drive readout

system, the calibration was expected to give valid results.

“1

2.3.b.2. Results of the Calibrations
The results of the calibrations of the target angle
are given in Table 2.3. The quantities, --RMS, MAX, and

N--are defined in section 2.3.a.2.

TABLE 2.3.—-Summary of the results of the calibration of
' the target angle.

 

RMS MAX N
The deviations, 5, for aAG = 10°
from an arbitrary point (defined
in 2.3.a.2.):
1) Slow 0.l° 0.3° 66
2) Fast + Slow 0.3° 0.9° 61
The deviations, 5, for any A6
up to 130°:
1) Slow 0.3° 0.70 66
2) Fast + Slow 0.“° 3.9° 50
The reproducibility of the drive
system (defined in 2.3.a.2.)
With no vertical change
1) Slow 0.2o 0.“° 70
2) Fast + Slow 0.20 0.60 5“
With vertical change:
1) Initial shift 6.0° l
2) Repositioning with slow
drive 0.3° 0.7° l2
Backlash (defined in 2.3.a.2.):
1) Slow 6.2° 6.7° ll

2) Fast + Slow 5.7O 6-5° 13

 

“2

It was noted that the deviation from the standard
increases as A6 increases. This tendency is very evident
in the fast + slow mode and only slightly apparent in the
slow mode.

2.3.c. Target Height
2.3.c.l. The Reference Used and
the Calibration Procedures

The reference used for the target height readout
system was a 6" vernier height gage with a least count of
1 mil. A dial indicator was attached to the slide of this
gage. The dial gage, capable of reading to 0.5 mil, was
used to indicate the relative height of the vernier gage to
the top of the target shaft.

The vernier gage was held securely on the surface of
the secondary arm such that the dial gage could properly
contact the top of the target shaft. The target shaft was
manually run up and down in a combined fast + slow mode
in 0.500 inch steps as indicated on the digital readout.
The corresponding changes in the height as shown by the
reference were then found. These changes were compared to
the 0.500 inch to obtain the deviations for a AH = 0.500
inch.

Limit switches were set using the digital readout
as the reference. When the target shaft was run UP to its

highest position, the limit switch which defines this

“3

upper bound of travel was adjusted so that the bottom of
the target ladder was 3.750 inches above the top surface of
the main arm. This height corresponds to the beam height
for which the system was designed. The digital counter

was then set at 9.989 which takes into account a backlash
of 11 mils (2.3.c.2) of the drive and allows the bottom

of the target ladder to be defined as the 0.000 position
for the target shaft traveling DOWN.

The first target at the bottom of the ladder was
chosen to be a standard, 0.500 inch high target. The next
three targets were chosen as those targets which could be
selected automatically. The target frames that were picked
to be compatible with the switch locations are 1.125 X 2.000
x 0.06 inch frames. Different sized frames would work
but the switches would have to be readjusted. Switches #1,
#2 and #3 correspond to the vertical centers of these
target frames which are at corresponding distances from
the ladder bottom of 1.062, 2.187, and 3.312 inches. One
of these distances appear on the digital counter when the
corresponding control switch is activated and the search is
completed in the proper direction of travel.

The microswitches on the goniometer were adjusted in
'their vertical as well as their radial positions with
IPespect to the target screw shaft. The vertical height
‘was defined as satisfactory when the switch stOpped the

drive to within 5 mils of the proper location with the

““

drive running DOWN. The radial location of each switch
was set so that the switch was activated near the radial

peak of the cam on the target screw shaft.

2.3.c.2. Results of the Calibrations

 

The results of the calibrations of the target height
readout system are lsited in Table 2.“. The definitions
of the quantities RMS, MAX, and N are given in section

2.3.a.2.

TABLE 2.“.-—Summary of the results of the calibration of
the target height.

 

RMS MAX N
The deviations for a AH = 0.500"
(defined 2.3.a.2.): 0.6 mil 1.0 mil 55
Total deviations for any AH: 1 mil 2 mils 25
Reproducability of the drive
system (defined in 2.3.a.2.):
1) Manual mode 0.“ mils 0.5 mil 38
2) Automatic mode 0.6 mils 1.5 mils 20
Backlash (defined 2.3.a.2.) 11 mils 12 mils 8

 

2.3.d. Concentricity Checks

The concentricity of two rotating elements can be
expressed in terms of total indicator runous (maximum
fluctuation of dial gage), TIR. A TIR of 6 mils indicates
that the centers of the two elements are separated by 3
mils. To make those tests on the various elements of the

goniometer, a dial indicator capable of reading to 0.5

“5

mil was fastened to one element, the base element, and
was set in contact with a cylindrical surface on the
second element. Table 2.5 shows the results of these

tests.

TABLE 2.5.--Summary of the results of concentricity

 

 

 

checks.
Base Element Second Element TIR
1. Secondary Arm Target Shaft (R)* 3 mils
(Fully extended)
2. Secondary Arm (R) Target Shaft 3 mils
3. Secondary Arm (R) Target Well 1.5 mils

“. Main Arm (R)
with Sec. Arm free (R) Target Shaft 1.5 mils

5. Main Arm (R)
with Sec. Arm fixed to
M. A. Target Shaft 3 mils

6. Main Arm (R)
with Sec. Arm fixed in
space Target Shaft 3 mils

7. Main Arm Target Shaft (R) “.5 mils

 

*R = Rotating element

2.“ Installation of the Goniometer on
the Beam Line--Figure 3.1

 

A prOper installation of the goniometer on the
external beam line is required in order to utilize its
precision to the fullest. To obtain the precision of
0.02°, it is necessary that the main arm rotate in a plane

COntaining the beam line to a tolerance of better than

“6

i 16 mils at the full radius of “ feet. It is also neces-
sary to locate the axis of rotation of the goniometer so
that it intersects the beam line to better than :8 mils.
During the calibration it was found that the main arm
rotates about an axis which is within 2 mils of the axis of
the target shaft; therefore, an alignment of the center of
the target shaft on the beam line defines the axis of rota-
tion of the main arm to within the tolerances. It was
also found that the plane of rotation of the main arm
could be leveled to within 2 mils over the entire length
for one full revolution. Considering these facts, there-
fore, it can be concluded that the goniometer can be
aligned well enough on a beam line to make use of its pre-
cision.

2.“.a. Determining the Beam
Direction

 

The limiting factor in the alignment of this precision
instrument on the beam line is the accuracy to which the
beam direction and the beam location at the center can be
determined and reproduced. The beam line elements are
shown in Figure 3.1. The alignment procedures were carried
out at a beam energy of “0 MeV which was the energy at
Which this thesis experiment was done.

The beam from the Michigan State University Sector-
fOcused Cyclotron was analyzed by the 90° analyzing

System, M3 and M“. The switching magnet M5 was then set

“7

for the field determined by the analysis system and the
calibrations for the magnets M3, M“ and M5(Sn 67). The
positions of quadrupole magnets, M7 and M8, were adjusted in
a direction perpendicular to the beam direction such that the
steering effects of these magnets were eliminated. The

beam was then focused to a 1/8" wide spot inside of vault

#2 at various locations in a 10 foot region about the
intended location of the goniometer. At each of these
locations a burn was taken on a 1/“ inch thick quartz

plate. A plumb line was then used to transfer the center

of the burn to the floor. The jig transit, TR #1, described
above in section 2.3 was then leveled at the beam height

and adjusted such that its line of sight was colinear with
the points on the floor. The transit was then used to
transfer the beam direction defined by its Optical axis to
survey targets located on the walls of vault #2.

The beam height was also defined in the above proce-
dures by a burn taken at the intended center location of
the goniometer. The center of this spot was transferred to
the wall of vault #2 by TR #1 which had been carefully
leveled.

The accuracy to which the beam direction was deter-
mined for a “0 MeV beam was estimated by how well the
centers of the burns could be identified and how well they
Could be transferred to the floor. The estimated uncertainty

Was about 1/8 inch in 10 feet or about 0.1°.

“8

2.“.b. Placement of the Goniometer
“on the Beam Line

 

 

A second transity, TR #2, was set up in valut #2
to intersect the intended center location of the goniometer
at the beam location. The line of the intersection of the
vertical planes determined by TR #1 and TR #2 was then
defined as the axis of rotation of the goniometer. The
goniometer was placed at the center to $0.5 inch by using
a four wheel dolly. The four legs were then lowered so
that the feet rested on four, thin, compressed styrofoam
pads on the concrete floor. These pads provide an inter-
face between the floor and the steel feet.

The goniometer was raised so that the beam height,
as defined by TR #1 was 3.750 inches above the top surface
of the main arm. The distance of 3.750 inches was defined
by a sharp scriber point located on a vernier height
gage. Using this technique the arm was leveled and adjusted
to the prOper height.

The center of rotation of the goniometer was defined
by a 90° point on the end of a brass sleeve which fit over
the upper end of the target shaft. Using the adjustable
X-Y base the center was adjusted to the proper location.
The arm, however, had to be simultaneously leveled and
also adjusted to the prOper height.

To level the arm it was necessary to consecutively
adjust the base as well as possible and then to adjust

the arm braces on the main arm. With enough successive

“9

approximations of the various adjustments, the arm was
found to be level to :2 mils over its entire length, to be
at the proper height to within i2 mils, and to be on center
to within :5 mils.

When the goniometer was aligned, the four feet were
held securely to the floor by clamps consisting of 3/“
inch steel plate and a 3/“ inch bolt screwed into the con-
crete floor. After the goniometer was clamped to the floor,
locknuts on the legs and the bolts on the base and arms

were tightened, making sure that the alignment was preserved.

2.“.c. Faraday Cupe—Figure 3.1.

 

The Faraday cup which is used with this system is
used only as a beam dump and is not intended to be used for
measurements of absolute charges. The end of this beam
stop is a 1/2 inch thick aluminum cap on the beam pipe
about 12 feet beyond the target location. The shielding
of the Faraday cup consists of solid concrete and paraffin
blocks. The concrete blocks form a stack about 6 feet
wide and 7 feet high which extends from the wall of vault
#2 behind the stOp to a point about 6 feet from the center
of the goniometer. The beam stop fits into a hole extend—
ing the length of the stack. The region in this hole around
the beam pipe and an access hole to the end of the beam
pipe are plugged with paraffin. To provide additional
Shielding for the detectors at small angles from the beam

Stop, a paraffin ring about 1.5 feet long and 15 inches in

50

diameter is located around the beam pipe at a distance of
about three feet from the target chamber.

Measurements were made to varify the effectiveness
of this stack in reducing the neutron background in vault
#2. A neutron counter was used to monitor the thermal
neutrons around the outside of the stack. Readings were
taken in locations which were both shielded and unshielded
from the beam dump. The readings at the protected locations
were reduced by about a factor of 10.

The beam stop is isolated by a Delrin¥beam pipe section
from the remaining sections extending from the shield to the
target chamber. Another Delrin section is located before
the target chamber. These insulators serve to isolate the
goniometer from local ground connections, and prevent ground
loop problems from occurring as well as to allow the pipe

to act as a charge collector of sorts.

*E. I. DuPont C.

CHAPTER III

EXPERIMENTAL PROCEDURES

3.1 Cyclotron and Beam Transport System

 

3.1.a. Cyclotron

 

The “0 MeV proton beams used in this experiment were
produced by the sector-focused cyclotron at Michigan State
University (B1 66). This is a variable energy, isochronous
machine designed to accelerate a variety of particles.
Protons, for example, can be produced with energies from
20 to 50 MeV. The accelerated particles are extracted at
a radius of about 30 inches by a combined electrostatic
deflector and magnetic channel system. Typical H+
internal beam currents used during this experiment were
30A and typical extraction efficiencies were about 80%.
The extracted beam entered the external beam transport

system shown in Figure 3.1.

3L1.b. Beam Transport System

Two small, horizontal bending magnets, M1 and M2,
and two quadrupole doublets, Ql and Q2, were used to align
the beam parallel to the beam pipe axis and to focus it on

the object slit, 81, of the analysis system. The two

51

52

  

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primary elements of the analysis system, M3 and M“, are
“5° bending magnets. The properties of this analysis
system have been well studied and are described elsewhere
(Ma 67) (Sn 67).

Slits 81 and 82 are separated by about “8 inches are
used to define the beam divergence. The analyzed beam is
focused on slit S3, which is the object for the switching
magnet, M5. During this experiment, typical horizontal
slit apertures were 70 mils for 81, 150 mils for S2, and
70 mils for S3. These slit settings provide a beam with
a calculated resolution of 5.“ parts in 10“, or 22
keV, and a maximum beam divergence of :5 mrad.

When the analysing magnets are set up through a stand—
ard cycling procedure, the energy of the transmitted beam
can be determined to :100 keV from the decapot settings On
the magnet power supplies. These precautions were taken
during this experiment to insure that the energy of the
protons used were “0 i 0.1 MeV. Nuclear magnetic resonance
fluxmeters in M3 and M“ were also used to verify the
energy of the proton beam (Sn 67).

3.1.0. Alignment of the Beam
into the Target Chamber

After being analyzed, the proton beam was deflected
through an angle of “5° into vault #2. The quadrupoles Q7
and Q8 were adjusted to the settings which were determined

during the installation of the goniometer described in

5“

section 2.“. With the detectors removed from vault #2 the
beam was allowed to enter the vault, pass through the
target chamber and enter the beam dump (Faraday Cup,
F.C.).

A 1/8 inch diameter hole was drilled in a tantalum
strip which was thick enough to stop “0 MeV protons. This
strip was located in the target ladder inside the target
chamber such that the hole was along the beam line and
on the axis of rotation of the goniometer. With the beam
passing through this "hole target" the beam currents were
monitored on the annular slit, S“, located in the input
coupling to the target chamber (Appendix I) and in the
F.C. By slightly adjusting the quadrupoles, Q7 and Q8,
and the switching magnet, M5, the current on S“ could be
minimized and current on the F.C. could be maximized,
thus providing a focus of the beam at the target location.
The typical slit settings shown above produced a beam
spot of about 1/8 inch in diameter. With a beam current
of 30 nA in the F.C. a current of 0.2 nA was read on the
annular slit.

3,1.d. Faraday Cup and Current
Integrator ‘5

 

 

The beam stop used in this Faraday Cup is described
in section 2.“.c. The beam pipe sections which extend from
the paraffin shield around the beam pipe to the target

chamber were designed specifically for this experiment.

55

Just beyond the target chamber was a 12 inch long piece of
3/“ inch copper pipe. This pipe is connected to a 20 inch
long, l-l/“ inch diameter copper pipe which in turn is
clamped to a standard beam pipe section containing the
paraffin shield ring. This "tapered" construction of the
Faraday Cup snout allowed the detector to reach a scattering
angle of almost 13°.

The end of this Faraday cup snout next to the target
chamber is sealed by a 1 mil Kapton foil glued to the copper
pipe. The interior of the entire F.C. assembly was main-

tained at a pressure of approximately 25 X 10-3

Torr during
the experiment.

The beam current passing through the target and into
the insulated beam dump was measured by an Elcor current
integrator model A310B. Since th F.C. was in contact with
the paraffin and cement blocks of the shielding, and since
the restrictive input snout could provide a loss of charge,
the total charge through the target was not measured on an
absolute scale. This arrangement, however, did provide the
relative numbers for the total incident charge from run to

run and served to check the results of the relative

normalization as measured by the monitor counter.

56

3.2 Set Up of the Goniometer

 

3.2.a. Target Chamber

The target chamber used in this experiment with the
goniometer is the 8 inch diameter chamber presented in
detail in Appendix I. The foil window was used on this
chamber during the experiment and permitted detector angles
from about 13° to 160° with respect to the beam. This
window consisted of a 1/2 mil Kapton foil glued to an
aluminum frame which was bolted to the target chamber
through an O-ring seal. The scattered beam as well as

the exit beam passed through this window.

3.2.b. Targets

 

A 1 mil polystyrene target and a target of gold on a
l/“ mil mylar backing were used in checking the detectors.
The nickel targets used were isotopicly enriched, self-
supporting foils purchased from Oak Ridge National Labora-
tory. The isotOpic purity and areal density for each of

these targets is listed in Table 3.1.

3.2.0. Detectors

 

The monitor detector consisted of an ORTEC silicon
surface—barrier detector 270 microns thick and mounted in
a transmission geometry. This detector was located outside
the target chamber in a mount which contained a 1 mil
Kapton window. This mount was clamped to the KF-lO Leybold

vacuum fitting at -“5°.

57

TABLE 3.1.--The selfssupporting foil targets used.

——

 

Target Purity Areal Density
(%) (mg/cm2)
58Ni 99.95 0.89 t 0.3%
6ONi 99.83 0.70 i o.u%
62Ni 99.06 0.53 i 0.“%
°“Ni 99.81 0.47 : o.uz

 

Two Ge(Li) detectors were used to obtain angular
distributions of the scattered protons during this experi-
ment. These Ge(Li) charged particle detectors were
fabricated by C. Maggiore, T. Kuo, and L. Samuelson. The
sensitive volumes of these detectors were about 7 mm X 7 mm
X 10 mm. Each detector was contained in a package which
was described in section 2.1.b.

The collimator located inside the detector package
consisted of two slits in a configuration which has been
described before (Gr 68). One is a 1/16 by 1/8 inch slit
in a sheet of 1/32 inch tantalum. This slit is placed on
the back surface of the second slit 1/8 by 3/16 inch
in a l/“ inch thick piece of brass. The edges of this
thicker slit were beveled. This type of collimator caused
the detected particles, which had gone through slit scatter-
ing in the thicker slit, to be degraded by about 10.2 MeV.
The result is the removal of the slit scattered events from

the region of interest.

58

These two detectors differed only in the type of
structure which was used between the detector cap and the
target chamber window. The detector located at the small
scattering angle, Det. #1, had a snout about “.3 inches
long made from 3/“ inch copper pipe. This snout was coupled
to the aluminum detector cap through an O—ring seal. There
was no window on the detector cap but instead the l/“ mil,
aluminized mylar window was glued over a l/“ inch hole in
the end of the snout.

The detector located at the larger angle, Det. #2,
contained a l/10 mil Havar window on the detector cap. A
KF-20 Leybold vacuum fitting was fastened to the cap through
the O—ring seal. Fastened to this flange was a short brass
vacuum pipe which contained a 3/8 inch hole covered with
l/“ mil mylar through which the scattered particles passed.
A vacuum valve was also fastened to this section allowing
it to be evacuated during the experiment.

These two detectors were securely fastened into the
dual detector mount on the detector carriage described in
Appendix I. The mounts were adjusted so that the carriage
could be pinned to the main arm and at the same time have
the ends of the snouts on the detector packages as close
as possible to the target chamber wall.

By using a transit which was aligned through the
center of the target chamber, each detector was oriented

so that the hole in the end of the snout and the center of

59

the detector cap were along the line of sight of the
transit. The internal collimator was also on this line
as defined when the detector package was assembled.

When the detector packages were in place, Det. #1 was
at a distance of 9.78 i 0.06 inches from the target with a
0.75 inch air gap between the target chamber window and the
window on the end of the package snout. Det. #2 was located
at a distance of 9.28 i 0.06 inches with a 0.“0 inch air gap.

Part of the data obtained for 58

Ni was taken with only
one detector. The detector used at that time was Det. #2
described above. The setup procedures used for this group

of data was identical to that described above.

3.3 Electronics

 

The electronics used with the two Ge(Li) detectors is
shown in the block diagram in Figure 3.2. The bias for the
detectors was provided by an Ortec Model 210 power supply.
The bias applied to Det. #1 was 600V and to Det. #2 was
330V.

The signal from each detector was input to a modified
Ortec 109A, charge sensitive preamplifier which gives as
output an analog pulse of 2 usec decay time. Also input
were pulses from an Ortec Model 20“ pulser coupled to an
Ortec Model “22 dual decade attenuator. These pulses were
adjusted in amplitude so that they were stored in about

channel 100 in the multichannel analyser.

60

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The pulses from the preamps were fed into Ortec
Model “08 biased amplifiers which were used to cut off the
lower 30 MeV of the spectra. From here the pulses entered
Tennelec, TC 200 amplifiers. The pulses from these ampli-
fiers were input to a Nuclear Data, dual ADC, “096 multi-
channel analyser, ND-160.

The pulser which is in each detector circuit is also
counted in an Ortec Model “30 scaler. The Ortec Model “10
multimode amplifier and the Ortec Model “20, timing single
channel analyzer, TSCA, shown in this circuit were used to
provide the proper pulse shape to drive the scaler.

The electronics used with the monitor counter are
shown in Figure 3.3. The 100V of bias used for the counter
is provided by the Ortec Model 210 power supply. The pulses
from the detector were passed into an Ortec 109A, charge
sensitive preamp and from there into an Ortec Model ““0
selectable, active filter amplifier, a Model “20 TSCA, and
a Model “30 scaler. The remaining elements in Figure 3.3
were used to facilitate the adjustment of the window of the
TSCA. This window was set to allow all the pulses from the
detector which were greater than or equal to the pulses from
the elastically scattered protons to be scaled.

During the early runs only one Ge(Li) detector was
used. The electronics during these runs were the same as
those described above with the exception that the pulser was

not used during the time the data was being taken.

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3.“ Data Acquisition

 

Before the actual data retrieval was begun the
electronics were tested with the pulser. The pulses were
analyzed in the ND-l60 and a measurement of the noise
characteristics of the electronic circuits was obtained.

A typical value for the full width at half the maximum
height of the peak, FWHM, was 6 keV.

The typical times required to obtain the necessary
statistics in a spectrum was from “5 minutes to two hours
depending upon experimental parameters such as beam current
and detector angles. The beam current was limited by
analyzer dead time. In order to minimize pile up effects,
it was necessary to keep the dead times below about 5%.
Following this criterion, beam currents were increased to
“00 nA as the detectors were moved to larger angles and the
counting rates decreased.

The angular distributions of the nickel isotopes were
taken in 5° intervals from about 15° to 90° in the laboratory.
The automatic angle increment feature of the goniometer was
used during the experiment to increase the angle in the
necessary 5° steps. When an angular distribution was
finished, the completed target was removed from the target
chamber and the new target inserted by use of the target
transfer lock. This allowed the target transfer to be
completed in about 5 minutes due to the fact that the vacuum

in the target chamber was not broken.

6“

The experiment also had to be stopped about every 10
hours to fill the dewar for the Ge(Li) detectors with LN2.
During the experiment it was also necessary to retake a few
of the data points due to serious gain shifts in the
electronics.

When a run was completed, the data contained in the
ND-160 analyzer was dumped into the memory of the Sigma-7
computer and then punched onto computer cards. While accumu-
lating data for the next angle the cards for the previous
run were plotted and listed using a Calcomp plotting program
written by P. J. Plauger. These plots were then examined
for any indication of a new problem which might have arisen.

Representative spectra, one for each of the nickel
isotopes, are shown in Figures 3.“-3.7. The resolution
obtained in this experiment ranged from “5 keV to 85 keV
FWHM. The worst'resolutions occurred for the runs with high

incident beam currents.

65

 

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CHAPTER IV

DATA ANALYSIS

“.1 Experimental Analysis

 

Only relative cross sections were obtained in this
experiment. To obtain the absolute cross sections, the
elastic angular distributions of this experiment were
normalized to the results of elastic scattering studies

58 60Ni

done by M. Fricke (Fr 67a) on Ni and

A monitor counter was used to provide the relative
normalizations of the runs. This counter, setting at a
fixed scattering angle during the entire experiment,
monitored the product of charge and target thickness. The
existence of this monitor counter eliminated the need to
know the exact areal densities of the targets, the exact
target angle, and the precise total charge incident on the
target.

There are, however, various quantities which did
affect the relative results between two data points. First
of all, the fact that a multiple counter setup was used
requires one to know the relative solid angles of the
detectors. It was also observed that there was a need for

dead time corrections in those few runs which had unusually

large data rates.

69

70

“.1.a Computer Programs Used

 

“.1.a.l. PEAKSTRIP by R. A. Paddock

 

This program was used to obtain the centroid, the
net area, and the statistical error in the area for the
peaks in the spectrum. The input required for this program
consisted of two boundary channel numbers for each peak
along with the background at each of these channels and
the identifying number associated with the peak. An option
of this program allowed one to choose what fraction of the
peak to be used in finding the centroid.

The background used for each channel contained in a
peak is the result of the fit of a linear curve between the
background given at each boundary channel. The fractional
standard error for the net area of each peak is defined by
the formula,

(N + 2B)1/2

AN = N “.1

 

where N is the net yield and B is the total background

under the peak.

“.l.a.2 RELTOMON by R. A. Paddock

 

The input to this program was the output of PEAKSTRIP
plus information concerning the reaction involved, the
laboratory scattering angle, the monitor counts, and the
dead time associated with the spectra. This program

calculated the center-of—mass cross section for each peak

71

at each angle using the monitor counts for the normaliza-
tion and making allowances for the dead time.

The output of this program was separated into sections,
one section for each peak number used. The output for each
peak contained the laboratory and center-of-mass scattering
angle and cross section.

There was an option in this program which was used
during this analysis. This made it possible to multiply
the angular distribution obtained for each state by a con—
stant normalization factor. This factor was used to con—
vert the relative angular distributions into absolute

distributions.

“.l.a.3. FOILTARCAL by R. A. Paddock

This program was used to determine the excitation
energies of various peaks. The input used was the output
of PEAKSTRIP plus information concerning the target compo—
sition and orientation, the reaction involved, and the
detector angle for each spectra.

A further piece of input required for FOILTARCAL
was a set of energies for reference peaks (standards). The
program used these standards to find a calibration curve
of selected order which was then used to determine the
excitation energies of the unknown peaks. The effects of
target thickness and relativistic kinematics were accounted

for in these calculations

72

“.1.a.“ SIGTOTE

 

This program was written to extract the deformation
parameters, BL, from the experimental angular distribu—
tions obtained for each state. It required as input the
experimental and theoretical angular distributions along
with identifying numbers which indicated which theoretical
distribution was to be compared with the experimental dis-
tribution.

All of the data points of a state which occurred at
the same angle were combined into one point using a weighted
average. The theoretical data was then interpolated to the
same angles at which the experimental points occurred
using a 6-point Lagrange interpolation. The resulting
theoretical distribution and the experimental data were

integrated according to the equation,

0 0(01) sin 6i A01 “.2

int = i=1

where A01 is an angular region defined by the equation,

For the end points in the distributions the angular
region was terminated at 01.
The ratio of the experimental to the theoretical

integrated cross section was found for each state. The

73

square root of this number resulted in the deformation
parameter for the state

An error was calculated for each 82 resulting from
the errors which were input with the experimental distribu-
tion only. These input errors produced an uncertainty in
the integrated cross section which was calculated using
standard propagation techniques (Be 62). This resulting
error in B2 was added in quadrature to an input systematic
error due to normalization uncertainties. This resulted in

a total uncertainty for 82.

“.1.b. Lab Angle Calibration

 

The angular position of Det. #1 relative to the beam
direction was defined during the experiment to coincide
with the position of the main arm as indicated by the
digital readout. The position of Det. #2 relative to Det.
#1 was found by sighting the center of one of the detector
caps with a transit. The main arm was then rotated until
the second cap was aligned in the sc0pe. The relative
angle was found to be 20.l°.

The laboratory angles obtained for the detectors
during the experiment relative to the beam direction were
only approximate. To obtain a better determination for
these angles for each detector, measurements were obtained
for the cross-over (Ba 6“) of the ground states of the
carbon and oxygen impurities with some of the more isolated

excited states of the nickel isotOpes.

7“

The experimental cross-over point was obtained in
each case by plotting the centroids of the nickel and con-
taminant peaks versus the laboratory angle as measured by
the goniometer. The centroids used were those determined
by the computer program, PEAKSTRIP. The theoretical cross—
over angles were determined from calculations of the
relativistic kinematics of each target nucleus with the
program KINE written by P. J. Plauger. These calculations
were done every 0.01°. This allowed the accurate deter-
mination of the point at which the apparent excitation
energies for the peaks were equal.

Since the kinematics calculations were done every
0.01°, the cross-over points could be determined better
than 0.01° for a given incident beam energy. The effect
of the uncertainty of $100 keV in the incident energy
was found to be about i0.07° in the cross-over point.

The errors in the experimental results that were con-
sidered included the uncertainties in the shapes of the
curves drawn between the points on the centroid vs. lab
angle plots and the errors in the centroids themselves.

The total error in each measurement amounted to
about 0.3°. There were a number of measurements, however,
of the angular correction needed for each of the three
detector setups. The resulting standard errors, therefore,

in the results ranged from :0.1° to t0.2°.

75

“.1.0 Elastic Cross Sections

 

The absolute cross sections for the experiment were
obtained through the normalization to the elastic proton

58Ni and 60Ni obtained by M.

angular distributions on
Fricke (Fr 67a). Each elastic peak was analyzed by choos-
ing the boundary channels such that the yield at each
channel relative to the maximum peak height was consistent
with the corresponding results obtained for the other
spectra. These tests of consistency were made only between
spectra for the same target taken with the same detector
setup.

There were several peaks, however, for which one of
the boundary channels could not be set at the consistent
location as a result of poor peak-shapes caused by pileup
or close lying contaminant peaks. In these cases correc-
tions were made in the net areas and estimates of the errors
in these corrections were added in quadrature to the statis-
tical errors. There were also uncertainties in the loca-
tion of the "consistent" channel which produced an uncer-
tainty in the net peak area. These errors were added in

quadrature to the errors from above giving a total relative

error for the net area of each elastic peak.

76

“.l.d. Normalization of the Data
to Obtain Absolute Cross Sections

 

“.l.d.1. Dead Time

 

The average dead time occurring for each spectrum
during the later stages of the experiment was found by
using the net area of the pulser peak. This peak was
generally superimposed onto a smooth background and was
easily integrated to obtain the net area. The area of the
peak was then divided by the total number of pulses pre-
sented to the analyzer as indicated by the scaler (section
3.3). The dead times for these spectra had a mean of “.2%
and a standard deviation of 3.6%.

The spectra obtained in the earlier runs did not
contain the pulser peak with which to determine the dead
time. Instead the dead time meter on the analyzer was
used. These runs were taken with beam currents of approxi—
mately 30 nA and with dead times less than 2%.

“.1.d.2 Ratios of the Monitor
Counts to the Integrated Current

For each spectrum taken there was a value obtained
for both the monitor counts and the total integrated
current. The ratio of the monitor to the integrator was
calculated for each case. This ratio varied with target
angle and with the target used.

The data obtained for 58Ni was taken during two

separate times and the ratio was not expected to be the

77

same. They were, in fact, different, but the values obtained
in each set had a fairly constant value shown by the fact
that the measurements had a standard deviation of less

than “.0%.

For 6ONi the data was taken at one time, but the tar—
get angle was changed after eight data points had been
taken. The ratios obtained for the runs after this change
had a standard deviation of less than 3%, but the runs
before the change had a standard deviation of more than 13%.

The spectra obtained for both 62Ni and 6“Ni were
taken during the same three—day run, and the target angle

was not changed. The standard deviations of the ratios

for these targets were 2.9% and 5.1% respectively.

“.l.d.3 Method of Normalization

For 6ONi, 62Ni, and 6”Ni, there were two sections

 

of the angular distributions which had to be multiplied by
an independent constant factor in order to obtain the
absolute cross sections. In each of these distributions,
however, there were angles which had been measured by both
detectors. By adjusting the relative normalizations of
the two parts of each distribution, all of the repeated
points were made to simultaneously overlap.

58

For Ni there were no repeated data points and the
elastic angular distribution for 58Ni, obtained by Fricke
(Fr 67a), was used to find the relative normalization of

the two detectors use in the latter run. All of the

78

resulting factors were averaged to give the relative

solid angles for Det. #1 and Det. #2 of,
AOl/AO2 = 1.08 i 0.0“ “.3

The elastic angular distributions obtained in this

58Ni and 60Ni were normalized to those

experiment for
obtained by Fricke who had estimated absolute errors of

from 5% to 9% for the majority of points between 0° and

90°. To obtain an absolute normalization for the 62Ni
and 6“Ni data, however, the elastic distributions obtained
60

in this experiment by Det. #l were normalized to the Ni
elastic distribution of Fricke in the forward angle region
between 10° and 20°. Since this region of the distribution
is effected predominantly by Rutherford scattering and the
mass dependence is small, the results for the different
nickel isotopes are expected to be the same. The standard
errors for all of these factors were estimated using the
total relative errors from this experiment as a guide.
Using the factor obtained from Det. #1 in each case and the

relation “.3 the absolute normalizations for the 62Ni and

6“Ni data were found.

“.l.d.“ Corrections

During the analysis of the inelastic peaks it was

found that the data at a few particular angles in 6ONi,

62Ni,and 6”Ni consistently had an improper normalization

79

relative to the neighboring angles. These discrepancies
were attributed to dead time effects and a faulty monitor
counter. I

It was noted above (section l.d.2) that the early
runs taken for 60Ni had a 13% standard deviation in the
values found for the ratios of the monitor counts to the
integrated current. A calculation of the expected ratio
in these earlier runs was done by using the mean ratio
found in the runs taken after the target angle was changed
and correcting for the variation. The results showed that
the two ratios corresponding to those data points which
had a consistently bad normalization differed from the
expected value by 23% and “5%. These problems could have
been caused by shifts in the monitor electronics during
these initial runs. Considering these large discrepancies,
it was concluded that the relative normalizations were
faulty for these two cases, and the integrated current
was used to give the normalization.

There were several spectra in this experiment which
had dead times more than one standard deviation from the
mean. The corresponding states also were consistently low
relative to nearby points in the angular distributions. As
a result of these findings it was necessary to make cor-
rections in the results of those spectra.

To estimate the correction factor the results of 60Ni

were examined. The results for the 1.33 MeV, 2+, and “.0“

MeV, 3‘, states obtained by Fricke (Fr 67a) were used as

80

references. The angular distributions obtained in this
experiment were compared with Fricke's results. The points
corresponding to those angles with a high dead time were
raised in order to be consistent with the Fricke distribu—
tions. The correction factor that was required was found
to be relatively constant for all points which were taken
with high dead times. In addition to this, the high dead
time runs were examined for the other targets and the
factors which would give smooth results were estimated.

The final correction factor used was an average of
the results obtained in the above comparisons with the 60Ni
results carrying the largest weight. This averaged factor
was then used for all spectra for which the dead time was
larger than 8.5%.

An error in this factor was estimated taking into
account the errors in the angular distributions that were
compared. This error and an estimated error for the monitor
correction above were then added in quadrature to all the
data points in each of the corrected spectra resulting in

total relative errors.

“.l.d.5 Final Results

 

After the above corrections were made in the monitor
counts and in the total relative errors, the final normali-
zation constants were determined for all of the detectors
used and for all of the target nuclei. These factors

along with the final elastic peak information were then

81

put into the program RELTOMON which provided an output of
the absolute angular distribution along with the total
relative errors associated with each point.

The systematic errors in this data were the results
of the errors in the constants of normalization of the
present data with Fricke's. This error was estimated
graphically and added in quadrature to the total relative
errors of the data whenever total errors were required.

“.1.e. Inelastic Angular
Distributions

 

 

After the elastic peaks had been analyzed, the net
areas and statistical errors were determined by the program
PEAKSTRIP (section “.1.a.) for each of the inelastic peaks
of the nickel isotopes as well as the contaminant peaks.
The centroids of these peaks were determined by using the
upper 2/3 of the peak. During this analysis special care
was taken to provide consistent peak boundaries and con-
sistent backgrounds for each peak considered.

The carbon and oxygen contaminants were removed where-
ever possible. A laboratory angular distribution was con-
structed for both oxygen and carbon using only clearly
separated peaks and plotting the net counts divided by the
associated monitor count. This distribution was then used
to estimate the net area of the contaminate located under
a nickel peak. This area was subtracted from the net

peak area output from PEAKSTRIP and was added to the

82

background yield, B, in equation “.1 giving a new statis-
tical error in the net area of the peak.

There were also several multiplet peaks. These multi—
plets were separated by using a graphical technique of
comparing peak shapes. Here again the errors were accounted
for in a consistent manner.

The net areas and the statistical errors for each of
the peaks along with the monitor counts and the normaliza-
tion factors were input into the program RELTOMON treating
each detector independently. The final results of this
analysis were compiled into four decks, one for each target
nucleus. These decks were then used in all succeeding calcu-
lations. The angular distributions for all of the

analyzed states are tabulated in Appendix IV.

“.1.f Excitation Energies

 

The excitation energies for the states of the nickel
isotopes have been determined to i7 keV by Tee and Aspinall
(Te 67) using inelastic proton scattering at 11 MeV.

There are states excited in the present experiment, however,
which lie in regions of many states. It is necessary,
therefore, to determine the excitation energies of those
particular states which were excited in this experiment.

In each of the target nuclei there exist two
strongly excited states, the first 2+ state and the first
3' state. The energies and the centroids of these two

states along with the ground state were used as reference

83

points with a linear calibration curve in the program
FOILTARCAL (section “.1.a.3) to obtain estimates of the
excitation energies of the remaining states. The centroids
used as input to this program were found in PEAKSTRIP using
only the top 2/3 of the peak. These estimates were then
compared to the previously determined excitation energies
(Te 67). When the estimate was within 15-20 keV of a known
state which is separated from its neighboring states by
50—100 keV, the corresponding peak for this experiment was
assigned the known energy and added to the list of standard
peaks.

The final group of standard peaks was used in FOIL—
TRACAL to determine a cubic energy calibration curve and
consequently the excitation energies of the unknown states
independently for each spectrum. Precautions were taken
not to include as a standard any peak which was contaminated
by carbon or oxygen. The resulting excitation energies
for each unknown peak were then averaged making sure to
remove any contaminated or otherwise questionable peaks.
These mean energies along with the standard deviations
are given in Tables “.1—“.“. Also presented here are the
standard energies which were assigned to peaks observed in
this experiment along with the excitation energies deter—
mined by Tee and Aspinall. The latter states are listed

only up to an energy where the density of states becomes

8“

 

 

TABLE “.l.—-Excitation energies for 58Ni.

Ex(MeV) Ex(MeV) Ex(MeV) Ex(MeV)

i 7 keV Present i 7 keV Present

Te 67 Data Te 67 Data

l.“56 1.“56* “.517

2.“58 2.“58* “.538

2.773 “.578

2.900 “.75“ “.75“*

2.9“0 “.920

3.035 3.035* “.965

3.260 3.260* 5.063

3.“l“ 5.089

3.52“ 5.128 5.128*

3.588 5.165

3.615 3.62:0.01 5.171

3.773 5.383

3.895 3.895* 5.“3u 5.u3:0.01

“.103 “.lli0.02 5.“60

“.290 “.30:0.03 5.“75

“.3“3 5.506

“.3“9 5.589 5.589*

“.380 “.38:0.01 5.706

“.“01 5.77:0.02

“.““3 6.08:0.0“

“.“72 “.“72* 6.35:0.08
6.75:0.02
6.98:0.08
7.3 i0.1

 

Note:

*
This state was used to determine the calibration
curve in each spectrum.

The highly excited states of Te 67 are not shown since

the higher states observed in this experiment cannot
be uniquely identified with any single state in this

reference.

85

 

 

TABLE “.2.-—Excitation energies for 60Ni.

Ex(MeV) Ex(MeV) Ex(MeV) Ex(MeV)

i 7 keV Present i 7 keV Present
Te 67 Data Te 67 Data
1.331 1.331* 3.86“

2.156 . 3.891

2.28“ 3.927

2.502 2.502* “.011

2.621 “.021

3.119 3.119* “.0“2 “.0“2*
}3.l87 “.082

3.271 .

3.316 . “.32i0.02
3.390 3.36:0.02 . }5.1“iO.10
3.589

3.619 . }5.“5iO.13
3.671 }3.69:0.02

3.732 5.7 :0.2

 

*This state was used to determine the calibration
curve in each spectrum.

Note: The highly excited states of Te 67 are not shown since
the higher states observed in this experiment cannot
be uniquely identified with any single state in this
reference.

86

 

 

TABLE “.3 Excitation energies for 62Ni.

Ex(meV) Ex(MeV) Ex(MeV) Ex(MeV)

i 7 keV Present : 7 keV Present
Te 67 Data Te 67 Data
1.169 1.169* 3.“6“

2.0“3 3.518

2.2““ 3.750 3.750*
2.33“ 2.33“* 3.8““

2.890

3.050 3.99 : 0.02.
3.150 “.1“8::0.009
3.168 3.168* “.6“ : 0.02.
3.2“9 “.98 : 0.03
3.265 3.270: 0.009 5.61 : 0.06
3.363

 

*
This state was used to determine the calibration

curve in each spectrum.

Note:

The highly excited states of Te 67 are not shown since
the higher states observed in this experiment cannot
be uniquely identified with any single state in this
reference.

87

 

 

TABLE “.“.~—Excitation energies for 6“Ni.

Ex(MeV) Ex(MeV) Ex(MeV) Ex(MeV)
i 7 keV Present : 7 keV Present
Te 67 Data Te 67 Data
1.3““ 1.3““* 3.6“7

2.275 }3.7“8

(2.“77) 3.795

2.608 2.608* 3.808

2.865 3.8“9 3.8“9*
}2-971 3.965

3.028

3.165 3.165* . “.60:0.06
3.273 . “.80:0.0“
3.393 5.“ :0.2
3.“59 5.8 10.2
3.“83

3.560 3.560*

 

*
This state was used to determine the calibration
curve in each spectrum.

Note: The highly excited states of Te 67 are not shown since
the higher states observed in this experiment cannot
be uniquely identified with any single state in this
reference.

88

too dense to be able to make a unique association between

states observed in the two experiments.

“.2 Theoretical Analysis

 

“.2.a. DWBA Theory

 

The analysis of the data presented in this thesis
employs the collective model, distorted wave theory. This
theory is described in detail elsewhere (Ro 61) (Ba 62)
(Sa 6“). For the reactions presented here the distorted
wave approximation has been shown to give satisfactory
results (Fr 67c). Calculations using this theory were
compared with the experimental results and values for the
nuclear deformation, BLRO, were obtained for each state
observed. The RO here is the radius of the real well in
the optical potential used in this experiment. Some of
the basic relationships used in this theory for inelastic
scattering are summarized in the following paragraphs.

A general form for inelastic scattering can be written

as
A(a,a')A* “.“

The total Hamiltonian for this system with a projectile, a,

and a target nucleus, A, is

H =_H€ + TO + U(rO) + V(§O, E) “.5

where

89

E designates the internal coordinates of the target
and the projectile.

designates the separation vector between the

51

centers of mass of the projectile and the
target.
T is the relative kinetic energy operator of the two
colliding systems.
U(ro) is the central optical potential describing the
elastic scattering.
V(ro,€) is the interaction potential producing the

inelastic scattering.

The eigenfunctions for this total Hamiltonian, 0, are

solutions of the SchrOedinger equation

The eigenfunctions, v(£), of the Hamiltonian, Hg’
representing the internal states of the target and possibly

the projectile are solutions of the equation,

(En - H§)Vn(€) = 0 “.7

where the subscript, n, can represent either the initial,
1, or final, f, states.

The solution of interest for equation “.6 has an
asymptotic form comprised of an incident plane wave and an
outgoing spherical wave. This solution with Coulomb

effects omitted can be written as

)/r'

W(+) __+ vi(€)eigi . g0 _ O

z
(r-m) f

where the cross section for a particular final state in the

target is

do _ 2
51'2" ”ii"

A transition amplitude can then be defined such that
2 _ 2 2 2
IAifI - (u/2nh ) Itifl

and the cross section for inelastic scattering can be

written

 

2
—— 2 It I “.8
2flfi i av if

The p is the reduced mass of the system and 8v designates
the average over the spins of the initial states and sum
over the spins of the final states.

The transition amplitude, t can be represented by

if’
the equation,

tif = <vf<t> X(;)IV<30,£)lw (+) >

This is just the matrix element of the interaction poten-

tial which connects the total incident wave of the system

91

with that wave which represents the exit channel of interest.
) is the solution of the SchrOedinger

The function X(-

equation,
[-V2 + 33- U (r > - k2] x(‘) = 0
f h f o f f

which satisfies incoming spherical wave boundary conditions.

The total wave function for this system is intract-
able and, therefore, tif cannot be calculated exactly. The
Born approximation makes the assumption that

(+) N (+)

which gives,
(“) (5,. £0)|V(§O,€)lvi(€) X(+)(Ei,zo)>

< vf(E) X
“.9

tif ”

The form of V(§O, g) is assumed to be central and

can be expanded in multipoles as
_ Z M c M c
V(£O’€) “ LM gL (130,5) YL (E) YL (r0) “.10

Each internal nuclear state has a well defined J and m;

therefore

92

J Ji
V (E) = v (E) and v (E) = v (E)
f i m
f 1
Using the Wigner-Eckart Theorem (R0 57) the integration

over 5 gives

J J
f* M A i _
f d5 vmf (E) gL(€,rO) Y L (E) vmi(€) -
(Ji L mi M Imef) FL (r0) “.11

The cross section can then be written as

2
__._ L . u .21: . IBLMI I...
21m2 k. 2Ji + 1 LM 2L + 1

Q.

 

Q

where

B = f dr X(-)*(k r ) F (r ) YM*(r ) X(+)(k r )
LM —0 f —f’—o L o L o i —i’—o

The FL(rO) is a radial dependent factor which depends
on the model used for the interacting systems.

In the collective model the excited states are
attributed to excitations of deformations about a Spherical
shape. It is assumed, then, that the deformed nucleus has
a deformed optical potential associated with it. The
total interaction representing the inelastic scattering

can be written in the form

93

UT = U(r — R(0')) “.13

where 0‘ are coordinates in the body fixed system.
The radius of a deformed nucleus can be written in

a multipole expansion,

v = Z O I
R(0 ) ROEl + L 8L YL (0 )J “.1“
if axial symmetry is assumed. The total potential can be
expanded in a Taylor series about the spherical shape,
R = R

O,

_ l 2 3 U ,,,
UT(r-R) - U(r-R0) + AR + 2 (AR) -—— |

9.! |
BR R=R
0

where

= _ — Z O I
AR (R R0) — R0 L BL YL (e )

The first term in equation “.15 is the spherical
optical potential and describes to first order the elastic
scattering. The second term describes to first order the
inelastic events. The usual approximation is that the
interaction potential of equation “.5 can be equated to
the second term of equation “.15 giving

fig 0 I
.0 ' 0 BL 8r (P-RO) Y (9 ) “.16

L

9“

This relation is then transformed from the body fixed
system to one that is space fixed by a spherical harmonic

addition theorem (Ro 57)

M

* A A
M (r) YL (a)

_ . 8
(8', 0) — (“fl/(2L + 1)) § YL

where g is the relative angle of the body and space
fixed axes, and equation “.16 becomes

11 M*A MA
) j Y (rO)YL(€)

2L+1

V<:O.a> = - E E0 BL g; (r—RO) <—51— L

This is compared to equation “.10 for V(§O,£) to find an
expression for gL(rO,§) in equation “.11. For even-even
nuclei experiencing a rotational collective motion the

nuclear wave functions can be written,

0 A
Vi(€) - Yo (€)¢intrinsic
Mf A
Vf(§) = YJf(€)¢intrinsic
where ¢intrinsic are parts of the wave function which remain

A

unchanged in a rotational excitation. The angle 5 repre-
sents the nuclear collective coordinates which are rele—

vant. Using these wave functions along with the gL(rO,€)
found above and the fact that J = 0 and m = 0 for an

i i

even-even nucleus the form factor (equation “.11) becomes

95

“n . 8U Mf

% * A M A o A
(m) BLRo-37f YJf (5.) YL(€) YOU.) d5

FL(r)

30
O8? °J L °MfM ”'17

-%
- (2L+1) BLR
f

This form factor is then used in equation “.12 to deter-

mine B which is used in turn to give the calculated cross

LM
section for inelastic scattering. Then by normalizing
these angular distributions to the data, the nuclear

deformation, BLRO,can be extracted.

“.2.b. Vibrational Model Parameters
and Reduced Transition Probabilities

 

 

The spectra of the even nickel isotopes have char—
acteristics of vibrational nuclei (section 5.1). The
formal results in the collective, distorted wave calcula-
tions for a vibrational model are the same as those shown
above for the rotational model. The difference between
these two approaches is that for the vibrational case, the
nuclear deformation is dynamic in the space fixed coordi-
nate system.

The nuclear deformations for the vibrational model
are evaluated from the experimental results in exactly
the same fashion as for the rotational case. The vibra-
tional model, however, relates the nuclear deformation,

0 = BL R0, to the quantities, D

L and CL’ which appear in

L

96

the Hamiltonian describing a system with small oscillations

o LM LM
where
H0 is the Hamiltonian which describes the static
nucleus
and

HLM is the Hamiltonian of the deformation with

angular momentum, L, and projection, M.

In terms of generalized coordinates,

_l - 2 1 2
H ‘2'DLIO‘LMI +'2'CL|°‘LM| +

The DL is defined as the mass transport parameter and CL

the surface tension parameter. These are related to the

excitation energy, E = no by the relation (La 60)

L L’

EL = n(CL/DL)% “.18

and to BL by (Ba 62)

2-
BL - (2L + l) th/ZCL
OP
Bi = (2L + l)/2(cL DL/h2>“ “.19

97

In the comparisons of experimental results it is more
meaningful to compare the nuclear deformations, 6L = BLRO,
rather than the 8L alone (B1 63). As a result of this
the reduced transition probabilities and the vibrational
parameters were derived in terms of the OL's or OL/Ro where
RO is an interaction radius, R0 = rOAl/3.

The surface tension and mass transport parameter are

found from equations “.18 and “.19

 

 

R 2
a (2L + 1) o
CL 2 62 EL “.20
L
2
DL = (2L + 1) R0 g_ u 21
‘67 2 5: EL

The reduced transition probability is given by the

equation (La 60),

2L-2 “.22

Ze(2L + 1) <r >)2 1
L-2 2 8
“w R0 2(DLCL/h )

 

 

B(EL; L+0) = (

Using the fact that B(EL; 0+L) = (2L + 1)B(EL; L+0)(A1 56),
and using 6L and the relation “.19, equation “.22 can be
rewritten

Ze(2L + 1) <r2L_2>

)2
“n R L'2 R
o

6

I...
J:-

 

B(EL; O+L) = ( .23

[\J

O

98

where (La 60) it has been assumed that the matrix element

<rL> is given approximately by:
<rL> = erp(r)dr/f p(r)d§ “.2“

where p(r) is the charge density distribution. The single
particle estimate for the reduced transition probability

is defined as (La 60),

(2L + 1) 2 L 2
BSP(EL; 0+L) = “—E?‘—‘ e <flr |i>
but can be estimated by the relation,
. _ (2L + l) 2 L 2
BSP (EL, 0+L) "_—_FF—__'e <r > “.25

The ratio, G, of the results of equations “.22 and “.25 is
the reduced transition probability expressed in terms of

single particle, Weisskopf units,

0 = B(EL; 0+L) / B (EL; O+L)

SP

“.2.c Sum Rules

 

The non-energy—weighted sum rule, NEWSR (La 60), is
based on the shell model. This rule gives the maximum
value of the sum of the reduced transition probabilities
for transitions from the ground state of an even-even
nuclei to n states with the spin, L, is given by

e2Z 2L
ZBn(EL; 0+L) = —“F <r > “.26

n
A second sum rule is an energy—weighted sum rule,

99

EWSR, for transitions to states with T = 0. It is (Na 65)

2
2 2 2
28 L h (2L+1) <r2L-2>

5 (En - E0) B (EL; L+O) = 8" AM

“.27

This sum rule is independent of any model of nuclear
structure except that it assumes a velocity independent
Hamiltonian. It also depends on the charge distribution
in the ground state through the quantity <r2L'2>, but
this distribution can be found from electron scattering

data (El 61).

The expression “.27 can be rewritten in terms of the

hydrodynamic limit for the mass transport, (DL)HYD (La 60).
(DL)HYD is written as
(D ) = g£_1_l AM <r2L-2> u 28
L HYD L F? ‘E2L3F’ '
o

where AM is the total nuclear mass. Using equations “.28,

“.23, and “.21 the EWSR can be expressed as

(D )
Z L HYD _
r1 .,.__)___DLn __ 1 “.29

“.2.d. Optical Model Parameters

In order to perform the DWBA calculations, the opti—
cal potential had to be defined for each target nucleus.
The parameters of the potentials used in this analysis

were derived from work of Fricke et a1. (Fr 67b) who did

100

elastic polarization studies for eleven targets throughout
the periodic table. The optical potential used in this work

was of the form
_ d
V(I’) - V00?) - V0f(x) - 1(WO-“WD air)f(X')

19..
r dr

+ (fi/m"0)2 vs( > f(xs) g - .9:

where Vc(r) is the Coulomb potential for a uniformly
charged sphere of radius 1.25A1/3. Also, f(x) = (ex-+1)"l
and x = (r - Ro)/a. In this study the potential parameters
were found for 58Ni and 60Ni, but of more importance a

set of average parameters was found for all of the

targets. These average parameters are listed in Table “.5.

TABLE “.5.--Average optical potential parameters used.

 

r0 = 1.16F a = 0.75F
r0' = 1.37F a' = 0.63F
rs' = 1.06“F as = 0.738F
Vs = 6.0“ MeV

 

It was concluded in this study that these fixed parameters
provide a reasonable optical-model description for elastic
scattering and polarization of protons at “0 MeV. As a

result of this work, therefore, the average parameters were

101

used in the present experiment for 62Ni and 6“Ni. In

addition the values of those remaining parameters found

by Fricke et al. for 58Ni and 60Ni were used.

The remaining parameters needed in the present analy-

6“
sis were the potential strengths for 62Ni and Ni. To

obtain a set of starting parameters, an extrapolation of

58 60

the form VO = K + K (N - Z)/A from the Ni and Ni

1 2
values was performed for each potential strength (Fr 67b).
An optical model parameter search code, GIBELUMP, was
used to search on the parameters and obtain fits to the
elastic angular distributions. The criterion used to
determine the necessary variation of a parameter was the

minimization of the quantity X2 where

O

2
=l[(oTH(ei) - 0EX(01))/AOEX(01)]

N
|
HMZ

where N is the number of data points, OTH(81) is the
calculated value of the cross section of angle 01,
0EX(61) is the experimental value at that angle and
AOEX(01) is its standard error.

The parameters searched on were V0 and WD. Since

changes in W0 and W produce about the same effects on

D
the resulting angular distributions, only one needed to

be varied. The optical potential depth parameters which

were determined in the study by Fricke et al. for 58Ni,

60Ni and those found in this work for 62Ni and 6“Ni are

102

listed in Table “.6 along with the resulting

X2/N.

TABLE “.6.--Optical potential strength parameters used.

 

2 b 2 C

 

Target VO(MeV) WO(MeV) WD(MeV) x /N X /N
58Nia “5.05 6.63 1.22 3.6
6ONia “5.7u 5.u7 2.50 5.6
62Ni uu.86 “.38 3.13 2.2 “.8
°“Ni 45.25 3.37 3.20 0.55 3.0

 

aFricke's parameters
bUsing the final parameters listed

CUsing parameters that were extrapolated from
Fricke's results.

The calculations using these parameters are compared to

the data of the present experiment in Figure “.l.

“.2.e DWBA Calculations

 

The DWBA calculations were done using a FORTRAN—IV
version of the Oak Ridge computer code JULIE (Ba 62) on
the SDS, 2-7 computer. These calculations included Coulomb
excitation with rC = 1.25F and the deformation of the
complete Optical Potential.

The Optical potential parameters used in these

calculations are those given in Tables “.5 and “.6. The

103

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'00 l I l I I I I '00 I I I 1 T I
58m (0.9) 60Ni (pm)
40.0 MeV ' 40.0 MeV
v,=45.05 MeV \4 = 45.74 MeV
W°=6.63 MeV w.=5.47 MeV
x‘sss x’=5.6
I
. S
‘2
b
| >— I -—I
I I
O.I I l I l 1 l l 1 0| 1 I 1 l 1 I l I
o , 4O 80 I20 '0 4O 6 80(d , I20
9‘)
Bummeg) cm
'00 I 17 T I T I I I '00 I I I I T I I
62Ni(O.P) 64Ni(p.p)
40.0 MeV 40.0 MeV
v.=44.86Mev v0: 45.25Mev
w,=4.3s MeV w,= 3.37 MeV
IO -— wp :3-'3Mev -- IO — W,=3.20MeV _j
x' = 2,2 X'=O.6
K
9 §=
b b
I — I — ._
0, I I I I I I I I 01 I“, I I I I 4 I
‘ o 40 so I20 0 4o 6 so (6 ) I20
00
cm.
6am. (dog)
“.1

Comparisons of the experimental, elastic scattering

results and the theoretical calculations using the

Optical potential parameters given in Tables “.5

and “.6.

10“

resulting angular distribution, ODW’ for inelastic
scattering is related to the experimental distribution

by the relation,

921E131: l 32.2.5113... “30
d9 (2L + 1) L 2JA + 1 DW '

where L is the transferred orbital angular momentum. For

inelastic proton scattering from an even-even target

JA = 0 and JB = L; equation “.30 becomes
d EXP 2
“EEO-'2’ = 8L ODW “'31

“.2.f Extraction of Deformation
Parameters, BL

 

The relation “.31 was used in the comparison of the
theoretical and experimental angular distributions through
the computer program, SIGTOTE (section “.l.a.“). In these
comparisons the value of the momentum transfer, L,
associated with each state observed Was needed in order to
extract a definite value for the associated nuclear
deformation.

In Tables “.7—“.10 are tabulated the values of J1T
that have been determined for the various states in the
stable, even nickel isotopes through other experiments.

Also listed here are the L-values that were assigned to

the states with the excitation energies shown in the table.

105

mam Co moCmComom

.mm om ooCmCmmmmm

mum on ooCOComomo mwm CH moCoComom

mum we ooCOCommmm

 

 

o n
+3+Im pom.»
3 Im o.omm.s
+3 oom.sImH.~
Im no.0Im.o
+3 nmm.m
+m nom.m
Im 950.0
+3 nom.m
+m++3 nom.m
+3 n03.m
o mma.m +m nma.m
3 3ms.3 +3 +3 s3ms.3
m ~53.3 m Im Im mNN3.3
3 mm.3 +3 mHO3.3
A+mv mmoa.3
m mmm.m +m +m mmmm.m
A+mv mmss.m
3 mw.m 3 +3 +3 mmam.m
+H mmmm.m
+3 mamm.m
A+mv o3H3.m
m owm.m m m +m +m womm.m
m mmo.m m +m +m ammo.m
+o o03m.m
+H moom.m
m +m +m mmss.m
3 mm3.m 3 3 +3 +3 mmm3.m
m mm3.H m +m +m omm3.H
as as en so
A A>mzvxm >02 m >02 mma >02 m.om >02 3.3m
xCoz pComOCm A.Q.dv A.m.ov A.a.ov A.a.dv

CH own: mosam> m o o a A>mzvxm

 

mosam>Iq UCm mOHwCOCo Coapmpaoxm 0C» UCm Hz

.pCoEHCoaxm man CH poms
mm

Cfi wepmpm Com mpCoECmfimmm :wII.>.3 mqm<e

106

TABLE “.8.—-JTr assignments for states in 60Ni and the

excitation energies and L—values used in this experiment.

 

 

a b Values used in
Ex(MeV) (aa')3“.“ MeV present work
Jw J“ Ex(MeV) L
1.332a 2+ 2+ 1.331 2
2.158a 2+ 2+
2.286a 0+ 0+
2.506a “+ “+ 2.502 “
3.625a 3+
3.123a 2+ 3.119 2
3.11b 2+(“+)
3.195a 1+
3.35b 2+
3.700 “+
“.022a 1+,2+
“.0“0a 3- 3- “.0“2 3
“.079a 1+,2+
“.332a 1+,2+
“.300 “+
“.“96a 1+,2+
“.50b 2+
“.555a 1+,2+
“.583a 1+,2+
5.0b 5-
5.lb
5.102a “+ “+
5.6b 3-
5.85b 2+
6.16b 3-
6.53b 3-
7.00 3-,“+

 

aReference Ra 68
bReference Ja 67

107

TABLE “.9.-——JTr assignments for states in 62Ni and the

excitation energies and L-values used in this experiment.

 

 

a“ 63 b 3 Values used in

Ex(MeV) J Cu(d, He) present work
Jw Ex(meV) L

1.172a 2+ 1.169 2
2.0“7a 0+
2.293a 2+
2.336a “+ 2.33“ “
3.75la 3- 3.750 3
“.02b ( )+
“.7uo ( )+
“.85b ( )+

 

aReference Ve 67

bReference Hi 68

108

TABLE Ll.lO.--JTr assignments for states in 6“N1 and the
excitation energies and L—values used in this experiment.

 

 

a 65b c Values used in
Ex(MeV) w 3Cu (da') present work

J (d,JHe) 30.5 MeV Ex(MeV) L
1.3M8a 2+ 1.3uu 2
2.272a 0+
2.6053 4+ 2.608 U
2.863a 2+
3.16la 2+ 3.165 2
3.55ua 3- 3.560 3
3.79b ( )+
3.85c 5- 3.849 5
u.29b ( )+

 

aReference Ve 67
bReference Hi 68

CReference He 68

109

There were states observed, however, that could not
be associated with a unique state identified in reference
Te 67 (see Tables u.1-u.u). This ambiguity is a result
of the errors involved in the determination of the energies.
When this was the case, the observed state could not be
given a definite L-value. Furthermore, some states in
reference Te 62 were given only tentative assignments or
no spin assignments at all. In these cases several values
of L were used in the comparison of experiment and theory,
and the BL for each case was found. The program, SIGTOTE,
described in section 4.1.d, was used for this comparison
by the method of normalizing the integrated cross sections
for the theoretical and the experimental results. All of
the L-values which were used in the calculations are
shown in Appendix IV along with the nuclear deformations,
6L = BL R0, which were found. The experimental angular
distributions of known L are shown in Figures 4.2-“.6 along
with the normalized theoretical data. The angular distri-
butions which cannot be associated with an L—value are
plotted in Appendix IV. Also in Appendix IV are plots
of the DWBA theory. All of these plots of experimental
and theoretical data are presented on the same scale to
facilitate comparisons.

In addition to this procedure a second method was
used to evaluate the nuclear deformations. This method

involved comparisons of the ratios of the cross sections

llO

 

 

 

L456 MeV

   

 

3.6 2 MeV
43
B4=O.068

3.995 MeV
fi2= 0.038

I L I l l L, l 1
0.0. 0 4O 80 '20

(EEJL

A.2 Comparisons of the experimental inelastic scattering
results and the theoretical DWBA calculations for
states in 58N1 with known J" assignments.

 

 

 

 

11.3

111

 

IO

 
 

 

 
 

 

 

 

E l’ I I I I I I I 5
: “Ni (p.p') :
' s” ‘2‘
IO 1;
4.38 MeV 3
4+ :
3:007? .
E' ,
1g 1 2:4Jfi2hmeV' :
v k - -
,3 I . Bfono _
s i
., f
I I 4.754 MeV 1
I 4*

*1 ”‘1 B4=O|Ol ~
IL I 5.|28 MeV 1
I I 6* a
g B; 0.096 3
_ J
OJ 5' I} 'E
E 5.589Mev 5
: 4* 1
_ 34:0.079 -

00' l L l l L l l l

0 40 so I20

Q9CJL
Comparisons of the experimental inelastic scattering
results and the theoretical DWBA calculations for
states in 58Ni with known JTr assignments.

112

 

ICX): I I I I I I I I

1111!]

8
Z.
.3
'0-

1 L11

1 l

 

L33I MW

1 l Illll

1 1 11111

I L

2.502 MeV

da/dw (mb/sr)

L 1 lllJlll

 

1 I 11111

:25. I I0 MeV
[3; 0.056

 

 

 

 

A.“ Comparisons of the experimental inelastic scattering
results an the theoretical DWBA calculations for
states in 0N1 with known J1T assignments.

 

'00 T T I I T [1T T

1 1141111

  
  

l0

T l V 11111.
1 1 1 111111

l.|69MeV

1 1111111

I

‘FD
11
.0
“O
C)
C”

I:

 

1" fliiilfl'

da-ldw (mb/sr)

1 1 1111111

 

.1

AN
*0:
o:
4:.
§
<1

111111

1

3.7 50 MeV
3-
B4=O.l80

1 1 #11111

 

 

 

CAL

4.5 Comparisons of the experimental inelastic scattering
results and the theoretical DWBA calculations for
states'in 62Ni with known J1T assignments.

lllI

 

ICX) I I‘ I I I I I I

|.344MeV ‘:
2+
BZ=0.I83

1 L11

2 .608 MeV
4+ ‘5
B4=0.075 3

dcr/dw (mb/sr)

 

3.|65MeV

3.660 MeV
B; 0. I94

 

g8 49 MeV
. a; 0.079
I l I L l 1 I
0‘0'0 40 so I20

tatji
A.6 Comparisons of the experimental inelastic scattering
results and the theoretical DWBA calculations for

states in 6“Ni with known J1T assignments.

 

 

 

l

 

115

for the excited states to the ground state for the theory
and the experiment. This type of procedure eliminates the
need for knowledge of the relative normalization of the
data at the various laboratory angles. Since there were
normalization problems (see section A.l.f.2) in this
experiment, this method did prove to be helpful. It also
has the potential to provide a better measurement of the
6L's since only the statistical errors contribute to the
final error. By the former method, in comparison, there
are systematic errors which also contribute.

Involved in the ratio are two statistical errors,
one for the ground state and one for the excited state.
Furthermore, the angular distributions of the ratios have
the general trend of increasing in magnitude with increas-
ing angle. These facts result in a change of the weights
of the terms comprising the integrated cross sections in
equation 4.2 compared to the first method. The exact
nature of this effect was not examined in detail, but the
results indicated the larger weight tends to be given to
the points at the larger angles. This effect is different
from the method involving the absolute cross sections
where the forward angles are weighted more.

The result of this change in weighting is that the
errors for a particular 6L as found by the ratio method
may in fact be somewhat larger than that found by the more

customary method. The results of the ratio method,

116

however, did agree in general with the values obtained by
the customary procedure. This enhances ones confidence
that the relative normalizations of the experimental data
were correct.

In addition to the observed states upper limits to
the differential cross sections for the second 2+ states
were obtained. Several energy spectra at various detector
angles for each nuclei were examined at the points at
which these states should appear. The statistical fluctua-
tions of the background at these points were compared to
the net peak heights for the first 2+ states. The estimated

upper limits are shown in Table A.ll.

TABLE H.ll.--Estimated upper limits for the 5L for the
second 2+ states.

 

 

58N1 60N1 62Ni 6uNi
Ex(MeV) 2.773 2.156 2.293 2.863
5 0.103 0.138 0.121 0.102

L

 

CHAPTER V

DISCUSSION OF THE RESULTS

A vibrational collective model was used in the
distorted wave theory to extract a nuclear deformation
for each observed state. These deformations were then
used to find reduced transition probabilities and the
corresponding parameters of other models.

According to Lane (La 64) transitions which involve
"collective" motions exhaust greater than 5% of the sum
rule. This is considered to be a rough means of identi-
fying collective motion. The fraction of each sum rule
contained in each state is presented in Appendix IV.A.

The energy weighted sum rule is deflected by more than 7%
for the first 2+ state in each nuclei and by more than 12%
for the first 3— state. The non-energy—weighted sum rule
shows even larger fractions exhausted for these states,
and there are a number of additional states which contain
more than 5% of the limit. These results indicate that
the spectra of the stable, even nickel isotopes contain

a number of states which can be associated with collective

motions according to the criteria of Lane (La 64).

117

118

Vibrational characteristics of the energy level
structure of a nucleus include the uniform spacing of
the levels and the systematic occurrence of a given type
of level in neighboring nuclei (La 64) (Bo 67a).

58 60 62

The low lying energy levels of Ni, Ni, Ni,

and 6“Ni are approximately evenly spaced as shown by the
fact that E = is and E = l E . The systematic

appearance of the strongly excited 2+ and 3' states in
even-even nuclei support a collective interpretation of
these states.

The optical potential strength parameters used in
this analysis for this experiment are shown in Table 4.6.
The values of X2/N indicate that the starting parameters

for 62Ni and 6”Ni derived from the work of Fricke et al.

on 58Ni and 60Ni resulted in reasonable fits. This
indicates that the searches on the parameters for 62Ni and
6“Ni were probably not necessary.

According to Glendenning and Veneroni (G1 66) inelas-
tically scattered protons are a valuable tool for examining
details of nuclear structure well inside the nuclear surface.
This probe, on the other hand, is not conclusive in deter—
mining spins and parities as compared to the strongly
absorbed particles such as alpha particles.

The results of the collective distorted wave calcula-

tions provide very good fits in many cases to the angular

distributions for the states of known spins and parities.

119

As a result of this there is some value in comparing those
states of unknown Spins and parities to the calculations.

This does provide tentative assignments of the orbital

 

angular momenta, L, associated with some of the states.

The tabulated results of such comparisons are pre—
sented in Appendix IV.3. The X2/N can be used here to
indicate how the experimental distributions are fit by the
calculations for various L-values. Plots of the calculated
distributions were also compared with the data to check
that the shapes were indeed consistent. The tentative L

assignments for various states are given in Table 5.1.

TABLE 5.l.--Tentative L assignments.

58 6O 62 64

N1 N1 N1 N1

 

Ex(MeV) L Ex(MeV) L Ex(MeV) L Ex(MeV) L
u.11 (u) 3.67 (M) u.1u8 (5) u.60 (5)
6.89 (3) 5.7 (3)

7.3 (3)

 

The quantity <rx> (section 4.2.b) was used in the

calculations of the reduced transition probabilities and
sum rule limits which gave the results tabulated in
Appendix IV.4. The value of this radial moment depends on

the type of charge distribution used. These different

120

distributions were used here. A comparison of the B(EL)'s
for these three cases show that there can be factors of 2
variations in the results for the 2+ states, factors of 4
for 3- states, and up to factors of 10 for 4+ states. The
conclusion is that the reduced transition probabilities
obtained in (p,p') experiments are extremely sensitive to

the model used for the matter distribution.

5.1 Comparisons with Other Experiments

 

The nuclear deformations obtained in this experiment
are compared to other experimental results in Tables 5.2—5.5.
The quantities shown are mostly for states with a known

L-value. For 58Ni and 60N

1, however, there were deforma-
tions obtained for states which have uncertain energies
and L—values in reference In 68. If the excitation energy
determined in this experiment agreed with that in In 68 to
within the errors, a value of 8L R0 was obtained for the
state. The BL's found for each of these states in the
present experiment were, in general, constant to within
a few per cent for the different L assignments. An average
of the deformations shown in Appendix IV.3 for each of these
states of undetermined L is shown in Tables 5.2 and 5.3.
The values obtained for the reduced transition
probabilities along with results from other experiments

are presented in Table 5.6. Listed here are the results

for the three charge distributions given in Appendix IV.4.

121

.4 CH hpcflmBLmoc: on» on 030 Logic mg» magaocfl poc on mmpmpm @060» Low whoppm one

 

 

*
:Hm.0 00.: “Am0m.00 mm.0
0Hm.0 00.m “Azmm.00 00.0
mmm.o “0.: “Amma.00 ss.m
500.0 mm.MH*AH0m.00 00.m
Hmm.0 man“ 00.0 asmfimm.0 00.0 “mmm.0 0 000.m
00m.0 ma.m “Hm0.0 0 mma.m
000.0 was“ 0m.0 0000mm.0 00.0 Amm0.0 0 005.0
mmm.0 sme.0 00.Hflmmm.a K00.0 ms 6 ms.0 ”maflss.0 ms.0 mm.m “m0s.0 m- ms0.0
00H“ 0m.0 0mm000.0 00.m H0zm.0 0 0m.0
00H000H.0 00000H.0 0H.m HHAH.0 m 000.m
s0m.0 00flflmzm.0 Rmmfimm.0 mm.m wm0m.0 0 00.m
00.0000:.0 0Hm.0 00“ mam.0 00.0 “mmm.0 m 00m.m
“mmflszm.0 0Hm.0 m0afl0mm.0 0H.m “000.0 m mm0.m
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124

TABLE 5.6.--Comparisons of reduced transition probabilities, B(EL; O+LL in units of

 

 

 

30L
_ I 1,. 0
Ex’MeV) L Coulomb Exoitaticn / Ge F-ebent Results
‘ St 05 :0 . Cr (1 a b c
SBN1
1.u56 2 1050 906 1030 1030 1230 1720
£101 110 1:08 1&7 :57 :79
3.035 2 1;. 9A 112 156
‘ "0 :6 t :10
3.260 2 n.0 153 182 25a
1;: :9 :10 :1u
u.u72 3 107%0 2" c- 17uC0 2&800 68000
0730 +800 :11u0 23160
1 r
2.u68 u 1 ng10 1 .xicg 1.67010; 1.3Ux102
:3 5x10 :0.08x10 t0.07xlO
3.62 u 80010” 0 0x103 1.0 x10; 8.1 x105
. :3 ux10 10.06x10 :0.5 x105
6ON1
1.331 2 397 1217 1" ‘ 1300 1600 2200
: 15 :13 :__: :88 1106 :1u5~
u.ou2 3 u05f0 3:310 21200 30100 80700
:12: :1u00 21900 25200
2.502 u 2 7x10” 1 11x10? 2.0x10? 1.6x106
:3 0ax10: 10.2x10) 10.1x106
62Ni
1.169 2 1210 1:63 1290 1530 2080
:115 :10 _ 113 :135 :183
3.750 3 302u0 22300 31700 82600
:778 :1250 :2730 17100
6uNi
1.3uu 2 1253 1070 1270 1710
:2u5 1180 :21U 2288
aUniform charge distribution with r0 = 1.20?
bFermi equivalent, uniform charge distribution with r0 = 1.31F

cFermi charge distribution with r0 =

1,10F and a =

0.566F

125

The force constant,CL, which was found in this
experiment using a uniform charge distribution with
r0 = 1.20F is shown for each of the first 2+ excited states
in Table 5.7. Also shown in this table are the results of

calculations (W0 68) of C which used the values of the

L
B(E2)'s obtained from studies of electromagnetic transi-

tions (St 65).

TABLE 5.7.—-Experimental surface tension parameters,

 

 

CL(MeV).

We 68* Present work**
58N1 10M 0 9 106 i 5
6ONi 74.8 1 5.7 77.7 _ 5.1
62Ni 79.3 0 6.9 7u.u i 6.5
6“Ni 91.3 t 1u.9 107 :17

 

*
Using a uniform charge distribution with r0 = 1.2OF.

**
r = 1.2OF
c

Crannel et al. (Cr 61) evaluated the mass transport

parameters, D In these calculations the D 's were cal-

L' L
culated from the B(EL)'s found in their experiment with
inelastic electron scattering. They used a Fermi charge
distribution with r0 = 1.05F and a 2 0.57F. Their results

along with those obtained in this experiment are shown in

Table 5.8.

126

TABLE 5.8.--Experimental mass transport parameters DL/h2
in units of (MeV' ).

 

 

 

Ex(MeV) L Cr 61a Present Workb
58Ni 1.u56 2 7O 1 9 50 1 9
3.260 2 160 i 38 150 i 8
60N1 1.331 2 65.21 7.8 an 1 3
58
Ni u.U72 3 103 i 1“ 29 i l
60
Ni H.0u2 3 88.5i 1U 28 i 2
58N1 2.158 n 61AO 1 1800 258 1 12
3.62 U 1196 i 270 288 i 17
60N1 2.502 A 3uoo 1 650 227 1 17
aUsing a Fermi charge distribution with r0 2 1.05F

and a = 0.57F.

br = 1.2OF
o

5.2 Comparison with Theory

 

The nickel isotopes have been described (Au 67) by
N. Auerbach in terms of strongly admixed spherical shell-
model configurations of neutrons in the 2p3/2, lf5/2’ and
2pl/2 orbits. The B(E2) values from these calculations
are shown with the present experimental results in Table 5.9.
The experimental B(E2)'s shown here were calculated

using the uniform charge distribution with

r = 1.2OF.
O

127

TABLE 5.9.-—Experimental and theoretical results for B(E2)'s
for the nickel isotopes.

 

 

 

 

Theorya Experimentb
B(E2' 0+ + 2+)(Fu)
’ 1 1
58N1 585 1030 1 A7
60N1 1001 13u0 1 88
62N1 1235 1290 1 113
6“N1 1129 1070 1 180
B(E2' 0+ + 2+)(Fu)
’ 1 2
58N1 75 <15
6ONi 30 <27
62Ni 1.u <21
6“N1 9.0 <15

 

aAu 67

bUsing a uniform charge distribution with r0 = 1.2OF

A modified Tamm—Dancoff approximation has been applied
to the even nickel isotopes by Raj gt_al. (Ra 67). In this
work several interaction potentials were used and reduced
transition probabilities were found. The results were
calculated for the various potentials for transitions
between the first and second 2+ states and the ground state

in each nuclei. The results of these calculations and of

128

the present experiment are shown in Table 5.10. The
uniform charge distribution with r0 = 1.20F was used in

the extraction of the experimental results.

5.3 Conclusions

 

From the comparisons made in sections 5.1 and 5.2
between the results of this experiment and other experi-
ments and theoretical calculations it is apparent that
certain precautions should be taken. Comparisons of the

nuclear deformations, 6 in Tables 5.2-5.5 show that the

L’
present results agree to within errors for a large

number of cases. These comparisons, however, need not
necessarily show an agreement for all the reactions con-
sidered. The different projectiles used need different
optical potentials which are then incorporated into the
collective model distorted wave calculations. These
potentials commonly have different, real well radii. The
effects of this are compensated for by the use of BRO
instead of 8 alone in the comparisons for different
reactions. This procedure has been pointed out, however,
to still have its deficiencies (Be 69). The radius which
should be used is not well defined in all cases since the
8's which are obtained are often the results of calcula-
tions which deform both the real and the imaginary well.
These wells usually have different geometries. Also the

strongly absorbed particles, i.e., deuterons, 3He and “He,

require much more absorption than protons. The fact that

129

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130

the real and imaginary geometries are quite different
could affect the extraction of a deformation.

This problem points out a need for a standardized
procedure for the extraction of B or BR. This would make
comparisons of the type shown above more meaningful.

Unless the interaction radius can be defined more pre-
cisely, therefore, comparisons of BR's should be viewed
with caution.

It has also been shown that, irrespective of the above
problem for B's, there is also the problem of obtaining the
reduced transition probabilities and the sum rule limits
in an inelastic proton experiment in a manner which is
insensitive to the matter distribution. Also the sum
rule limits and the mass transport and surface tension
parameters found from electromagnetic measurements depend
on the model used for the charge distribution. As shown
in Table 5.6 and Appendix IV.“ the results of the three
models are fairly consistent for the L = 2 states, but for
the higher spin states the results can differ by factors
of more than 10.

The model which gives the most consistent results with
electromagnetic measurements can be found by comparing the
results in Table 5.6 for all the L-values shown, L = 2,3,“.
It can be seen that the calculations using a Fermi equiva-

lent, uniform charge distribution are most consistent.

131

As shown in Tables 5.7 and 5.8 the vibrational
parameters, DL and CL’ obtained from this experiment
agree in general, to within experimental errors, with the
results of electromagnetic measurements for L = 2 states.
The values for the higher spin states in Table 5.8, how-
ever, disagree more.

It should be reiterated that for inelastic scattering
the values for the mass transport and surface tension are
deduced from the experiment in a fashion which is insensi-
tive to the matter distribution in contrast to these
parameters as deduced from EM experiments. On the other
hand the B(EL)'s found in studies of electromagnetic
transitions are insensitive to the charge distribution in
contrast to the sensitivity of the B(EL)'s deduced from
inelastic proton scattering.

Keeping in mind the above discussion of the model
dependent uncertainties for the results of this experiment
for the measurements of the B(E2)'s, the results in Tables
5.9 and 5.10 can be compared. Table 5.9 shows that
Auerbach's shell-model calculations agree in general with
the results of the present work. The calculations for
58Ni, however, do seem to be somewhat inconsistent with
the experimental results and yet here the only serious
disagreement is in the results for the 0: + 2: transition.

The main disagreements in the comparisons made in

+

Table 5.10 involve the 01 + 2: transitions. The result of

132

the EIA(B) theory for 62Ni about 7 times greater than the

estimated upper limit. Also the results of the EIC(b)

theory for 62Ni and the EIC(a) theory for 6“Ni are rather
high. In this comparison the most consistent theoretical
results are produced by the Q-Q interaction in contrast to

its predictions of the excited states (Ra 67).

APPENDICES

133

APPENDIX I

DETAILS OF THE CONSTRUCTION AND

OPERATION OF THE GONIOMETER

Table of Contents

I.1 Goniometer Base
1.2 Main Arm

.a Construction
.b Calculations of the vertical deflections

I.3 Rotary Table and Drive Chain for the Main Arm
.3.a Rotary Table
.3.b Drive Motor
.3.c Gear Train
.3 d Calculations for the Main Arm Drive
I.3.d.l Motor Requirements
I.3.d.2 Gear Strengths
I.3.d.3 Strengths of the Pins, Keys,
Bearings and Shafts
1.4 Calculations of the Main Arm Configuration
1-55 Readout of Main Arm Position
I.6 Central Column
1'7 Target Drive
1'8 Target Holder
1'9 Target Chamber
1°10 Target Lock
1°151 Detector Carriage

1°12 Local Power Supply

13“

1.13

1.14
1.15
1.16

1.17

Remote

I.13.a
I.13.b
I.13.c
1.13.d

Surface

135

Control Station

Control Panel

DC Motor Power Supply
Electronics Bin

Power Distribution Chassis

Finishes

Suggested Improvements

Documentation

Assembly and Maintenance Suggestions

I.17.a
l.l7.b
I.17.c
I.17.d
I.17.e

I.17.f
I.17.g

List of

Backlash Adjustment of the Rotary Table Gears
Assembly of Main Arm Drive
Installation of Main Arm Synchro Motor
Installation of Target Well
Assembly of Target Drive and Central
Shaft
Electrical Fuses
Lubrication

the Major Components.

APPENDIX I

DETAILS OF THE CONSTRUCTION AND
OPERATION OF THE GONIOMETER

In this section the details are presented of the
construction of the goniometer system described in section
2.2.. In addition the calculations used in the design and
suggestions for maintenance of the system and assembly of
the more involved components are given. To facilitate
‘the use of this section a table of contents is provided to

aaid in the location of the particular topics of interest.

I.1 Goniometer Base--Figure 2.2A

The goniometer is supported entirely on four legs.
These legs are constructed from 1 inch diameter, NFT,
threaded steel rod. The length of these legs was made
sufficiently long to allow the detector support to be
pofiiistioned at 12 inches below the scattering plane as well
as at a typical working distance of 3—3/A inches.

There was some question about the stability of the
83731; em when the longest leg extensions were used. The
fiJléll design, however, results in a rigid structure. This
is 1Jnsured by using a counterbalanced, load carrying system.

This guarantees that there exist only vertical forces on the

136

137

legs under static conditions. Under dynamic situations the
legs are held securely by threading them into the base
plate through l-l/A inches of steel and using two lock-nuts
to rigidly tighten each leg in place.

Each of the legs is located at the lower end by a
foot. The rotating joint between this foot and the leg is
close fitting both vertically and radially. This permits
the goniometer to be securely located when the feet are
fastened rigidly to the floor.

The primary base-plate which supports the goniometer
is made of 1/2 inch steel with each corner built up by an
additional 3/A inch of steel to permit a stronger and more
rigid leg coupling.

A 1/2 inch thick steel, secondary, base-plate rests on
tun: aluminum spacers which are 7 inches high. To this
pliate is rigidly fastened all of the drive elements of the
goniometer. The spacers are attached to the main plate by
2L/2-l3 machine screws through slotted holes in the plate.
The spacer is fastened to the secondary plate in a similar
fasrlixmn Between each spacer and the main plate and between
one Spacer and the secondary plate are adjustment screws
Whifilll function like turnbuckles. The position of the
goniometer in two perpendicular horizontal directions can
then be adjusted by loosening the bolts between the spacer

and the plates and then using the turnbuckles to accurately

locate the base .

138
I.2 Main Arm--Figure 2.2C

I.2.a Construction
The rotary mill table (section I.3.a) is securely

fastened to the base and the main arm is connected rigidly

to the table surface by 8, 1/2 inch bolts and T-nuts. The

main arm is supported by a central column constructed from

a 22-1/2 inch length of standard 8 inch black pipe.

The main arm is made up of two aluminum beams. Each

is a total of 6 feet long and is fastened to the central

column such that the portion which supports the detector

extends A feet from the center of rotation. Each beam of

‘the arm is made of two rectangular bars which are pinned

annd bolted together. The top bar is 1/4 x l-l/2 inch and

tune leg is 1/2 x l-l/2 inch. Hardened steel drill bushings

wdtth.l/A inch ID are located in the tOp surface of each

beam and are accurately spaced 6 inches apart. These bush-

ings are used to locate the detector mount on the arm.

Between the dual beams of the 2 foot section of the

arn1 capposite the detector support is located an aluminum

POXi LJSGd to hold a counterweight if it is needed. This

box; its large enough to hold at least 8 lead bricks each

weighing 25 pounds. Two 3/8 inch bolts and two dowels

com'lect the box to the arm in such a way as to permit the

31““ ‘bo flex a small amount. The need for this flex is

31Ven below in section 1.1%.

139

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MO 000000O0 0:0 000050000 o0 0005 E00
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1A0

The end of each beam is supported by a brace which
extends to the base of the column. This brace is made of
aluminum and consists of a 1/2 x 1-1/2 inch bar with a
l/2 x 1/2 inch bar bolted to it to reduce the bending of
the brace under load.

With only the detector support considered Figure I.1
shows the basic configuration of the structure. This
schematic was used in the calculations to determine the
location of the point at which the brace should meet the
arm beam, point (A). For simplicity the beam was assumed
to have no vertical deflection under load at point A. The
point at which the arm meets the central column, C, is a
Itigid vertical support, and the beam does not twist about
tfluis point since each beam is held to the column at this
point by 3, 1/2 inch bolts.

There are two sections of the beam, therefore, which
caJi experience deflections under load--section x which is
betnween the central column and point A, and section y
Whj0231': is beyond point A. Point A can be taken as a pivot
IKxirrt or as rigidly fixed. The criteria which was used to
°a143141ate the position of point A was that the maximum
deflection of section x be equal to that of section y for
a rigid support at A. This calculation is shown below in

secrtqion I.2.b. and point A was found to be located 9 inches

from the end of the arm.

A (mils)

26

24

22

20

Results of the calculations and measurements of
the vertical deflections in the main arm under a

lLil

 

 

___.Poim‘ A is rigid

___Point A is o pivot

. Measured values

 

 

 

 

load of 100 lbs.

142

The deflections of each beam were estimated using
equations 1.1, 1.2, and 1.3. The results of these calcula-
tions are presented in Figure 1.2 where the vertical
deflection, A, of the arm under 100 lbs load is plotted
as a function of the distance, Z, of the load from that
point located A feet from the end of the arm. Calcula-
tions were done for both a rigid and a pivoting connection
at A. The deflection for the beam for points beyond A in
the second case were estimated by considering the ratios of
the deflections calculated for both cases for corresponding
points inside of A.

Also shown in Figure 1.2 are the results of measure-
Inents of the deflections for a lOO lb load. The fact that
'the value near A is about 9 mils shows that the brace does
rust provide a rigid vertical support. The comparison of

tine locations of the peaks in the curves also shows that A
is probably a pivot point.

The final dimensions of the dual beams were deter—
mined by successive attempts to find a configuration which
WCHJJLd satisfy the load and structural requirements discussed
1‘1 E3ections 2.1 and 1.4. The moment of inertia about the
Veilt‘tzical axis of the goniometer for the arm system loaded
W143!) the maximum of 100 lbs at 4 feet and 200 lbs at 2 feet

was calcualted to be

2852 lbs - ft2

lA3

This result will be used in some of the succeeding
calculations.
I.2.b. Calculations of the
Vertical Deflection
The following equations give the deflection, A, of

sections x and y in terms of the quantities a, b, and c
as defined in Figure 1.1. For rigid support at A

Wa3b3

A = SEI:_§ (Ma 6“, p. 397) I.1
x

Ay = 3—E-I-‘r (M3- 614: p- 393) I.2

For pivoting at A

 

3 2
Ax = wa b (3X+§) (Ma 6M. p. 395) I.3
12 E1* x
where E = modulus of elasticity

1* a Areal moment of inertia of the support cross-
section (Ma 64, p. 358)

2
II

load

The maximum deflections for a given load will occur
‘when the load is in the center of x and at point B for

section y; hence, a = b = x/2 and c = L - x.

14A

A = ””3 I 1'
x "19"‘2E‘I'3F °

Ay = "3"E—T'I

u'—u" = 3.67'

F‘
II

2.92'

>4
II

This means that A is 9 inches from the end of the 4 foot
detector support if the radius of the central column is con-

sidered.

1.3 Rotary Table and Drive Chain
for the Main Arm--
Figure 2.2B

 

1;;3a Rotary Table

The primary positioning element for the main arm con-
sists of a 15 inch diameter rotary mill table (1). This
table contains an oil reservoir and has an entirely enclosed
90:1 worm gear drive whose center distance of the worm drive
is adjustable, thus allowing the backlash to be maintained
within tolerable limits. There are also adjustments for
all thrust bearings which allow compensation for wear. This
table is supplied with a vernier scale on the worm gear
shaft which has a least count of 20 seconds, or 0.006°.

In order to use this mill table there was a need to

<determine if it could operate under loads associated with

145

its use in the goniometer. The vertical load capability
was checked by placing about A00 lbs on the table surface.
The worm wheel shaft was then turned and found to have
little added resistance compared to the no load condition.
The calculations of the limiting strengths of the gears in
the table are shown in section I.3.d.2. The details of the
main arm construction were then designed so that these cal-
culated limits would not be exceeded under anticipated

operating conditions.

I.3.b Drive Motor

In order to have a system that WOUld faCilitate
anticipated computer control and function accurately and
reliably under possibly heavy loads,a bifilar, Slo-Syn motor
(2) was chosen. These motors Operate with 200 steps per
revolution in a DC stepping mode and can also be operated
in an AC synchronous mode at a speed of 72 RPM. The motor
is connected to the rotary table through a u:l gear train
resulting in a 1.0 degree change in the main arm position
for each motor revolution.

The size of the motor required depends on two aSpects
of the system-—the maximum torque that the motor must
supply and the moment of inertia that is rigidly attached to
the motor. The maximum torque requirements occur at the
Inoment the system is set in motion. There are two modes
(bf operation which had to be considered--the AC synchronous

Inode and the DC stepping mode.

146

The calculations which were done to determine the
loads on the motor under various conditions are given in
section I.3.d.l. These calculations show that the motor
must be able to supply 750 oz-in of torque and must be
able to drive a moment of inertia of 10 lbs-in2.

The Slo-Syn motor that was selected as a result of
these calculations is the 881800-1006. The engineering
data needed for this motor was obtained from the Slo-Syn
motor catalog #SSl265—2. For the AC mode of operation of
the bifilar motor the engineering data for the 3 lead Slo-
Syn motor was used. The bifilar motor can supply a torque
of 1800 oz-in in the AC mode and 1600 oz-in in the DC mode
operating at 20 steps/sec. In addition, the moment of
inertia that it can drive is 16 lbs-in2.

To run this bifilar motor in an AC synchronous mode
a 195 Volt, lKVA, power supply is used with a phase shifting
network consisting of a 75 Ohm, 300 Watt resistor and a 25
mf, 460 VAC capacitor. 1n the AC mode this motor runs at a
speed of 72 RPM and drives the main arm at 72°/min. 1n the DC.
stepping mode the motor is driven at about 20 steps per

second rotating the main arm at a rate of 6°/min.

I.3.c. Gear Train—-Figure 1.3.

The gear train between the motor and the rotary table
luas a 4:1 ratio to provide a 10 main arm rotation for each
:revolution of the motor. The gears that were used are

stock, 12 pitch, spur gears. The gears on the motor shaft

147

 

 

 

 

 

m
//i' W/fl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F C

I.3 Section view of the 4:1 gear train for the main arm drive:
A - Spur gear, B - Spur gear, C - Gear box sides, D - Gear
shaft, E - Ball bearing, F — Box spacer, G - Box cover,

H - Bearing cover plate, 1 - Brake.

148

(A) and that on the rotary table shaft (B) is a 3/4 inch
faced steel spur gear (3) and a cast iron spur gear (4)
respectively. These gears are mounted in a box (C) which
maintains the center distance for the gears. The center
distance for these gears was empirically determined by
placing the gears in close contact and measuring the dis—
tance between two shafts placed in the gear bores with a
micrometer; 1 mil was added to provide for an appropriate
backlash. This center distance was then verified by locat-
ing two shafts in a block of aluminum at the determined
distance and observing that the gears ran smoothly.

These gears were then modified so that they press fit
onto two separate shafts, for example (D). A ballbearing,
for example (E), is placed on either side of each gear (5)
(6). The outside diameter of each of these bearings makes
a close, clearance fit in a hole located in the side plates
of the gear box. The side plates are bolted together with
1/2-13 bolts and are maintained at the proper spacing with
steel spaces (F) over the bolts. A 0.06 inch aluminum
sheet (G) is wrapped around the outside of the side plates
to provide for a completely enclosed gear train.

The small gear shaft is pinned to the motor shaft
with a l/8 inch diameter, soft steel dowel. The large gear
shaft is held to the rotary table shaft utilizing the 1/8
inch Woodruff key supplied with the table. Calculations

were done to verify that the pin, key, table shaft and gear

149

bearings, could take the torque and resulting loads
supplied by the motor. These calculations are presented
in section I.3.d.3.

When this gear box was first installed and the motor
was turned on, it was found that there was a severe rattling.
On examination of the gears it was found that there were
two problems that produced this effect. First, the stepping
action of the Slo-Syn motor, even in an AC synchronous mode,
produced an unforeseen problem. The motor makes discrete
steps and suddenly stops after each, but the larger gear
is allowed to coast a small amount because of the backlash
in the gears. When the motor makes the next step the motor
gear sharply strikes the table gear like a hammer. Secondly,
the large diameter spur gear tended to ring after the
hammer-like contacts of the gear teeth.

It was found that a friction drag on the larger gear
eliminated the noise and produced a smooth and quiet opera-
tion. Two methods were used to provide this drag. First,
thrusting screws were placed in cover plates like (H) on
either end of the large gear shaft which were in turn
securely fastened to the outside of the gear box. These
screws were used to apply opposing thrusting loads on the
two bearings on the gear shaft. This appeared to provide
the necessary affect,but the adjustment of the screws was
difficult and not very exact. The actual result was that

there was a thrusting load on a bearing inside the rotary

150

table causing severe wear and ultimate failure of this
part.

As a result of this failure, a needle, thrust bearing
(7) was placed inside the rotary table to replace the
original thrust bearing (Bridgeport #RT—26 and #RT-27).
When the thrust screws were used after this modification,
it was found that they did not produce the necessary drag
on the gear drive.

These thrusting screws were, therefore, replaced by
a brake system (I) which constituted the second method.
This brake consists of two fiber-covered, spring-loaded,
aluminum plates which are located between the gear and gear
box sides. The springs for this brake provide a sufficient
friction drag to insure a very quiet drive for both the AC
and the DC mode of operation.

Calculations were made to determine the safe loads
which the various gears in the drive chain could support.
These calculations are shown in section I.3.d.2. These
computations verify that the spur gears used are strong
enough, and that the worm gear in the rotary table can
safely supply 67 lbs-ft. of torque.

Also included in this system are two limit switches
which stop the clockwise and counterclockwise rotation of
the arm. These switches are mounted to the base of the
rotary table and are actuated by cams which are located in

a groove around the circumference of the rotary table.

151

I.3.d.l Motor Requirements

According to Slo-Syn motor specifications for a three-
lead, 72 RPM motor,the motor reaches its Operating speed
within 5° of shaft rotation. Since the main arm is attached
to the motor through a 360:1 gear train, however, the arm
is brought to speed in 0.0l4°. The final velocity of the

main arm is

_ 72 RPM
“"766—

= 0.021 rad/sec

The angular acceleration needed to attain this final

velocity in a distance A6 is

02/2A6

$2
ll

4

A6 0.0140 = 2.4 x 10’ rad

0.92 rad/sec2

Q
II

In the stepping mode a rate of 20 steps/sec is chosen——
O.l°/sec--for the main arm. It was assumed that during a
single step the arm was rigidly attached to the motor. This
is, of course, not strictly true, but this is a limiting
case and does provide for some safety factor. therefore,
one step moves the arm through an angle of 0.005° in 1/20

sec. This results in an angular acceleration of

152

N
D
CD

a = = 0.07 rad/sec2

3.:

The above calculations for the accelerations and the
moment of inertia of the main arm can then be used to cal—
culate the torque the motor must supply. The largest
acceleration of the arm is 0.92 rad/sec2. A factor of about
5 was then used to account for friction in the drive system

and to allow for some safety factor.

Therefore, the torque needed at the arm is

T(arm) = 85,500 oz-in

The torque that must be supplied by the motor, however, is

effected by the gear ratio, N, shown by the relation

T(motor) T(arm)/N

T(motor) 2H0 oz-in

The moment of inertia seen by the motor is also

effected by the gear ratio, N, as shown by
I(motor) = I(arm)/N2
Using the moment of inertia of the arm calculated above

I(motor) = 3.2 lbs—in2

153

Using these results along with the fact that a safety factor

of at least 3 should be included, a motor was needed that

could drive an inertia of at least 10 lbs-in2 with a torque

of 750 oz-in.

I.3.d.2 Gear Strengths

The safe load for a spur gear is found by using the

Lewis formula

Where w

Wr

R

S

(Ma 6M, p. 715).

Fsyc/Pd 1.4
safe torque

gear pitch radius (in)

face width (in)

diametral pitch = # of teeth/pitch diameter
tooth outline factor

velocity factor = 600/(600 + v)

pitch line velocity (FPM)

pitch diameter

RPM

safe working stress

For the calculation for the 2.u17 inch diameter, 12 pitch

gear used at 72 RPM

'< “:19:
II

0)

V

12
0.75"
0.32 for 30 teeth, 1” 1/20 (Ma 6“, p. 717)

8000 PSI

15M

d = 2.417"

R = 72 RPM

v = 45.5 FPM
c = 0.93

r = 0.1'

w = 149 lbs.

And the safe torque is

Wr = 14.9 lbs-ft

For the 9.667 inch diameter gear

r = 0.U'

y = 0.37
Therefore

w = 172 lbs

And the safe torque for this gear is
Wr = 69 lbs—ft.

The calculations for the worm gear contained in the
Bridgeport rotary table was a little more involved. The
specifications for these gears were supplied by Bridgeport
(Bridgeport parts: #RT-H and #RT—5). The worm gear in the

table has the following properties

155

1. 90 teeth
2. Diametral pitch = 12

. Pitch diameter

7650"
14 l/2°

3
4. Pressure angle
5. Addendum = .08"
6. Material is better than gray cast iron.
The worm has the following prOperties:
1. Axial pitch = .2618
2. Lead angle = 3°u9'
3. Pitch diameter = 1.25"
u. Material is hardened steel
Two equations were used to calculate the safe load
for this gear. First, the limiting strength load was found
by the equation (Ma 64, p. 793)

T = 0.625 beS Q m D cos La

Where

T = torque limit (lbs—in)

Sb = bending stress factor > 6000 PSI (Ma 6“,
‘ p- 79“)

XS = speed factor

Q = arc length of worm tooth measured along

the root
m = .3183 ° (axial pitch of worm)

D = pitch diameter

F‘
ll

lead angle

156

To find the velocity factor for the very slow speeds used,

a graph was made of the tabulated valves given for X8

(Ma 64, p. 795). This plot, shown in Figure I.4,shows

that for speeds less than 6 RPM, Xs is greater than 0.6.
The valve for Q was found by scaling from the draw-

ings provided by Bridgeport (Bridgeport #RT-4) to be 0.83

inch. Summarizing these values gives

Sb > 6000 psi
XS > 0.6
Q = 0.83"
m = 0.083"
D = 7.5"
cos La = 1
Therefore

T > 1160 lbs-in = 97.0 lbs-ft

The strength of the worm wheel is not a limiting factor
since it is made of steel and has great strength because of
the large effective face width it has. It is not necessary,
therefore, to calculate the limiting strength of this drive
component.

The second equation that was used to determine the
safe load for the worm gear was a modified form of the
Lewis formula, equation I.4, used above for Spur gears.

This modified form is

157

000.

.zmm .mpfiooao> pmazwcm mamho> .mx «hopomm woman map mo poam

00.

six

0.

 

Z.—

 

_P__

_

_

_

_

_

_

_

____a_

:2:

_

r

_

_

_

d:__ q __

:2. __

fl

_

 

 

:.H

0.0

6.0

md

Where

F(min)

158

F(min) syc/Pd

1.125 {<do + 2e)2 — (
outside diameter of t
D + 2a

addendum = 0.3183 pn
clearance = ht - hk
0.7003 pn + 0.002
0.6366 pn

lead = nD/ # of teeth

For the rotary table gear

Pn

F(min)

Therefore

Wr

l2

II

I?

I2

l2

l2

0

1

0.37 for 90 teeth, 14
8000PSI

0.26"

l"

246 lbs

And the safe torque is

Wr

246 1bs x 0.27 ft =

do - 4a)2}11 (Ma 64,
p- 776)
he worm

1/2° (Ma 64, p. 717)

66.7 lbs—ft

159

Considering both of the results, it was decided that
67 lbs-ft would be used as the maximum safe_load that the

rotary table could support.

I.3.d.3. Strengths of the
PinngKeysJ Bearings and Shafts

 

 

Shearing torque for a key is (B1 55)

wLSsd
TS = -—--—— 105
2

The shearing torque for a shaft in rotation is (B1 55)

nd3s
8

TS '-'- T I.6

Where

d = shaft diameter

S = elastic limit > 3 x 10” PSI (B1 55)

w = key width

L“
ll

key length

The Woodruff key in the rotary table shaft is 1/8" x

1/2" and the shaft is 5/8 inch diameter. Therefore

T8 = 41 lbs-ft

The pin in the motor shaft is 1/8 inch diameter.

The w'L in TS equation is the cross section of the key

160

exposed to the shearing forces at the circumference of
the shaft. Replacing this cross section with that of a
round pin with radius, r, through a shaft of diameter, d,

equation I.5 becomes

2
Ts WP Ssd
Therefore, for the 5/8 inch diameter motor shaft the safe

load is

Ts = 12.5 lbs-ft

For the rotary table shaft

T8 = 51 lbs-ft

All of these values are larger than the torque that the
motor can supply--9.4 lbs-ft, on the motor shaft and 37.6
lbs-ft at the table shaft.

The radial load that the ballbearings had to support

was also calculated using the equation (Ma 64, p. 726)

P = L/cos ¢
Where
L = maximum force supplied by the motor at the
gear circumference
¢ = pressure angle of the gear = 14 1/2°

161

The motor supplies a maximum of 9.4 ft-lbs of torque to the
gear fastened to its shaft; therefore, using the 2.417 inch
pitch diameter of the smallest gear in the gear train,
there is 94 lbs of force applied at the pitch diameter of

this gear. Therefore
P = 97 lbs

For a larger diameter gear this force is less, but these
radial forces could easily be met by the ballbearings

used.

1.4 Calculations of Main Arm
gpnstruction

 

The construction of the main arm was finalized after
the safe load for the rotary table had been determined.
The maximum load of the gear is produced when there is a
maximum load on the arm (i.e. 100 lbs at 4 ft along with
the 200 lbs at 2 ft).

The forces that can appear on the worm gear can arise
from various sources. First, there is a force arising
directly from the motor. Consdier, for example, the
torque that would be applied to the worm gear if the table
were prevented from rotating. The torque of the motor is
increased by the gear ratio in the gear train (360:1).

Therefore, the torque applied to the gear is

T = 3380 lbs-ft

162

This result shows that the main arm must never be locked
or must never run into an immovable object. For this
reason the looks that were supplied with-the table were
removed.

A second load on the worm gear is the main arm itself.
Consider what happens when the motor steps. A worm gear
system cannot be drivenfby the worm gear but only the worm
wheel. Therefore, when the motor stops, the worm gear is
locked in place. Because there is a large amount of energy
contained in the loaded main arm while in motion, there
will appear large forces on the worm gear which decelerates
this motion. Since the Slo-Syn motor can also start in a
very short time there is a similar effect when the motor

starts. The torque, T, needed to accelerate the arm is

AL

T=E

where At is very small if the arm is assumed to be rigid.
Therefore T is very large.

To reduce the required torque, it is sufficient to
increase the time during which the arm is being accelerated.
To accomplish this, the arm was made slightly flexible.

The calculations presented below show that the final arm
design described in section I.2 provides sufficient flex to

bring the torque within safe limits.

163

The following calculations were made for a set of
operating conditions which provide for a maximum stress

on the drive system. The rotation of the arm very close

 

to the axis of rotation will be assumed to start or stOp
instantaneously. This assumption is not far from being
exact when a Slo—Syn motor and worm gear drive are used.
The case that is considered below, therefore, involves the
instantaneous stopping of the center of rotation of the
main arm from a maximum initial angular velocity of 72 RPM

or
w = 2.1 x 10-2 rad/sec

The limiting torque that the worm gear in the rotary table

can provide is
TG = 67 lbs-ft (see section I.3.d.2)

The major source of energy in the rotating arm system will
arise from the load on the arm; therefore the contributions
of the arm structure itself are neglected. The load on

the arm consists of

W" 100 lbs at L" = 4 ft
And

W!

200 lbs at L' I 2 ft

This configuration has moments of inertia using mass

units instead of pound-mass units

I. 2

62.5 slug—ft

I' 2

3102 Slug-ft

The total kinetic energy is

KE = KE" + KE'

4

KB" = — 138 x 10' ft-lbs

[\JII-J
H
8

I

4

KE' 68.8 x 10‘ ft lbs

I .
2 I w

When the rotation of the axis suddenly stops, this
total kinetic energy is converted into potential energy by

the flexing of the arm. That is

KE k' (e'max)2 + % k" (8"max)2

[UH-4

Where 6 represents the angle corresponding to the deflection

at the ends of the arm. But
|TI = k6
k = ITI/B

Now a fictitious force, W, is considered to act
horizontally at the end of the arm of length L causing the

arm to deflect by an angle 0. Then

165

WL =

*3
II

k8

1 __e_
I? LW I.7

The deflection, A, caused by the fictitious force,
W, on the arm L units long is given by equation I.2
3
WL
A = W I.2
This deflection can also be given in terms of the arm

length and the angle of deflection, if it is assumed that

the deflection is small.

D
II

L8

I.8-

tflb

The expression for A from equation I.2 is then
used in equation I.8 giving a relation for 8 which is used

in equation I.7,

 

l _ ___ = _______ _
E- - 109

Considering only one beam, the kinetic energy before
deflection can be equated to the potential energy after

deflection giving

166

KB

ll
"U
F1

NIH
H
E

u
mp4
>7
CD
H
L.
o

The preceding equations can now be applied to each
end of the beam. From equation I.9 an expression for the
ratio of the force constants, k, for each end of the beam
can be found. Using the fact that E and I* are the same
for both parts

k! L"
'12" = E!
Taking into account the fact that the beam is held

rigidly for 4 inches on either side of its "center"

L' + 20 inches

L" + 44 inches

This is not strictly true for all of the L's used in this

development, but it will give a result to i 10%. Therefore

'
k = 2.2 1.11

’3

Using equation I.10 for both ends, a ratio of the

angles of deflection can be found

6'/e" = {(k"/k') (I'/I")}* 1.12

But

167

1" = 21'

And also using results I.ll equation 1.12 gives

0'/8" = 0.48 1.13

Now the total kinetic energy before deflection is

equated to the total potential energy after deflection

— i 2 l; n "2
KE — 2 k'e' + 2 k e
=%k1912{1 + (kn/kt)(e"/ev)2}
k'26'2 = 2(KE)k' {l-+(k"/k') (6"/e')2}"l 1.14

The maximum torque which the rotary table must supply

in order to stop the rotary motion of the arm is
._. v! "n
TM k 8 M + k e M
=k'e'M {l + (k"/k') (0"/8')} 1.15
But this torque is limited such that
T > k'B'M {l + (k"/k') (0"/0')} I.16

G

where the fact that 0"/8' = constant has been kept in mine.

168

Therefore

kvevM < TG {1 + (k"/k') (e"/e')}'l 1.17

Using 1.17 in equation 1.14

k' < G {1 + (k"/k') (e"/e')}‘2

x {1 + (k"/k') (e"/e')2} 1.18

Using this result in equation 1.16, 8' can be solved for,

M
giving

< 2%531 {1 + (k"/k') (e"/e')} {1 + (k"/k') (8"/8')2}"l
G

8
e M

1.19

The value of 1* needed to limit the amount of torque
the worm gear must supply can now be found. Using equa-
tions 1.2 and 1.8 and eliminating A with the maximum values

used for W and 8

WML3
LBM —-3fiT 1.20
Also
W L = T 1.21

169

Combining 1.20 and 1.20 gives

*
T = 31 E8M
M L
This expression can be applied to both ends of the
main arm, giving

* 1
31 E8 M
M L'

I-3
II
H
N
[\J

31*E8"M 31*E8'M
M T = “T— {(e"/e')<L'/L")} 1.23

“2.
u

The application of the restriction on the allowable
torque which the worm gear can supply is used now to put
a limit on the total moment of inertia of the arm structure.
This results in

= I n
TG > TM (total) T M + T M

Substituting the results of equations 1.22 and 1.23 into
this relation

3I*E8'M
TG > ‘71— {1 + (8"/8')(L'/L")}

L'T

G n v c H ”l
1*<-3-§9—,—1-v-I-{1+(e/e)(L/L)}

170

The expression 1.19 for 8'M can be used in this, along

with the expression

:1:
II
818.

L'T2G {1+ (k"/k')(8"/8')2}
1* <

 

6E(KE) {l + (0"/8')(k"/k')} 2

Using parameters associated with the final goniometer

design,
Total kinetic energy = KE = 206 x 10-“ ft-lbs
TG = 67 lbs-ft
E = 1.48 x 109 lbs/ft2 (Ma 64, p. 426)
L' = 1.67 ft
k"/k' = 0.45
8"/8' = 2.1

The results of equations 1.24, 1.19 and 1.18 are

1* < 3.2 x 10"5 ft“

8' < 2.3 x 10'2 degree

k' < 8.6 x 10“ ft-lbs

And by the relations 1.13 and 1.11
8"M < 0.0480
k" < 3.9 x 10L‘ ft-lbs

171

Now that a value for k" has been found, the period,
T, for the detector support section of the main arm can be

evaluated

21/8
(kH/I")%

0'"
II

Where 8

But 1" is evaluated above as

I"

62.5 slug—ft2
Therefore

0.25 sec

a
II

Those results show that the final design of the detector

support has an oscillation with a magnitude at the end of
the arm of 0.05 degree and a period of 0.25 sec. when it

is stopped in the fast mode.

1.5 Readoutqof the Main Arm Position—-
Figure 1.3

 

 

There are two different devices'used to indicate the
angular position of the main arm. First there is a vernier
dial (J). The primary scale is 5—1/2 inches in diameter
and is divided every 0.050 of table rotation for a total
of 4 degrees. The vernier scale subsequently can be used
to divide each of these divisions by ten resulting in 0.0050
as the smallest division. This readout is fastened to the
worm wheel shaft on the rotary table and provides the most

direct readout of the arm position. The second mode of

172

readout incorporates a synchro-motor (K) (8) which is
attached directly to the motor shaft through an Oldham
flexible coupling (9).

An estimate of the errors in the digital readout
system was made considering only the backlash in the gear
systems involved.

1) Main drive spur gears--0.005" (Ma 64, p. 693),

0.00070
2) Worm gear--0.0010" (I.17.a)
0.016°
3) Digital counter gear train-+0.001" (Ma 64, p. 697)
0.00130
The total error is the algebraic sum of these since back-
lash errors are accumulative--0.018°.

The error that might be expected is 18 minutes
for each synchro motor* or a total error of 25 minutes in
the pair. This corresponds to an error for the readout
system of 0.0014°. This was added in quadrature to the
backlash errors giving an estimate of the total error of

the readout system of about 0.0160

1.6 Central Column--Figure 1.5
The central column consists of two sections of welded
steel construction. The lower section (A) is bolted to the
rotary mill table (B). The upper section(AA) is bolted to

the lower at the flange (0). An off—set is machined in

 

*
Bendix Synchro Engineering Catalog #25.

173

Section View of central column: A - Lower column
section, AA — Upper column section, B - Rotary
table, C - Flange, D - Tapered roller bearing, E -
Tapered roller bearing, F - Secondary arm hub, G —
Bearing nut, H - Secondary arm, 1 - Vernier scale,
11 - Tapered roller bearing, J - Bearing nut, K -
Clamp, L - Clamp housing, M - Clamp, N - Clamp shaft,
0 - Miter gears, P — Target well, Q - Ball bearing,
R - Clamp, S - Target shaft, T - Connecting rod, V —
Worm gear, W - Worm gear, X - Limit switch, Y -
Central shaft, Z - Target screw.

 

 

\wwflx \\

 

 

 

 

 

 

 

 

 

 

 

 

118/ng222 ,9. s

 

174

this flange to insure the radial alignment of the two
column sections relative to each other. A hardened steel
dowel is also located in this flange to provide a secure
coupling of the two sections.

In the lower flange of the lower section is located
a taper roller bearing (C) (10). The seat for this bearing
was machined to be concentric with the alignment seat of
the upper flange. The lower surface of the lower flange was
also machined to be perpendicular to the axis of the column.

There are two tapered-roller bearings (E) (11) (12)
located in the upper column section. The bearing seats are
machined to be concentric with each other as well as con-
centric with the lower flange seat of this column section
at (C). These bearings are used to support the secondary
arm hum (F). The bearing nut (G) on the lower end of this
hub is used to tighten the hub in the bearings.

The secondary arm (H) is fastened to this hub with
four 3/8-16 machine screws. This arm is made from a 3/4
inch thick, 606l-T6 aluminum plate. It has a maximum
radius of 21.5 inches. There are 1/4 inch, inside diameter
hardened-steel, drill bushings inserted into the top of
this arm. These bushings are located every 3 inches on
three radial lines separated by 15°, each of which inter-
sects the axis of rotation of the arm. This intersection

is insured by a close clearance fit of the arm and hub.

175

The angular position of the secondary arm is indicated
relative to the main arm by a vernier scale (I). The scale
is fastened to the main arm and is scribed every degree.

The vernier contains four indices and is located by a slip
Joint on the hub allowing the position of the arm to be

read to 0.1". This part can be locked in place by a locking
screw in the secondary arm plate.

There is located in the bottom of the hub another
tapered-roller bearing (11) (10). Between this bearing and
the one located in the bottom flange of the lower column
section is located the central shaft (Y). The bearing nut
(J) is used to adjust these bearings so that there is no
radial or axial play of the central shaft. This nut is
adjusted through a 1/2 inch hole in the side of the lower
column section (A).

The central shaft extends up into the interior of the
hub. This shaft is also hollow and contains a 1/2 inch
inside diameter, 2 inch long, hardened steel, drill bushing
in the upper end. The lower end of the central shaft extends
through a 1 inch diameter hole in the rotary table (B)
into a 1-1/2 inch thick anchor assembly.

This anchor contains a 4 inch diameter, brass, split
collar (K) which is clamped to the shaft. This collar has
a tab which is then clamped between two colinear bolts in
the aluminum plate (L) which is in turn bolted to the

secondary base plate. The result of this assembly is to

176

provide a shaft (Y) which is fixed to the base and extends
up through the center of the central column.

The secondary arm can be clamped to the stationary
central shaft by the use of th split clamp (M) located
inside the hub. This clamp is activated through the
shaft (N) and the miter gears (0) (13). .

Located inside the hub is the target well (P) which
is a part of the vacuum chamber containing the targets.
This well is held in alignment at the top by a ball bearing
(Q) (14). At the bottom it is clamped to the central shaft
by a split brass clamping collar (R).

There is a hole in the bottom of the target well
which contains a double O-ring seal allowing the 1/2 inch
diameter target shaft (S) to enter the vacuum system. This
shaft is made from drill rod which was specially ground to
fit the drill bushing in the top of the central shaft and
is straight, to 0.3 mil, over its entire length. A tapered
length of drill rod was also made to screw into the tOp of
the target shaft to facilitate the insertion of the shaft
through the 0—ring seal.

The need for the 2 inch drill bushing is apparent
at this point. A certain amount of clearance between the
bushing and shaft is necessary in order to have a slip
fit. The beam line, however, is 9 inches above the drill
bushing in a typical experimental configuration. Since

the drill bushing provides the alignment for the target

177

shaft, there is an amplification at the beam height of the
play in the bearing. To decrease this effect for a given
clearance it is sufficient to increase the length of the

bearing used.

1.7 Target Drive--Figure I.5

 

The target shaft (S) is pinned to a 1/4 inch diameter
shaft (T) which extends to the lower end of the central shaft.
At this location the target screw shaft (Z) is pinned to
(T). This target screw contains a 1/2-10 Acme thread.

There is a keyway located along the side of this screw to
accommodate a 1/8 inch square key.

The target drive contains two similar sections, one
for the target height and one for the target angle. Each
of these sections contains a worm gear assembly. One end
of each worm wheel shaft is connected to a drive motor system
and the other end is connected to a synchro motor (15).

The target angle, 60 tooth worm gear (V) (16) was
modified to contain a 1/2 inch bore with an 1/8 inch key-
way. The target height, 100 tooth worm gear (W) (17) was
modified to contain a 1/2-10 Acme internal thread.

The drive motor for the target angle is a Slo-Syn
#SSSO-lOOl bifilar motor. This motor is used both in AC
synchronous and DC stepping modes. To run this bifilar
motor in an AC synchronous mode, a 24 Volt, 1 Amp, power
supply is used with a phase shifting network consisting of

a 2 Ohm, 25 Watt resistor and a 50 mf, 100 VAC capacitor.

178

The drive motor assembly for the target height consists of
two motors coupled by a magnetic clutch (18). The fast
motor is an 1800 RPM, 22 oz—in torque, Globe synchronous
motor (19), while the other is a 72 RPM, 50 oz-in torque,
Slo—Syn motor #8350. These two motors use only 110 VAC
power. In the AC synchronous mode the bifilar motor drives
the target at 432°/min. In DC stepping mode, 20 steps/sec
are applied to the motor driving the target at 36°/min.

The Slo-Syn motor in the target height drive moves the
target at 0.072 inches per minute. The Globe motor pro-
vides a motion of 1.800 inches per minute.

Below the target drive units is located the target
position, limit switch assembly (X). This unit consists of
five microswitches, two of which define the upper and lower
limits of travel and three of which define the vertical
positions for three targets. These switches are activated
by a cam fastened to the lower end of the target screw (Z).
Each switch is mounted so that it can be adjusted in its
vertical position as well as in its horizontal position

relative to the cam.

I.8 Target Holder-~Figure I.5

 

The target holder consists of two parts fastened to
the target shaft. There is a steel collar which is fastened
to the target shaft with a brass set screw. This collar

has a tongue on it which meets with a groove in the ladder

179

base and prevents any rotation of the target ladder relative
to the target shaft.

The target ladder is a U-frame structure which accepts
6 inches of target frames that are 1/16 inch thick and 2
inches wide. The bottom of this U—frame fits over the
target shaft and rests on the steel collar. A short 1/4-28
machine screw goes through a hole in the ladder base and
screws into the top of the target shaft. This method of
fastening the ladder to the shaft permits the ladder to be
easily removed or fastened in place while the target shaft
is in its lowest position inside the target well. It also
provides a secure location of the ladder on the shaft.

The sides of the ladder contain grooves in which are
located bent, phosphor-bronze springs. These springs pro—
vide the necessary tension to hold the target against the
edge of the groove. The upper ends of the sides of the
ladder contain a lead which facilitates the insertion of

the targets into the ladder.

1.9 Target Chamber--Figure I.6

 

The target chamber shown in Figure 2.2D is a section
of the goniometer which depends on the experiment for the
exact design which is used. For this reason it was con-
structed in such a way as to facilitate modifications for
various requirements.

The target chamber consists of three basic aluminum

components. The top and bottom have general usefulness

 

 

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181

while the median plane section has a configuration which
depends on the experimental requirements. The bottom mates
with the top of the target well (Figure 1.5P) through an
0-ring seal. These two sections are bolted together with
four, 10-32 machine screws. 0n the upper surface of the
bottom section there is a 6.625 inch diameter O-ring

located in a dovetail groove. This forms the vacuum seal
between the bottom and median sections. The top section has
a similar construction as the bottom except that it contains
a 4 inch Marman flange which is the type of standard coupling
used in the beam line.

The center section of the target chamber which was
used for this thesis work will be described here. This
section is 8 inches in diameter and contains various beam
entrance and exit ports. There are two fixed monitor ports-—
one at —45° and one at -l35°. These ports consist of KF-lO
Leybold vacuum flanges.

The beam input port consists of a coupling which
fastens to the standard beam pipe and tapers down to slip
into a 1 inch diameter hole in the target chamber through
a double O-ring seal. The inside of this coupling has a 6
inch section of 1/2 inch diameter hole through which the
beam must pass. To facilitate the alignment of the beam
into the chamber, there is an insulated, 9/16 inch inside
diameter, annular, tantalum slit located just before this

restricted section.

182

The final beam port is for the scattered beam. This
port is a slot in the side of the chamber extending from
—15° to +177°. There is an O—ring groove 1/16 inch out-
side of this slot on the outside surface of the chamber.
This port can be used in two basically different ways. One
utilizes a foil window for the beam to pass through while
the other incorporates a sliding vacuum seal similar to a
type that has been used before (Fe 66) (Bo 67).

The details of the sliding vacuum seal are shown in
Figure 1.6. Above and below the 0-ring groove (A) is
located a 1/4 inch wide ball bearing (B) (20). Beyond
these bearings are located removable spacing rings (C). The
seal strap used is 10 mil stainless steel and covers the
entire slot area and the two bearing surfaces.

The clamping strap (D) provides the O-ring compres-
sion. This strap contains a slot which has the same
dimensions as the slot in the target chamber. There is a
piece of 20 mil Teflon sheet between the clamping strap
and the stainless steel strap. The clamping strap and
Teflon are bolted to the target chamber through holes in
the spacing rings (C). When the bolts are tightened this
assembly provides the prOper 0-ring compression. The stain-
less steel strap is clamped between the Teflon and the ball
bearings. The bearings move with the seal strap and the

strap slides on the Teflon as the seal is moved.

183

The scattered beam port coupling is inserted into the
stainless steel strap. The necessary torque to move the
seal is supplied to the strap through this exit port
coupling. To facilitate the replacement of the seal strap,
this coupling utilizes an O-ring vacuum seal.

The core of this coupline (E) is made of stainless
steel and contains a shoulder on the portion extending inside
of the seal strap. Between this shoulder and the strap is
a spacer (F) which has an 8 inch diameter. cylindrically
curved surface on the side in contact with the seal strap.
0n the opposite side of the strap is located a 1/16 inch
O—ring (G) and beyond that another spacer (H) which has a
cylindrically curved surface in contact with the O-ring.
Finally, there is a spacer (I) which slides over the spacer,
(H) and the O-ring (G) and is in contact with the seal
strap on a cylindrically curved surface. The final component
is a brass thrusting collar and KF-20 Leybold flange (J).
The collar is threaded onto the core (E) and presses against
the ends of the two spacers (H) and (I). There is a double
O-ring seal between the collar (J) and the core (E).

When this beam port coupling is properly assembled
the seal strap is clamped in place and a vacuum seal is
formed. The strap is clamped between the spacers (F) and
(1). The vacuum seal is formed by the O—ring (G) and the
two spacers (H) and (I). The spacer (1) produces the com-

pression of the 0—ring against the core while the spacer

184

(H) produces the compression against the seal strap. This
type of coupling limits the smallest obtainable forward
angle to about 20°.

The thrusting collar (J) fits into a clamping plate
(K) which is then bolted between the two collars (L).

These two collars fit over ball bearings (M) (21) which are
located on the top and bottom of the target chamber. When
the sections (J), (K), and (L) are rigidly bolted together,
the exit port coupling is secured at a fixed radius. As a
result, one does not have to worry about bending the thin
stainless steel strap or breaking the seal by inadvertently
moving the exit port.

The torque needed to move the sliding vacuum seal is
supplied by the main arm through the coupling (M) to the
clamping plate (K). In order to move the sliding vacuum
seal, a fair amount of force is necessary. This force can
be supplied to the seal strap by the main arm. A counter-
torque, however, must also be supplied to the target chamber
body to prevent it from rotating with the seal. In the
original design this torque was to be supplied through the
split ring which clamps the vacuum chamber to the fixed
central shaft (see Figure I.5R). It was found, however,
that this clamp could not be tightened sufficiently without
restricting the movement of the target shaft in the very
close fitting bushing located in the upper end of the central

shaft.

185

Since this was the case, the needed torque had to be
supplied from some other source. This other source is the
coupling between the target chamber and the beam line.

There is some play, however, between this coupling and
the target chamber, and as a result, the target chamber
did rotate a few degrees when.the seal strap was moved.

This sliding seal was originally designed to be used
with an internal Faraday cup. Some preliminary work, how-
ever, showed that this method of charge collection is, in
general, not compatible with many types of experiments for
which this system is to be used. The alternative method
of charge collection for this target chamber is to run the
beam through the stainless steel strap into an external
beam dump. This method was found to produce background
levels that were too high for many types of experiments.

The thin foil, exit port construction is a simple
structure in comparison to the sliding vacuum seal. This
window utilizes the clamping strap of the sliding seal
(Figure 1.6D). This strap is clamped to the target chamber
through the holes in the spacing ring (Figure 1.6C), and the
vacuum seal is formed between the O-ring and the inside sur-
face of the strap. A thin foil is glued to the outside of
the strap. This is the type of window that was used for
this thesis experiment and further details of the particular

window that was used will be given in section 3.2.a.

186

From the above description of this 8 inch diameter
target chamber, it can be seen that there are features
which limit its usefulness. These features include its
fixed monitor ports, its lack of a primary beam, exit
port, the limit of 20° as a minimum scattering angle
attainable,and the need for additional countertorque for
the sliding seal.

In an attempt to improve this system, a 16 inch
diameter median plane section was designed (Ma 69). This
new chamber has a sliding vacuum seal with an angular
range from 8° to 110°. The design of the chamber, however,
allows the detectors to cover a range from 8° to 172° if
necessary by permitting the inversions of the median plane
section for the angles from 90° to 172°. The reduced range
of the seal was used in order to keep the necessary torque
requirement for moving the seal at approximately the same
value as that needed for the 8 inch chamber. There is
also a fixed port at the beam exit which has a design that
is similar to the input port used for the smaller chamber.
Provisions were also made to supply the counter torque for
the vacuum seal by coupling the chamber to an anchor post.

Details of this larger target chamber are not given
here since this was not included in the original system.
It is mentioned here, however, to show the utility of the

modular design concept.

187

1.10 Target Lock--Figure 2.2E

Fastened to the Marman flange on the tOp of target
chamber is the target transfer and hold lock. The lock
assembly consists of three aluminum units-~a ported
vacuum coupling, a vacuum valve, and a small chamber con—
taining a transfer operation.

The next section is a vacuum valve similar in con-
struction to a ball-type valve. This valve has a cylindri-
cal aluminum core which contains a 3/4 x 2-1/2 inch slot
which aligns with a similar slot in the valve housing when
the valve is opened. At each end of the core there are
O—ring seals. There are also two O-ring grooves located
on the surface of the core 90° on either side of the slot.
These two O-rings are glued in place using Eastman 910
adhesive. These seals are shaped in such a way as to
encircle the hole in the valve housing when the valve is
closed. This arrangement of O-rings allows the valve to
be used in either direction. The only fact that unsym-
metrizes this valve is the existence of a KF-10 Leybold
vacuum fitting in the valve housing on one side of the
valve permitting that side to be evacuated with an external
pump. Dow Corning high vacuum silicone grease has been
successfully used in these valves.

When this valve is closed and evacuated there is a
double O-ring seal between vacuum and atmospheric pressures.
This arrangement of O-rings can cause some problem, however,

if certain precautions are not taken. To be specific,

188

there are isolated regions between the valve core and
housing when the valve is either fully Opened or fully
closed. Because of this, the vacuum can be broken when

the valve core is turned for the first time after evacua-
tion. To prevent this from occurring, it is sufficient to
turn the valve to the half-opened position while evacuating
the valve.

Using one valve in the target lock permits the
insertion of targets into the vacuum chamber without break-
ing the vacuum. The use of two valves, on the other hand,
permits the transfer of a target without exposing it to the
atmosphere.

The third section of the target lock is a small,
cylindrical, vacuum chamber. In the top and on the axis of
this chamber there is a target transfer mechanism. This
mechanism consists of a 3/16 inch steel rod inside of a 5/8
inch steel shaft. The larger shaft enters the top vacuum
chamber through a double O-ring seal while the smaller
enters the vacuum chamber through a double O-ring seal in
the top of the larger shaft.

The part which grasps the target frame is a split,
conical, phosphor-bronze jaw. This fits into a conical
hole in the lower end of the 5/8 inch shaft. The smaller
shaft is screwed into the top of the jaw and is spring

loaded to keep an upward pressure on the jaw mechanism.

189

The transfer of a target into the target chamber is
accomplished by placing the target in the transfer jaws
while depressing the inner shaft. Releasing this shaft
allows the spring to tighten the jaws on the target frame.
The chamber is then fastened to the top of the valve and
evacuated. The valve is Opened and, while being sure that
the target is aligned properly, the target is lowered
through the hole in the valve and into the target ladder.
A clamp around the shaft is provided on the top of the
vacuum chamber and prevents the transfer shaft from being

unexpectedly drawn into the evacuated chamber.

I.1l Detector Carriage-—Figure 2.2F

 

The detector carriage consists of a base and a LN2
dewar. The exact configuration of the base depends on the
experiment which is to be done. The primary base component
consists of an aluminum block which rests on the dual beams
of the arm. In that portion of the block which rests on
each beam is located 6, 1/4 inch inside diameter, hardened
steel, drill bushings spaced at 1 inch intervals. A steel
dowel on each side of the base is used to align one of these
bushings with one of the bushings located in the beam
itself thus fixing the radial position of the detector
mount with respect to the target center. The surface of
the base which comes in contact with the beam surfaces is

covered with a self-adhesive, felt cloth which prevents

190

the beam surface from being scored while moving the
detector carriage over it.

The LN dewar is a welded stainless steel construction

2
large enough to hold two vertical cryostat, detector pack-
ages. The inner wall is a 1/32 inch thick tubing and the
outer wall is 1/16 inch thick tubing. There is a bellows
vacuum valve on the side of the dewar which permits evacua-
tion when necessary. To aid in the thermal insulation of
the dewar,the outside is wrapped with two layers of 5 mil
polyethylene sheet and heavy aluminum foil. These in turn
are wrapped with a heavy, 3 inch wide plastic adhesive
tape.

The best performance of the dewar was Obtained when
it was pumped out with a diffusion pump (D.P.) for several
hours. The pressure obtained at the D.P. was about
6 x 10"7 Torr. During the pump down the dewar was also
heated with an air gun to permit the outgassing of the
inner walls. Having done this, it was found that the dewar
had a pot life of about 12 hours which gives a useful life—
time of about 10 hours in an experimental setup using two
detector packages simultaneously.

The form of the detector mount support which is
used on the base depends on the detector setup used in the
GXperiment. The original support was designed for a single
detector package. This consists of a detector clamp which

18 bolted onto an aluminum block which slides for 1 inch on

191

two parallel steel rods mounted in the base. This slide

in conjunction with the drill bushings permits the detector
to have a continuously variable radial position over the
useable region of the main arm.

The second detector support is designed to hold two
detector packages side by side with a separation of about
20° at a radius of about 9.5 inches. The detector clamps
are independently mounted to the base and have a total of

one inch of radial adjustment.

1.12 Local Power Supply

 

The necessary AC electrical power needed for the
various driving motors is supplied from a local power supply
located in the experimental area. This supply is connected
to the goniometer drive unit by three 20 AWG, 15 conductor
cables in a bundle and a 48 pin connector.

This power supply along with a power distribution
chassis are totally enclosed in a mobile, steel rack. The
fact that these are totally enclosed helps to isolate the
other electronics in the experimental area from the contact
noise arising from the relays in the chassis. These
relays are used in the selection of motor speed and direc-
tion,.in the automatic target selection system, in the
limit switch circuits, and in the main 110 VAC control
circuit. There are also two time-delay relays used in the
fast motor reversing circuits for the main arm and target

height drives. These relays are incorporated to prevent

192

the instantaneous reversal of the motor direction.

Instead, there is a two second delay between the time

the reversal signal is received and the power is turned

off and the time that the power is reapplied in the reverse
direction. The contacts of the relays which control the

AC power to the main arm and target angle motors as well as
those for the main AC power line are all protected with
Thyrector diodes.

The electrical chassis ground in the local power
supply is provided through the interconnecting cable from
the remote power supply. The goniometer itself, however,
is n93 grounded through its control system. All the 110
VAC circuits which are connected to the remote 110 VAC
circuits are completely isolated from the local 110 VAC
power.

A local control box, Figure 2.3, fastened to about
30 feet of 22 AWG, 25 conductor cable is connected to the
local power panel through a 25 pin connector. This control
box is grounded in order to isolate the switch contact
noise, and it contains all of the controls which appear
on the remote control panel except the automatic angle
increment feature of the main arm (see section I.13.a.3.a).
In addition to these, however, this control box contains
a limit switch override which allows the operator to go

past the limit switches for the main arm if he desires.

193

The controls on this box are in the form of momentary
push-button, microswitches (22).

The operation of the buttons on this box are the
same as those on the remote control panel except for
three cases. First, the red, limit abort button must be
used if the arm must be positioned beyond the limit
switches. This is accomplished by pushing this button
while moving the arm over the limit switch. It-need not,
however, be pushed to return in a CW direction over the
switch which limits the CCW motion, etc.

The other two buttons are the target angle, FAST
button and the target height, SLOW button. To permit
these buttons to provide a choice of speed at the local
station, the operator must set the remote controls for
the target angle in the SLOW mode and the target height in

the FAST mode.

1.13 Remote Control Station

The remote control station is located in an equip-
ment rack in the data room at MSUCL. This station is con—
nected to the local power supply and control circuits by a
series of multiconductor cables and 47 pin connectors.
This method of connection was found to be very useful since
it allows thecontrol panel to be easily connected either
locally or remotely to the other system components. This
also allows the entire system to be transported in several,

easily managed components.

194

The remote station consists of four interconnected
units--the control panel, a DC motor power supply, an
electronics bin, and a power distribution chassis. The
chassis ground for the entire system is connected at this

location to earth ground.
1.13.a Control_Panel—-Figure 1.7

I.13.a.l Digital Counters
and Driving Systems

 

The front of the control panel is a 1/4 inch aluminum
plate. The synchro motors which indicate the positions of
the various elements on the goniometer are connected to
identical synchros located on a shelf near the top of the
control panel. Each of these motors is then connected to
the digital counter by a series of gears mounted on 1/4
inch shafts turning in 1/4 inch, inside diameter, ball
bearings (23). The main arm system contains a 1:1 gear
train connected to a dual-bank, 4 wheel, digital counter
(24) giving a least count of 0.02°. The zero on this
counter corresponds to a scattering angle of 0.0°. The
readings increase in either direction from this point
allowing the lab scattering angle to be directly read on
the counter.

This counter, as well as the others, are connected
to the gear train through a friction coupling (25). This
allows a hand-wheel to be attached to the counter shaft

permitting the zero to be easily set when necessary.

195

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I.7 Remote Control panel: A - Graphic display, B -
Main arm controls, BB - Digital counter windows,
0 - Target height controls, D - Target angle controls,
E - Preset digital counter, F - Run button, G —
Main power switch.

196

These hand-wheels penetrate the front surface of the
control panel by about 1/8 inch, and each has a protective,
movable cover to prevent the accidental movement of the
wheel.

The target angle system has a 1:6 gear train con—
nected to a 4 wheel digital counter (26) giving a least
count of 0.02°. The target height system has a 10:1 gear
train connected to a 4 wheel digital counter (26) giving a
least count of 0.2 mil. This gear system also contains an
electromagnetic brake system. This brake was found to be
needed because of the tendency of the synchro motors to go
into a free running mode when the drive was started or
stopped while using the fast operating mode. This brake
is released only when the target height, drive motor is
activated and is immediately applied when the drive is
stopped. A braking action is also utilized on the gonio—
meter itself in the target height drive system. Here the
high residual torque of the Slo-Syn motor used in the
drive system is utilized by activating the electromagnetic
clutch between the two motors whenever the fast motor is
turned off.

The digital counters are viewed from the front of
the control panel through cylindrical lenses (27) mounted
in blackened frames, (BB), and through blackened masks which
incorporate the decimal points. The lens and counter spac—

ings provide for an approximate magnification of 2 for the

197

numbers on the counter wheels. Each of these digital
counter systems includes a 24 VAC incandescent lamp for
illumination of the digits.

1.13.a.2 Graphic Display——
Figure I.7A

 

 

Coupled into the gear systems which drive the
counters for both the arm and target angles are two small
sychro motors (28). These motors are used to drive the
synchros in a graphic display system located in the control
panel (A). This display provides a pictorial view of the
relative angular positions of the main arm, the manually
positioned arm, the target, and the incident beam direction.
Each of these elements is represented in a plexiglass disc
by an engraved line which has been filled with India ink.
These discs were found to be very soft and easily scratched
but could be polished with a buffing wheel. This display
also contains four 24 VAC incandescent lamps which provide

for the illumination of the elements.

 

I.B.a.3 Push Button Controls

The front of the control panel is separated into 3
sections, one for each drive system. The controls located
on this panel are illuminated switches (22). Those
switches which initiate the manually controlled motions of
the driven elements are distinguished by a red border
around the white switch faces. The remainder of the switches

are pale orange except for the main power, on-off switch,

198

which is red. The switches on this control panel which
control 110 VAC have 0.05 mf, 1000 VDC, disc capacitors

across them to prevent contact noise.

1:13.a.3.a Main Arm Controls--
Figure I.7B, '1 ‘

 

 

In this case the slow and fast controls are separated
into two separate sections. When running in either mode,
only those lights in the section for that mode are lighted
indicating at a glance which mode is active.

There is an automatic angle increment feature incor-
porated into the slow mode drive system of th main arm. In
this slow mode the arm is moved by the motor operating in
a DC stepping mode. To determine the angular increment, it
is sufficient to count the steps of the motor driving cir-
cuits. This is accomplished by the use of a pre-determined
electromagnetic digital counter (E) (29). Each step on
this counter represents 0.01° of main arm rotation.

Implementing this system requires that the arm-be
set at its starting position using either of the driving
speeds. The SLOW button is pushed to activate the stepping
circuits. The direction of rotation is set as CW or CCW.
The AUTO—MAN button is set in the MAN position. The
preset counter is set for the desired angular increment
and the reset button on the front of the counter is pushed.
When the automatic mode is desired, the AUTO—MAN button is

set in the AUTO position. This action may also initiate

199
the motion of the arm; therefore, it should not be pushed
until necessary. When the increment is needed, the RUN
button (F) is pushed. To make the next increment the
counter is reset and the RUN button activated.

To run in a manual mode, the AUTO-MAN switch must be
in the MAN position. When the RUN button is then pushed
the motor will make 0.01° steps at a rate of lO/second as
long as the button is depressed.

It should be recalled at this point that there is a
2 second time delay incorporated into the fast drive
reversing circuits (section 1.12). Due to this delay,
when the arm has been running in a CW direction, for
example, and the CCW button is pushed, there will be a
delay of 2 seconds before the arm and the digital counter
begin to move in a reverse direction.

1.13.a.3.b Target Height
Controls--Figure 1.70

 

 

The target height controls include a FAST—SLOW
mode switch, an UP switch, a DOWN switch, three automatic
target positioning switches--#l, #2, #3--and a manual RUN
switch. It may be recalled here that there is a time
delay in the reversing circuits. If the target shaft is
moving in a downward direction, the DOWN switch will be
lighted. If it is now desired to have the shaft move

upward, the UP button may be pushed. The light, however,

200

will not come on nor will the counter move until after a
2 second delay.

The RUN button will produce a motion of the target
shaft whenever it is depressed. The motion that is pro—
duced depends on the state of the three mode switches dis-
cussed above.

The three automatic target positioning switches are
used in conjunction with the three limit switches mentioned
in section 1.7. Whenever one of these switches is pressed,
the target shaft will move until it activates the associated
microswitch. The microswitches were set initially to be
activated when the beam height was 1.062 inches above the
bottom of the target ladder for target #1, 2.187 inches
for target #2, and 3.312 inches for target #3. These
locations were chosen such that the incident beam would
pass through the vertical center of standard target frames
which are 1.125 inches high. These three targets are the
first three located just above a 0.500 inch high standard
target which restson the bottom of the target ladder.

These locations are properly defined only when the target
shaft is moving DOWN and the reference point correctly
determined. This reference point, 0.000, is found by
running the target shaft UP until it reaches the upper
limit switch. The digital counter should then read 9.989

which allows for the 11 mils backlash in the drive system

201

(see section 2.3.c). The details of the setup of these

switches are given in section 2.3.0.

I.13.a.3.c Target Angle
Controls--Figure I.7D

 

The target angle controls include a mode switch--
FAST or SLOW--and two directional switches--CW and CCW.
The target angle changes as long as one of the directional
buttons is depressed. There are no limit switches in
this system.

The fast mode was found to rotate the target at
too great a speed for convenient use. The slow speed
operation was found to be more useful since only small
changes are usually made.
1.13.a.4 Main Power ON-OFF
COntrol--Figure 1.70

The main power control switch is located on the
lower right side of the control panel. This switch con—
trols all of the power in the entire system. It turns
on the 110 VAC power not only for the remote control

panel but also for the local power supply as well.

1:13.b. DC Motor Power Supply

The DC motor power supply is located behind the
control panel. This supply has an output of 35 Volts at
6 Amps. It is protected with an MDL-4, 4 Amp slow-

blowing fuse on the transformer primary and contains a

202

switch for the 110 VAC input and a pilot light located
between the fuse and the transformer primary.

An AGC-4 fuse on this supply was found to be blown
at frequent intervals during the early operation with the
goniometer. It was believed that this was a result of
surges produced when the AC power is switched on or off.

This was corrected when the slow-blowing fuse was installed.

I.13.c. Electronics Bin

 

The electronics bin is also located behind the control
panel. This bin is an Elco Varipak card bin and contains a
regulated power supply and the logic and power amplifier
circuits necessary to drive the DC stepping motors. The
stepping logic for eachEflo-Syn, bifilar motor is provided
by two DTpL9lll, parallel gated, clocked flip-flop, inte-
grated circuits. The clock pulses are provided by an
oscillator built around a A7100 high speed differential
comparator, integrated circuit and a differentiating, RC
network. The stepping logic and amplifier for each of
the two motors is contained on three cards. The amplifiers
for the motors are identical even though the power require-
ments of the two motors are quite different. This was done
to facilitate the construction of the circuits and to permit
the swapping of cards if necessary from one drive to the
other. The Zener regulated power supply which is in this

bin contains outputs of +5VDC, -6VDC, +12VDC, and -12 VDC.

203

1313.d Power DistributionfChassi§_

The remote power distribution chassis is located
behind the control panel. There is a plug-in, 24 VAC-DC
power supply located here. This supply provides the
necessary AC power for the 24 Volt incandescent lamps in
the control panel and the DC power needed to drive various
reed relays in the electronics circuits and the electro—
magnetic clutchirIthe target height drive, section I.7.

Since the clutch is a large load on the power supply,
its being switched on caused the lamps in the control panel
to dim. To prevent this, a dummy load, equivalent to the
clutch load, is put on the power supply whenever the clutch
is disengaged.

Also located on this chassis is a plug—in card of
miscellaneous electronics and reed relays used in the main
arm stepping circuits. There are three momentary relays,
one of which is a spare, and one latching relay located
here. The contacts of the main power relay are protected
with Thyrector diodes and 0.05 mf, 100 VAC capacitors.

All the relay contacts which switch 100 VAC have 0.05 mf
capacitors across them for noise suppression.

Finally, this chassis has a number of multipin con—
nectors into which are fastened cables from the various
components of the system. Not one of these connectors is
the same as another except where an interchange would
cause no problem; this eliminates any question of the way

the components are interconnected.

204

1.14 Surface Finishes

 

The eXposed steel surfaces of the goniometer base
and central column were painted first with a steel primer
and then with several coats of enamel. The exposed alumi-
num surfaces of the goniometer base, which do not come in
contact with other components during operation, have a sand
blasted finish. This surface is easily cleaned and provides
a uniform finish of these parts.

The local control box face contains the identifying
lettering for the various bottoms. This lettering is
engraved into the surface and filled with black ink.

The surface of the remote control panel is also sand
blasted. There is no lettering on this surface, but
instead the lettering is located on the digital counter
window frames, on the switch faces, and on the graphic

display components.

1.15 Suggested Improvemenps

 

There are certain difficulties that arise due to
some features of thetarget readout and driving systems.
First, the digital counters have a least count which is
too small for practical use. Second, the target height
drive raises thetarget by too small a distance for each
revolution of the motor, resulting in the need for the
1800 RPM motor and the braking system. Also, the target
angle drive rotates the target through too large an angle

per revolution of the motor. Finally, the need for a

205

1:6 gear increasing drive between the synchro and the
counter produces a limitation of the usefulness Of the
fast drive mode for the target angle.

The following changes could be made to remedy
these problems. The least count on the digital counters
could be increased by a factor of 10 by providing for an
additional 10:1 gear train for each system. This would
give a 100:1 system for the target height and 5:3 system
for the angle. The 5:3 gear reduction would be a great
improvement over the 1:6 gear increase. The resulting
least count for the target height and target angle would
be 2 mil and 0.2° respectively, which are more realistic
figures.

The remainder of the difficulties could be removed
by a redesign of the gear boxes used in the drive system.
The type of change that could be made is to replace the
100 tooth single thread worm gear in the target height
box with a 40 tooth, 4 threaded worm gear (30) driven by
a 200 RPM Slo-Syn motor (31) or a precision Slo-Syn step-
ping motor (32). This not only reduces the speed of the
motor needed but also increases the travel of the target
per motor revolution and eliminates the need for a dual
motor system.

The 60 tooth worm gear in the target angle drive
could be replaced with a 360 tooth worm gear (33). This

would provide for a smaller angular change per revolution

206

of the motor and would also reduce the problems at the
digital counter. The fact that the target screw in the
drive system is used for both turning and raising the target
can also produce some difficulty. This arises from the fact
that the target changes in its vertical position for a
change in its angular position. The size of the angular
change, however, is less than 90° in a majority of cases,
this produces a change in height of 25 mils. This is not

a serious problem, however, since this can be compensated
for if the operator is aware of the peculiarity. Further-
more, in order to eliminate this problem completely would
involve a complete redesign of the target drive system

resulting in a much more complicated mechanism.

1.16 Documentation

 

When the goniometer was completed and operated satis-
factorily, all of the mechanical and electrical drawings
were updated to insure the existence of a complete set of
as—built prints which can be used as reference for future
modifications or additions. The mechanical drawings of
the goniometer drive unit are filed at MSUCL under the
project number HA-llO . . . while the electrical and
electronics drawings as well as the control panel mechanical

drawings are filed under the project number FC-151 . . . .

207

1.17 Assembly and Maintenance Suggestions

 

I.17.a Backlash Adjustment of
the Rotary Table Gears

 

Before this rotary table was assembled into the
final system, the proper backlash was set for the worm
gear drive. It may be necessary from time to time to check
this figure and to readjust the table gears. The technique
which can be used to set the backlash is the following:
First there can be no endplay in the worm wheel shaft. This
can be checked by supplying an alternately CW then CCW
torque on the rotary table platform and observing if there
is any inward or outward movement of the shaft. If there
is a movement,a nut inside the housing around the worm
wheel shaft must be tightened.

With the worm wheel shaft secure, a dial indicator
can be placed to show any motion at the circumference of
the table platform. With the indicator in place a CW and
CCW torque can be applied to the table,and the movement of
the indicator is observed. A movement of about 2 mils was
found to produce a smooth operation. If the movement is
not around 2 mils,the backlash is adjusted making sure
that the four 1/2 inch bolts holding the table to the
secondary base plate are loose. The alteration is accom-
plished by utilizing the adjustment mechanism on the end of

the worm wheel shaft opposite the spur gear drive assembly.

208

I.17.b Assembly Of Main Arm Drive

First the rotary table and central column can be
assembled loosely with the central shaft extending through
the rotary table and beneath the secondary base plate.

The central shaft anchor clamp, Figure I.5K, and anchor
housing, Figure 1.5L, loosely fastened around the central
shaft to confine the center of rotation of the rotary table
to an acceptable area.

Next, the motor is hung loosely on its mounting screws,
and the rear gear box plate is placed over the motor and
table shafts. The large gear shaft containing its two ball
bearings is placed on the table shaft and slipped into the
bearing hole in the gear box plate. The position of the
motor can then be adjusted to allow the small gear shaft
with its two bearings to slip over the motor shaft and into
the box plate when the two motor mounting screws have been
tightened. When this adjustment is completed, the rear box
plate should be flat against the mounting plate on the
rotary table, the motor mounting plate, and the edge of the
secondary base plate. The box plate can then be securely
bolted into place.

The gear plate is made to rotate about the worm wheel
shaft. 1f, when all the mounting bolts have been tightened,
there.is a binding of the ball bearings in their respective
seats, the motor must be loosened and readjusted so the

bearings slip into their seats with only a slight pressure.

209

Next the gear shafts can be removed and the "rear"
brake plate installed. The gear shafts are placed on the
respective shafts. The 1/8 inch pin which couples the motor
and gear shafts, is inserted with only a gmgll force and
held in place with a small set screw. The rotary table can
now be bolted in place. The remainder of the assembly is
self explanatory from here.

I.17.c Installation of the Main
Arm Synchro Motor

 

 

For a proper assembly the synchro housing must be
concentric with the motor shaft. Access to the clamp used
to fasten the Oldham coupling to the synchro shaft is
obtained through a hole in the bottom of the housing.

I.17.d Installation of Target
Well TFigure 1.5)

 

 

The collar (R) on the bottom of the target well (P)
contains a #10 socket head, machine screw and is adjusted
with a special, long handled, allen wrench. Access to the
clamp screw is obtained through a hole in the side of the
upper column section (AA) and one in the sides of the
secondary arm hub (F). The main arm must be rotated to the
appropriate position before the two holes and the screw

are aligned properly.

210

1.17.e Assembly of Target
Drive and Central Shaft
(Figure 1.5)

 

 

Before the anchor is attached to the central shaft a
dial indicator is used to check to see that the central
shaft (Y) assembled in the two central column sections
(A)(AA) stays fixed when the rotary table is turned through
one revolution. If not, the 8, 1/2 inch bolts which hold
the central column to the rotary table must be loosened.
Then the central column may be shifted on the table plat-
form to insure that the central shaft does not move when
the rotary table is rotated.

Now the central shaft (Y) can be removed from the
central column assembly by unbolting the flange (C) and
loosening the clamps (J and R). The target screw (Z)
which is pinned to the connecting shaft (T) by a tapered
pin, which does not extend above the surface of (T), is
inserted into the lower end of the central shaft. The
target shaft (S) is greased and very carefully inserted
into the top of the central shaft being careful nOt to get
gay dirt in the grease. Shaft (S) can then be pinned to
the shaft (T) through a hole in the side of (Y) using a
tapered pin which does not extend above the surface of (S).
Making sure that the bearing nut (G) is tightened and the
bearings lubricated, the central column can be reassembled
at flange (C) making sure that there is no dirt on the

flange surfaces.

211

The clamp ring (K) is attached to the lower end of
the central shaft about 1/32 inch below the secondary base
plate and tightened securely. The aluminum anchor plate
(L) is bolted in the secondary base plate. The page bolt
in (L) can be tightened onto (K) now that was loosened
during disassembly, preventing any assymmetric loading of
the parts.

The two target drives can be assembled straight for-
wardly. The target angle drive assembly is placed in the
proper orientation under the anchor block while the target
shaft is in its highest position. It can then be raised so
that shaft (Z) goes through the worm gear. The 1/8 inch key,
which has well rounded leading and trailing edges, is placed
in the keyway in (Z). (Z) is then oriented to permit the
key to enter the worm gear. The assembly is then raised
to meet block (L) and securely bolted in place taking care
not to cause the target screw to bind.

In order to provide enough room for the target height
assembly to fit between the fully raised target screw and
the main base plate, the secondary table must be loosened
and raised a little. Having done this, the target height
drive can be located beneath the target screw shaft. The
assembly is now raised so that the screw enters the worm
gear. By activating the target angle drive, the screw
shaft can be slowly screwed through the gear and beyond the

bottom of the housing. This assembly can then be raised

212

bolted to the target angle housing taking care not to
cause binding to the target screw.

The 1/4 inch plate of the switch assembly is then
bolted to the rest of the drive. The switch mount assembly
can finally be placed in position through the hole in the

main base plate and bolted to the 1/4 inch mounting plate.

1.17.f Electrical Fuses

 

1. Local Power Fuse #
a. Main power AGC-lO
b. Main Arm MDL-6
0. Target Angle MDL-l/2
d. Target Height MDL-l

2. Remote Power

a. Main Power AGC-8
b. 35 VDC Motor Power Supply MDL—4
c. Electronics Bin (on back

side of bin) AGC-l
d. 24 VAC-DC power supply AGC-l/2

1.17rg, Lubrication

 

The rotary table, section I.3.a, contains a dipstick
to check the oil level in the internal reservoir. The oil
contained in this table is a heavy oil (Sunoco way oil)
and should be checked once a month. There are also three
other points which need to be oiled once a month. Two have

access through holes on the edge of the table platform, and

213

the third has access through a hole located on top of the
worm wheel drive shaft just outside the table housing.

The lubrication which is used for the target shaft
(Figure 1.58) is a 2:1 mixture by weight of Apiazon L
vacuum grease and Welch, Duo—Seal, mechanical pump, vacuum
oil. Care must be taken when greasing this shaft that no
dirt is allowed to get into the grease which could cause a
ceasure of the shaft in the hardened bushing in the top of
the central shaft.

The target screw shaft (Figure 1.52) is lubricated with
a light, good quality machine grease every two months. This
is done by lowering the target shaft to its lowest position
and applying the grease to the exposed threads.

When the target drive, worm gear boxes were assembled,
grease was packed around the worm gear. The shaft bearings
in this mechanism are oil impregnated and, therefore, need
not be checked. Once a year grease can be pumped into the
worm gear cavities through the hole in the side of each
housing containing a small brass plug.

The bearings used in the remote control panel are
all either ball bearings or oil impregnated bronze. There—
fore, the only lubrication which is necessary is to apply
a small amount of light grease_to the teeth of the gears
once every six months.

Finally, in order to prevent them from rusting, the

hardened drill bushings in the main arm, the secondary arm,

214

and the detector carriage, should be swabbed with a light

oil or preferably a rust preventative oi1* after every use.

1.18.

List of the Majpr Components

 

This list contains information concerning those com-

ponents of special interest mentioned in the text.

Part No.

1.

2.

l3.
14.
15.
l6.
17.
18.

Bridgeport Machines Inc., Bridgeport, Conn.
Superior Electric, Bristol, Conn.

Boston gear # GD 29

Boston gear # GD 116

New Departure #3305

New Departure # 3307

Torrington #NTA 1423, #TRC 1423, # TRD 1423

Bendix synchro transmitter, MK.10, Mod. 4, Type 3HG
Pic # T3-3

Timken #15520B

Timken #L624510B

Timken #47825B

Boston #G462Y

Split Ballbearing #45—56—P

Henschel synchro transmitter MK.6, Mod. 9, Type 5HG
Boston #G1040

Boston #G1049

Simplatrol #FFK-43

 

*
DOALL, rust preventive mist

19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.

215

Globe #CLCLL 142A146

Realistim #KA75CP

Realistim #KA60XP

Micro Switch, Freeport, Illinois.

New Departure #R—4

Durant #4-4—Y—8823-R—CL

Pic #R3—3

Durant #4-Y-8823-R-CL

Edmond Scientific Co., Barrington, N. J.
Arma synchro motor MK.8, Mod. 1B, Type 1F.
Hecon #FA-043—6-1—10-l2-DC-2-C

Boston Q1344

Slo-Syn #HS5O

Slo—Syn #TSSO

Pic #Q1-13.

APPENDIX 11
CALCULATIONS OF THE ANGLES IN REFERENCE I

USED FOR THE MAIN ARM CALIBRATIONS

See Figures 11.1 and 2.5 for the definitions of the

various quantities. Assuming a perfect 90° triangle:

cos(a) = B/H 11.1

sin(a) = A/H 11.2

cot(d) = B'/A' 11.3
B' = B-X cos(a) = X B/H

A!

X sin(a) = XA/H

Therefore:

cot(d) = g (% — 1) 11.4

The quantities used in equation 11.4 were:

A = 32.000 feet
B = 33.500 feet
H = 46.327 feet
X = n-(7.000 feet) where n = l to 6

216

217

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one mo COHpHmOO gmasmcw one mpmHSOHmo Op pom: mhuoEoow on» mo oapmsogom H

4 .15.

 

 

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APPENDIX III

COMPOUNDING OF THE ERRORS IN THE POINTS

FOR THE MAIN ARM REFERENCE ANGLES

A. The sources of the errors in reference 1 and the
size of the uncertainty in each case is broken down in
the following summary. The "adding" of errors was done
in quadrature in all cases. It might also be noted here
that the errors used in this section are the result of
empirical measurements. That is, the errors shown in
the majority of the cases are the results of estimates of
the maximum errors in the measurements. These errors are
hard to compare with standard errors but they will be con—
sidered pessimistic estimates of the standard errors.

1. Points A and B, Figure 2.5

a. Alignment of the scope between the two points
0.021" at 132'
b. Center point, 0, Figure 2.5
1). 0.010" for transit errors
2). 0.005" for errors in the placement of
the point.

Total center error is the sum of b(1,2)

0.011"

218

for

219

Adding the results of la and lb, the total error
points A and B about the center point is:
0.016" at 66' or 0.0012°.
Points 0 and D, Figure 2.5
a. These points depend on how well the line between
points A and B was defined by the line of sight
of TR #1.
0.0012°

b. Alignment of the cross hair in TR #2 with:

l). Pointer-—0.005" at 8' 0.0031°
2). Center point--0.005" at 24' 0.001°
3). Pointer image—-0.0l5" at 40' 0.0018°

Total error in the perpendicularity of the line
of sight of TR #2 to the line of sight of TR #1
is the sum of results of b(1,2,3). 0.0036°
c. Placement of the targets on the line of sight
of TR #2.
0.020" at 70' 0.0014°
d. Center point location errors
0.010" at 35' 0.0014"
Total error of point C and D about the center

point is the sum of 2(a,b,c,d): 0.0043°

Point E, Figure 2.5
a. Error in line AB 0.0012°
b. Alignment of TR #1 on line AB--0.010" at

66' 0.00080

220

c. Transfer of point to the floor--
0.005" at 32' 0.0004°
The total error of point E about the

center is the sum of 3(a,b,d) 0.0015°

Point F, Figure 2.5
a. Error in line CD 0.0043°
b. Alignment of TR #1 on line CD--
0.005" at 35' 0.0008°
0. Transfer of point to floor-—
0.005" at 33.5' 0.0008°
The total error of point F about

the center is the sum of 4(a,b,d) 0.0044°

The 90° angle between lines OE and OF, Figure 2.5.
The error about the center in this angle is the sum

of the errors in points E and F 0.0047°

Checks of consistency of transit and scale measure-
ments——-A check was made to see how well the tape
and transit measurements compared for the 90° triangle
constructed on the floor. Also the sensitivity of
the checking procedure used was examined.
The points E and F were located on the floor and
the error in the 90° angle was determined—--0.0047°
a. Comparing tape and transit measurements---The
linear tape was used to measure the distances,

A and B,from the center point to points E and F

221

respectively and the distance H between the
points E and F. The source of error which was
considered in the linear measurements was that
which arises because of different tensions
applied to the tape during the measurements. A
vernier caliper was used to measure the differences
in the measurements due to variations in the ten-
sion of the tape. The variations in the measure-
ments in a 32 foot length were found to be
10.012". This is the error which is associated
with each linear measurement. The other sources
of errors will be checked in the following para-
graphs.

If it is assumed that the central angle is

exactly 90° then

A = 32.000 1 0.003 feet
B = 33.500 1 0.0013 feet
H = 46.327 1 0.0010 feet

2 2

A + B = 2146.25 _ 0.120 feet2

+

H (calc) = 46.438 1 0.001 feet

This demonstrates that the transit and the tape
measurements were of equal quality and that the

assigned error is not a bad estimate.

222

Sensitivity of check 6a—-—In checking 6a it
was assumed that the central angle was exactly
90°. The question remains as to what size of
error in H might be expected for the size of
error determined for the 90° angle.

Considering Figure 1.5:

H2 = A2 + B2 - 2 AB cos 6

Where 8 = 90° + O for 8 small
Also
A = B

Then

2 2B2 (1 + ¢)

:11
u

:13
I2

/2§(1 + %)

Therefore the difference in H due to the error,

8, is
~ ¢
AH — B/2 g
For 8 = 0.0047° and B = 32 feet
AH = 0.022"

This shows that the error in the 90° angle

determined only by the transits would produce a

223

change in the H of an amount only slightly
larger than the estimated error in H. This
verifies that the estimated errors given above

are consistent in these tests.

7. Points G, H, I, J, K, L—--There are two sources of
error in these points. First, there are the errors in
the linear measurements of the quantities used in
Appendix 11. Second, there is an error which arises
from the fact that the central angle has an uncertainty.
This uncertainty effects the equations 11.1 and 11.2.

a. Errors from linear measurements---Using standard
procedures for compounding errors in a functional
relation of several measured quantities (Be 62), the
uncertainties of the points on the hypotenuse were
found. The associated error for each point is

given in Table 111.1.

TABLE 111.1.-—Estimated standard errors for the primary
angles in reference I for the main arm due to errors in
the linear measurements.

 

Point Error

 

0.00140
0.00250
0.0020°
0.0030°
0.0025o
0.0017°

Ewen—4mm

 

224

b. Errors due to central angle--—

Equations 11.1 and 11.2 can be rewritten

B2 + H2 - A2

2BH

 

cos(a) =

But:

H2 = A2 + 32 - 2AB cos (90° + o)

 

2 o
cos(a) = 2B — 2A§BHOS (90 + O)
= g (1 - (A/B) cos (90° + ¢>>
cos(a) = g (l - (A/B) O) 111.1
sin(a) = % sin (90° + ¢)
= % cos ¢
sin(a) 2 g (1) 111.2

\

Using equations 111.1 and 111.2 in equation 11.3

B-X(B/H) (1 + (A/B) I)

COt(d) 1' f(A/H)

I2

cot(d) % ((H/X) -1) - o 111.3

225

The 8 in this case is 0.0047°.
The associated error for each point on the hypotenuse

is given in Table 111.2.

TABLE 111.2.--Estimated standard errors in the primary
points in reference 1 due to the error in the central, 90°

 

 

angle.
Point Error
G 0.0017°
H 0.0007°
1 0.0018°
J 0.0032°
K 0.0042°
L 0.0047°

 

C. Total errors—--The total error in these points is
the sum of 7(a,b). Table 111.3 shows the results using

angles relative to line OC.

TABLE 111.3.—-Total estimated standard errors in the primary
points in reference I.

 

 

Point Error
9.649° 0.002°
22.474° 0.003°
38.379° 0.003°
55.580° 0.004°
71.283° 0.005°

83.844° 0.005°

 

226

8. Points in quadrant BC, Figure 2.5-——The points in this
quadrant are the result of the 90° transfer of the
points in quadrant AC. The errors in these points are
the result of:

a. Errors in points G --- L, see Table 111.3.~
b. Alignment of TR #2 on the center point and the
point, J, on the hypotenuse (see Figure 2.6)
1). Center 0.010" at 25' 0.0020°
2). Point J 0.003" at 6' 0.00240
0. Alignment of cross hair in TR #2 with
l). Pointer 0.005" at 12' 0.0020°
2). Pointer image 0.020" at 58' 0.0020°
d. Placement of targets on the line of sight of TR #1
0.010" at 30' 0.0016°

Note: Center errors are included in 8a.

The total error in these secondary points is the sum of
8(a,b,c,d) and is shown in Table 111.5 where the angles are

relative to line OA.

TABLE III.5.--Tota1 estimated standard errors in the
secondary points in reference I.

 

Point Error
96.155 0.0049°
108.717 0.0054°
124.420 0.0054°
141.621 0.0060°
157.525 0.0067°
170.351 0.0067°

—-——

APPENDIX IV

EXPERIMENTAL DATA

1V.l Tabulated Angular Distributions
The following pages contain listings of the center-
of—mass differential cross sections and scattering angles

58 6ONi, 62Ni and 6“Ni. All of the excited states

for Ni,
which were observed in this experiment are presented here
along with the total relative standard errors (see
sections 4.1.d). All shown here is the systematic
experimental error which is associated with each distribu—
tion. The values of the cross sections are to be read as

1.60s + 03 a 1.60 x 103.

227

228

SENIIPIP'ISSNlfi EP-40.0 MEV
THE Esnsns Sheww ARE THE TOTAL RELATIVE EXPERIMENTAL assess.
THE SYSTEMATIC EXPERIMENTAL ERROR Is “4.5x

EX'00OOO HEV

ANGLE CH SIGMA CH ERRBR
(DEG) (MB/SR) (X)
17-20 1-6OE+03 0-43
1907“ 7076E+02 0034
24083 8032E+01 0071
29091 4030E*01 008“
34099 1022E+02 0035
“0006 1032E+02 0033
45013 7OSSE+01 0043
50019 2057E*01 0973
55024 1016E§01 1'08
60029 1043E+01 1012
65024 1052E+01 0067
70027 IOZOE+01 . 0076
85033 2046£+00 1074
90034 2052E+00 1'72

5X810456 MEV

ANGLE C“ SIGMA CH ERROR
(DEG) (HS/SR) (X)
17021 1037E+01 4079
19075 1°02F+01 3012
24.84 8011E+OO 2-3“
29092 4088E+co 2057
35000 2037E+00 2076
40007 1088E000 , 3007
45014 2052E+00 _3087
50020 2074E000 2043
55026 1096E000 2089
60031 8078E-01 4078
65025 4°79E'01 5'1“
70029 5051E-01 4077
85035 4047E-01 “009'

90036 20715-01 5053

_4—_:=Ih

 

 

229

saNIIP,PvIsaNI. :p-uo.o MEV
THE ERRORS SHOWN ARE THE Tam. RELATIVE EXPERIMENTAL Emacs.
THE SYSTEMATIC EXPERIMENTAL ERRBR 13 4.5%

EXI20458 HEV

ANGLE CH SIGMA CM ERROR
(DEG) (NB/SR) (X)
17021 1002E000 32030
19076 1015E000 13031
24084 90535-01 7083
29093 8027E-01 6070
35000 1001E+00 4078
40008 80365‘01 5008
45015 4075E001 6044
50021 2098E'01 8003
55027 1066E-01 11011
65026 1035E'01 9013
70030 1065E'01 7068
85036 60975.02 10037
90037 5044E-02 14034

EX'30035 “EV

ANGLE CM SIGWA CM ,ERRSR
(DEG) (HS/SR) (X)
17021 1023E+00 29024
19076 1021E*00 13071
24085 8001E-01 9015
29093 4045E-01 9074
35001 20005.01 15012
40008 10145-01 24014
45015 10395-01 16065
50022 10205-01 15050
55028 10312-01 13025
60033 10002-01 17068
65027 10115001 27071
70031 8076E'02 12096
85037 40345-02 18072
90038 20352-02 26067

230

58N[(P,P')SBNIO EP'4000 MEV
THE ERQORS SHOWN ARE THE TOTAL RELATIVE EXPERIMENTAL ERRORS.
THE SYSTEMATIC EXPERIMENTAL ERROR (S 405%

EX=30260 ”EV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
17021 2058E+00 15029
19076 1023E+00 12072
24085 1006E*00 7028
29093 50625-01 8057
35001 4019E~01 8073
40009 30285-01 9063
45016 3018E-01 9049
50022 30252-01 7077
55028 20772-01 .7092
60033 1061E-01 12077
65027 1027E-01 10002
70031 10085-01 28021
85038 1001E901 11006
90038 50115-02 15014

5X830610 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
17022 1062E+00 22097
19076 1028E+00 13048
24085 5080E'01 10073
29093 4009E-01 10003
35001 4005E'01 9054
40009 4036E-01 8057
45016 2077E-01 9079
50022 1076E'01 11010
55028 1047Ev01 11093
60034 1014E'01 16041
65028 1015E-01 10034
70032 10055¢01 11032
85038 20325'02 30077
90039 30078

2001E-02

231

58Nl(ppp')58NI' EP.uo.o MEV
THE ERPBRS SHOWN ARE THE TeTAL RELATIVE EXPERIMENTAL Ennens.
THE SYSTEMATIC EXPERIMENTAL ERRQR Is 0.5x

EXIB0895 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
17022 6074E'01 “3080
19076 4077E001 30087
2‘085 10725-01 28076
2909“ 10H4E'01 25052

.35002 80625-02 29039
40009 1075E-01 18049
“5016 1024E-01 1704“
50023 8098E-02 18056
55029 “098E-02 24032
6003“ “0025-02 33011
65028 10‘4E-02 “7007
70032 101OE'02 61025

EXl40100 ”EV

ANGLE CM SIGNA CM ERROR
(DEG) (MB/SR) (8)
17022 80762.01 45008
19076 10965-01 750Q3
2‘085 60335.02 63035
2909“ 8072E-02 33062
35002 10275-01 23034
“0009 10055-01 22028
45017 8095E-02 21027
50023 2099E'02 #4009
55029 50385'02 35000
6003“ 10795002 67080
65029 3076E-02 23000
70032 3031E-02 25000
85039 802kE-03 69082
90040 8020E-03 66018

232

SANTTP,P')58NI0 EP-uo.o wEv
THE EPQBRS SHOWN APE THE TOTAL RELATIVE EXPERTMENTAL [92529.
THE SYSTEMATIC EXPERIMENTAL ERRen IS 4.5x

EX0k0300 ”EV

ANGLE CH SIGMA CM 59903
(DEG) (MB/SR) (X)
19076 30752.01 35049
2“085 10‘3E'01 2603“
2909“ 8042E-02 42086
35002 107#E-01 16080
“0010 10b4E-01 19063
“5°17 5021E-02. 33033
50023 60806-02 2‘000
55029 10025.01 17011
60034 “029E902 37050
65029 h0H9E-02 20093
70033 30795-02 23060
85039 10205'02 37050

EXI40380 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) ‘ (X)
17022 70125-01 3“092
19076 7092E'01 18058
24085 60172-01 21085
2909“ 60375'01 13068
35002 6090E'O1 7086
40010 60225-01 8042
“5017 4061E'01 13062
50023 2093E'01 23072
55029 1051E'01 210“3
6003“ 90835.02 “7027
65029 1062E-01 11016
70033 1001E-01 19086

233

58NI(PIP')58NI* EP04000 MEV
THE ERRaRs,5HewM ARE THE TaTAL RELATIVE EXPERIMENTAL ERRORS-
THE SYSTEMATIC EXPERIMENTAL ERRaR Is 405%

EXI40472 ”EV

EXI40754 HEV

5022E-02

ANGLE CH SIGMA CM [8839
(DEG) (MB/SR) (X)
17022 40995+00 9023
19077 0.77E0oo 5030
24085 40982000 3094
29094 40072000 3033
35002 304OE+00 2049
40010 203IE+00, 2091
45017 1042EOOO 5045
50023 1011E000 6097
55029 1007E+00 ' 4063
60035 1014E+00 5019
65029 70672-01 3085
70033 60175‘01 5070
85039 30865.01 6080
90040 30135.01 7038

ANGLE CM SIGMA CM ERRaR
(DEG) (MB/SR) (X)
17022 2016E+00 17081
19077 2006E*00 11023
24086 10162400 7044
29094 10052+00. 6066
35002 90695.01 5017
40010 904SEP01 4094
45017 70415.01 5068
50024 ~4097E-01 6018
55030 2097E-01 7066
60035 2093E-01 9052
65029 20395-01 6083
70033 20052-01 7097
85040 6029E902 13068
90040 16029

 

 

 

 

 

234

SaNII°;P')58NI0 ER.uo.o MEv
THE ERReRs SHOAN APE THE TaTAL RELATIVE EXPERIMEHTAL ERReRs.

THE SYSTEMATIC EXPERIMENTAL ERRBR IS 405X

EX850128 MEV

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
17022 1056E+00 23046
19.77 7029E-01 25000
24086 4025E-01 15050
29094 4072E-01 19075
35003 40412-01 9055
40010 4057E-01' 7098
45018 4058E-01 7073
50024 0.24E-01 6090
55030 4001E'01 6061
60035 2097E-01 8098
65030 2088E-01 6007
70.30 2016E-01 7067
85040 8039E-02 11029
90041 70535-02 12087

EX'50430 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
17022 70505.01 52010
19077 50965-01 26075
24086 2029E-01 25025
29095 1'05E'01 34017
35003 2052E°01 13099
40011 3049E'01 12004
45018 2038E-01 13074
50025 20055-01 12034
55031 1092E-01 10054
60036 1089E-01 12073
65030 10055-01 13001
70034 1055E-01 10040
85041 40125.02 19016

235

58N1(p:P')58K10 EP04000 MEv
THE ERRaPs SHOWN ARE THE TeTAL RELATIVE EXPERIMEVTAL EQReRs.
THE SYSTEMATIC EXPERIMENTAL EPReR Is «05x

EX'S0589 ”EV

ANGLE CH SIGWA CM ERROR
(DEG) (MB/SR) (X)
17022 1014E+00 36015
19077 8055E001 21059
24086 60215.01 11032
29095 60315.01 9041
35003 5063E-01 8021
40011 5062E'01. 11096
45018 50025.01 7033
50025 3037E-01 8036
55031 2053E'01 8054
60036 10975.01 11099
65031 10435'01 9060
70034 1°06E-01 11040
85041 8084E-02 11018
90.41 5074E-02 1407s

EX85077C NEV

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
17022 1017E+00 36069
19077 50675-01 29086
24086 2004E-01 26084
29095 1'14E'01 31079
35003 1045E-01 23036
40011 1079E‘01 17062
45018 8028E-02 28058
50025 60125.02 29007
55031 8047E-02 19051
60036 10028.01 21026
65031 70545'02 16023
70035 60825.02 17035
85041 7049E-03 76020
90042 56067

1001E-02

236

saMTTP,Pv)58MI0 EP-4O0O MEv

THE ERRORS SHOWN ARE THE TOTAL RELATIVE EXPERIXENTAL ERRORS0

THE SYSTEMATIC EXPERIMENTAL ERROR IS 405X
EXI60080 MEV

ANGLE CM SIGMA CM ERROR

(DEG) (MB/SR) (X)
17023 1°08E+00 43016
19077 4034E-01 40074
24086 3067E-01 13032
29095 1077E-C1 24073
35003 10675-01 24055
40011 1012EF01- 32017
45019 10195-01 26033
50025 90115-02 25028
55031 1095E'01 11056
60037 1048E’01 16082
65031 1047E'01 11008
70035 1001E'01 13035
85042 2062E-02 22069
90042 1094E-02 34038

EX'60350 MEV

ANGLE CM SIGMA CM ERRBR

(DEG) (MB/SR) (X)
17023 20985'01 131035
19077 6030E'01 29002
24087 3014E-01 20066
29095 20225-01 21037
35004 1092E-01 23012
40012 20165'01 20080
45019 1024E'01 24063
50026 10055-01 20066
55032 8074E-02 20092
60037 30755.02 47086
65032 30285002 34069
70035 3038E-02 29051
85042 1095E002 34038
90043 2024E'02 30057

 

 

 

237

58NI(20P')58N10 EP-4O0O MEv
THE ERReRs SHowN ARE THE TeTAL RELATIVE EXPERIMEN7AL ERRORS0
THE SYSTEMATIC EXPERIMENTAL ERRaR Is 0.5x '

EX'60750 HEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
17023 60925.01 66019
19078 5053E-01 37079
24087 60425.01 13053
29096 5018E'01 12027

.35004 20615901 18006
40012 20915001. 17001
45019 10435-01 27076
50026 1017E'01 22055
55032 1027E-01 13032
60038 70152002 32020
65032 6070E'02 20074
70036 5017E'02 22075
85043 3074E-02 23016
90043 2024E-02 38074
EXI60890 MEV

ANGLE CM SIGMA CM ERReR
(DEG) (MB/SR) (X)
17023 1081E+00 34093
13078 1026E¢00 21083
24087 1043E+00 7065
29096 90025.01 7085
35004 7069E-01 8038
40012 4095E'01 '11077
45020 2096E001 1 017
50026 2024E-01 13083
55032 2094E001 9.82
60038 30295001 14013
65032 1085E'01 9035
70036 1066E001 9076
85043 80435.02 14080
90044 1003E-01 11049

238

SRNI(PIP')58NI. E984000 MEv
THE ERRORS SHBNN ARE THE TeTAL RELATIVE EXPERIMENTAL ERR8R30
THE SYSTEMATIC EXPERIMENTAL ERReR IS 405%

EXI70300 MEV

ANGLE CH SIGMA CH ERRGR
(DEG) (MB/SR) (X)
17023 3084E+00 20052
19078 2033E+00 15017
24087 1023E+00 9012
29096 1013E+OO 7064
35005 8046Eco1 8046
40013 5079E-01' 10058
45020 50025-01 10046
50027 4021E'01 9073
55033 3047E-01 9016
60038 20895.01 12083
65033 207OE'01 7091
70037 1078E-01 10018
85044 10325'01 10026
90044 9054E-02 11048

239

60N1(p09')60NI* EP-4000 MEV
THE ERRGRS SHOWN ARE THE TBTAL RELATIVE EXPERIMENTAL ERRORS0
THE SYSTEMATIC EXPERIMENTAL ERROR IS 505X

EX000000 MEV

ANGLE CM SIGMA CH ERRDQ
(DEG) (MB/SR) (X)
12092 3039E+03 1063
18001 1025E403 3003
23009 20502+02 19089
28017 2062E+01 17085
33024 1021E+02 0031
38031 1050E+02 0084
43038 1004E+02 6003
.48044 3094E+01 6006
53050 1016E+01. 0077
58055 1044E+01 0089
63059 1063E+01 0084
68063 1025E+01 0096
73066 705EE+CO 1.49
78068 30555+00 1088
83070 2042E+OO 2026
88070 2072E+00 2016

EX010332 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
12092 1049E+01 12076
18001 1032E+01 5067
23009 1000E+01 17096
28017 70715000 17084
33025 3056E000 3003
38032 20715400 6075
43039 20725000 9072
48045 3042E¢OO 6097
53051 2069E+00 1096
58056 10065000 3098
63061 60335.01 6026
68064 70225.01 5036
73067 1006E000 3097
78070 80992-01 3071
83071 6079E-01 4028
88072 40025?01 5064

240

60NI(p02')60NI* ERI4O0O MEV
THE ERRORS SHOWN ARE THE TBTAL RELATIVE EXPERIMENTAL ERR8R80
THE SYSTEMATIC EXPERIMENTAL ERROR IS 505%

5X820532 MEV

"ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
12093 2007E+00 32054
18001 1048E+OO 17024
23010 1015E000 20035
28018 1011E000 19038
33026 9020E'01 4077
38033 80365.01 14041
43040 70085001 10063
48047 3055E-01 12048
53052 2008E-01 6091
58057 1040E'01’ 25060
63062 10605'01 10078
68066 10225.01 ‘11093
73069 9049E'02 33033
78071 7054E-02 12080
83073 70355002 13002
88073 7040E002 16017

EX830119 MEV

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
12093 3069E-01 137080
18002 5009E-01 37032
23010 6029E-01 24035
28019 30685-01 23011
33026 3059E001 8087
38034 5003E-01 19080
43041 20522-01 18002
48047 1096E-01 18086
53053 1039E'01 8086
58058 ’9011E-02 15083
63063 60435.02 23074
68067 8080E'02 28095
73070 80495-02 14000
78072 50565'02 19049
83073 40482-02 21086
88074 1091E-02 40053

241

60NI(PIP')60N1' Ep'4000 MEV
THE LRQOPS SHOWN ARE THE TBTAL RELATIVE EXPERIMENTAL {895250
THE SYSTEMATIC EXPERIMENTAL ERRBR IS 505%

EXI30360 “EV

EX'30690 MEV

ANGLE CM SIGMA CM ERRfiR
(DEG) (MB/SR) (X)
12093 50905.01 104.56
18002 20645001 77043
23010 1039E'01 50021
28019 10‘95'01 38092
33027 1014E’O1 21053
38034 1011E'01 56082
43041 90238.02 36045
48047 60058.02 38037
53053 20288’02‘ 30060
58058 30415.02 30033
63063 30“4E'02 34000
68067 30715.02 28031
73070 3041E-02 37061
78072 P060E'02 31095
83074 1062E-02 “6'77
88075 1040E'02 49000

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
12093 10145000 67058
18002 1003E+00 23044
23011 4096E-01 26068
28019 4062E-01 22025
33027 3064E001 8099
38034 5003E001 19080
«3.01 3033E001 17002
48048 2081E-01 16049
53054 10805.01 7090
58059 1053E001 11084
63063 1084E-01 11016
68067 1036E-01 12070
73070 1032E-01 15002
78073 6006E002 19004
83074 3049E002 27021
88075 1091E002 41067

242
. 69N((P0P')6ONI0 EP04000 MEV
THE ERRORS SHOWN ARE THE TBTAL RELATIVE EXPERIMENTAL ERR6R50
THE SYSTEMATIC EXPERIMENTAL ERRQR 15 5.5%

EXQ40038 HEV '

ERROR

'ANGLE CM SIGMA CM
(DEG) (MB/SR) (X)
12093 3061E+OO 22095
18002 4092E+00 6024
23011 5003E+DO 17099
28019 50272000 17087
33027 3085E+00 1094
38035 30525000 5087
43042 1081E+00 8013
,48048 1048E+00 7088
.53054 1037E+00. 2034
58059 10305000 3014
63064 9074E-01 0 3075
68068 6068E'01 4058
73071 4098E-01 6025
78073 4052E001 6028
83075 30655-01 6041
88075 3017E-01 6073
EX'40310 MEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
12093 80485-01 79057
18002 40055001 50067
23011 4067E001 27016
28019 4011E-01 24085
33027 2045E-01 14005
38035 2021E-01 36091
43042 1065E-01 31'05
48048 1057E'01 26032
53054 ,7077E002 16038
58060 8027E-02 18082
63064 50645-02 24082
68068 60145-02 24025
73071 4033E-02 31073
78074 30775002 27034
83075 4023E002 25065
88076 2036E-02 43008

2u3
60NI(P:P')6ONI0 EP-4O00 MEV
THE ERPQPS SHOWN APE THE TaTAL RELATIVE EXPERTwEwTAL annens.
THE SYSTEMATIC EXpERIMENTAL ERROR 18 5.5%

Ex-s.1so nzv

ANGLE CM SIGMA C" ERROR
(DEG) (NB/SR) (X)
12094 10998000 53009
18003 20585+00 14046
23011 20998000 19066
28020 2033E+00 18070
33028 1092E+00 3048
38036 2050E+00 8044
43043 10718000 8057
.48049 1046E+00 8031
53055 80755-01- 3055
58060 70255-01 5023
63065 50938.01 5085
68069 40625-01 7023
73072 4004E001 8005
78074 2098E'01 8'14
83076 20618.01 8075
88077 10845'01 10049

EX85046O MEV

ANGLE CM SIGMA CM ERRBQ
(DEG) (MB/SR) (X)
12094 1°47E*00 48048
18003 80945-01 24017
23012 60685'01 24094
28020 60508.01 21089
33028 4066E-01 8021
38036 20915.01 34060
43043 20515-01 22042
48050 30098.01 15036
53056 20375'01 7080
58061 2038E-01 10028
63066 20015.01 11049
68070 10678'01 13073
.73073 1001E-01 17077
78075 1007E'01 15014
83077 5060E'02 21042

244
6OkI(°:P')60NII EPs4O0D MFV
THE anews ShewN AQF THE TeTAL RrLATIVE EXPER VEqTAL ERRaRS.
THE SYSTEMATIC EXPFPIMFNTAL EQRBR Is 505%

5X350700 MEV

AVGLV CV SIGqA CV E899?
(ECG) (NB/SR) (X)
12094 1084E+00 4C053
18003 1008E+CO 26019
23012 70225’01 24069
28020 30765-01 25055
33028 30195.01 10086
35036 30225-01 36044
43043 20328-01 27069
48050 1094E'01 21041
53056 1047E'01 11078
58061 10495-01 13080
63066 90145'02 20099
68070 7087E-02 22001
73073 50828-02' 26034
78075 3027E‘C2 34038
23077 2099E¢02 34038
88078 4091F-02 22086

245

52NITP,P')62NI0 EP0uo.o MEv
THE ERRaRs SHONN ARE THE TaTAL RELATIVE EXPEQI“EVTAL ERRBRS-
THE SYSTEMATIC EXPERIMENTAL ERRBR Is 805%

EX!00000 MEV

EX810169 MEV

ANGLE CM SIGqA CM ERROR
(DEG) (MB/SR) (X)
13002 60142003 17024
18010 10252003 0034
23018 10352002 2008
28025 3008E+01 1030
33033 10452402 0085
38040 10692002 0061
43046 7.885001 0025
48052 2082E+01 0077
53057 1019E+Cl 0099
58062 1074E+01 0067
63066 10872001 0065
68070 10305001 1002
73073 60155400 1045
78075 3025E+00 1075
83076 206IE+00 1062
88077 2083E+00 1058

ANGLE CM SIGMA CM ERRB?
(DEG) (MB/SR) (X)
13002 202IE+01 17083
18010 1057E+01 5043
23018 10015+C1 2036
28026 60782400 2006
33033 30132000 4077
38040 2027E+00 5090
43047 20922000 1044
48053 30612400 1062
53058 2031E000 2077
58063 10452+00 2079
63068 6069E-01 2075
68071 70975.01 3093
73074 10015400 3076
78076 9006E'01 3011
83078 50998-01 3047
88078 30552-01 4067

246
62Nl(902')62NI* E904000 “CV
THE ERRORS. SHOWN ARE THE TBTAL RELATIVE EXPEquEVTAL £2385th
THE SYSTEMATIC EXPERIMENTAL. ERROR IS 805X

EXI20334 HEV

ANGLE CH SIGMA C" 28808
(DEG) (MB/SR) (X)
13002 2035E+00 27053
18011 10192000 20079
23019 1014E+00 7049
28027 90996-01 5004
33034 8076E-01 9089
38041 50905'01 11097
43048 40822‘01 3095
48054 3000E'CI 5075
53060 20338'01. 9003
58065 10745.01 8056
63069 1090E'01 5042
68073 1071E'01 12078
73075 10022.01 14048
78078 80448.02 11034
83079 70225.02 11008
88080 60442-02 12001

EX=30168 MEV

ANGLF CH SIGMA CM ERRGR
(DEG) (MB/SR) (X)
13002 7067E'01 56090
18011 6031E'01 24075
23019 3065E'01 15047
28027 40142'01 9'30
33035 30392.01 17079
38042 20538.01 22078
43049 20118-01 7082
48055 1072E'01 8076
53060 80452002 15079
58066 8057E002 13060
63070 70035-02 14046
73077 4046E'02 25071
78079 30642.02 19079
88081 10342-02 39048

247

62~1TP,P'T62NT0 _ [904000 MEv
THE Ennons snow ARE THE TOTAL RELATIVE EXPERIMENTAL ERRoRs.
THE SYSTEMATIC EXPERIMENTAL ERRBR Ts 805%

Ex030270 MEv ’

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
13002 10725000 29087
18011 90328.01 17070
23019 7083E'01 8073
28027 80478'01 5086
33035 90188.01 10000
38042 80892001 9052
43049 40842001 4014
.48055 ' 30272'01 5092

.53061 1047E901- 11028
58066 1029EP01 9092
63070 1024E001 9003
73077 9044E-02 17057
78079 10028.01 10058
88081 . 50942.02 13038

EXs30750 MEV

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
13003 8030E+00 18032
18011 6096E+00 4089
23019 6007E+00 2049

' 28028 5048E000 2008
33035 40552000 3091
38042 3045E+00 “002
43049 10728000 1069
48055 10502000 2046
53061 10562000 2095‘
58066 10412400 2057
63071 1003E+00 2001
68074 70018.01 3037
73077 30218.01 8073
78080 40662001 4051
83081 4052E'01 4012
88082 30808.01 4054

248
6PNT(°:P'T62NI0 EP04000 MEv
THE ERRORS SHOWN ARE THE TeTAL RELATIVE EXPERIMENTAL ERRBRS0
THE SYSTEMATIC EXPERIMENTAL ERRBR IS 805%

EX'30990 “EV

ANQLE CM SIGMA CM ERRBR
(DES) (MB/SR) (X)
13003 8096E'01 56002
13011 70902'01 26073
23020 30232.01 22008
28028 2079E'01 15059
33035 20452'01 26081
38043 20218'01 30073
43049 1077E-01 8060
48056 10372'01 12050
53061 1037E'01‘ 14092
58066 1048E'01 11031
63071 90995-02 9050
68075 7069E'02 14082
73077 60385.02 20060
83081 2074E002 23031
88082 20545'02 22070

EX840148 MEV

ANGLE CM SIGMA CM ERReR
(DEG) (MB/SR) (X)
13003 40628-01 96028
18011 30762.01 53063
23020 3073E-01 18049
28028 30272'01 12026
33035 40218'01 18032
38043 5006E'01 15091
43050 4026E001 4044
48056 30062401 7009
53062 2088E001 8055
58067 10912.01 10006
63071 10192001 8015
68075 70892.02 15015
73078 60122-02 21°25
83082 4096E-02 15025
88082 3097E'02 16083

2249

ezuxcPoPtT62N10 EP-ao.o MEv

THE ERRORS swam ARE THE TeTAL RELATIVE EXPERIMENTAL ERRORS0

THE SYSTEMATIC EXPERIMENTAL ERReR Is 8.5: '
EX04064O MEV

ANGLE CM SIGMA CH ERROR
(DEG) (NB/SR) (X)
13003 1052E+00 37088
18012 1019E000 19069
23020 6010E-01 11027
28028 5077E-01 8014
33036 5000E'01 18060
38043 30442001 21078
43050 2018E-01 8007
.48056 2.64:001 8070
153062 20705.01- 9009
58067 203OE-01 9066
63072 10805001 6056
68075 1040E-01 10003
73078 1025E-01 12066
78081 I 7052E-02 14066
83082 8010E002 12015
88083 8026E-02 11081

Ex-4.980 MEV

ANGLE CM SIGMA CH 'ERRQR
(DEG) (MB/SR) (X)
13003 3033E+00 23068

‘ 18012 10342000 17040
23.20 9.14E001 8067
28028 8016E'01 7024
33036 6065E-01 14043
38043 6042E'01 14084
43050 3016E-01 6030'
48057 20932'01 7050
53062 2063E001 9068
58068 10825001 12038
63072 1030E'01 9032
68076 1004E'01 12091

T 73079 1005E-01 15099
78081 9070E-02 12019
83083 8072E-02 12045
88083 7091E-02 11037

 

250

62MI<P.P'I62NI. . EP0400O MEV
THE ERReRs SHOWN ARE THE TeTAL RELATIVE EXPERIMENTAL ERRORS.
THE SYSTEMATIC EXPERIMENTAL ERROR Is 0.5X ‘

EX050610 HEV

ANGLE CM SIGMA cM ERRaR
(DEG) (MB/SR) (X)
13003 2074E+00 25042
18012 1040E+00 17015
23021 8080E-01 10011
28029 9025E'01 6073
33037 60198901 19036
38044 70778.01 13084’
“3051 3044E901 6064
.48058 50268501 5075

*53063 30652.01‘ 9024
58069 20388001 10085
63073 2041E001 .6037
68077 10525.01 12003
73080 10632-01 13071
78082 . 10655-01 9086
83084 10462.01 9004
88085 8.12E0oa 13024

251
64NITP,P')64N10 ‘ EP04000 MEV
THEERRORS SHOWN ARE THE TOTAL RELATIVE EXPERIMENTAL ERRSRSO
THESYSTEHATIC EXPERIMENTAL ERROR IS 1505X
. EX'00000 MEV
ANGLE CM

EX010344 MEV

SIG"A CM ERROR
(DEG) (MB/SR) (X)
13001 4074E+03 9001
18009 10408403 9081
23016 1099E+02 18080
28024 70462401 18079
33031 10972002 1'58
38038 1098E¢02 0093
43044 10112402 0089
48050 3033E+01 0092
~53055 1073E¢01' 1036
58060 20332001 9000
63064 2017E+01 ~ 9000
68067 10292001 9000
73070 5053E+00 9011
78072 ~ 30992400 8055
83073 4007E+00 1051
88074 30975400 2006
93074 30212000 2033

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X)
13001 1073E+01 15021
18009 1039E+01 5086
23017 9047E+00 16069
28025 6067E000 16065
33032 20732400 10015
38039 20212400 8039
43045 2096E+00 3009
48051 30612000 2002
53056 2055E000 2087
5806 7066E001 5047
6306 4092E001 6053

‘ 68069 60402-01 5079
73071 6023E'01 5001
78073 9063E'01 3046
83075 60362001 3096
88075 3072E'01 5099
93076 2080E'01 6021

252

EP-4000 MEV
THE ERReRs SHOWN ARE THE TOTAL RELATIVE EXPERIMENTAL ERRBRS-

64NI(P:P')64NII

THE SYSTEMATIC EXPERIMENTAL ERROR 15 15.5%
‘ EX=20608 HEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (x)
13002 10385*00 57063
18010 1039E+00 20061
23018 ' 1009E¢00 18049
28025 9025E'01 17078
33033 7019E'01 17026
38040 1004E+00 14031
43046 40215.01 9064
048052 20665.01 7096
.53057 10945.01. 9088
58062 10275-01 13017
63066 10045.01 13020

‘ 68070 8057E'02 15086
73073 5053E-02 37050
78075 _ 6043E'Oa 16092
83076 5086E-02 14098
88077 4066E~02 20030
93077 60615.02 12080

EX330165 MEV

ANGLE CM SIGMA CM ERRBR
(DEG) (MB/SR) (X1

~ 13002 10565000 42031
13010 1018E+00' 22064
23018 5064E'01 22005
28026 6025E-01 18058
33033 50915‘01 17071
38040 5062E'01 22062-
43047 40275.01 9097
48053 30325.01 7066
53058 1031E-01 13027
58063 9092E'02 17031
63067 1011E'01 13035
73073 5023E~02 20058
88078 40195902 21086
93078 17015

3068E'02

6&NI(P,P')64NI0 ER-uo.o MEV
THE ERReRs_sHewN ARE THE TeTAL RELATIVE EXPERIMENTAL ERRsRs.
THE SYSTEMATIC EXPERIMENTAL ERRBR IS 15.5:

EXI30560 MEV

EXI30849 MEV

ANGLE CM SIGMA CH ERRBR
(DEG) (MB/SR) (X)
13002 1001E+01 10097
18010 9017E+00 4056
23018 9016E+00 16061
28026 8053E+00 16057
33033 50835400 9'01
38040 4035E+00 6001
43047 2052E+00 3013
.48053 20265000 2048
.53058 2032E+001 2043
58063 1056E¢00 2088
63067 1001E+00 3034
68071 6003E-01 5019
73074 4021E'01 9086
78076 6063EP01 4049
83078 6022E-01 “019
88078 $0415.01 5016
93078 30675901 6001

ANGLE CM SIGMA CM ERRQR
(DEG) (MB/SR) (X)

E 13002 ~1004E+00 87079
18010 1053E+00 17089
23018 7005E'01 20010
28026 70345'01 180380
33033 9038E'01 18006
38041 50985901 23066‘
43047 50605'01 8095
48053 4004EI01 8024
53059 30145.01 8060
58064 20045501 10°60
63068 10095.01 15027
68071 8014EIOE 21092
73074 60325'02 20002
78077 6033E¢02 20054
83078 5068E'02 18053
88079 40195'02 24022
93079 40225002 25064

254

64NI(P0P')64N10 EPI4000 HEV
THE ERRORS-SHOWN ARE THE TOTAL RELATIVE EXPERIMENTAL ERRORS0
THE SYSTEMATIC EXPERIMENTAL ERROR IS 15052

, Ex-u.aoo HEV

ANGLE CM SIGMA CM ERROR
(DEG) (MB/SR) (X)
13002 70785.01 112050
18010 5067EP01 40010
23019 4080E'01 23048
28026 3066E'01 23015
33034 20375.01 27063
38041 4054E'01 26084
43048 30445.01 14058
‘48054 3034E¢01 8086
53059 30148-01' 9014
58064 2008E901 11020
63069 1050E'01 12004
68072 10195.01 17032
73075 10075-01 14058
78077 1022E'01 13003
83079 70975-02 35063
88079 5018E'02 23051
93079 50045002 21044

255

IV.2 Plotted Angular Distributions

In the following pages are contained plots of the
experimental center-of-mass angular distributions for which
there exists no definite L-value. The initial plot in the
group for each target is a plot of the calculated distorted
wave distributions for each L—value from L = 2 to L = 6.

All of the plots appearing here as well as those
appearing in section 4.2.f are shown on the same scale which
allows a direct graphical comparison of the theoretical

and experimental data.

256

 

 

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260

 

 

 

 

 

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265

 

 

 

 

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268

IV.3 Tabulated Nuclear Deformations

 

All of the values of the nuclear deformations, BLRO
which were obtained from this experiment are tabulated

58Ni, 6ONi, 62Ni and 64Ni along with the L-value

here for
assigned to the corresponding excited state. The value of
RO used here was 1.16F x Al/3 where A is the atomic mass of
the target nucleus. Also presented is the X2/N which is
the result of the normalization of the theoretical

data to experimental results using the assigned L-value

shown

269

 

 

 

 

 

RC 1'

“301 6001
EX<MeV)a I e R xg/n Ex’MeV)a L s R 2

_ L o "“ L‘o XL/N

1.056 2 0 862 1 2.35 6.9 1.331 2 0.972 1 3.3% 7.0
2.058 0 0.391 + 2.5; 10.7 2.502 0 0.018 1 3.7% 13.0
3.035 2 0 260 1 3.1C 8.2 3.119 2 0.250 1 0.5% 0.1
3.260 2 0.332 1 2.85 5.8 3.36 2 0.150 1 8.7% 3.8
3.620 0 0.305 1 2.9: 6.0 3.36 3 0.163 1.2
3.895 2 0.171 1 5.1% 2.9 3.30 0 0.173 3.8
0.11 2 0.100 1 6.1% 0.0 3.69 2 0.295 t 0 25 8.0
0.11 3 0.108 2.5 3.69 3 0.313 8.6
0.11 0 0.153 1.1 3.69 0 0.327 5.0
0.30 2 0.166 1 0.0% 5.7 0.002 3 0 22 1 3.2% 18.5
0.30 3 0.166 2.3 0. 2 2 0 223 1 5.6. 2.8
0.30 0 0.171 2.5 0.32 3 0 236 3.3
0.38 0 0.306 1 3.05 3.0 0.33 0 0 205 2.3
0.072 3 0.763 1 2.3: 13.0 5.10 3 0 605 t 3 2; 19.0
0.750 0 0.050 1 2.55 9.0 5.10 0 0 677 19.2
5.128 6 0.031 1 2. z 9.0 5.10 5 0 736 19.1
5.03 3 0.265 1 3.3% 16.8 5.05 2 0 309 1 0 1% 7.1
5.03 0 0.270 12.8 5.05 3 0.327 3.7
5-03 5 0.301 8.0 5.05 0 0 301 6.0
5.589 0 0.355 t 2.8% 9.2 5.7 2 0 272 t 0 9% 0.0
5.77 2 0.193 1 0.0% 7.6 5.7 3 0 286 0.0
5.77 3 0.198 3.9 5.7 0 0 300 6.0
5.77 0 0.207 3.9
6.08 2 0.225 1 3 9" 9.3
6.08 3 0.229 5.3
6.35 2 0.198 t 0 o 1.7
6.35 3 0.202 2.0
6.35 0 0.211 2.8
6.75 3 0.251 1 3.9% 2.3
6.75 0 0.260 0.6
6.89 3 0.382 1 2.9% 3.3
6.89 0 0.000 10.3
7.3 3 0.031 1 2.8% 5.1
7.3 0 0.009 15.0

1 .

b‘ui o“Ni

1.169 2 0.901 1 0.0% 38.3 1.300 2 0.809 1 7.9% 27.8
2.330 0 0.381 1 0. g 11.3 2.608 0 0.308 1 8.3% 21.2
3.168 2 0.220 1 5.2% 6.0 3.165 2 0.270 1 8. % 8.0
3.168 3 0.230 7.8 3.560 3 0.900 1 7.9% 67.2
3.168 0 0.203 2.6 3.809 5 0.367 1 8.3 15.1
3.270 2 0.326 1 0.6% 28.2 0.60 3 0.270 1 8. 5 5.6
3.270 3 0.300 03.9 0.60 0 0.288 6.7
3.270 0 0.363 15.0 0.60 5 0.311 2.3
3.750 3 0.826 1 0.3% 32.9 0.80 2 0.251 1 8 7% 3.0
3.99 3 0.230 1 5.5% . 3.3 0.80 3 0.260 2.2
3.99 0 0.208 0.0 0.80 0 0.270 0.9
3.99 5 0.266 12.3 5.0 2 0.251 1 8.6% 0.0
0.108 3 0.275 1 5.0% 19.0 5.0 3 0.260 5.5
1.108 0 0.289 13.3 5.0 0 0.278 7.9
0.108 5 0.312 2.9 5.0 5 0.297 7.0
0.60 2 0.298 1 0.8% 23.0 5.8 2 0.325 1 8.2% 5.3
0.60 3 0.312 7.0 5.8 3 0.339 10.8
0.60 0 0.326 16.0 5.8 0 0.362 23.6
0.98 2 0.331 1 0.7% 17.0 5.8 5 0.385 15.0
0.98 3 0.309 10.9
0.98 0 0.367 22.9
5.61 3 0.381 1 0.6% 13.1 .
5.61 0 0.399 22.5
5.61 5 0.032 35.2

 

aThese are the excitation

energies assigned to the excited states observed

in this experiment (section 0.1.f).

270

IV.0 Tabulation of Quantities
Calculated from the Nuclear
Deformations in IV.3 Above

 

 

 

In the following pages are tabulated the values of
parameters calculated from the nuclear deformations. The
BL given here is normalized to an interaction radius of
1.25F x Al/3. There are radial moments, <rA> section
0.2.b, which must be evaluated in these calculations and
the model used is shown for each set of parameters.

There are three models represented below: a uniform
charge distribution with r0 = 1.20F, a Fermi equivalent
uniform charge distribution with r0 = l.3lF (E1 61),
and a Fermi charge distribution with r0 = l.lOF and

a = 0.566F (Du 67).

271.

 

 

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Ba

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62

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66

67

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