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Proton Induced Reactions on N and O
and the Creation of Elements Lithium, Beryllium
and Boron

presented by

Helmut Wolfram Laumer

has been accepted towards fulfillment
of the requirements for

Ph.D. Physics

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ABSTRACT

PROTON INDUCED REACTIONS ON l4N AND 160 AND

THE CREATION OF ELEMENTS LITHIUM, BERYLLIUM AND BORON

by

Helmut Wolfram Laumer

Measurements of cross-sections for production of masses
6 to 11 by proton spallation of 14N and 160 have been carried
out. The proton energy range covered was 17 MeV to 42 MeV.

These cross-sections are indispensable in attacking
an unsolved astrOphysical problem, the origin of the light
elements Li, Be and B. A number of theories have been proposed,
and proton spallation of C, N and O is found to play a
dominant role in several of them.

Two methods were employed in the cross-section measure-
ments. For the main body of data collected particle identifi-
cation was accomplished with a time-of-flight technique based
on the narrow proton burst width of the M.S.U. Cyclotron.

The particle energy measured with a silicon surface barrier
detector and the particle flight time from target to detector
yielded mass identification of spallation products. Angular
distributions were collected and an integration over angle
determined total cross-sections. For these measurements

gas targets were used, contained in a specially designed

gas cell with an exit beam window areal density in the range

50 ug/cm2 to 130 ug/cmz. As a check on the time-of-flight

ll

. 7 .
technique we measured Be and C cross-sections for proton

14N at 21.7 MeV using radioactivation followed

spallation of
by y-ray detection. Gas targets in a gas cell designed for
y-ray counting with the Ge(Li) detector were used. Good
agreement was obtained for the cross-sections measured by
the two methods.

A specific model for Li, Be, B production, proton
spallation in the surfaces of stars, based on a theory by
Bernas, is tested using the newly acquired cross-sections.
A proton spectrum of the form E-Y, based on solar flares,

14

is considered. It is found that N proton spallation is

a large contributor to light element production in spite

of the low 14N abundance compared to 12C and 160. To produce
the ratio 113/103 % 4 as observed in the earth and in meteorites
a value of y low compared to that of proton spectra measured

for solar flares is required. The ratio 7Li/6Li = 12.5 as
observed for earth and meteorites, on the other hand, can

be produced only by proton spectra with improbably high

values of y. A depletion mechanism for 6Li or alternate

production mechanisms for 7Li are the more likely explanations

for this ratio.

PROTON INDUCED REACTIONS ON l4N AND 160 AND

THE CREATION OF ELEMENTS LITHIUM, BERYLLIUM AND BORON

by

Helmut WOlfram Laumer

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics

1971

ACKNOWLEDGMENTS

I would like to thank my thesis advisor, Dr. Sam
M. Austin for his guidance during the period of this
experiment. I would like to thank Dr. Cary N. Davids
for convincing me of the importance of this experiment
and for introducing me to the intricacies of the
experimental technique.

In constructing the apparatus required for the
experiment I found Mr. Norval Mercer a most helpful
teacher and master of his trade.

I would like to thank Mr. Lolo M. Panggabean for
the many days spent in assisting in data collection,
and Mr. Stan H. Fox and Mr. Duane Larson for acting
as seconds when called upon.

Dr. Ron Goles, Dr. Richard Todd and Mr. Larry
Samuelson generously provided the help I needed to
do the y-ray counting.

The assistance of the Cyclotron technical staff
in the running of the Cyclotron is gratefully
acknowledged.

I would also like to thank the National Science
Foundation and Michigan State University for their

support during the experiment.

ii

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

Chapter
1.,

INTRODUCTION

1.1 Nucleosynthesis in Stars

1.2 Need for Cross-Section Measurements
1.3 Difficulty of Measurements

1.4 Time-of-Flight Technique
EXPERIMENTAL EQUIPMENT AND TECHNIQUES FOR

TIME-OF-FLIGHT MEASUREMENTS

2.1
2.2

2.3

2.6

The M.S.U. Cyclotron Facility

Target Choice

Gas Cell Design

2.3.1 Introduction

2.3.2 Slit System Design

2.3.3 The Shell, Collimation Slit and
Formvar Window Support

2.3.4 Gas Cell Construction

Formvar Windows

Pressure Measurement

2.5.1 Equipment

2.5.2 Beam Heating

Beam Integration

iii

Page

b P‘ F‘

11
11
11
12

14
18
19
21
21
21

23

2.7

2.8
2.9
DATA

3.1

DATA

4.1

4.2

Particle Detectors

2.7.1 Spallation Product Detection
2.7.2 Proton Elastic Peak Monitor
Time-of-Flight Electronics

The 17 MeV Measurement

ACQUISITION

On Line Setting Up Procedure For Data
Taking

3.1.1 Introduction

3.1.2 Software

Data Taking

Dead Time Correction

Mass Band Resolution

REDUCTION

Energy Spectra and Low Energy Cutoff
Correction

Time-of-Flight Cross-Section Calculation

RADIOACTIVATION AND DECAY MEASUREMENTS

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9

Introduction

Cell Construction

Irradiation Technique

Counting Method for 7Be and 11C Decays
Data Reduction

Cross-Section Calculations for 11C
Cross-Section Calculations for 7Be
Error Analysis

Cross-Section Comparison

iv

Page

23
23
24
26
31
34

34
34
34
37
39
39
43

43

75
133
133
133
136
136
139
141
144
146
146

6. REVIEW OF PAPERS ON ASTROPHYSICAL THEORIES
OF LiBeB PRODUCTION
6.1 Introduction
6.2 Early Theories of Nucleosynthesis of
LiBeB
6.3 Current Theories of Nucleosynthesis
of LiBeB
7. IMPACT OF NEW CROSS-SECTIONS
7.1 Introduction
7.2 Isotopic Ratio Calculations
7.3 Energy Requirement of (BGRS 67) Model
7.4 Observations
APPENDIX A Ions Traversing Kapton
APPENDIX B Slit System Design Calculations
APPENDIX C Formvar Film Thickness Measurement
APPENDIX D Gas Heating Model
APPENDIX E Calculations for Beam Degrader
APPENDIX F Band Resolution Calculations
APPENDIX G Time-of-Flight Cross-Section Integration
Related Formulas
APPENDIX H Set Up Procedure

BIBLIOGRAPHY

Page

149
149

149

158
167
167
167
181
182
184
186
189
191
195
197

200
202
204

10.

11.

12.

13.

14.
15.

LIST OF TABLES

Beam Heating Comparison Data
Electronics Module Identification
Individual Contributions to A(Et2) in Terms

of Percentage of Et2

Band Resolution of Spallation Data from 14N
by a 41.9 MeV Proton Beam

Validity of Stopping Power Equation

Energy Cutoff Limits

Error Contributions Not Associated With
Particle Detection

Individual Cross-Section Calculations for
14N and 16O Targets

Summary of Measured Cross-Sections For

14 16

Proton Spallation of N and 0

Summary of Cross-Sections For Proton

12c (DLA 70)

Spallation of
Error Contributions to the Radioactivation-
Decay Measurements

11C and 7Be Cross-Section Measurement
Comparison

Abundances of Interest in LiBeB Production
Compilation of Other Spallation Data Used
Isot0pic and Elemental Spallation Production
Ratios From a Target Mixture C:N:O (3:1:5)
by Proton Spectra E-Y

vi

Page

22
28

41

42

73

74

79

80

113

114

147

148

150
169

180

Table Page

16. Proton Energy Loss in Kapton 184

vii

Figures

1.

8.

9.

10.

11.

12.

13.

14.

LIST OF FIGURES

Curve of Relative Abundances from (BBFH 57)
Based on Suess and Urey

Schematic Drawing of the Beam Transport
and Analyzing System

Schematic Drawing of a Gas Cell and its
Slit System

Gas Cell Design

Schematic Drawing Showing Slit System —-
Table Center Geometry

Monitor Electronics Block Diagram
Electronics Block Diagram for Charged
Particle Time-of-Flight

Start, StOp and TAC Pulses

Stop Pulse Timing Adjustment

Mass Band Displays

Selected Energy Spectra from Proton Spallation

14 16

of N and O Targets

Angular Distributions for Masses 6 to 11

14 16

from Proton Spallation of N and O

Cross-Sections for Masses 6, 7, 10, 11 from

Proton Spallation of Targets 14N and 16

O in
the Energy Range Ep = 17 to 42 MeV
Partial Assemny Drawing of Gas Cell for

Activation and y-Ray Counting

viii

Page

10

13

15

17

25

27

30

35

36

44

115

132

134

Figure

15.
16.

17.

18.

19.

20.

21.

22.

23.

y-Ray Counting Electronics Block Diagram
Data Points of 0.511y Decay Curves for
Nitrogen and Helium Filled Gas Cells and
the Curve ReSulting from Taking Their
Difference

Sample Fits to the 0.511 7 Difference
Decay Curve

Total Cross-Sections as a Function of
Proton Energy for Spallation Products

Mass 6 to Mass 11 from Targets 12C,

14N and 16O

The Net Contribution from the Targets
C:N:O (3:1:5) to the Yield of Masses 6,
7, 9, 10 and 11 by Proton Spectra of the

Form E
Isot0pic Spallation Ratios as a Function
of Proton Spectra

Geometry of Slit System with Beam at

90°

Approximate Range of Path Length
Difference

Range of Flight-Distance for 90% of

Particles Reaching the Detector

ix

Page

137

140

142

171

178

179

186

187

198

1. INTRODUCTION

1.1 Nucleosynthesis in Stars

One of the more spectacular successes of nuclear astro-
physics is the explanation (CL68) of many of the features of
the natural abundance curve of the elements. The correlation
of nuclear properties of heavier elements with the observed
abundances is so striking that the mechanisms for their
production are quite well established. Figure 1 shows a
relative abundance curve with regions labeled by their
dominant production mechanisms in stars. During the lifetime
of a star the fusion reactions in its interior fuse nuclei
in an ascending sequence of mass. Hydrogen-burning converts

hydrogen into 4He, and if 12C and 16O are present these are

14

converted largely to N if the star's mass is large enough.

Once the hydrogen fuel is exhausted the star contracts until

the temperature at the center is high enough to overcome the

coulomb barrier of 4He + 4He, and the helium burning process

begins. The major products are 12C and 16O, with 20Ne and

24Mg also perhaps possible (IE 66, TU 71). Once 4He is also

exhausted 12C + 12C and later 160 + 16O are expected to

react, to form nuclei up to 32$. The temperature necessary
to burn the next most likely fuel, 24Mg, is so high that
(y,p), (an) and (Y’a) reactions become dominant before it

is ever reached. These reactions convert the products

1

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Figure 1. Curve of Relative Abundances From (BBFH 57) Based

on Suess and Urey.

from the last burning stage, A near 28, to the more stable
nuclei with A near 56. This last process is called silicon
burning or photodisintegration rearrangement. Recent
calculations (AC 70) show that explosive carbon, oxygen
and silicon burning can give good agreement with observed
abundances in the range 20§A§62. At temperatures higher
than necessary for silicon burning,the photodisintegration
and net production of iron group nuclei becomes balanced.
This is called the equilibrium or e process. The elements
heavier than those of the iron peak are more abundant than
expected from these processes. The mechanism for their
production is neutron capture. Two processes, r (rapid)
and 5 (slow), are postulated. In the 5 process there is
time for B decay after (n,y) reactions have produced a B-
unstable nucleus; a neutron capture chain climbing the
valley of stability of the nucleidic chart is the result.
In the r process fast neutron captures produce a highly 8-
unstable, neutron rich nucleus near the neutron drip line.
Subsequent B— decay then leads to the resulting stable
nucleus. There are some proton rich heavy isotopes which
cannot conceivably be produced by the r or 3 process.
Their abundances are considerably lower than those of
isotopes accessible by the r or s process. Presumably
(p,y) and (y,n) reactions on nuclei synthesized by the

r or 3 process can account for the abundances. In Figure 1

the abundance of Li, Be, and B is seen to be anomalously

low compared to their neighbors. In the nuclear burning
processes in stars described above, they are largely by-
passed. They are also very fragile so if present or

produced during hydrogen burning,(p,d) reactions quickly
destroy them (BGRS 67). For example 7Li can be produced

in hydrogen burning by the reaction chain:

H + 1H + 2H + e+ + v

H + 1H + 3He + y

He + 3He + 4He + 1H + 1H

He + 4He + 7Be + y

7

\IMWNH

Be + e- + Li‘+ v

only to be destroyed by 7Li + 1H + 4He + 4He. As a result

even the low abundance of Li, Be and B becomes difficult to
explain. Spallation reactions on the more plentiful nuclei
are the suggested (FBB 55) mechanisms for their production.
In the case of 7Li cosmological production is also a possibil-
ity (WFH 67).
1.2 Need for Cross Section Measurements

Since 12C, 14N, and 16O are the most abundant of the
nuclei heavier than Li, proton induced spallation of these
targets is the process most likely involved in forming the
light elements Li, Be and B (FEB 55). The reaction cross-
sections for these targets are thus of great interest.

12

While data for C exist at most energies (DLA 70, AER 67),

16

only a few cross-section measurements for 0 above 100 MeV

proton energy are available, and there was little data on

14 11

N until the recent C and 7Be cross-section measurements
by M. Epherre and C. Seide (ES 71) . The threshold region
for light element production cross-sections is of special
interest for several reasons. Theoretical calculations
are most unreliable for this region,hence predictions
valid at higher energies are of marginal value here. Proton
spectra encountered in nature (FW 63) usually vary as a
negative power of the energy, hence there are considerably
more protons available for reactions at lower energies
where in addition the cross-sections are also often larger
than at high energies. Due to differences in threshold
energies for their production, the formation ratios of
isotopes vary most drastically in the threshold region; in
view of the proton spectrum cited above, relative abundance
calculations will be sensitive to these cross-sections.
1.3 Difficulty of Measurements

The sparse cross-section data for Li, Be, and B production
is not due to lack of interest on the part of experimenters,
but is the result of extreme experimental difficulty encountered.
The most straightforward technique used in the past is radio-
activation analysis. This is limited to radioactive products
however and thus cannot yield all the cross-sections of interest.
Mass spectrometry has also been employed in some measurements,
but this technique is beset by difficulties such as sample
contamination and variable sensitivity to isotOpes; hence,
it is very time consuming (see for example (YI 68)). Attempts

have also been made (JU 70) to use emulsions; but contributions

to cross-sections from break up which leads to more than
one free neutron could not be measured. The data collected
also suffered from poor statistics.
1.4 Time of Flight Technique

The method used in my measurements is the time-of-flight
technique reported in (DLA 70), as modified for application
to gas cells. A collimation system limits the volume from
which particles may reach an energy sensitive particle
detector. By choosing a flight path which is long compared
to the dimensions of this gas volume, particles can be
assigned a flight time which in conjunction with the energy

measurement determines the particle mass:

LT]
ll

particle energy

t = flight time

D = path length
E = mv2/2 = m (%)2/2
2
hence m = EEE— .
D

Angular distributions are obtained by integrating spectra
over energy for each particular mass. An integration of
a distribution over angle then yields the total cross-section
for the mass.

It may seem that particle mass identification is in-

sufficient since 11B and 11

C, for example, cannot be distin-
guished. For the astrOphysical application however the
information is quite complete since only one isobar per mass

number is stable in the region GiAill. All other isobars

of the same A detected in our experiment decay to it on

astrophysical time scales with two minor exceptions. The

9 14

C production threshold from N is at a proton energy

of 39 MeV. Since 9C(B+) 9B+p(2a) this does not lead to

9 16

Be. The production threshold of 9C from O is at 50 MeV

proton energy, hence it cannot be produced in our access-

ible energy range. Although 10Be does decay to 108, its

10

half-life is 2.7 x 106 years; fortunately Be production

is low at least at the high proton energies measured (YBDFGB 68,

o.3:o.2 mb for 135 MeV protons on 16

14

O). The threshold for

160 it is 36 MeV.

its production from N is 34 MeV, from
The time of flight technique does have the weakness that
it fails for very low energy products. Since at 22 MeV

proton energy 7Be and 11C are the only isot0pes of A=7

14N, I performed a

and A=ll produced from spallation of
cross-section measurement based on their radioactive decay
to check the time of flight technique; this is presented in
chapter 5.

The MSU Cyclotron is particularly suited to make measure-
ments with proton energies from 22 MeV to above 40 MeV.
In this range the beam intensity needed (2500 n amp), and
narrow pulse width (0.2 n sec has been achieved) of beam
bursts essential for the success of the time of flight
technique can be routinely obtained. This energy range is

also important for relevant theories of nucleosynthesis

of LiBeB as pointed out above.

The experimental equipment used in the time of flight
measurements is discussed in chapter 2. Chapters 3 and 4
treat data acquisition and reduction respectively. Chapter 5
contains theradioactivation-decay measurements and chapter 6
presents the major developments in astrophysical theories
on the production of LiBeB. Conclusions and calculations
based on the newly acquired cross-sections and pertinent

to these theories are presented in chapter 7.

2. EXPERIMENTAL EQUIPMENT AND TECHNIQUES FOR TIME-OF-FLIGHT

MEASUREMENTS

2.1 The M.S.U. Cyclotron Facility

The proton beam of the MSU cyclotron was used for all
experiments. The time-of-flight technique depends most of
all on the narrow beam burst width that can be achieved
with this cyclotron. Widths as low as 0.2 nsec FWHM have
been measured. The widths during our experiment have usually
varied from 0.3 nsec to 0.5 nsec. The spacing between beam
bursts depends on the frequency of the cyclotron RF and is
therefore beam energy dependent. This spacing is 53 nsec
at 42 MeV and 72 nsec at 22 MeV. As explained below (Appendix
F) this spacing limits particle detection at low particle
energy.

A schematic drawing of the beam transport and analyzing
system is shown in Figure 2. The time-of-flight measurements
were done in the large scattering chamber shown. Lately.
this is a 40 in. diameter chamber; in the early parts of the
experiment a 35 in. diameter chamber was in its place.

The irradiations for y-ray counting were done in the small
scattering chamber associated with the Enge split-pole-
spectrograph because it allows faster access. 8

On-target-beam—spots were 0.030" to 0.050" wide by
less than 0.1" high and beam currects from 300 to 800 namp
were routinely obtained. Usually 3 to 4 uamps were extracted
with 100% efficiency from the cyclotron under these conditions

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with beam loss occurring at the various slits in the analysis
system.
2.2 Target Choice

At room temperature N and O are gases, so if a solid
target is wanted one must select some compound which contains
the desired target elements as a constituent. The contribu-
tion to the observed yield due to the other elements in the
compound must be determined however. The use of gas targets
appears advantageous in this respect. They are also desirable
for other reasons. Target thickness measurements for solid
targets in the 100 ug/cm2 range are not easily performed to
an accuracy of better than 10%. For gas targets a pressure
measurement need only be made. Here 1% accuracy can be easily
achieved in the range 0.1 to l atmospheres. Target stability
under bombardment is also no problem for N and 0 gas. There
are also some disadvantages encountered in using gas targets.
The gas cell design described below minimizes them so the
experiment could be carried out successfully.
2.3 Gas Cell Design
2.3.1 Introduction

All gas cells must have a thin foil or "window" which
confines the gas and through which the beam enters and
reaction products leave to be detected outside the cell.
The foil is hence chosen as thin as possible subject to
the limitation that it must withstand the required gas

pressure and stand up to the irradiating beam. A common

12

foil used for gas cells is Kaptonl available in 0.00025",
0.0005", or 0.001" thicknesses. For the relatively heavy,
low energy reaction products which are to be detected in

14N and 16

spallation of 0, this still implies a large and
unacceptable energy loss (see Appendix A). While a specially
thin window must be used for these products, in our case
it is a 30 ug/cm2 formvar film, Kapton is quite acceptable
as proton beam window; the energy loss for a 22.0 MeV proton
traversing a 1/2 mil foil is only 0.040 MeV.
2.3.2 ASlit System Designv

When measuring yields with solid (foil) targets, the
volume from which reaction products originate is usually
well defined. One need only use one aperture in front of
the detector to fix the solid angle for particle acceptance.
In gas cells reaction products can originate anywhere along
the line segment joining the point of entrance and the point
of exit of the bombarding beam. Since the nuclear debris
from the gas cell wall is not what one wants to measure,
an additional slit is needed to limit the volume from which
particles may reach the detector.

For the time-of-flight technique the slit system must
be carefully designed. In Figure 3 the acceptance angle
determined by slits 1 and 2 is shown. The beam intersects

the rays of angle 8 at points Al and A2. Reaction products

falling on the detector may originate from any point on

 

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the line segment AlA2. This means that there is a range

of flight distances. This manifests itself in terms of

an uncertainty in the flight time of reaction products.

In Appendix B the calculations relating the slit geometry

to counting rate and flight time resolution are presented.

The conclusions one can draw are that 82 should be as close

to the origin of reaction products as possible. The width

of 82 and the width of the beam are then equally critical

as far as flight time resolution is concerned. Making 82

smaller than the width of the beam would gain little for

flight time resolution but would lower the yield, an obvious

disadvantage. The size of $1 is not as critical and is

mainly determined by the active area of the detector. 81

represents the horizontal extent of the aperture in front

of the detector. The vertical dimension of this aperture

has even less effect on differences in flight path length.

The dimensions of the aperture used were .125" wide x

.25" high.

2.3.3 The Shell, Collimation Slit and Formvar Window Support
The above considerations led to the gas cell design

shown in Figure 4. The important element is a cylindrical

shell sliding in a keyway in the cell. The end of the shell

closest to the beam acts as defining slit 82. It also

supports a formvar film which acts as the cell exit window

for the spallation products. Since 32 must be fixed with

respect to the detector, and since 82 is rigidly secured

to the gas cell, the slit, cell, and detector must rotate

together when the detection angle is to be changed.

 

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The shell is milled in two parts which are then sweat-
soldered together. The curved surfaces are milled last,
after which the shell is polished. The lips at 82 are
rounded by buffing. This ensures that the stresses causing
rupture of the formvar window under pressure are better
distributed. The slit end of the shell is also tapered so
it can be moved as close to the beam as possible.

Reaction products lose energy not only in the formvar
window but also in the gas they must traverse. Depending
on the detection angle the shell is positioned to minimize
this distance. At 1/10 atmosphere the density of N2 is
125 ug/cm3. It would seem desirable to work with low gas
pressures to minimize energy loss; however the yield and
hence the time needed to perform the experiment is directly
proportional to the gas pressure. Also background events,
are largely independent of gas pressure; this implies a
minimum pressure for a successful experiment. For a
nitrogen pressure of 25 torr and a 30 ug/cm2 formvar exit
window we can obtain an average total exit areal density
of 50 ug/cm2 at 90° and 130 ug/cm2 at 15° detection angle.

In order to avoid repeated mechanical adjustments of
the shell, but to still minimize energy loss in the gas ,
we simply mounted the gas cell and slit system slightly
off center on the scattering chamber table. As shown in
Figure 5 table rotations between 15° (or 165°) and 90°

can be carried out with one shell setting. The distance

between the beam and the closest point of the shell is

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18

about constant and as a result practically minimum in-gas
flight distance is achieved at all angles in this range.
The vertical extension of $2 is 0.750". Since the
detector aperture is 0.250" high and the beam was always
less than 0.1" high, this represents a big margin of safety
for vertical alignment. The variation of the beam height
with respect to the cell center was always less then i3/32"
as seen by beam spot burns on the Kapton window.
The horizontal dimension of the shell was chosen to
be 7/16" so 82 widths up to 1/4" could be accommodated.
2.3.4 Gas Cell Construction
The gas cell structure is made of brass. Two 5" disks
were silver soldered to a spacer which had been milled with
a keyway for receiving the shell. The spacer subtends 60°
from the center of the cell. After silver soldering, the
cell diameter was turned down to 4.75". A chamfer was
then milled at the mouth of the keyway. This forms one
surface of an O-ring vacuum seal; the other is the side
of the sliding shell. The pressure needed for the seal
is exerted with a clamp screwed to the body of the cell.
The geometry of the shell and the vacuum seal determine
the minimum detection angle. This is the reason for the
non-circular design of the shell. A tube of 1.125" diameter
in a gas cell of the same diameter would allow a minimum
detection angle near 20°, while for the actual design it

is 10°.

19

A 0.25" Imperial Eastman vacuum fitting soldered into
the top disk of the cell serves the double function of
evacuation outlet and gas inlet. Kapton foil 0.0005"
thick was bonded to the gas cell using the epoxy Ciba
Araldite 502. The brass surface was prepared by light
sanding or filing just prior to the epoxy application.

At pressures up to 50 torr and beam currents up to 800

nano-amps the Kapton held up indefinitely.

2.4 Formvar Windows

Formvar (H1608C4)1 is available in powder form. To
cast formvar film a 2% solution by weight of formvar in
l, 2 Dichloroethane is prepared. A 6" diameter glass
beaker is filled with distilled water (care must be taken
that no soap residue is in the beaker, since the surface
tension of the water would be reduced). A 14 B.S. gauge
wire is dipped into the formvar solution and a line is
drawn with the wire tip across the water surface. A thin
layer of solution spreads on the water and within a few
seconds the l, 2 Dichloroethane evaporates, leaving a
formvar film.

This film is lifted from the water with a square wire
loop. The plane of the loop is held perpendicular to the
water surface during the lifting process. A double layer
of formvar clings to the loop and is transferred immediately

to the slit end of the shell by passing the shell through

 

1Available from Shawinigan Resins Corporation, Springfield 1,

Mass .

20

the wire loop. This process is repeated until a formvar
window of the desired thickness has been built up. Air
drying for a few hours cures the formvar film. The drying
may be speeded up by using an infrared heat lamp. Very
thin wrinkle free formvar films are produced by the technique
just described. To measure the average thickness of formvar
film produced by the above technique, 44 double layers were
cast and transferred to a 5/8" i.d. copper tubing. The
energy loss of the 5.48 MeV alpha particles from an americium
source was used to calculate the thickness. The electronics
to process pulses suitable for a Nuclear Data 160 multi-
channel analyzer was the same as for the energy signals for
particle identification described under data acquisition
and shown in Figure 7. The electronics was checked for
linearity with test pulses, making sure E=0 corresponded
to channel 0 of the ND 160. The 5.48 MeV peak centered in
channel 587 shifted by 9.5 channels when the built up formvar
film was introduced between the source and the silicon
surface barrier detector. The calculation in Appendix C
shows this represents an average thickness of 2.4:0.2 %%2/
double layer.

A 30 ug/cm2 formvar window over a 0.040" slit sustains
a pressure of 25 torr for many hours. The films are weakened
by the variable stress occurring during repeated pumping down

to vacuum and letting up to air pressure.

21

2.5 Pressure Measurements
2.5.1 Equipment

The gas pressure was measured and monitored at first
with a Wallace and Tierman Type FA 145PP12296 aneroid
gauge, later with an oil manometer designed and constructed
by Lolo Panggabean. It has a range of 135 cm of oil; each
miniscus can be read to :0.5mm, hence the net error is
z :1 mm for a pressure measurement. The oil used is the
pump fluid Octoill. At 25°C its density is 0.983 g/cm3;
its vapor pressure is 2 x 10.7 mm Hg.

A manifold interconnects gas cell, scattering chamber,
manometer and target gas source. During data taking one side
of the manometer is held at scattering chamber pressure
(vacuum) while the other side is connected to the gas cell.

During pump down all components are held at the same pressure,

evacuation proceeds through the scattering chamber pumps.

2.5.2 Beam Heating

To calculate the target gas density, besides knowing
the pressure, one must know the gas temperature. Since the
beam loses energy as it traverses Kapton and gas, it is not
obvious what the temperature of the irradiated volume is.

To obtain a rough estimate of how much the gas in the
beam trajectory might be heated, the naive model described
in Appendix D is considered; for our average operating

conditions it predicts a temperature rise of 2 25°C above

 

1Octoil is manufactured by Consolidated Vacuum Corporation.

ambient gas temperature.

To experimentally check the effect and compare it to
values given by the model, the beam was focused to produce
a beam spot 0.025" wide, 0.045" high on the Kapton window.
A cesium-iodide crystal mounted on a phototube was used to
monitor the proton spectrum for scattering of 35 MeV protons
from 20Ne. The proton counts from the ground and first
excited state were used to monitor the product of beam

20

current and Ne density. A 500 nano amp beam and a 100

nano amp beam were compared, results are given in Table 1.

TABLE 1. Beam heating comparison data.

 

 

Beam Monitor Pressure Integrated
Current Counts (cm oil) charge
(nano amps) (10‘7 coulombs)
500 152,277 53.35i0.2 3375.4
100 4,494 53.10:0.l 100.1

 

 

 

 

These date imply Tsoo/Tloo = 1.00:0.015. The model predicts
Tsoo/Tloo = 1.06; the discrepancy is most likely due to more
efficient gas mixing than postulated. To first order any
error in charge integration is the same for both cases so

the error in the ratio due to the pressure readings and

total charge collected is negligible compared to the statisti-
cal error of 1.5% for the 100 nano amp beam measurement.

To make sure the beam spot was of the same dimensions in

both cases, slits near a beam antinode were used to cut the
beam from 500 n amps to 100 n amps; this should not have

influenced beam spot size which is determined by the object

23

slits.
2.6 Beam Integration

A 57" section of 4" diameter beam pipe served as
Faraday cup for charge collection. The beam was dumped
on an aluminum plug at the end of the pipe. The section
was insulated from the scattering chamber by a 1.5" plastic
ring. Charge integration was performed with an Elcor
model A3103 current indicator and integrator. Performance
of the integrator was checked with a 1.35 volt mercury
cell in series with a 1% 4.5 meg. ohm resistor. This test
was performed both at the input to the integrator in the
data room and at the Faraday cup. The maximum deviation
between expected and observed total charge was 1.6%. The
average deviation was less than 1%. Two successive 9 min

calibrations were consistent to within 0.17%.

2.7 Particle Detectors
2.7.1' Spallation Product Detection

Particle energy was measured with silicon surface
barrier detectors manufactured by Ortec. Thinner detectors
have faster rise times, hence yield better timing pulses
for low energy signals. For this reason thin detectors,
75p and 85p thick, were used for all proton beam energies
below 40 MeV. At or above 40MeV a 150 u detector was used
for the 14N target. Minimum detector thickness was set by
the requirement that all spallation products heavier than

mass 5 be stopped in the detector. A 250 u detector placed

behind the thin detector served as veto for particles not

24

stopped in the first detector. This was done to minimize
computer processing time for uninteresting events.

To achieve best possible energy resolution, the detector
was cooled by pumping alcohol cooled to near dry ice tempera-
ture through a copper yoke which held the detector. It was
also usually overbiased by 50% to insure short collection
times and hence achieve optimum timing signals. The energy
resolution, checked with the 5.48 MeV a peak of an americium
source, was always better than 40 keV FWHM. The detector
holder, solid angle defining aperture, and gas cell are all
mounted rigidly on a rail held in a block of aluminum which
is provided with pins that fit precisely into positioning
holes of the rotary scattering chamber table. This system
assures reproducibility of geometry.

2.7.2 Proton Elastic Peak Monitor

To calculate the cross-section corresponding to an
experimental yield measurement, one has to know both the
integrated charge of the proton beam and the density of
the gas target. A gas leak during a bombardment would
present a difficult pressure monitoring problem. It is a
common technique to use a monitor cross-section to integrate
the product of gas density and beam intensity during a
bombardment. The proton detector is set at a fixed angle
and the proton energy spectrum is recorded. The number of
events in the elastic peak for each bombardment represents

the integration. The pressure must then be accurately

known only for a calibration point (see Chapter 2, section 2.5.1).

25

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26

A cesium iodide crystal mounted on a phototube was
used to monitor the proton spectrum. (This detector was
designed and constructed by Larry Learn of the MSU
Cyclotron Lab.) Figure 6 shows the electronics used to
record the spectra. A single channel analyzer was set
to accept only pulses from the elastically scattered proton
peak. The proton spectrum was also collected in a Nuclear
Data 160 multichannel analyzer so gain shifts in the photo-
multiplier could be detected and scaler counts could be

corrected if necessary.

2.8 Time-of-flight Electronics

A schematic of the electronics configuration is shown
in Figure 7. Table 2 identifies abbreviations, manufacturers,
and model numbers.

Reaction products of interest are stopped in a silicon
surface barrier detector, labeled E detector. It is connected
by a 3ft, 22pfd/ft Microdot cable to a time-pickoff unit
and then to a preamplifier. The time-pickoff in conjunction
with a time-pickoff control derives a timing pulse from each
energy pulse. This system employs leading edge timing. A
time-to-amplitude converter (TAC) is started by this timing
signal. The stop pulse is obtained from the cyclotron RF
system.

To avoid the non-linear region of the TAC (=15% of the
100 nsec range), it is desirable that the RF stop pulse

occurs at least 25 nanoseconds after the start pulse. To

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28

Table 2. Electronics Equipment.

 

 

 

Unit

Model Number and

Manufacturer

 

(ADC) Analog to digital converter
AMP amplifier

COMPUTER

Detector, E and Veto

i i i e
Fast ant co nc denc one module

Fast coincidence

Gate generator, 25 and 30 NS, one
module
TAC time to amplitude converter

Time pickoff

Time pickoff control

SCA Single-channel analyzer
Slow coincidence

Linear gate stretcher

PRA preamplifier

629 Northern Scientific
440 ORTEC

SIGMA 7 XDS

Si surface barrier ORTEC

C102B/N EG+G

121LRS

437 ORTEC

260 ORTEC

403A ORTEC
420A ORTEC
418 ORTEC

442 ORTEC

109A ORTEC

w

29

do this in a fashion which also maintains the dynamic

range of particle flight times, logic has to be done on

the start and stOp signals. The start signal triggers

a discriminator which is set to give a 25 nsec long positive
going pulse. This pulse and the RF pulse are presented

to a fast coincidence operated in anticoincidence mode.

Only RF pulses which come later than 25 nsec after the

start pulse yield an output signal. Figure 8 represents
three situations of the start and step pulse relationship.
Time increases from left to right. In each set of pulses
the first line represents StOp pulses, the second line is
the 25 nsec gate pulse generated by the start pulse in

line three. Line four schematically represents the height
of the TAC pulse by the length of the rectangular pulse
shown. The first set shows the st0p pulse arriving later
than 25 nsec after the start pulse; the second set is an
example of the first stOp pulse coming within 25 nsec of
the start pulse and the third set illustrates the nonlinear
effect for stop pulses arriving 225 nsec after the start
pulse. To avoid the nonlinear effects for signals which are
close to the edge of the 25 nsec pulse and hence are partially
attenuated (see Figures 7,8), the second channel of the LRS
model 121 is used to provide a negative going 30 nsec pulse
for each accepted RF pulse. This negative pulse and the
original RF pulse appropriately delayed are fed into the
second channel of the fast coincidence module. A uniform

RF stop pulse with the correct time relation to the start

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TAC I
STOP
\
v V
GATE :\
S R I I
l I
199.] L

 

TIME -—--

Figure 8. Start, Stop and TAC Pulses.

 

 

31

pulse is obtained by this means. Of course the start pulse
presented to the TAC has to be delayed by the time needed
to perform these logic Operations. With the noted choice
of start and stOp pulses, fast particles, hence short flight
times, are associated with large TAC pulses, while slow
particles are associated with small TAC pulses. A pulser
simulating events should produce a flat, continuous random
time spectrum. The smallest TAC pulse should represent
25 nsec delay between start and stOp, while the largest TAC
pulse should represent (25 nsec + 1-RF-period) delay.

The energy pulse from the preamP is fed into an amplifier.
A single-channel analyzer in the integral mode provides a
logic pulse for each energy pulse above a set level. Similarly
the TAC pulses are fed into a single channel analyzer for
logic pulses. To be able to discriminate out particles
passing through the front detector, a detector placed behind
it provides veto pulses. The single channel analyzer
pulses from the energy signal and TAC signal are fed into
the coincidence input of a slow coincidence circuit while
the veto pulses are fed into the anticoincidence input.
Linear gate-stretchers for energy and TAC linear signals
are gated by the coincidence logic output. These are
presented to 8192 channel ADC's. The ABC's are then read

by the XDS Sigma 7 Computer.

2.9 The 17 MeV Measurement
The lowest proton energy available with good timing

characteristics and sufficient beam intensity is presently

32

near 22 MeV. The cross-sections for masses 7, 10, 11 from

14N are still large at this energy.

proton spallation of
It was thus very desirable to perform a cross-section measure-
ment at a lower energy, lowering the beam energy by intro-
ducing a degrader. In Appendix E are calculations to choose
degrader material and thickness. Aluminum is better than
heavy elements such as lead in terms of energy spread caused
by degrading the beam by a fixed energy differential.

Aluminum is also advantageous since when irradiated by

protons the radioactive products have comparatively short
half-lifes and handling equipment after irradiation is less

of a problem. The beam emerging from the degrader also has

an increased angular spread. It is therefore important to
position the degrader as close to the gas cell as possible.
Since the resolution is still quite marginal for masses 10

and 11, it was desirable to have the display for the non-
degraded beam as a guide. Therefore a mechanism for inserting
and removing the degrader was devised. A solenoid was
designed to lift the degrader in and out of the beam path

at 0.25" from the Kapton gas cell window. The mechanism
could be actuated in less than a second. This made it possible
to compare instantaneous beam intensity ratios with the
degrader in and out of the beam. Due to the angular spread
not all of the degraded beam was collected in the Faraday

cup. Spot checks were made throughout the experiment to
determine the ratio. The total charge collected was scaled

by the average of these rather constant ratios.

33

The beam degrader chosen was 0.085" thick 6061 aluminum
alloy. For the proton beam energy of 21.65 MeV the degraded
beam energy is calculated in Appendix E to be 16.8 MeV.
Experimentally the degraded beam energy was determined to
be 17.2 MeV :0.2 MeV from the cesium iodide monitor spectra for

degraded and direct beam.

3. DATA ACQUISITION

3.1 On Line Setting Up Procedure for Data Taking
3.1.1 Introduction

When the proton beam is first brought into the scattering
chamber, the detector-gas cell assembly is removed. The
beam is focused on a plastic scintillator at the center
of the scattering chamber. The beam spot on the
scintillator is viewed by remote TV. Once a satisfactory
spot, appropriately centered on the scintillator, is obtained,
the gas-cell-detector assembly is positioned in the scattering
chamber. Manometer, gas cell and scattering chamber are
evacuated. The gas cell is then filled with the gas target
of interest to the pressure desired. The detector is replaced
and the detection angle is set to 15° with respect to the

beam which is again brought into the scattering chamber.

3.1.2 Software

Data taking is done under the all purpose code TOOTSIE,
written by Douglas L. Bayer (BA 71). Data is displayed at
run time on a Tektronix 611 storage scope. Data and display
are manipulated and interacted with by both teletype and
switch commands.

The EDE mode of TOOTSIE is used for choosing the correct
delay for RF stop pulses. In this mode TOOTSIE plots two
variables, x-axis=energy pulse, y-axis=TAC pulse as shown in
Figure 9. ,

Starting with the first display, where the timing pulse

of the fastest particle arrives sometime between RF stop

34

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pulses, delay is added to (or subtracted from) the RF stop
pulses until the second display, with the timing relation
indicated, is obtained. Optimum delay is such that the
fastest particle of interest has the longest TAC pulse

(25 nsec+l RF period). The slowest particle that can then
be identified will come one RF period later and will have
a TAC pulse equivalent to 25 nsec. Once the RF delay has
been determined, the E*T**2 Option of TOOTSIE is entered.
In this mode the quantity [A+E*(TAC-TZERO)**2/NORM] is
plotted against E on a two-dimensional analyzer. E is the
energy signal and TAC is the time signal. The parameters
A, TZERO, and NORM are selected at run time to display

data in the most convenient form (see Figure 10).

3.2 Data Taking

Once the parameters are satisfactory, data is accumu-
lated. Energy spectra of the various masses can be derived
from the two-dimensional display. An option in TOOTSIE
makes it possible to define upper and lower bounds of a
mass band. This is done by choosing points with a cross
which is moved from scape switches. Up to a ninth degree
polynomial fit can be performed on these points. The
resulting curve is then one of the mass band boundaries.
Given upper and lower bounds, TOOTSIE generates energy
spectra by summing all counts in the band identified by the
same horizontal (energy) channel number. Since data is taken
on a 128x128 array, the energy spectra are 128 channels long.

Sample energy spectra are shown in Figure 11, The complete

38

two-dimensional array as well as the energy spectra derived
from it were punched on cards. The data, as read from the
ABC's can also be stored on tape. The tape can later be
read by TOOTSIE and the data can be reanalyzed. It is thus
possible to use different parameters to display portions

of the data for easier analysis. Figure 10 shows four

150 for 37.9 MeV

oscilloscope displays for the data from
protons with the detector at 15° to the beam. One display
shows all data up to mass 16; by using a different set of
values for the parameters NORM and A, and by displaying

only those channels which have N or more events, one obtains
the other three displays (N=l, N=8, N=30). The valley

between mass 11 and 12 can thus be seen on the (N=30)
oscilloscope display. The nonlinearity (mass defect) of

the mass bands toward low particle energy is due to incomplete
charge collection by the detector.

Background events, presumably neutron induced reactions
in the silicon detector,contaminate the spectrum at low
particle energy as is evident in Figure 10. This data
represents the most severe case. For lower energy proton
beams the background is considerably less. Since 14N
spallation cross-sections are considerably larger, back-
ground is less of a problem even at high proton beam energy
for that target. For the 41.9 and 37.9 MeV data, background
runs were taken with no gas in the cell. Cross—section
calculations in Table 8 and angular distributions for these

runs are labeled "Vac". The cross-sections summarized in

Table 9 are corrected for this contribution.

39

3.3 Dead Time Correction

Dead time of the analog to digital converters (ADC)
is monitored using the option "channel zero" in the program
TOOTSIE (BA 71). A logic pulse presented to channel 0
is counted only if the ADC's are free to accept an event.
Thus the ratio of the number of counts in channel zero to
the number of pulses presented is the fractional lifetime
of the ADC's. The source of pulses for channel zero has
to be chosen carefully. For example if the beam intensity
fluctuates, then a random or fixed frequency pulser will
indicate less deadtime than is actually the case. Suppose,
for example, that the beam is off for 9 sec and on for 1 sec
periodically; then even if the ADC's are completely dead
during the 1 sec, the channel zero count will indicate only
10% deadtime while actually the deadtime is 100%. This shows
the channel zero pulses should come from a source which is
directly correlated with scattered particle intensity. The

proton elastic peak monitor was used for this purpose.

3.4 Mass Band Resolution

For the correct choice of TZERO the quantity (TAC—TZERO)
is proportional to the flight time t of the particle. Beam
bursts have a finite duration; flight path length varies
for different particles; and the energy resolution of the
detector is not perfect; hence what is ideally a series of
sharp lines representing the energy spectra of different
masses, becomes a set of bands. As shown in Appendix G

the width of a band is governed by the equation:

40

width of band = A(Et2) = Et2[(AE/E)2 + 4((Ax/x)2+(At/t)2)]5

E = energy,

X = flight distance,

t = flight time,

AB = energy resolution,

AX = uncertainty in the flight distance

At width of the beam pulse.

Suppose the quantity Et2 is given in mass units. To
separate one mass band from the next, A(Et2) should be less
than one mass unit. From the equation for A(Et2) it can be
seen that the higher the mass, the more difficult it is
to resolve it.

To resolve mass m the fraction A(Et2)/Et2 must be less
than l/m. This represents 17% resolution for mass 6 and
9% resolution for mass 11. Table 3 summarizes individual
contributions to the mass resolution as discussed in Appendix
G. The observed band width can be accounted for by these
contributions. Table 4 gives a specific example. It is
fortunate that for low energy particles where energy resolu-

tion starts to become significant, the beam time-resolution

is less limiting than for higher energy particles.

41

Table 3. Individual Contributions to A(Et2) in Terms

of Percentage of Etz.

M
Particle Energy AE

Source: Detector resolution of 5.48 MeV a is z 40 kev
Max: 8% (for a 0.5 MeV particle)

Min: 0.2% (for a 20 MeV particle)

Time Resolution (Cyclotron) 6t.

Source: Average width of cyclotron beam burst was
0.5 nsec (.3 to .7 nsec were measured)

Min: 1.2% (slowest particle, flight time 3 84 nsec)

Max: 8% (fastest particle, taken to be 20 MeV
mass 6, flight time 3 12 nsec)

Time Resolution due to Ad
(flightypath length uncertainty)

Source: geometry; beam width 0.040", front slit SZ=O.040"
Min: 0.8% (detector at 90°, holds for all particles)

Max: 5% (detector at 15°, holds for all particles)

-__.
1

 

 

 

42

Table 4. Band Resolution of Spallation Data from 14N

by a 41.9 MeV Proton Beam.

 

 

 

 

Geometry: Detector angle 15°, beam width 0.040", front slit

$2 = 0.040 .

Particle energy considered: 5.48 MeV.

Observed mass resolution: 611 channels FWHM for mass 11,
4i0.5 channels FWHM for mass 6.

One mass unit = 9.6iO.l channels.

 

 

Theoretical Resolution Contributions to A(Et2) in % of Et2
Mass 6 Mass 11
Due to AE=40 kev .7 .7
Due to beam burst 4.4 3.3
width 6t
Due to flight path length 5.0 5.0
uncertainty Ad
Contributions combined 6.7 6.0
in quadrature
Observed band spread 7.010.9 6.9il.l

percentage of Et2 (FWHM)

 

 

4. DATA REDUCTION

4.1 Energy spectra and low energy cutoff correction

Energy spectra were obtained directly from the data
taking routine TOOTSIE as outlined in section 3.1.2. An
alternate method was also employed based on the two
dimensional array obtained in card form. A fortran program
was written for converting the two dimensional data into a
set of mass spectra by generating line-printer plots of
the events stored in the set of channels in a line parallel
to the (Etz) axis. The mass band fitting could then be done
off line. This was of advantage for two reasons; time did
not have to be spent at run time to perform all band fits,
and, as can be seen from Figure 9, mass separation for mass 11
is not always easily determined on the scope display. A
second fortran program was written to generate 128 channel
energy spectra from the two dimensional data, given the band
fits determined from the printer plots.

A few energy spectra are shown in Figures 11 to 39.
They are representative in the sense that the 37.9 MeV
data is the lowest quality taken, while that at 25.6 MeV
is among the better data sets. The energy spectra collected
all have a low energy cutoff. This is usually due to the
finite flight time available and the energy losses in gas
and formvar window. The energy cutoff for particle detection
due to detector and time pickoff sensitivity limitations is
near 0.5 MeV; this represents the limiting factor for masses

6,7 for proton beam energies below 30 MeV (since then the

43

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mo\>mz mH.o

 

 

 

 

 

umzzmxo nmzzmxu
o 2 on o o 2 on
. q . 4 .. . 4 4 .fi . 1m . . __uq . . A..1 4 .
a H _ . __._ r
1 3
0
1 nu
”N
1 1
co
I4
m mmc: 18 k m2:
nozzczo nozzmxu
o 8 o
. . . . .
1
I no
0
1 nu
”N
1 .1
ea
o.mm¢: 1 ..mmm:
8m

 

 

 

 

 

 

SINDOD

o...

SINDOD

om

9mm"... com ...msm 2 $5915 mmeumam yommzm

46

(continued)

Figure 11.

mo\>mz ma.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Buzzmlo szz¢Iu
o a. on o o 3 cm
_ — _ _ _ 41 d A q . _ _ .. _ n... _ _
1 _ 1
__.
... 3 1
0
1 DH l
um
.I II. 1
Co
I J
m mmm: no: A mmmz 1
omzzqu Buzchu
o o. on o o a. on
_. «I p _ . A q A 4 .fi fi11. A d u A. .4
L «J P 1
0
.I- m l
1 I. L
l S J
o. mmm: 1 2 mmmz J
om

SlNFIOD

om

SiNflOO

o...

m.mmu.m OT. “25 z $59.5 amBmam 5E2...

47

(continued)

Figure 11.

 

 

 

mo\>mz mH.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SINHOD

or

SINDOD

om

nozzcxo nozzmzo
co. co co. om
_ 41 A . 1. .1 4 1. d . m ., d1 d a a
. . r L
M.
.J :111 1
mw A
um
IL 1
II. 8 IL
mmmmz 12.. kmmmz 1
nuzzcru nmzzczo
02 on o so. am
. . 1m _ A A q 1. A1 _ L . . . ._ A #114
1 1
u a 1
0
l m IL
1 II. I.
1 Q. 1
OHmmmz 1 ..mmc: 1
oo. ,
mfimnlm .8 "elm 2 £591.”: EBEm Emmzm

48

(continued)

Figure 11.

mo\>mz mH.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

umzzmru Buzzmro
o 2 on o o 2 on o
. _ _ _ _ . q _ . . _ _ . q _ .

L 1
:C 1 3 1 3
nu nu
1 nu 1 nu
um ”N
.L ll— 11 l
1 co 1 a:

m mmm: .1 m mmm: 1

om ‘ or
.32ch... ..mzzmxu
o 3 on , o o O. on o
_ _ . _ . _ _ .1 _- . _ _ _ _ _ a _ _ . _

if: .1 3 1 3
0 0
.1 n .1 n
”N um
1 1i 1 11
co 1 ca

2 mmm: .. 2 mmm: ..

om om

 

mnmulm 0mm 1.5.. 2 £59.15. $1595 532.“.

49

(continued)

Figure 11.

 

.522qu

on:
.14 a _ _ . 4

m mmm:

 

 

 

szzqu
o o.

o. mmc:

 

 

J1;

l

l

L L

 

 

@811“.

.8 "male

mo\>wz mH.o

SLNDOO

SINHOD

o...
2 rpmomck cmhummm ymmmzm

13.2ch0
o o.

om

 

 

m mmc:

 

 

 

..wzzqu
o o.

 

 

2 mmm:

 

 

 

SINDOD

0...

8114003

om

mo\>mz ma.o

 

 

 

 

 

 

 

 

50

 

 

(continued)

 

 

 

 

...mzzmIo buzzczoo
o 2 on o o o. o
.4 . . _ .1 _ . _ _ _ifiggfilm . _ . _

1 3 2mg 1 3 .
nu nu

l n I n
”N um

I. II. I I...

1 Q. 1 Q.

m mmaz 1 k mmm: 1
om cm
.322qu ..mzzmruo
o o. on o o o. o
. _ _ _ _ . ., _ . . =d , _ . _ _ .

1 no 1 «J
nu nu
um um

I l 1 I...

L S l S

S mmm: 1 2 mud: ___m__§‘ ..
r 2.

 

 

 

 

Figure 11.

 

mnmulm a 2.1.5.. 2 550%: cmeumnm 552m

51

(continued)

Figure 11.

 

Juzzmlo

"mm... 0

com
3 mm:

 

 

 

szzmlo

 

 

 

 

l

[J

JLliv

 

 

mU\>OE ma.o

o

SiNDOO

SINDOO

o.

mnmunm 2 Z BEE

szchQ

 

 

 

 

 

 

 

 

 

 

ch
m
mm: 1

 

 

ameumnm yoawzm

om

SINDOD

SINDOO

Figure 11.

Ep=25.8

TRRGET H N

ENERGY SPECTRR

52

 

 

 

 

 

 

 

 

(continued)
0
o -—1
(”CD _JCD
00|| 53
U) -'1
0E
IZaD ‘
._l
n—l
-CD
U)
-
anus-=1
111111
2F c:
SiNflOD
3) 4
ofl\ dc”
c3
UNI —~
00 g; ‘
a:
24> ‘
-
...O
U)
.4
c:::::
——‘
llllll,
3' c3

SINDOD

CHRNNEL

CHRNNEL

 

U0 °

00

RS

2:

L98

CD

100

 

 

H

SiNflOD

50

 

llliillLLI

O

CHHNNEL

0.13 MeV/CH

Fi

53

(continued)

Figure 11.

 

m0\>mz ma.o

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

umzzmzo guzzaxu
3: on. , o 3: on o
4 IA
fiJ fiJ
0 0
m m
I I. I.
Q9 I Q4
m mam: .. m mmc: I
com om
umzzcxo szzmxo
ooi om o
fl q I4 I‘ a _ A Ifi .
m I m
m I m
IL 1 IL
Qu I Q4
gamma: I fiflmmmz I

com com
mNmuJ 92 ...mSm 2 £583 mmbmam >396

54

(continued)

Figure 11.

 

 

 

 

 

 

 

 

 

 

 

 

m0\>wz mH.o

 

 

 

 

 

 

 

 

SiNFIOfJ

or

SiNf‘IOD

om

..mzzmru owzchu
S: on ,o _..:pof.1d. om: _ _ _
3 J
nu
n -
um
I. I]. .L
I. S l
m wmmz now u mmm: I
umzzcxo ..mzzmro
C on: on
_ _ I _ fl dingo _
H a I
I W L
L I. l
i S I
2 mmm: J : mmm: I
oo—
mNmuJ com ...msm z EDEE cmSmmm yommzm

 

dzzmxo 5%: 2.0

 

 

 

 

 

55

(Continued)

 

 

 

 

 

Figure 11.

o 3 on o
m _q.‘712iw _ fi I1 L L
L n, _ _ .l
M T 3
x nu
,2 nu
_, N
, Ii
q.
m mmm: I or
...mzcho
Q on
a g _ _
no
0
n.
_N
IL
L A:
2 mmm: I
om

o4w22¢10o

jig:

 

 

 

m mmcz
szzmIo

 

 

 

 

 

 

L1 LI

2 mmm:

 

 

 

SiNflOCJ

SLNFIOZJ

or
mxmufi om: ...mSo z 550%: $5QO $32”.

guzzmxo axsgrmdo umzzcxu

 

 

 

 

 

 

 

 

 

 

 

56

 

 

(continued)

 

 

 

 

 

 

 

 

 

 

Figure 11.

 

H L
_ _o_o _ o . doqo om... Jo
3 I 3
0 0
n I n
N N
1 IL I IL
I S L S
m mmm: I I ..\. mwcz I
or or
szzclo szzmIU
o 3 o 2 on I o
_ _ . d 4 _ 4 4 u d _ ... u
3 I 3
0 0
n I n
N N
i I i
S I S
aflmmcz I dimmmz i
c... or

mxmufi 0mm ...mSo z ZEEE $5QO Samzm

57

(continued)

Figure 11.

 

 

 

mo\>mz mL.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

szzcxo szzmzu
o L: o o L: on , o
L L L L L L L L L L
L
fig 1 do
0 0
nu I nu
”N um
L .1. L IL
co co
m mmm: I m mmm: I
or or
szzcro .fizzmro
o 3 on o o 2
L L L L L a L L L L L L L L L IL L
I no fig
0 U
I n H
um um
.1 II— I. 1
AD L:
J ll
2 mmc: I LL wmmz I
om om
mxmumm 0mm ....msa z 350%.: mmbmqm 3&3

 

mo\>mz mL.o

szzmIQ ..szzmIo
o L: on , o o 2 cm

L LI L L L 4 L L L L L L L LI fiI

 

 

 

 

1 I 41
SlNHOD

I I II I 1 J, I I I-
SLNHOU

 

58

 

 

 

 

 

(continued)

 

 

 

 

 

 

 

 

Figure 11.

 

m mmm: or m mmm: oL
IszzmIo .szzmIo
o L: o L: on ,o
L L L L IL L L LI L L L L L L HIL
i
.flu I flu
nu nu
nu I nu
um um
1 IL L IL
Ga Ga
I .4
L: mmmz I LL mmm: I
om om

mNmuJ o 2725 2 ZEomE. mmSEm yommzm

Figure 11.

(continued)

 

EP=37.9

 

J i

l

IIIn I

l

l

 

 

 

TRRGET 1% N

 

 

ENERGY SPECTRR

 

 

SLNHOO

 

59

100

 

 

 

 

 

 

 

 

 

 

a
U) L
0)“) do
J gum _2
uJ CE 3
3: 22a: -
CZ: L
J:
U 2%
Lo
U7
{3
q
4 I I L L I LLI
CD CD
SLNUOQ
.4
O
U)
(3)3- o
o
J gug _L
LU a: J
3: 22a: 4
I:
a: 1
{5 L
O
U)
-(
I I I I I I ,
o O
(U

SLNFIOU

o . 15 MeV/CH CHHNNEL

CHF-‘INNEL

60

mo\>mz mL.o

 

(continued)

 

 

 

 

 

 

 

 

 

 

Figure 11.

 

Luzzmlu Lmzzmxo
L _o_oL_ L _ L on .110 L _o_oL_ L L LgL LL
#41 J
I m I
I m = I
I... ll- .1
I S
"2.. "2.. I
ommxmmmm Im ammo. mcm I
m.mmu¢m z 3 SEE mmBmmm yommzm

SiNflOD

 

61

(continued)

Figure 11.

 

 

 

 

 

mU\>mz mL.o

 

 

 

 

 

 

 

 

 

 

SlNr'lOfJ

 

 

 

 

 

 

 

 

 

 

 

or

Sle‘IOO

 

 

cor

.322qu Lmzzmxo
o L: on o o 3 cm
L L: L L L L IL L C L
I 3 I
1 MW L
I m I
L S l
m mmm: I2. m mmcz I
...wzzalo .szzcxu
o L: on o o L:
L L IL 1. L_I L L LI L L LI L L
, L L I m I
, I. n .l
L N
L I m I
L: mmm: I LL mmc: IL
or
QKm "J o 2 ...mSo a 250mg mmbumm yommzm

mo\>mz mL.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

62

 

 

(continued)

 

 

 

 

 

 

 

 

 

 

Figure 11.

 

Lmzzcro szzcro
o 2 on o o L: on o
I I L L L L L L L L_ I_ _L L L L
I , L. I L
L m M I ‘2 I I.
I I g L I
I 3 I. I I I, I 3
nu _I .2 nu
l n I L l n
1 UN . J um
IL I I.
I Go I L on
I I
m mmmz If m mmm: IL:
.szzmro IGZZIIQ
o 3 o 3 00 o
L IL L LIaL L L L LI L L L LI L IL L
L
«J I n4
0 0
AM I nu
”N um
Ii I IL
I Q9 I c:
L: 3% I LL mmm: I
or com

mNmIJ com “$5 a BEES ESEm yommzm

63

(continued)

Figure 11.

 

 

mo\>mz mL.o

 

 

 

 

 

 

 

 

 

SiNflOD

 

 

 

 

 

 

 

 

 

 

 

om

SiNflOD

 

 

 

ooL

szzmxo Lmzzcxo
ELL , on , o as on
L L L L L LfiI LLJ%;W_L L L L L L a:
E: I
I no
0
I nu
um
I .i
. I no
m mmmz Iom m mmm:
Lmzzmxo szzmxo
o L: on o o 2 on
L L L L L L L L n L L L L L A L
I no
0
I nu
um
I IL
I co
2 mmm: I LL mmc:
m
mNm "mm om: ...mSm a 2535 mmanLm $52.“.

64

(continued)

Figure 11.

 

 

mo\>mz mL.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

Lmzzmlo .62ch0
ooL a 3: on o
L L. L L L. fid I L. L L L L. L— L‘ _ I
I I
I nu L nJ
0 0
l n l m
L I mm I IL
I S I S
I I
m mmc: I m mmc: I
L: r L:
Lmzzqu Lmzzcxo
L LOLOLL L L L OWL fl L o L LOLQLL L L LIOLID L L o
E L I
I do I nu
0 0
I nu I nu
”N um
I Ii I IL
I S L 8
0L mmm: I LL mmm: I
m 8
mNmuJ 08 ....mSo a £5.55 $5”me SEE

65

(continued)

Figure 11.

 

Lmzzmlo
o L: on

 

L L .2 LIIL L :wdflHfiflmwch

 

 

 

 

 

 

 

 

 

 

 

m mmm: I
Lmzzcxo
o 3 on
L L L L L L L
i
2 mmm: I
mNmInJ own ...mSm

mo\>mz mL.o

o

SiNflOD

om

SLNHOO

oL

szzclo

 

 

 

 

 

 

 

 

 

om

 

 

m mmm:
LmzzmIQ
92
L L 1L L L 4

LL mmm:

 

 

 

 

SLNHOD

SLNFIOD

om

® mLHmmmmh mmhummw >ommzw

66

(continued)

Figure 11.

mU\>mE oL.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lmzzmxo Lmzzmxo
o L: on. , o L: on
L IL LI L L L O L L L. L L LI 0
.L I: I
I 3 I
0
.1 n II
”N
l I. i
I Q4 L
m 8% Im n 8% Im
Lmzzmzo Lmzzcro
o 2 o 8 on o
L L LI LI L IL L
3
nu
nu
”N
I .i
I Ga
2 mmc: I1 LL mmm:
m m

mNmIIJ o8 “2.6 a 2535

 

SLNHOU

SLNHOD

$3.0me >ommzm

67

(continued)

Figure 11.

 

 

 

 

 

 

 

 

mU\>mz oa.o

 

 

 

 

 

 

 

 

 

 

 

 

SiNfiOO

oL

SLNHOD

om

szzmru umzzmxo
o 2 on o o 2 8
A L L \L 1L L L L L L L L q L L L
L
L
«J l
0
n L
.. m. L
s L
J 1
m wmmz 107 m mmm: 1
Juzzcxo Luzzmzu
o 2 on o o 2 on
L! L L L ‘L L |4‘ a \fi= L L L L a L L L d L
I 44
0
1 nu
mu
1 I;
L ea
2 mmm: L 2 mmmz ..
om
mNmnmm o moLumfim z 3.59%: cmwommm >ommzm

68

(continued)

Figure 11.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

..mzzcxu 8%: 35 ..wzzczo
o 2 on a o o 2 on
L L L1 L AL1L L L L 14 fi
1 fig
0
1 0
un
1 .i
3
m mmm: 18 m mam:
Luzzmxu umzzmxo
o e on o o 2 on
L L L 1‘ L L 1H L L q L L1 L L L L L
1 flu
0
1 nu
”N
1 .i
1 S
S mmc: 1 : mmc:
om
mNmuJ 02 “25 0%

SLNHOD

or

SLNHOD

om

Hmomme mmhummm yummzm

69

(continued)

Figure 11.

.mzzcxo 5%: 3.0 dzzcxu

o 3 on

 

 

 

 

 

 

 

 

 

 

L L LL: L L L a L L o
1 3
0
1 0
un
1 I.
o:
1
mmmm: ..
Lmzzclu om
2:
L L L L L
3
0
n
”N
1 I.
1 8
Emma: 1
m

 

 

mxmufi com “Lisa um:

 

 

ooL on
L L

LLLLQ LLo

L

 

 

 

111 1 LL_1 J
‘3an03

 

 

 

 

 

 

 

 

n mmm: L
szzmlo o
02
L LL L L a L
3
0
nu
N
1 I.
1 S
2 mmc: 1
m

hmmmE. mmhuwmm >omwzm

70

(continued)

Figure 11.

16222.5

 

 

 

 

 

 

 

 

 

 

 

 

m

mo\>mz oL.o

L o

SiNflOD

SiNfiOD

m mmm: L1
Lmzzmzo
LILI=fiOLoHL a L L r
L: mmm: . 1
mNmuJ on: 125 LE;

 

Lmzzcxo

m mmm:

 

 

 

Lmzzcio
0 2

LL mmcz F 1

 

 

 

 

m

SiNf‘le

SlNF‘IOD

Hmommh mmhummm >©mmzm

71

(continued)

Figure 11.

Lmzzcxu axseLodo Lmzzcxo

 

 

 

 

 

 

 

 

 

 

L
L LoLoL L L 10
T:
r
L1 3
0
1 n
1 N
IL
1 S
mmmm: 10m
LmzzmIQ
com on o
q — L L L L L
1 3
0
1 n
N
1 IL
1 S
a: mmc: 1
m

 

 

mNmuJ com 1.25 um:

 

 

 

 

 

 

 

 

 

 

L L oLoLfiW L on J
. 1
L
L
m mmm: 1
Lmzzmro
o L: on
L L L L L L 11 11
1
Lmecz 1

 

 

Sle‘IOD

SLNFIOCJ

.T

Hmommh mmhummw yommzm

72

(continued)

Figure 11.

 

 

mox>mz mL.o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

szzmxu Lmzzczu
3: on o , 02
L L L L L L L‘L L L L L L
L
l
I 44
0
1 nu
1 1N1
1 Cu
com "mam 1 am: 121m
m mmc: m 0. mm:
Lmzzmxo Lmzzmzu
S: on 1 LL as 8
L1 L L 1L L1 L11L1 Léfiwgfif. L L L L XL L qqllacLL
L 1
1 flu
0
1 nu
L m
1 Cu
08 "use 1 EL 121m
a mac: m o. mmc:
mxmumm um: BEE mmSanm Lomwzm

 

 

 

om

SlNDOD

SLNHOU

73

RF period is longer at low beam energy). To account for
energy losses in gas and formvar window a formula for
stopping power from (SE 68) modified from a theory by

Lindhard e£_§l, (L8 61) is used:

 

2 7.39 x 104 zi'20722 %
(dE/dR)Mchm /g = e
A (ZZ/3+ Z2/3)3/2
2 1 2
Zl = atomic number of projectile
22 = atomic number of target
A2 = atomic weight of target

a = the specific energy of the projectile in MeV/nucleon

Experimental stopping power data of carbon on carbon (NO 63)

is compared to the values obtained by this formula in Table 5.

Table 5. Validity of stopping power equation
W

Stopping power of Carbon on Carbon (Mchmz/g)

 

(21:6, 22:6, A2=12)
e = 0.01 s = 0.1
Experimental 1870 5760
Calculated 1890 5980

 

LLL=====================
In the calculations for projectile energy loss it is
assumed that e, the energy per nucleon, is 0.1. This is
valid since the energy cutoff for mass 6 is near 0.5 MeV
and for mass 11 it is near 1 MeV. As explained in section
2.3.3 reaction products traverse varying areal densities
of gas depending on detection angle, hence the low energy

cutoff also depends on angle. Table 6 summarizes the range

74

of the cutoff effects. In Appendix G some more details of
the calculations can be found.

The front surface electrode of the detector is a
40 ug/cm2 gold layer; the energy loss it causes is negligible
as shown in table 6, and since the time cutoff limit is
usually above the detector sensitivity limit, it has no

effect on particle detection.

Table 6. Energy cutoff limits
_
Energy in MeV

 

Product ion: 6Li 11C

Minimum cutoff due to EP=22MeV 0.3 0.6
finite beam burst spacing EP=42MeV 0.5 0.9
energy loss in 15° detection angle 0.4 0.7
exit window 90° detection angle 0.2 0.3
energy loss in gold electrode of

detector 0.02 0.03
............L1 -—-—-—-—-—-—-—-—-—.

 

The number of channels which the energy loss in the exit
window represents is added to the number of channels for the
low energy cutoff obtained from the energy spectra. The
energy calibration curve necessary for determining the
energy/channel ratio is determined from the two-body final
state peaks appearing in the energy spectra. A low energy
cutoff correction is performed by multiplying the number of
cutoff-channels by a weighted average (60:30:10) of the number

of events in the last three low energy channels of the energy

75

spectrum. The resulting number is added to the total number
of counts in the spectrum and this represents the yield Y.
One-half of the low energy extrapolation contribution is
assigned as error. The justification for the low energy
extrapolation and error assignment is that phase space
considerations (see Sternheimer (ST 63) for example) for
multiparticle breakup assure that the energy spectra show

zero yield at zero particle energy.

4.2 Time-of-Flight cross-section calculation
The equation relating differential cross-section and

yield at a specific angle is:

dO/dQ = Y/nintAQ .

Y = yield in counts.
ni = no. of beam particles.

nt = no. of target atoms/cm2 traversed by beam as seen

from detector

A0 = solid angle subtended by aperture 81 in steradians

Y is found by summing the events recorded in the 128
channels of an energy spectrum and adding the energy cutoff
extrapolation as outlined in 4.1.

ni = Q/(1.6 x 10‘19

)

Q(coul) is the integrated charge.

ZXSZXR 273.1 19

 

t=mXT XPX2.687X10 .

This is an approximation, but for our geometry the maximum

76

error introduced is less than 0.02% (shown by comparison
with the program G-FACTOR based on (SI 59) and written by

Dr. R. A. Paddock at the M.S.U. Cyclotron laboratory).

82(cm) is the front slit width,
R(cm) is the average flight distance to SI,
R(cm) is the distance between 51 and 82,
0(deg) is the angle between particle trajectory and
proton beam axis,
T(°K) is the gas temperature,
P(atm) is the gas pressure.
The factor of 2 enters since N and O are diatomic gases.

Aw—
R

A(cm2) is the area of aperture 81,

R(cm) as above.

Once g% is known at all angles, the total cross-section

is obtained from
o = 2nf(do/d0)sinede

In the actual experiment performed 3% is measured only at

a few angles Ai. To perform the integration some arbitrary

method must be chosen to fill in the missing points.

. do . do _ gg_ .
Given afi-(Ai), it was assumed 55 (a) - d9 (Ai) for e in the
range

(A1 + Ai_1)/2 < e < (Ai+1 + Ai)/2 .

There was always a maximum angle, A , beyond which no

max

data could be obtained because of the low energy cutoff.

77

Depending on the behavior of the angular distribution
. 91.2 -
for Amax < 6': 180 , d0 (0) was either assumed to be equal
to gg-(Amax) or it was assumed to go linearly to 0. Similarly
do _ do .
for 0 < 6 < Amin' afi-(e) — d§'(Amin) was assumed,no large
error contribution is expected from this source except
possibly for mass 11 at 26 MeV or below where the mass 11
yield is comprised largely or entirely of 2-body-final-state

do _ do

breakup. A modification of the afi-(e) (A ax) extrapo-

- 55' m
lation, taking account of peaks falling below the low energy
cutoff, was used for these cases.

All angular distributions used in calculating total
cross-sections are shown in Figure 12, p. 115. A fortran
program was written to carry out the total cross-section
calculations. Basic equations in the program are shown in
Appendix G. Table 8 presents individual cross-section
calculations. Table 9 and Figure 13 summarize all cross-
sections measured. Table 10 reproduces the cross-sections
from 12C published in (DLA 70).

The abbreviations in Table 8 stand for:

N = number of monitor counts for calibration run,

P = pressure for calibration run,

integrated charge in coulombs x 10_4,

distance between 81 and $2,

= distance from 81 to the center of the cell,

on so :11 0
II

= width of front slit 82.

Lab angle: angle at which data was taken (6),

 

Diff. Cross Sect. gives the calculated differential cross

 

section at the angle given in the same row (mb/Sr),

78

Contrib. to total cross sect. gives the result of the

integration step from (Ai +Ai)/2 : 6‘: (Ai +Ai)/2 (mb),

-1 +1
Assigned error: error due to low energy cutoff and the

statistical error combined in quadrature (mb),
Yield is obtained from E spectra as explained in

section 4.2 (counts),

Low E corr.: the low energy cutoff correction as explained

 

in section 4.1 (counts),

Monitor counts: the events in the elastic proton peak

 

of the cesium iodide detector used to integrate

beam current and particle density,
225‘ yield from extrapolation of integration to 6=0° (mb),
EEEE‘ yield from extrapolation of integration to

6 = 180° (mb),

Total cross section: the result of the angular distribu-

 

tion integration (mb).

The "total error" quoted in Table 8 is arrived at as
follows: For each angle the statistical error of the yield
and the low energy cutoff error are combined by their square.
These are then added linearly, weighted by the contribution
of the corresponding yield to the total cross-section.

This conservative error estimate is used since all cutoff
corrections may very well be in error in the same direction.
The last value under the column "Assigned error" is the sum
of these errors. One half of the back angle extrapolation
and 0.2 of the extrapolation to 6=0 are also added as error

contributions. This final sum appears as the total error of

 

 

79

the cross-sections in the tables. Table 7 summarizes other

error sources entering into the cross-section calculation.

Table 7. Error contribution not associated with

particle detection.

 

w
Error Source Error in % Measuring Apparatus

A = area of back 0.39 Traveling Microsc0pe
aperture 81

82 front slit width 1.2 to 1.7 Feeler gauge
R the average particle 1.0 Steel rule and micro-
flight distance to 81 meter (sensitive to

beam centering)

H distance between 81 0.3 Steel rule and micro-
and 82 meter
T temperature 0.7 Thermometer
T temperature (beam 1.5
heating)
P gas pressure .33 Oil manometer
P gas pressure .7 Aneroid gauge
Q integrated charge 2.0 Elcor A3103 current
integrator

 

f

 

 

 

Added in quadrature these error contributions yield:

Jig? = 3.3%.
When folded in with the smallest "total error" appearing
in Table 8, namely 8.0%, the probable error becomes 8.7%.
Hence these error contributions are negligible compared

to the low energy cutoff correction.

Table 8.

14 N P SPALLATIBN CRBSS SECTION FOR MASS 7 3

Individual Cross-Section Calculations for

16

80

and O Targets.

...-......-.----.00-....-.--...-.......-.--...-.....-...-...
O

NI 15470 P32021CH HG 0:0765E 00 H82301CM

LAB
ANGLE

3000
#500
60’0
7500

FOR
BACK

TBTAL CROSS SECTION I 3606 M831001 MB (TOTAL ERRBRIBB X

in N P SPALLATIBN

N. 15470 pl2091CH HG 0.0765E 00 H.2301CM

LAB
ANGLE

3000
4500
6000
7500

FOR
BACK

TOTAL CROSS SECTIEN - 26.4 M83110? MB (TOTAL ERRGR-ua % )

CONTRIBO
DIFFO TB TOTAL
CROSS SECT. CRBSS SECT.

0682E 01 07395 01
obZZE 01 .7225 01
0398E 01 0565E O1
.2905 01 .460E 01
01065 01

0103E 02

0366E 08

CRBSS SECTIBA FOR MASS 10 3

CONTRIB-
DIFFo TB TBTAL
CROSS SECT. CROSS SECT.

01335 C2 01445 02
.3725 01 '“315 01
0129E Cl 0183E 01
05825 00 0922E 00
02855 01

02075 01

02645 02

ASSIGNED
ERRBR

.1325 01
0162E 01
0135E 01
01255 01
0260E 00
.2815 01

.8615 01

ASSIGNED
EnReR

055“E 01
01725 01
04895 00
.232E CC
0109: 01
.5215 00

.9595 01

l4N
E'1700 MEV
9:2407CH 8.0109CV
Lew E MGNITBR
YIELD CBRRI CQUNTS
2018 1111 15170
1380 1125 18905
689 627 18875
295 3h9 19011

YIeLD

1918
306

201
66

E31700 MEV

9.2“07CM

880109CM

L6H E MBNITBR

CBRRO

4693
1190
226
63

CSUNTS

15470
18905
18875
14011

Table 8.

LAB
ANGLE

3000
4500
6000
7500

FOR
BACK

1# N P SPALLATIGN caess SgcTIBN FBR MASS 11 1 EI17.O MEV
N' 15‘70 P-EOEICM HG 000765L 00 H82301CM R-2417CM BHlO9CH
CBNTRIBO
DIFF. T3 TBTAL ASSIGNED LBW E MBNITBP
CRBSS SECT. CROSS SECTO ERRBR YIELD CBQQO CBUNTS
'110E C? 01205 02 0168E 00 5039 27 1587C
~073éE 01 0854E 01 01585 00 2987 18 18905
0720E Cl OIOEE 02 0208E CC 2371 12 18875
0‘01E 01 0635E 01 OZIZE 0C 875 13 14011
03365 01 .332E'01
DEBBE 02 0952E 00
06795 02 0173: 01

(continued)

81

TBTAL cness SECTION . 6709 M81161“ MB (TBTAL ERR5982“ z >

1“ N P SPALLATIBN

N. «31392 P.2121CM HG o-os1oE 01

LAB
ANGLE

15°C
30°C
“500
6000
7500
9000
10500
FOR
BACK

TOTAL Cnass SECTION .

CRBSS SECTIBN FBR MASS 6 3 532107 MEV
H82301CM RaZQo7CM 880109CV
CONTRIBO
DIFFo 70 TeTAL ASSIGNED LBW E MONITBR
CROSS SECTo CROSS SECTo ERRBR YIELD CGRRc CGUNTS
0130E 01 05535 00 OIERE 00 481 390 50768
01085 Cl 08835 00 0211: CO . 257 230 63776
04195 00 04865 00 08768-01 91 46 64291
0232E 00 03305 00 05745-01 47 20 6891“
0196E CO 03105 00 05375-01 36 11 63497
0162E 00 02655 00 0519E-01 27 11 63962
OSIZE'OI 08125-01 02215-01 11 O 5618“
07005.01 01585-01
09935-01 02715'01
OSOSE 01 06518 CO

301 M8:

.7 MB (YBTAL ERRBR.23 X )

82

Table 8. (continued)

in N P SPALLATIBN CROSS SECTION FOR MASS 7 1 5.21.7 MEv
N. 431392 Pa2121CM HG 0.15105 01 H.23.1CM R.2#.7CM 8:1109CM
CBNYRIB.
LAB DIFF. T0 TBTAL ASSIGNED Low E MeereR
ANGLE CRess SECT. CRess SECT. ERReR YIELD CeRR. CBUNIS
15-0 o113E 02 .479E 01 .4625 00 6099 1147 50768
30-0 18¢6E 01 .694E 01 .552E 00 3226 598 63776
«5.0 .643E 01 .745E 01 .8115 00 1652 450 64291
6000 1&63E 01 .658E o1 o7#3E CC 1012 295 68914
75.0 .304E 01 .481E 01 .6525 00 537 192 63497
9010 .210: 01 .344E o1 0508E 00 352 141 63962
10500 01866 01 .294E 01 0690E 00 214 185 56184
FOR .6o7E 00 .585E-01
BACK 0360E 01 .SuSE 00
.4126 02 .532E 01

TOTAL c9658 SECTIBN a 41.2 MB: 7.2 MB (TeTAL ERRBRIlS X 1

14 N P sPALLATIBN CROSS S£CTIBN FOR MASS 1o 1

No #31392 PaZoEICM HG QaOSIOE 01

LAB
ANGLE

1500
30-0
4500
6000
7500
9000
10500
FOR
BACK

TOTAL CRBSS SECTIBN . 6101 M811306 M8 (TeTAL ERRGRsae % >

CBNTRIB.
DIFF. T3 TOTAL
CROSS SECTO CRBSS SECTO

I306E C? 01305 02
02195 02 01795 02
'152E 02 0177E 02
07355 01 0106E 02
0658E-O1 07265-01
01025 00 01685 00
0466E-02 0738E-02
0164E 01

09035-02

06115 02

H.23o1C”

ASSIGNED

gRReR YIELD
92336 01 13125
.334E 01 6205
.3235 01 2599
0297E 01 9““
01985-01 111
0279E'01 24
07385.02 1
.2955 00
09035.02
.132E 02

EI2107 MEV

Lew E
CBRRO

7323
3677
2383
1206

- O
O
0

R32407CM BuolOQC”

MONITBR
CBUNTS

' 50768

63776
64291
6891“
63997
63962
5618“

83

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 11 1 5-21-7 "EV

N. 431392 P-Eo21CM HG 0..510£ 01 H-23.1CM R.24.7CM B-o109c~
CONTRIBO
LAB DIFF. TO TOTAL ASSIGNED Lew E HeNITeR
ANGLE CRess SECT. caess SECT. ERRBR YIELD CaRR. CeUNTS
15.0 .485E 01 .2065 01 .3865-01 3197 47 50768
30.0 .4115 01 .3375 01 .3295-01 1821 36 63776
45.0 .322: 01 .3735 01 .1225 00 1022 30 61291
60.0 .2755 01 .3905 01 .1425 00 772 21 68919
75-0 «3025 01 .4795 01 .1805 00 709 16 63497
90.0 .2665 01 .4105 01 .1735 00 618 12 63962
105-0 .9415 00 .1195 01 .1075 00 139 13 56189
FOR .2615 00 ousaE-oa
BACK .1555 02 .2635 00
03955 02 OIIIE 01

TOTAL CROSS SECTION I 3905 M81 900 MB (TBTAL ERROR-23 Z )

1“ N P SPALLATION CROSS SECTION FOR MASS 6 I E82508 MEV
N. 760607 P.4o27CM HG 0..503E 01 H.26.9CM R.27.5CM B..o7SCM
CONTRIB.
LAB DIFF. 78 TOTAL ASSIGNED Law 5 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERRBR YIELD C699. CBUNTS
15-0 .6315 01 .2685 01 .1925 00 917 527 30315
30-0 .1485 01 .368E 01 .589E 00 758 351 60967
65.0 .3515 01 .406E 01 .9525 00 322 280 59020
60.0 .1565 01 .2215 01 .4525 00 296 200 133142
75.0 .9655 00 .1505 01 .3975 00 177 196 182690
90.0 .5805 00 .1115 01 .328E 00 88 12» 174110
110.0 .2075 00 .4245 00 .1165 00 33 37 150363
FOR .3395 00 .6235-01
BACK .3255 00 .890E-01
0163E 02 03485 01

TOTAL CROSS SECTION I 1603 MB:

307 M18 (TOTAL ERROR323 %

84

Table 8. (continued)

1“ N P SPALLATIBN CROSS SECTION FOR MASS 7 } E'2508 MEV

Ni 760607 2.4.a7cv HG 00.5035 01 H'2609CM Q32705CM B'OO7SCV

CBNTQIBO
LAB DIFF. T6 TOTAL ASSIGNED Law 5 MONITBR
ANGLE CRess SECT. CRess SECT. ERRBR YIELD CERR. CBUNTS
1500 .5595 01 .2375 01 .1865 00 1089 139 30315
3000 oh82E 01 03965 01 0&86E 00 906 287 60967
45-0 .3765 01 .4355 01 .3905 00 539 106 59020
6000 .3055 01 .934E 01 .972E 00 769 205 133192
75.0 02255 01 .3576 01 .hSSE 00 6&6 293 182690
9000 01605 01 03055 01 0522E 00 388 196 174110
11000 01095 Cl 0213E 01 -“3OE 00 212 139 150363
FOR .300E 00 .2355-01
BACK .1635 01 .3295 00
.257E 02 .33uE 01
TOTAL CRBSS SECTION . 25-7 MB: 4.2 MB (TOTAL 53962.16 3 1
19 N P SPALLATIBN CRBSS SECTION FOR MASS 1c 1 5.25.8 MEV
NI 760607 p10027CM HG OBUSOBE 01 H82609CM R82705CM B'OO7SCM
CBNTRIBO
LAB DIFF. T6 TOTAL ASSIGNED L0. 5 MONITER
ANGLE CROSS SECT. CROSS SECT. ERReR YI£LD CBRR. CBUNTS
15-0 .2375 02 .1015 02 .1265 01 “069 1351 30315
30-0 01865 02 01535 02 02365 01 3189 1417 60967
65.0 .1265 02 .1465 02 .2785 01 1317 320 59020
6000 0730E 01 0104E 02 0250E 01 1208 1122 133142
75.0 .3555 01 .5625 01 .1675 01 571 331 182690
9000 01605 01 .306E 01 0111E 01 160 #26 174110
110.0 .5915-01 .1215 00 .6125-01 7 13 150363
‘ FOR .1276 01 .159E 00
BACK .9285-01 .3165-01
06055 02 0119E 02

TOTAL CRGSS SECTIBN I 6005 M81120? MB (TBTAL ERRBRIEO x )

85

Table 8. (continued)

14 N P SPALLATION cRess SLCTION FOR MASS 11 : 5-25.8 M5v

NI 760607 P.4.27CH HG 0-.503E O1 H-26.9CM R.27.SCM BIoo7SCH
CBNTRIBO
LAB DIFF. TO TBTAL ASSIGNED Law 5 HBNITOR
ANGLE CROSS SECT. CROSS SECT. eRRBR leLD CORR. COUNTS
15.0 .4045 c1 .1715 01 .1985 00 716 207 30315
30-0 .3185 01 .2615 01 .4215 00 537 250 60967
#5-0 .2725 01 .3155 01 .5365 00 312 155 59020
60-0 .2065 01 .2925 01 .3445 00 508 148 133142
75-0 -1665 01 .2635 01 .2475 00 542 114 182690
90'0 0199E CI 03805 01 .6635 00 476 250 170110
110.0 .1105 01 .2265 01 .5695 00 187 186 150363
562 .2175 00 .2515-01
BACK .3465 01 .872E 00
.228E 02 .3875 01

TOTAL CROSS 5551105 - 22-8 MB: 5-6 MB (TBTAL ERRBRIB5 % 1

1“ N P SPALLATIBN CROSS SECTIBV FOR MASS 6 3 Esagoé ”EV

N-1026222 2.4.115” HG 0..7485 01 HI26-2CM 8.27.6CM BI-C76CV
CONTRIBI
LAB DIFF. TO TOTAL ASSIGNED L0. 5 MONITBR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CBRR. CSUNTS
20.0 .6475 C1 .2485 01 .639E-01 1479 12 32621
25.0 .649E 01 .1505 01 .9555-01 1278 170 39030
30-0 .6395 01 .376E 01 .236E 00 1638 219 62753
45.0 .8075 01 .4725 01 .4155 00 1153 235 103680
60.0 .2655 01 .3765 01 .4205 00 738 203 132042
7500 0116E 01 IISHE 01 08925.01 45“ 18 168217
90.0 .7775 00 .1275 01 .1165 00 340 64 223078
105.0 .5085 00 .8055 00 .9135-01 223 57 228391
120.0 .4805 00 .6825 00 .1415 00 132 89 171014
FOR .6185 00 .1595-01
BACK .5905 00 .1225 00
.2205 02 .1815 01
TOTAL CROSS SECTION . 22.0 MB: 2.2 MB (TOTAL 58208.10 2 >

86

Table 8. (continued)

14 N P SPALLATIBN CROSS SECTION FOR MASS 7 1 5.33.6 MEV

NI1026222 P.4.11CM HG 0..7485 01 H226.25M R.27.6CH 8:.0765M
CONTRIBI
LAB DIFF. TO TOTAL ASSIGNED Low 5 MBVITOR
ANGLE CROSS $557. 08035 SECT. ERROR YIELD CORR. COUNTS
20-0 .3505 01 .1345 01 .5695-01 765 42 32621
25.0 .3405 01 .7875 00 .4455-01 690 68 39030
30.0 .3165 01 .1865 01 .1035 00 833 85 62753
45-0 .2555 01 .2965 01 .1865 00 775 95 103480
60-0 .2045 01 .2905 01 .242E 00 615 111 132042
75.0 .1505 01 .2375 01 .1485 00 547 60 168217
90-0 -1185 01 .194E 01 .1585 00 523 90 223078
105-0 -9085 00 .1445 01 .2035 00 364 136 228391
120.0 .6005 00 .8525 00 .9145-01 225 51 171014
FBR .3345 00 .1425-01
BACK .737E 00 .7905-01
01755 02 01335 01
TOTAL CROSS SECTION . 17.5 MB: 1.8 MB (TOTAL ERROR-10 % 1
14 N P SPALLATIBN CRBSS SECTION FBR MASS 10 1 5-28.6 MEV

N91026222 Psho11CM HG 03.748E 01

LAB
ANGLE

2000
25-0
30-0
“500
60-0
7500
90-0
105-0
120-0
FOR
BACK

TOTAL CROSS SECTION I 57-2 MB: 8-2 ”B (TBTAL ERRBRII“ %

CONTRIBI
DIFF. T0 TGTAL
CROSS SECT. CROSS SECT.

'182E 02 06955 01
.1755 0? 04055 01
01595 02 09355 01
-101E 02 0117E 02
0691E 01 09825 01
0391E 01 I620E 01
.197E 01 03235 01
.1205 01 .1905 01
.878E 00 01255 01
01735 01

.1085 01

05725 02

HI26I2CM

ASSIGNED

gRRBR YleLD
0364E 00 3761
.3725 00 3196
0687E 00 395“
01035 01 2833
-138E 01 1768
0119E 01 98C
.758E 00 547
ISBBE 00 251
o“76E 00 96
0908E'01
04125 00
I735E 01

R32706CM BIIO76CM

LEW E MOVITBR

CSRRO

421
707
667
597
687
607
478
408
308

)

CBUNTS

32621
39030
62753
103480
132062
168217
223078
228391
17101“

87

Table 8. (continued)

14 k P SPALLATION CROSS SECTION FOR MASS 11 1 [-28.6 MEV
N-1026222 2.4.115" HG 0..7485 01 HI26-2CM R.27.6CM B-.076CN
CONTRIBI
LAB DIFF. TO TOTAL ASSIGNED Law 5 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR Y15LD CORR. COUNTS
20-0 .4125 01 .1585 01 .180E 00 790 210 32621
25.0 .7125 01 .1655 01 .3605 00 895 693 39030
3000 I406E 01 02395 01 05525 00 637 543 62753
95-0 -1955 01 .227E 01 .3955 00 437 229 103980
60-0 -1565 01 .222E 01 .2995 00 411 144 132042
75-0 -1285 01 .2035 01 .1195 00 476 44 168217
90.0 08935 00 .146E 01 .938E-01 420 #6 223078
105.0 .1095 01 .1735 01 .3175 00 384 217 228391
120.0 .9705 00 .1385 01 .3445 00 225 221 171014
FOR .3945 00 .4495-01
BACK .238E 01 .596E 00
.1955 02 .3305 01
TOTAL CROSS SECTION I 19-5 MB: 4-6 M8 (TBTAL ERROR-23 % )

TOTAL CROSS SECTION I 23-1 M81 1-9 "B (TSTAL ERRBRI 8 K )

14 N P SPALLATION CROSS SECTION FOR MASS 6 1 [331.9 MEV
N3 1570“ P.5.36CM HG QIIIOOE 00 H32507CM RI2603CM 880076CN
CONTRIB.
LAB DIFF. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. [RROR YXELD CORR. COUNTS
15-0 .7155 01 .3035 01 .758E-01 2307 70 28419
30.0 .576E 01 .972E 01 .3366 00 1075 164 35519
45.0 .401: 01 .4655 01 .2715 00 2206 27“ 73288
60-0 .257E 01 .365E 01 .321E 00 504 96 71363
75.0 .1805 01 .2855 01 .2315 00 382 61 83930
90.0 .104E 01 .1715 01 .128E 00 282 35 107217
105-0 .5855 00 .9275 00 .8245-01 164 23 108880
12000 .4355 00 .6185 00 .673E-01 123 23 102567
FOR .384E 00 -9605-02
BACK .534E 00 .5835-01
.231E 02 .1586 01

Table 8.

14 N P SPALLATIBN CROSS SECTION FOR MASS

(continued)

88

N. 15704 pl5036CN HG 0.0100E 00 H.2507CM

LAB
ANGLE

15-0
30-0
4500
6000
7500
9000
10500
120-0
FOR
BACK

TOTAL CROSS SECTION I 1404 MB: 108 MB (TOTAL ERROR-13 Z )

14 N P SPALLATION CROSS SECTION FOR MASS 10 :

CONTRIB0
DIFF0 TO TOTAL
CROSS SECT0 CROSS SECT0

-2635 01 -112E 01
0214E 01 0175E 01
01785 01 02075 01
.2125 01 '301E 01
'144E 01 02285 01
-822E 00 -1355 01
07205 00 '11“: 01
05815 00 0825E 00
01415 00

07145 00

0146E 02

ASSIGNED
ERROR

-557E-01
-121E 00
0163E 00
04455 00
0271E 00
010“E 00
0102E 00
09155-01
-706E-02
07925-01

.144E 01

7 1 5-31.9 MEV
R.26.3CM B-.076C"
LOW 5 MONITOR
YIELD CORR. COUNTS

808 67 28419
411 49 35519
941 163 73288
353 142 71363
276 78 83930
226 24 107217
200 30 108880
159 36 102567

N. 15704 P05036CM HG 0.01005 00 H025.7CM

LAB
ANGLE

15-0
30-0
6500
60-0
75-0
90-0
105-0
12000
FOR
BACK

TOTAL CROSS SECTION - 45.9 MB; 5.2 MB (TOTAL ERROR-11 %

CONTRIB.
DIFF0 TO TOTAL
CROSS SECT. CROSS SECT.

'146E 02 0621E 01
.1145 02 09385 01
0746E C1 08665 01
0574E C1 08155 01
03805 01 I603E 01
0214E 01 0351E 01
0107E 01 01705 01
0554C 00 0787E 00
0787E 00

0681: 00

04595 02

ASSIGNED
52202

0263E 00
05786 00
.310E OC
010“E 01
0111E 01
0789E 00
0280E 00
.1545 00
0333E'01
0133E 00

0469E 01

El3109 MEV
R32603CM BIOC76CH
Low 5 MONITOR
YIELD CBRR. COUNTS
4477 390 28419
2171 289 35519
4311 304 73288
1006 335 71363
594 343 83930
361 290 107217
234 109 108880
116 70 102567

I

Table 8.

14 N P sPALLATION CROSS SECTION FOR MASS 11 1

(continued)

39

N- 15704 P.5.36CM HG 0..1005 00 H.25.7CM

LAB
ANGLE

15-0
30-0
4500
6000
7500
90-0
105.0
120-0

FOR
BACK

TOTAL CROSS SECTION I 2203 MB: 5-6 “B

14 N P SPALLATxeN CROSS SECTION FOR MASS 6 1

CONTRIB0
DIFFO TO TOTAL
CROSS SECT. CROSS SECT.

0572E C1 0243E 01
.6485 01 .5325 01
.3505 01 .4065 01
0178E 01 02525 01
09135 00 01455 01
0697E 00 01195 01
0748B 00 0119E 01
01015 CI 01435 01
03075 00

0297E 01

02235 02

ASSIGNED
ERReR

00055 00
01245 01
01015 01
0‘22E 00
01815 00
0107E OC
0825E'01
0309E 00
0513E'01
.5365 00

.4345 01

5.3109 MEV
R.26.3CM 80.076CM
LON E MONITOR
YIELD ceRR. COUNTS
1271 631 28419
746 649 35519
1091 1074 73288
280 135 71363
175 50 83930
182 30 107217
221 18 108880
194 144 102567

(TOTAL ERROR-25 %

)

No 78775 P-40SOCM HG 0:0588E 00 HI2403CM

LAB
ANGLE

15-0
30-0
4500
6000
7500
90-0
10500
12000
FOR
BACK

CONTRIB0
DIFFO T0 TOTAL
CROSS SECT0 CROSS SECT0

0813E 01 0345E 01
0696E 01 05715 01
04825 01 .5595 01
-3005 01 -427E 01
02035 01 03215 01
0149E 01 02455 01
-9035 00 0143C 01
01065 01 01515 01
04375 00

0130E 01

02945 02

ASSIGNED
ERRoR

0185E 00
0556E 00
05655 00
03595 00
036“: 00
0019E 00
0232E 00
0271E 00
02345-01
02355 00

0321E 01

[-3501 MEV
R.25.3CM 880076CM
Law 5 MONITOR
YIELD CORR. COUNTS
6514 763 78775
1835 434 55436
1153 283 71679
988 188 115309
594 165 122957
335 168 114468
208 94 109794
119 62 50231

TOTAL CROSS SECTION . 29.4 MB: 3.9 MB (TOTAL ERROR-13 % 1

90

Table 8. (continued)

14 N P SPALLATIBN CRBSS SECTION FOR MASS 7 I E03501 HEV

NO 78775 puk050CH HG 9.05885 00 H82403CH R.26.3CH BS0076CH

CBNTRIBO
LAO DIFF. TO TOTAL ASSIGNED Law 6 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15.0 .26SE c1 o112£ 01 .1206 00 1875 498 78775
30.0 .1726 01 .1416 01 .9876-01 495 65 55436
45.0 .181E 01 .2106 01 .2316 00 427 112 71679
60.0 01706 c1 .2426 01 .2996 00 508 159 115309
75-0 .124E 01 .1966 01 .2316 00 360 103 122957
90.0 .125E 01 .2056 01 .4406 00 243 178 114468
105.0 .924: 00 .1466 01 .2536 00 206 103 109794
12000 .5456 00 .7746 00 .1986 00 47 46 50231
FOR .1426 00 .1526-01
BACK .6706 00 .1716 00
olfilE 02 0206E 01
TBTAL CROSS SECTION . 14.1 MB: 2.4 MB (TBTAL ERR6R017 z 1
14 N P SPALLATION CROSS SECTION FOR MASS 10 1 5.35.1 MEv
NI 78775 PI40SOCM HG QIOSSBE 00 Hl2403CM R02603CM BB0O76CM
C8NT9180
LAB DIFF. TO TOTAL- ASSIGNED Lew 6 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15-0 .144: 02 o614E 01 .390: 00 11306 1632 78775
30.0 .127E 02 .1046 02 .138E 01 3038 1090 55436
45.0 .948E 01 .1106 02 .1986 01 1813 1013 71679
60.0 .5286 01 .7496 01 .8916 00 1581 485 115309
75-0 02746 01 04346 01 .6106 00 742 283 122957
90.0 .1956 01 .3206 01 .7846 00 337 320 114468
105.0 .239: 01 .3795 01 .1045 01 363 436 109794
120-0 .826E 00 .1176 01 .3956 00 47 94 50231
FOR .7776 00 .4946-01
BACK .1026 01 .3416 00
0493E 02 07855 01

TOTAL CROSS SECTION . 49.3 MBt 8.5 MB (TOTAL ERROR-17 % >

91
Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 11 3 EI35.1 MEv

N. 73775 R.4.50CM HG 00.5886 00 H-24-3CH

LAB
ANGLE

1500
3000
#500
6000
7500
9000
10500
12000
FOR
BACK

CONTRIBO
DIFF0 T0 TBTAL
CRBSS SECT. CRGSS SECT.

06126 01 .2606 01
04655 01 03815 01
0329E 01 03815 01
02335 01 0331E 01
01436 01 02275 01
.7376 00 01215 01
0314E CO 0“985 00
01315 01 01865 01
0329E 00

0323E 01

0229E 02

R.26.3CM 800076CM

TBTAL CRBSS SECTION I 2209 MB: 603 MB (TBTAL ERRBRIEB X 1

14 N P SPALLATION CROSS SECTION FOR MASS 6 1

NI 126329 p.2011CM HG 0.02745 01

LAB
ANGLE

1500
3000
“500
6500
8500
10500
FOR
BACK

CONTRIBO
DIFFO T0 TBTAL
CROSS SECT0 CRBSS SECT0

08515 01 03615 01
05752 01 04715 01
04542 01 06275 01
03025 01 0598E 01
02612 01 05685 01
01362 01 03935 01
00585 00

03385 01

0360E 02

ASSIGNED LBW E MBNITOR
ERROR YIELD CBRRo CGUNTS
0322E 00 412“ 1353 78775
05892 00 1052 464 55436
06765 00 636 344 71679
0868: 00 436 477 115309
00825 00 312 225 122957
09315.01 222 26 114468
0723E'01 79 26 10979“
05555 00 92 132 50231
0408E'01
0960E 00
.4666 01
5'3709 MEV
H'2‘H2CM 9:24.80” 8"108CM
ASSIGNED LBW E M5N1TBR
ERROR YIELD CORR. CBUNTS
0263E 00 2885 478 18191
0365E 00 1206 193 20822
0530E 00 707 132 22031
.569E 00 389 81 23691
0882C 00 234 99 21020
0727E 00 157 87 2077“
03335-01
0625E 00
0397: 01

TOTAL CROSS SECTION - 34.0 MB: 5.8 MB (TOTAL ERR0R017 x I

92

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 7 I 6'37o9 M6V
NI 126329 P.2.11CM HG 00.2746 01 H-24026M R.24.8CH 8-0108CM
CONTRIB.
LAB DIFF. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 03775 01 01605 01 01575 00 1203 285 18191
3000 .2836 01 .2326 01 .2726 00 533 155 20822
45.0 .2206 01 .3046 01 .3816 00 311 96 22031
65.0 .2386 01 .4716 01 .8556 00 239 131 23491
85.0 .2116 01 .4596 01 .8486 00 173 96 21020
10500 .1156 01 .2426 01 .3676 00 109 41 20774
FOR .2026 00 .1996-01
BACK .2086 01 .3166 00
.2106 02 .3226 01

TOTAL CROSS SECTION 0 2100 M81 403 MB (TBTAL ERRBRBEI % I

14 N P SPALLATION CROSS SECTION FOR MASS 10 3 5.37.9 MEv
N- 126329 P.2.11CN HG 0..274E 01 H024.2CM R.24.8CM B-o108CM
CONTRIB.
LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15-0 01256 02 .5306 01 .6916 00 3649 1281 18191
30.0 .9806 01 .8046 01 .1026 01 1787 598 20822
45.0 .7176 01 .9906 01 .1276 01 992 333 22031
6500 04666 01 09225 01 01396 01 518 206 23491
85.0 .2686 01 .5836 o1 .9806 DC 231 111 21020
105-0 01186 01 .2506 01 .4346 00 105 50 20774
FOR .6716 00 08756-01
BACK .2156 01 .3736 00
.4366 02 .6196 01

TOTAL CROSS SECTION . 43.6 MB: 7.4 MB (TOTAL ERROR.17 z I

Table 8.

I

LAB
ANGLE

1500
3000
4500
6500
8500
10500
FOR
BACK

14 N P SPALLATION CROSS SECTION FOR MASS 11 1 6037.9 MEv
N- 126329 P.2.110M HG 0..2746 01 H-24-2CM R.24.3CM B-.108CM
CONTRIO.
DIFF. TO TOTAL ASSIGNED Law 6 MONITOR
CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
.9026 01 .3836 01 .5816 00 2487 1077 18191
.6786 01 .5566 01 .1036 O1 1044 606 20822
.3786 01 .5226 01 .9296 00 453 245 22031
.2486 C1 .4906 01 .1136 01 210 175 23491
.7376 00 .1606 01 .2126 00 75 19 21020
08106 00 .1716 01 .1846 00 92 14 20774
.4856 00 .7366-01
.2946 01 .3166 00
.2626 02 .4456 01

(continued)

93

TOTAL CROSS SECTION . 26.2 MB: 600 MB (TOTAL ERROR-23 % I

VAC P SPALLATIGN CRGSS SECTION FOR MASS 6 1 [037.9 MEV
N' 10000 2020110M HG 0003006 00 H.24.2CM R024.8CM 80.108CM
COVTRIBO
LAB DIFF. TO TOTAL ASSIGNED LON 6 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 02956 01 01256 01 05496-01 2038 172 25004
3000 .1146 01 09336 00 .6126-01 414 45 25006
4500 09736 00 01132 01 .1442 00 258 80 30003
6000 01026 01 01445 01 09306-01 330 29 37027
FBR 01585 00 06966-02
BACK 0442E 01 0284E 00
0933E 01 06442 00

TOTAL CROSS SECTION .

903 MB: 209 MB

(TOTAL ERROR031

94

Table 8. (continued)

VAC P SPALLATION CROSS SECTION FOR MASS 7 1 6'37.9 MEV
N. 10000 P.2.11CM HG 0..3006 00 H.24.aCM R.24.gCM Bun-108CH
CONTRIB0
LAB DIFF. TO TOTAL ASSIGNED LOW 6 MBNITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15cc .1896 01 .8026 00 .3496-01 1316 100 25004
3000 09946 00 .815E 00 .968E-01 312 89 25006
#500 0774E 00 08985 00 .1295 00 197 72 30003
6000 .7256 00 .Ian 01 ~8556-01 224 32 37027
FOR 01025 00 .042E-02
BACK .3152 01 .262E 00
06795 01 06125 00

TOTAL CROSS SECTION 8

VAC P SPALLATION CROSS SECTION FOR MASS 10 3

N. 10000 P.2.11CM HG o..3006 oo H.24-ECM

LAB
ANGLE

15-0
3000
4500
6000

FOR
BACK

TOTAL CROSS SECTION 0

608 MB: 202 MB

CONTRIB.
DIFF. TO TOTAL
CROSS SECT. CROSS SECT.

01025 01 04315 00
00215 00 03455 00
0553E 00 06412 00
03712 00 05275 00
05465-01

01615 01

0361E 01

ASSIGNED
ERROR

0639E'01
02575-01
0059E'01
04035-01
08096.02
.1355 00

0323E 00

YIeLD

540
162
183
131

(TOTAL ERROR-32 Z

I

E33709 MEV

LOW E
C6990

221
8
9
0

R.2h.8CM BI0108CH

MONITOR
COUNTS

25004
25006
30003
37027

306 MB: 101 MB (TOTAL ERROR-32 % I

95

Table 8. (continued)

VAC P SPALLATION CROSS SECTION FOR MASS 11 3 E'3709 MEV

...-...U.......-.-.....-.--..---..-....-.-.-.....--......-.-

N' 10000 P02011CM HG 0003005 00 H.2402CM R82408CM 880108CN

, CONTRIBO

LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15cc .5905 00 .2506 00 .1176-01 431 11 25004
3000 0396E 00 0325E 00 02955.01 141 19 25006
4500 0357E 00 0414E 00 0449E-01 106 18 30003
6000 04305 00 06115 00 08282-01 116 36 37027

FOR 03175-01 0149E-02

BACK 0187E 01 02535 00

03505 01 .424E 00

TOTAL CROSS SECTION 0

14 N P SPALLATION CROSS 55CTION FOR MASS 6 1

No 80353 P01037CM HG QI0284E 01

LAB
ANGLE

1500

3000
4500
6000
7500
9000
10500
12000
13000
FOR
BACK

CONTRlao
DIFF0 T3 TOTAL
CROSS SECT. CROSS SECT.

0486E 01 02065 01
04355 01 03565 01
03395 01 0394E 01
0249E 01 03545 01
0155E 01 0245E 01
01035 01 01685 01
08275 00 01315 01
0607E 00 07275 00
08845 00 07425 00
02615 00

01635 01

02195 02

TOTAL CROSS SECTION I 2109 MB!

H.2601CM

ASSIGNED

ERROR YIELD
01915 C 1600
0387f 00 1099
0448E 00 911
04185 00 886
.351E 00 534
02835 00 305
02775 00 232
.1406 00 233
.1422 00 106
0242E'01
0313E 00
02985 01
308 MB

305 M8: 1.4 MB (TOTAL ERROR-39 X )

E04000 MEV

I.-.-----..---.-.-.--nouns-u.-......----¢.-----.----I--.OC-C

LOW E
CORRO

352
296
260
266
208
149
165
141

61

R02702CM BIOO76CM

MONITOR
COUNTS

29916
44452
66624

108429

124779

118344

123330

141192
37035

(TOTAL ERROR-18 X )

Table 8 .

14 N P SPALLATION CROSS SECTION r00 MASS 7 1

NI 80353 P01037CM HG 0002845 01

LAB
ANGLE

1500

(continued)

3000
4500
6000
7500
9000
10500
12000
13000
FOR

BACK

96

CONTRIBO
01550 T0 TOTAL
CROSS SECT. CROSS SECT.

02235 01 09475 00
01475 01 01215 01
0159C 01 01855 O1
01075 01 01525 01
09526 00 01515 01
08325 00 01365 01
05215 00 08255 00
06025 00 07225 00
06355 00 05335 00
01205 00

01175 01

01185 02

TOTAL CROSS SECTION I 1108 MB:

14 N P SPALLATION CROSS SECTION FOR MASS 10 3

N0 80353 901037CM HG 0002845 01

LAB
ANGLE

1500
3000
4500
6000
7500
9000
10500
12000
13000
FOR

BACK

CONTRIB0
01550 T0 TOTAL
CROSS SECT0 CROSS SECT0

07885 01 03345 01
07525 01 06165 01
05595 01 06495 01
.3942 01 .5606 01
02165 01 03435 01
01385 01 02265 01
09695 00 01535 01
08665 CO 01045 01
06936 00 05825 00
04235 00

06385 00

03155 02

H.2601CM

ASSIGNED

ERReR YIELD
01115 00 691
01065 00 398
02245 00 422
01745 00 389
02115 00 334
02035 00 263
01225 00 181
01265 00 245'
09545.01 81
01415.01
02095 00
01605 01

202 MB (TOTAL ERROR-19 X

5'4000 MEV

LON 5
CORRO

204
74
127
107
123
105
69
126
39

R02702CM B'0076CM

MONITOR
COUNTS

29916
44452
66624
108429
124779
118344
123380
141192
37085

)

[-4000 MEV

H026.1CM R.27.2CM
ASSIGNED LOW 5
ERROR YIELD CBQR0
04855 CO 2250 912
08885 00 1722 690
09395 00 1376 554
09785 00 1191 633
07075 00 613 426
04795 00 354 256
03495 00 256 209
.2925 CC 235 299
01695 CC 56 75
06145'01
01865 00
05535 01

88.076CN

MBVITOR
COUNTS

29916
44452
66624

108429

124779

118344

123380

141192
37085

TOTAL CROSS SECTION - 31.5 MB: 509 M8 (TOTAL ERROR-19 X I

Table 8.

LAB
ANGLE

(continued)

1500
3000
4500
6000
7500
9000
10500
12000
13000

FOR
BACK

97

14 N P SPALLATION CROSS SECTION FOR MASS 11 I 5040.0 MEv
N- 80353 Pa1037CM HG 0.02845 01 H32601CM R02702CM 580076CH
CONTRIB0
DIFF0 TO TOTAL ASSIGNED LOW 5 MONITOR
CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
01065 02 04525 01 01025 01 2351 1924 29916
06965 01 05715 01 01275 01 1243 992 44452
03275 01 03795 01 07745 00 669 458 66624
01525 01 02155 01 05165 00 367 334 108429
.1075 01 01705 01 04945 00 216 298 124779
05095 00 08345 00 08235-01 189 36 118344
05425 00 08585 00 08065-01 220 40 123380
05635 00 06755 00 .4745-01 312 35 141192
07895 00 06625 00 07075-01 126 23 37085
05725 00 01295 00
01455 01 01555 00
02295 02 04645 01

TOTAL CROSS SECTION 0 2209 MB:

14 N P SPALLATION CROSS SECTION FOR MASS 6 1

5.5 MB (TOTAL ERROR-24 x

I

N0 81252 P.2.16CM HG 0--260£ 01

LAB
ANGLE

15-0
3000
4500
6500
9000
11000
FOR
BACK

CONTRIB0
01550 TO TOTAL
CROSS 555T0 CROSS SECTO

06065 01 02575 01
05235 01 '429E 01
03915 01 0540E 01
02325 01 .5215 01
01555 01 03805 01
01085 01 02215 01
03265 00

01695 01

02555 02

504109 "EV
H.24.4CM R.24.7CM B-.108CM
ASSIGNED Law 6 MONITOR
gRROR YIELD CORR. COUNTS
.1455 00 5663 699 32758
.3935 00 2550 561 34451
.5416 00 1260 306 32341
.416E 00 557 93 28185
.4415 00 252 68 22688
.3956 00 212 113 30979
01835-01
03035 00
.2656 01

TOTAL CROSS SECTION 0 2505 MB: 306 MB (TOTAL ERROR-14 % I

98

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 7 8 E'4109 "EV

NI 81252 P02016CM HG 0802605 01 H'2404CM R02407CM 5"108C"

CONTRIBO
LAB DIFF. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0303E 01 01295 01 09325001 2736 «#9 32758
3000 .2605 01 ~213E 01 .209E 00 1251 295 3““51
45.0 .2242 01 .309: 01 .380E 00 681 210 32341
65-0 .150: 01 .346E 01 .362E 00 349 83 28185
9000 0125B 01 .305E 01 .3995 00 196 61 22688
110.0 .8315 00 .1705 01 .273E 00 175 76 30979
FOR .163E 00 .1185001
BACK .1315 01 .209E 00
01625 02 01945 01

TOTAL CROSS SECTION . 16'? M8: 2.6 MB (TOTAL ERROR-16 X 1

1. N P SPALLATION CROSS SECTION FOR MASS 10 a

No 81252 P.2016CN HG 0002605 01 H02404CH 8024075H 5801085M
CONTR180
LAB DIFF. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15-0 0885E 01 .376E 01 .0316 00 7167 2123 32758
30.0 .7175 O1 .5385 01 .421E 00 3661 598 30051
4500 0554E 01 07655 01 01045 01 1618 600 32341
6500 03215 01 07205 01 08395 00 696 203 28185
9000 0140E 01 03435 01 05605 00 199 90 22688
11000 0804E 00 01655 01 .2535 00 173 70 30979
FOR 04765 00 05455-01
BACK 01265 01 01945 00
03135 02 03805 01
TOTAL CROSS SECTxON 0 3103 M81 405 MB (TOTAL ERROR-1“ X )

504109 M5V

Table 8.

LAB
ANGLE

15'0
3000
4500
6500
9000
11000
FOR

BACK

(continued)

99

14 N P SPALLATION CROSS SECTION FOR MASS 11 : E-4109 MEv
N- 81252 P02016CM HG 0002605 01 H32404CM 9024075“ 5.01085”
CONTRIB0
DIFF. TO TOTAL ASSIGNED Lew E MONITOR
CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
.973E 01 .413E 01 .452E 00 7980 2229 32758
.6495 01 05325 01 .7435 00 2787 1072 34451
.417E 01 .575E 01 .100E O1 1390 578 32341
~155E 01 .348E 01 .716E 00 259 176 28185
.606E 00 .148E 01 .1685 00 105 20 22688
.642: 00 .132E 01 .109E 00 175 19 30979
05235 00 05725-01
.2025 01 .167E 00
02405 02 0342E 01

TOTAL CROSS SECTION . 24.0 MB: 4.5 MB (TOTAL ERRORs19 z )

14 N P SPALLATION CROSS SECTION FOR MASS

N- 760607 Pu4027CM HG 0005035 01

LAB
ANGLE

1500
3000
4500
6000
7500
9000
11000
FOR
BACK

TOTAL CROSS SECTION 0

CONTRIB.
DIFF. TO TOTAL
CROSS SECT. CROSS SECT.

09885 00 04205 00
07405 00 06075 00
06295 00 07295 00
.1325 CO 01875 00
02785901 04415901
.246E-01 .4715-01
.5916-02 01215-01
05315-01

09285-02

02115 01

201 MB:

9 I 532508 M5V
H8260959 R327.SCM BIOO7SCF

ASSIGNED LON E MONITOR

ERROR YIELD COQR0 COUNTS
.1015 00 119 107 30315
01815 00 75 108 60967
02625 00 31 77 59020
06385-01 14 28 133142
01205-01 11 0 182690
01575001 9 0 174110
06065902 2 0 150363
01285-01
04645.02
06595 00 -

07 MB (TOTAL 5RROR032 X

)

100

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 9 3 502806 M5V

N'1026222 P04011CM HG 0807485 01 H'26'2CM R027065M 8.00765H
CONTRIB.
LAB 01550 TO TOTAL ASSIGNED LOW 5 MBVITOR
ANGLE CROSS SECT. CROSS SECTo ERROR YIELD CSRR. COUNTS
20cc .235E 01 .901E 00 .123E 00 399 143 32621
2500 02235 01 05165 00 07465901 358 139 39030
30-0 01915 01 .112E 01 .195E 00 366 189 62753
“5'0 01345 01 01555 01 03765 00 237 219 103480
6000 05975 00 08485 00 01835 00 123 89 132042
7500 04165 00 06605 00 02345 00 50 119 168217
9000 02275 00 03725 00 01005 00 56 62 223078
10500 0763E-01 01215 00 03915.01 16 26 228391
12000 01245 00 01765 00 06155-01 18 39 171014
FOR 02255 00 03075'01
BACK 01525 00 05325-01
06655 01 01475 01

TOTAL CROSS SECTION 0 606 MB: 106 MB (TOTAL ERROR024 z )

14 N P SPALLATION CROSS SECTION FOR MASS 9 3 5'3109 M5V
N. 1570“ P350365M HG 0301005 00 H32507CM R326g3CM 88.0765H
CBNTRIBO
LAB DIFFn TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 .291: 01 .124E 01 .100E 00 822 147 28419
3000 01845 01 01515 01 01085 00 351 44 35519
4500 0109E 01 01265 01 06575-01 622 51 73288
6000 0809E 00 01155 01 0152E 00 145 44 71363
7500 02965 00 04705 00 08925-01 48 25 83930
9000 0240E 00 03945 00 01025 00 37 36 107217
10500 0206E 00 03275 00 01115 00 22 44 108880
12000 0864E-01 01235 00 03055-01 17 12 102567
FOR 01575 00 01275.01
BACK 01065 00 02645-01
06735 01 07995 00

TOTAL cness SECTION -

607 MB:

.9 Me (TOTAL ERROR613 z

)

101

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 9 I 5'3501 05V
NI 78775 P04050CM HG 0005885 00 14024035M R02603CM 8800765"
CONTRIBO
LAB DIFE0 TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT0 ERROR YIELD CORR. COUNTS
1500 0368C 01 01565 01 01695 00 2589 708 78775
3000 03175 01 02605 01 04155 00 707 326 55436
4500 02036 01 02355 01 03685 00 420 185 71679
6000 01175 01 01665 01 03605 00 263 196 115309
7500 09755 00 01555 01 04625 00 148 217 122957
9000 04935 00 08095 00 02425 00 68 98 114468
10500 02725 00 04315 00 01315 00 37 54 109794
12000 0117Eoo1 01665-01 .8335-02 2 0 50231
FOR 01985 00 02155-01
BACK 01445-01 07205-02
01125 02 02185 01

TOTAL CROSS SECTION 0 1102 MB: 202 V8 (TBTAL ERRBR'ZO % 1

14 N P SPALLATION CROSS SECTION FOR MASS 9 1

N- 126329 P02011CV HG 0002745 01

LAB
ANGLE

1500
3000
4500
6500
8500
10500
FOR
BACK

TOTAL CROSS SECTION 0 1105 MB: 201 PB (TOTAL ERROR-13 %

CONTRIB0
DIFF. TO TOTAL
CROSS SECT0 CROSS 85CT0

04035 01 01715 01
02435 01 01995 01
01755 01 02415 01
01215 c1 02395 01
06355 00 01385 01
03445 00 07255 00
02165 00

06245 00

01155 02

Hl24085M

ASSIGNED

ERROR YIELD
02255 00 1178
02005 00 480
03055 00 247
04435 00 122
02375 00 57
01665 00 27
02855-01
01435 00
01755 01

E83709 M5V

LOW 5
50020

413
111
76
66
24
18

R32408CM B30108CM

MONITOR
COUNTS

18191
20822
22031
23491
21020
20774

)

Table 8.

102

(continued)

VAC P SPALLATION CROSS SECTION FOR MASS 9 3 5'3709 M5V
N' 10000 PI2011CM HG 0803005 00 H'2402CM R02408CM O'OIOBCV
CONTRIBO
LAB 0155. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT0 ERROR YIELD C8990 COUNTS
1500 08435 00 I3585 CO 03625.01 512 120 2500“
3000 03945 00 03235 00 02605.01 150 9 25006
4500 0492E 00 05715 00 .417E-01 164 7 30003
6000 0292E 00 04142 00 04022-01 103 0 37027
FOR 04535-01 04585-02
BACK 01275 01 01235 00
02985 01 02725 00
TOTAL CROSS SECTION I 300 MB: 09 MB (TOTAL ERROR-31 )

14 k P SPALLATION CROSS SeCTION FOR MASS 9 3 504000 MEV
N- 80353 9.1037CM HG 0.0284E 01 H02601CM R02702CM Bu0076CV
CONTRIB.
LAB DIFF0 78 TOTAL ASSIGNED L00 E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 02685 01 01145 01 01885 00 725 351 29916
3000 0210E 01 0172E 01 0267E 00 468 205 44452
4500 01725 01 0199E 01 03425 00 392 200 66624
6000 0962C 00 0137E 01 02755 00 269 176 108429
7500 04585 00 07265 00 01435 00 136 84 124779
9000 03626 00 05935 00 0145E 00 84 76 118344
10500 034oE 09 05385 00 01615 00 67 96 123380
12000 0177E 00 02125 00 04195-01 69 40 141192
13000 03496 00 0293E 00 0787E-01 32 34 37085
509 01445 00 02385001
BACK 06435 00 01735 00
09365 01 01845 01
TOTAL CROSS SECTION 0 904 MB: 202 MB (TOTAL ERROR=23 % )

103

Table 8. (continued)

14 N P SPALLATION CROSS SECTION FOR MASS 9 1 204109 MEV
NI 81252 902016CM HG 00026OE 01 H82404CM R02407CM 800108CP
CBNTRIBO
LAB DIFF0 TO TOTAL ASSIGNED Law E MBNITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELC CORR. COUNTS
1500 03216 01 01365 01 01402 00 2687 686 32758
3000 02485 01 0203E 01 .2095 00 1178 295 34451
4500 01562 01 0216E 01 .3076 00 453 173 32341
6500 01275 01 0285E o1 0591E 00 211 145 28185
9000 0528E 00 01305 01 02785 00 65 44 22688
11000 0298E 00 06115 00 09516-01 67 23 30979
FOR 0173E 00 0178E-01
BACK 04685 00 0728E-01
0110E 02 0171E 01
TOTAL CROSS SECTION 0 1100 M81 200 MB (TOTAL ERROR018 x 1

VAC P SPALLATION

CROSS SECTION FOR MASS

NI 242535 P32016CM HG 0.07135 01

LAB
ANGLE

15.0
3000
4500
6000
7500
9000

FOR
BACK

TOTAL CROSS SECTION 0

CONTRIO0
01550 TO TOTAL
CROSS SECT0 CROSS SECTo

04115 CC 01755 00
04525 CO 03715 00
07505 CO 08695 00
05355 00 07605 00
07335 00 01165 01
05935 CO 09735 CO
02215-01

01625 01

05955 01

509 MB: 107 MB

9 z E04109 MEV
H.2404CM 2324075M B'C1O8CV
ASSIGNED LON E MONITOR
ERRBR YIELD CHRR0 COUNTS
01275.01 165 0 13384
03755.01 115 18 18256
01485 00 103 47 17289
09435-01 102 24 24702
02265 00 69 39 17147
01445 00 65 19 16961
01615-02
02395 00
09045 00

(TOTAL ERROR=29 2

)

104

Table 8. (continued)

16 O P SPALLATION CROSS SECTION FOR MASS 6 : E033.o MEv

N- 27783 P02027CM HG 0-0307E oo H024.1CM 8.2405CM 800109cM
CONTRlflo
LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0306E 00 0130E 00 0172E-01 52 7 15872
3000 0257E 00 0211E 00 .27oE-01 «7 0 27783
#500 0161C 00 0187E 00 0356E-01 21 0 27613
6000 0199E 00 02835 00 0590E-01 18 6 30965‘
7500 04995 00 0791E OO 0128E 00 36 7 24525
FOR 0164E'01 0218E‘02
BACK .1775 01 .286E 00
0339E 01 .5555 00
TBTAL CRBSS SECTION 2 304 MB: 104 MB (TBTAL ERROR=43 % 1
16 O P SPALLATIBN CROSS SECTION FOR MASS 11 ; £03000 MEV
N- 27783 2.2.27CM HG 0.03075 00 Hagu.1CM 9.24.5CM 800109CM
CONTRIB.
LAB DIFF. TO TOTAL ASSIGNED Ow E MBNITOR
ANGLE CROSS SECT. CROSS SECT. E998R YIELD CORR0 CBUNTS
1500 0133E c1 0565E 00 0760E-01 193 ea 15872
3000 0105C C1 0863E 00 .812E-01 165 27 27783
05.0 .261E 00 0303E 00 .605E-01 23 11 27613
6000 0332E-o1 .072E-01 .2365-01 A 0 30965
7500 0813E-01 01295 00 03685-01 7 0 24525
FOR 0716E-O1 0962E-02
BACK 0289E 00 08255-01
0227E 01 .370E 00
TOTAL CRGSS SECTION 0 203 MB: 05 MB (TBTAL ERRBR023 Z )

Table 8.

16 O P SPALLATION

(continued)

CROSS SECTION FOR MASS

105

N- 79059 2.20140H HG 000141E 01
C6NTRIBO
LAB DIFF. TO TOTAL ASSIGNED
ANGLE CROSS SECT0 CROSS SECT0 ERROR
1500 0401E CO 01705 00 02035-01
3000 OESBE 00 02085 00 OBIOE'OI
#500 06205 CO 0719K OO 07965-01
6000 0473C 00 06725 00 09185'01
7500 01765 CO 02795 00 09285.01
FOR 02165-01 0258E-02
BACK 0624E CO 02085 00
02695 01 05165 00
TOTAL CROSS SECTION I 207 98: 08 MB

16 O P SPALLATIBN

N- 79459 P02018CM HG 0:0141E 01

LAB
ANGLE

1500
3000
“500
6000
7500

FOR
BACK

TBTAL CROSS SECTION 0

CROSS SECTION FOR MASS

CONTRIB.
DIFF0 TO TOTAL
CROSS SECT0 CROSS SECT0

0378E 00 01605 00
0210E 00 01725 00
0403E 00 06675 00
03055 CO 04335 00
0976E-01 01555 00
02035-01

03Q7E 00

01755 01

108 MB:

H02606CM 8.27.2CM
ASSIGNED
. ERROR YIELD CORR-
.203E-01 151 43
0205E'01 95 21
.691E-01 53 14
0766E-01 29 9
.619E-01 S O
0258E'02
0139E 00
.390E 00
06 MB (TOTAL ERROR=32 z

H32606CM

YIELD

6 I E'3307 MEV

9:2702CH
LOX E
CORRo

163 “3
120 20
89 14
51 8
9 0

(TOTAL ERROR831 %

BIOO75CV

MOVITOR

)

COUNTS

#8808

97606 '

41575
37884
17240

7 3 E'3307 MEV

8:0075CM

wa E MONITOR

)

COUNTS

#88h8
97606
“1575
37884
17240

106

Table 8. (continued)

16 O P SPALLATION CROSS SECTION FOR MASS 1o 1 5.33.7 MEv
N0 79459 P.2o14CM HG 0.0141E 01 H-26o6CM R.27.2CM Ba-O7SCM
C8NTRIBo
LAB DIFFo TO TOTAL ASSIGNED LOw E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15cc 0790E co 0336E 00 .371E-01 323 83 #88b8
3000 ~413E 00 .339E 00 .514E-01 163 65 97606
45-0 .3436 00 0398E 00 07265-01 #0 17 41575
60°C 0281E 00 03995 00 01175 00 16 19 37384
75.0 09765-01 0155E 00 .619E-01 5 o 172ao
FOR 04255-01 .469E-02
BACK 0347E 00 .1395 OC
0201E 01 04865 00
TOTAL CROSS SECTION . 2-0 MB: .7 MB (TOTAL ERROR333 X

LAB
ANGLE

15-0
3000
#500
6000
7500

FOR
BACK

16 O P SPALLATIBN CROSS 85CTION FOR MASS 11 3 5033.7 MEV
NI 79659 9:201“CM HG 0.0141E'01 H82606CM RI2702CM BUOO7SCN
CGVTRIBO
DIFF. TO TOTAL ASSIGNED Lew E MONITOR
CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
osouE 01 .341E 01 .711E 00 2a13 1718 488“?
0477C CI 0391C O1 0805C 00 1555 1081 97606
0356C 01 04125 01 0104E 01 295 296 #1575
0108C 01 0154E 01 0250E 00 95 40 37884
07035 00 0111E 01 03195 00 17 19 17240
0432K 00 0900E-01
0250E 01 0715E 00
01705 02 0393C 01

TOTAL CROSS SECTION 8 1700 MB: 503 MB (TOTAL ERROR=31 z )

Table 8.

16 O P SPALLATION CROSS SECTION FOR MASS 6 :

(continued)

107

N- 257351 P.2006CM HG 0.0508E 01 H02402CM
CONTRIB0
LAB DIFF. TO TOTAL ASSIGNED
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD
1500 0101E c1 0428E 00 .997E-01 282
3000 0525E co 0431E 00 01166 00 97
4500 0479E CO 05565 00 01435 00 81
6000 04686 00 .6655 00 0175E oo 78
7500 04715 CO 07465 00 01755 00 90
90.0 .355E 00 05835 00 01835 00 39
FOR 05425.01 01265-01
BACK 0971E 00 0305E 00
0443E 01 0121E 01

TOTAL CROSS SECTION 0

16 O P SPALLATION CROSS SECTION FOR MASS

404 “8: 1'7 MB

7 }

533709 MEV

(TOTAL ERROR039 %

R324QSCM BIOIO8CM

Lew E MBNITBR
CGRRo CBUNTS
242 26977
110 37997
82 45689
84 56450
76 63796
63 53419
1
5'3709 MEV

N0 257351 P.2-o6CN HG 000508E O1 H024-2CN
CONTRIB0
LAB DIFF. 70 TOTAL ASSIGNED
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD
1500 07665 00 0325E oo 0578E-01 260
3000 06245 CO 05125 00 01225 00 131
4500 06826 00 0791E 00 02536 00 85
6000 04086 CO 0579E 00 0129E DC 80
7500 .059E oo 0728E 00 0190E 00 77
90.0 0265E 00 00305 00 0123E 00 3“
FOR 04125-01 07325-02
BACK 07245 00 02065 00
04135 01 01095 01

TOTAL CROSS SECTION 0

LBW 5
CBRRo

138
115
147
61
85
#2

#01 V8: 105 MB (TOTAL ERROR035 x

9.24085" 880108CV

MONITOR

)

COUNTS

26977
37997
45689
56450
63796
53419

108

Table 8. (continued)

16 O P SPALLATION CROSS SECTION FOR MASS 10 I 503709 MEv
N— 257351 P-EooOCM HG 0005085 01 H02402CM 802408CM B00108CM
CONTRIBO
LAO DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0221E 01 09375 00 0148E 00 788 359 26977
3000 01S9E c1 0130E 01 .1905 00 448 178 37997
4500 0429E 00 04985 00 0165C 00 so 96 45689
6000 0442C co 0628E 00 .2215 00 46 107 56450
7500 03435 00 0503E 00 .1755 00 44 77 63796
9000 0282E 00 0463E 00 0143E 00 32 49 53419
FOR 01195 00 0188E-01
BACK 07715 00 0238E oo
0526E 01 0130E 01

TOTAL CROSS SECTION I 503 MB: 107 MB (TBTAL ERROR-32 % I

16 O P SPALLATIBN CROSS SECTION FOR MASS 11 3 [037.9 HEv
N0 257351 P02006CM HG 000508E 01 H02402CM R.2008CM 800108CM
CONTRIO0
LAB DIFF. TO TOTAL ASSIGNED LOW E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0156E oz 0664E o1 0909E 00 5913 2220 26977
3000 0107E 02 0881C 01 0141E 01 2875 1356 37997
«500 06555 01 07595 01 0104C 01 1385 841 45689
6000 0336E 01 04785 01 01005 01 678 486 56450
7500 04425 00 0701E 00 .225E oo 57 99 63796
9000 0331E 00 0503E 00 .144E 00 46 09 53419
FOR 0801E 00 01156 00
BACK 09045 00 .240E 00
03085 C2 05495 01
TOTAL CROSS SECTION 0 3008 MB: 5.1 MB (TOTAL ERROR-20 x

109

Table 8. (continued)

16 O P SPALLATION CROSS SECTION FOR MASS 6 I E00109 ”Ev
N. 242535 'P02016CH HG 900713E 01 H02400CM R02407CM B00108CM
CONTRIBO
LAB DIFF. TO TOTAL ASSIGNED L00 E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0222C 01 .902: 00 .130E 00 1599 630 33506
3000 0182C 01 0109C 01 .201E 00 730 262 33823
4500 0165C 01 0191E 01 .275E 00 069 183 30187
6000 .210E 01 .3005 01 .093E 00 721 300 52009
75.0 .1515 01 .239E 01 .020E 00 033 233 51379
9000 0112E 01 0183C 01 .373E 00 211 100 37591
FOR .119E 00 .170E-01
BACK 0305C 01 0621E 00
01485 02 02545 01

TOTAL CROSS SECTION I 1408 MB: 401 MB (TGTAL ERRBR'EB % I

16 O P SPALLATION CROSS SECTION FOR MASS 7 1 5.11.9 MEv

N0 202535 2.2.16CM HG 000713E o1 H02404CM R.20.7CM B00108CM
CONTRIB0
LAO OIFF. TO TOTAL‘ ASSIGNED Lew E MBNITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 0258E 01 .1105 01 0150E 00 1870 726 33506
3000 01815 01 .1085 01 .197E 00 729 257 33823
05.0 0168C o1 .1958 01 .2636 00 090 17“ 30187
60.0 0156E 01 02225 01 .016E 00 088 287 52009
7500 .1365 01 .2165 01 .0295 00 366 236 51379
9000 .117E 01 .191E 01 .381E 00 223 103 37591
FOR 0139C 00 019$E001
BACK .3185 01 0630E 00
.101E 02 .209E 01

TOTAL CROSS SECTION 0 1001 MB:

0.1 93 (TOTAL ERRORaa9 %

110

Table 8. (continued)

16 O P SPALLATION CROSS SECTION FOR MASS 1o 1 5.01.9 MEv

N. 202535 P02016CM HG 0..7135 01 H02404CM R.20.7CM 800108CM

CONTRIBO
LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CeRR. COUNTS
1500 .0295 O1 .1825 01 .0275 00 2293 2020 33506
3000 02295 01 .1885 01 .3255 00 818 029 33823
4500 01515 01 0175C 01 02705 00 016 180 30187
6000 .1375 01 .1955 01 .3915 00 011 270 52009
7500 01855 01 .2905 01 .706E 00 027 392 51379
90.0 .6855 00 .1125 01 .2025 00 125 90 37591
FOR .2315 00 .5015001
BACK 01875 01 04035 00
.1365 02 .2825 01

TOTAL CROSS SECTION 0 1306 MB: 308 M5 (TOTAL ERROR-28 z I

16 O P SPALLATION CROSS SECTION FOR MASS 11 I

N. 202535 2.2.16CM HG o..7135 o1

LAB
ANGLE

1500
3000
4500
6000
7500
9000

FOR
BACK

TBTAL CROSS SECTION 0 4607 M821106 "8 (TOTAL ERROR-25 %

CONTRIBO
01550 T3 TOTAL
CROSS SECT0 CROSS SECT0

02105 02 08905 01
.1245 02 01025 02
07875 01 '913E 01
04745 01 06745 01
02895 01 04575 01
01385 01 02265 01
01135 01

03775 01

04675 02

ASSIG
ERR

.1555
.1625
01575
.1485
.125E
0672E
0197C
0112E

.947E

H.2404CM

NED

OR YIELD
01 13722
01 4639
01 2003
01 1322
01 581
00 177
00
01
01

5001.9 05v

LOW 5
CBRRO

7351
2153
1071
1030
690
256

R.20.7CM 80.108CM

MONITOR

I

COUNTS

33546
33823
34187
52009
51379
37591

111

Table 8. (continued)

VAC P SPALLATION CROSS SECTION FOR MASS 10 I 500109 MEv

NI 242535 P.2016CH HG 030713E 01 H02404CM R02407CM 810108CM
CONTRIBo
LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15.0 0364C 00 01555 00 01785001 119 27 13384
3000 0350E 00 02875 00 .3855-01 82 21 18256
4500 0550E 00 06385 00 06485.01 100 10 17289
6000 06165 00 08755 00 01805 00 88 57 24702
7500 .8102 00 01295 01 .2625 00 70 06 17147
9000 0536E 00 .8805 00 .2205 00 00 36 16961
FOR 01965-01 02255-02
BACK 01475 01 .3665 00
.5615 01 01155 01

TOTAL CROSS SECTION 0 506 MB: 109 MB (TOTAL ERRBRFS‘I X )

VAC P SPALLATION CROSS SECTION FOR MASS 11 I E04109 HEV

N- 242535 202016CM HG 0007135 01 H02404CM R32407CH 800108CN

CONTRIB.
LAB DIFF. TO TOTAL ASSIGNED Law 5 MONITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
1500 02325 00 09855-01 09535-02 93 0 13384
3000 04315 00 .3545 00 .435E-01 103 24 18256
4500 054SE 00 06325 00 01065 00 76 33 17289
60.0 .6075 00 .8635 00 .1035 00 100 03 20702
7500 04275 00 06775 00 09245001 53 10 17147
9000 .0385 00 .7185 00 .1355 00 02 20 16961
FOR .1255001 .121E002
BACK 01205 01 .2256 00
.0555 01 .756E 00

TOTAL CROSS SECTION 0

0.5 MB: 100 MB (TOTAL ERROR-30 X I

112

Table 8. (continued)

VAC P SPALLATION CROSS SECTION FOR MASS 6 I 5041.9 MEV
N0 242535 P02016CM HG 00.7132 01 H-2A.OCM R.24.7CM 8-0108CM
CONTRIBO
LAB DIFF. TO TOTAL ASSIGNED LON E MBNITOR
ANGLE CROSS SECT. CROSS SECT. ERROR YIELD CORR. COUNTS
15-0 012oE c1 05085 00 .7002-01 345 135 13380
30-0 0103: 01 0807C 00 01685 00 186 118 18256
“500 01195 01 01395 01 01975 00 176 63 17289
6000 0133: 01 0190E 01 0452E oo 166 148 20702
7500 0977E 00 01555 01 .336E oo 80 60 17107
9000 .1095 01 01805 01 .352E 00 97 58 16961
FOR 06635-01 09365-02
BACK .299E 01 .5852 00
0110E 02 0218E 01

TOTAL CROSS SECTION 0 1100 MB: 307 MB (TBTAL ERROR-33 X )

VAC P SPALLATION CROSS SECTION FOR MASS 7 1 E00109 HEV

N- 2&2535 P02016CH HG 0007135 01 H02404CH R.20.7CM 80-108CM
CONTR130 A
LAB DIFF. TO TOTAL ASSIGNED LON E MONITOR
ANGLE CRoss SECT0 CROSS SECT. zRReR YIELD CORR. COUNTS
15-0 0122E 01 05205 00 0102E 00 301 190 13380
3000 010RE o1 0852E oo 0198E 00 166 100 18256
05.0 0985C 00 01102 01 .1722 00 142 55 17289
6000 08915 00 01195 01 02245 00 127 71 24702
7500 08072 00 0128E 01 02u7E 00 76 03 17107
90.0 01oAE 01 01702 01 .363E oo 87 60 16961
FOR 0658E-01 01295-01
BACK 02835 01 0600E 00
09595 01 01925 01

TOTAL CROSS SECTION 0

906 MB: 300 MB (TOTAL ERROR835 X )

Table 9.

113

Summary of Measured Cross-Sections for Proton

Spallation of

14N and

160.

TOTAL CROSS SEcTIONS FROM PROTON SPALLATION OF 14 N

 

E (MEV) MASS 6 MASS 7 MASS 9 MASS1o MASSI1
P
1700 oo. oo 360611401 -0+ -0 260411102 6709016-4
2107 301‘ 07 4102* 702 009 00 610131306 390561001
2508 1603: 307 2507* 402 201: 07 60'5t1202 22080 506
38'6 22003 202 1705: 108 6063 106 S702: 802 19051 “-6
3109 23011 109 1604: 108 6073 09 45093 502 2203: S06
3501 2904* 309 1001: 200 1102: 2'2 49.31 805 2209: 6'3
3709 2808; 508 1609: 403 905: 201 4104: 700 2308: 6-0
4000 2109: 308 :11081 202 9040 202 31050 509 2209: 505
“109 1707; 2.5 903: 1.5 608: 105 2704: 3.5 2008: 3.5

TOTAL CROSS SECTIONS FROM PROTON SPALLATION 0F 16 0
W:

 

 

 

5 ("EV) MASS 6 HASS 7 HA5310 MA5311
p
3000 105; 05 00+ 00 000 00 2'3: 05
3307 207: 08 1°81 06 200: '7 17.0: 503
3709 40#1 107 “01g 105 5033 107 30.8: 601
“109 308; 105 “05: 105 8'0: 2'5 “2.211002

m

114

 

 

 

 

 

.Aon «any UNH mo GowumHHmmm aououm “Om mcowuommlmmonu mo Ka.n§.__=..9..n.. .oH manna

.0m 4.5m «.3 «:.ma 0. Hm.m o. H:.m 0.0 «3.8m m.m Hm.a~ 0.:8
oma “cam mum “Mood m. fl¢0m mo Hm.“ ¢om Naomm m.H “mom womm
.dm «.mm fi.m «5.58 S. «6.8 6. am." m.. «5.3m 8.“ am." 0.8m
.mm 0.8““ m.“ «m.od m. an.“ m. «m. ~.m um.mm ..8 «o.m o..m
owN H-HNH Bod «hem No HB- No H0. 00m ”Nam“ Cod “Moo Comm
.om «.mufi w.“ no.0“ o. .o. o. .o. fl.m «6.6 m. «0.. m.mm
.NN “com a.“ Hook 0. +0. 0. +00 00 «mom w. “mom 06mm
oha “0:0 @- Nhom 0. +00 0. +0. 00 +0. 0. +00 00¢N
.n «.m: 0. +0. 0. +0. 0. +0. 0. +0. 0. +0. h.am

a
damm<z ofimm«z m mw<x m mm<x n mm<x o mm<z .>wz. m

 

 

u we no 70~k<44<am ZOhoaa imam mzomkumm mmmmu J<pmk

5: M SS 7
1: E=17.0 MEL:
4
10;
El
5‘1 I I
...... j I
8% m9:
5 5'5
E. _
'1
a 101.071U10for r711.
\__J (2055191499 J
3
1 [1955 11
E 5‘: 2817.0 mu
1 1-
10.5
5'3
T
0
10 :5.
5‘3
'1
10 "0T T T {Nor T F L10
COS(9LPIB]
Figure 12.

115

HNGULHR DISTRIBUTIONS

 

 

 

 

 

 

 

 

from Proton Spallation of

Ln

0—5
C)

(H

0—0
O

Ln

0...
o

THRGET 1“! N

 

“LllhnflolllhuflbLllhm

[195$ 10
E=17.0 I’IEU

 

 

110' I 1 [“01 lT—Lh

 

C03 [9 LOO J

Angular Distribution for Masses 6 to 11

16

14 O.

N and

116

HNGULHR DISTRIBUTIONS

 

 

 

 

 

 

 

 

 

   

 

 

 

 

TRRGET H N
5 "953 ”955 7
E=21.7 MEU E=2l.7 neu
10 ° II
'I
,5 I I
I
’0? -1 l I I | I
(n, 10
S 5 l
7:
-2
'_Z_' 1 ”0T! I TmTjT L100 10 ”01 T 1 10:01 T T 1.1.0
B 505 [9 L88 1 C05 [9 LOO J
3 :
"95$ 10 - ”95$ 11
E 5 E=21.7 MEU 5 ‘2“ -E=21.7 ”EU
1 ’ I I 0'7 . .
10 I 10 .= ,
s s -
0 '5‘
10 10 a
5 5 E
-1 '2
10 1 0.0 - .‘o 10 1.0r ' T 'oIo' ' r1«1.0
505 [9 L88 1 C05 [9 L89 1

Figure 12. (continued)

117

RNGULRR DISTRIBUTIONS

 

 

 

 

 

 

 

TRRGET 1‘1 N
HRSS 6 M958 7
E=25.8 IIEu 5 E=25.B mm
10‘
I
S A I | I
T)? I o- I |
Q. I 10 E |
(I) I 5 I
2: I _
-1
E‘. 1 110' I T [M01 l 1 L1" 101.0! l T ToIoTT l I.“
... COS [91.88] C0319LBB]
3
HRSS 10 MRSS 11
Y E=2S.8 ”EU 5 E=25.B IIEu
b
‘1: | 1
l I 10
5 I
I - I I
I 0‘ ' ' '
10 .= l
5 :
. 47
0 1.'0I ' ' '0101 ' ' '-1.'0 101.0T r ' '010' ' 'j-l.
C05 [9 LOO] COS [91.88]
Figure 12. (continued)

 

 

 

 

 

 

 

 

 

do-Aw [IN NB/SR]

CD

018

D—I
010

0—0
0

CH

018

m8

0—0
O

118

RNGULRR DISTRIBUTIONS

 

 

 

 

 

”I IIquI °I 1111111! "I 111““

§ mass 6

-: E=28.6 neu

I.

5:...

T- I

j l

o 0

i I

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mass 10
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Figure 12.

 

Ln

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(continued)

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119

RNGULRR DISTRIBUTIONS

 

 

 

 

 

 

 

 

 

 

 

 

 

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; 5 M855 6 mass 7
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Figure 12. (continued)

120

RNGULRR DISTRIBUTIONS

 

 

 

 

5 NRSS 6
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Figure 12.

10

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(continued)

 

 

 

 

 

 

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121

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Figure 12. (continued)

 

122

RNGULRR DISTRIBUTIONS

 

 

 

 

 

5 93:90.0 neu
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Figure 12.

 

 

 

 

 

 

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(continued)

 

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123

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Figure 12.

 

 

 

 

 

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5 N955 7
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(continued)

Ila-Aw [ IN 99/39]

124

RNGULRR DISTRIBUTIONS

 

 

 

 

 

 

 

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Figure 12. (continued)

 

 

 

 

h
g; "I JLIJJJJI J 14111111 °I 1!I||||I

 

19999119 N

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125

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2" NIJLIIUH "1 1 1111111 °I

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JO'Aw[IN 98/89]

126

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Figure 12. (continued)

 

 

 

 

 

 

Ila-Aw [IN 99/99]

127

RNGULRR DISTRIBUTIONS

 

 

 

 

 

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Figure 12.

 

 

 

 

 

 

 

 

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11959 II
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(continued)

128

RNGULRR DISTRIBUTIONS

 

 

 

 

 

 

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3
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Figure 12. (continued)

 

 

 

 

 

 

RIO—AW [IN MB/SR]

129

RNGULRR DISTRIBUTIONS

 

 

 

 

 

 

 

5 I‘IRSS 6
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10‘
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Figure 12.

I0

C05 [9 L99-I
5 r1933 11
E=37.9 man

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5

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(continued)

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cos (9 L99 I

130

HNGULRR DISTRIBUTIONS

 

 

 

 

 

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Figure 12.

 

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l
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(continued)

131

RNGULRR DISTRIBUTIONS

 

 

 

 

 

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I’IRSS 6 FIRSS 7
5 E=‘11.9 neu 5 E='-I1.9 neu
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I
10" 10"
5 5
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035 [ems I C05 [91.99 I
Figure 12. (continued)

 

 

 

 

 

 

 

132

 

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Figure 13. Cross-Sections for Masses 6,7,10,11 from Proton
Spallation of Targets 1‘N and 16O in the Energy

Range RP - 17 to 42 MeV.

5. RADIOACTIVATION AND DECAY MEASUREMENTS

5.1 Introduction

Since the time-of-flight technique is limited by the
low energy cutoff, it is desirable to have an alternate
technique which could be used to check cross-sections at
one energy. A 22 MeV proton colliding with a 14N nucleus
at rest makes 20.5 MeV available in the center of mass.

11

This is just below the 20.7 MeV threshold for B production.

Thus the only mass 11 isobar produced at this proton beam

energy is 11C; similarly the only mass 7 isobar made is 7Be.

11C is by 8+ emission with a half-life of

The decay of
20.5 min, so its cross-section can be measured by counting
0.511 annihilation y-rays. The decay of 7Be is by electron
capture with a half-life of 52.6 days, and 10.310.16% (TM 62)
of the time it decays to the 0.477 state in 7Li; so finding

the intensity of this y-ray yields the 7Be cross-section.

5.2 Cell Construction
Finding a suitable nitrogen target is again an important
consideration. A small gas cell with Kapton windows to hold

the 14

N target gas was designed for y-ray counting with a
lithium-drifted-Ge detector. Figure 14 shows a diagram of
the cell assembly. The Kapton windows are pressed against
O-rings by the 1/16" thick aluminum disks. The ports, open
during irradiation, are plugged with 1/16" aluminum disks
when the y-ray counting is done. The aluminum stops even

11C decay. Hence all

the most energetic positrons from
y-rays originate within the cell volume or on the inner

133

134

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135

walls. The frustum design was chosen so no y-ray has to
go through more than 1/16" of aluminum plus 1/16" of brass
(11C positrons penetrate up to 0.5 mm of brass before
annihilation) to get to the detector. A y-ray intensity
attenuation correction can thus be made with confidence.
Assuming the average 11C y-ray traverses 1.5 mm of aluminum
and 0.75 mm of brass (one-half the maximum possible) the
attenuation correction factor is 1.091. In the absence of
a proper averaging procedure I assign an error of 33% to
this number. For the 7Be y-ray which only traverses 1.5 mm
aluminum the correction factor is 1.036 with better than
1% accuracy.

A 9559B-lMM Circle Seal valve with a 1/4" Eastman
Poly Flow fitting was soldered directly into the cylinder
of the cell body (not shown in Figure 14). The volume of
gas in the closed valve is less than 1% of the total cell
volume. Hence the resulting counting error due to asymmetry
of the volume holding the radioactive gas is quite negligible.

The Kapton windows are the main source of 0.511 MeV
and 0.477 MeV background y-rays. However a minimum thickness

11 7

of Kapton is needed to stop C and Be from escaping the

cell. For 11C,0.0005" Kapton windows are sufficient to stop
even the forward scattered nuclei. For the 7Be measurement
0.001" Kapton had to be used as exit window to accomplish

the same purpose (Appendix A).

136

5.3 Irradiation Technique

For each cross-section measurement two irradiations
were performed. Two identical gas cells were prepared.
One cell was filled with 14m, its twin with 4He. The
pressure was chosen to be 1 atmosphere so that no stress
was exerted on the cell windows before and after irradiation.
The chance that leaks would develop was minimized in this

4He filled cell the contribution to the total

way. With the
yield by the Kapton was determined. A Helium filled cell
rather than an empty one was used to ensure that any changes
in the Kapton are similar for both irradiations. The most
important effect is due to heating. Kapton in vacuum and

in contact with a gas should have different equilibrium
temperatures. Also the stress of 1 atmosphere pressure on
the heated Kapton may deform it.

5.4 Counting Method for 7Be and 11C Decays

The y-rays were counted with a lithium drifted Ge1
detector. An electronics block diagram is shownin Figure
15. For good counting geometry the gas cell was placed

at 10 inches from the detector. The detector efficiency

at this distance was established for the 0.511 y-ray using
a standard 22Na source (from the Bureau of Standards, 5%
accuracy quoted). The relative efficiency of the 0.477 MeV

y-ray with respect to the 0.511 MeV y-ray was found by

assuming log (y-energy) vs. log (relative efficiency) is a

 

1Manufactured by Nuclear Diodes, Prairie View, Ill.; Relative

peak efficiency 10.4%.

137

 

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138

straight line, determined by the 0.511 MeV y-ray and the
1.274 MeV y-ray of 22Na. A Ge(Li) detector for which a

more complete efficiency curve is available (DO 70) exhibits
this relationship in the range from 200 keV to 5 MeV.

The 8+ decay y-ray origin, and the frustum geometry
of the cell make precise positioning difficult. Consider
case 1, y-rays originate from all inner cell surfaces with
equal likelihood or, case 2, y-rays originate from the gas
volume only. To effectively place the cell at 10" from
the detector I find the cell position for the first case
is 0.024" closer to the detector than for the second case.
This still represents a negligible error of 0.24% in
distance or 20.5% in cross—section.

In the case of 7Be the irradiation time is short compared
to the half-life. For a cross-section calculation one then
needs the gas pressure, the total charge traversing the cell
and the distance traveled by the beam in 14N. In section
5.7 these measurements are combined with the measured
y-decay rate, detector efficiency and branching ratio to

7

yield the Be total cross-section. The 0.477 MeV y-rate

14

was measured by counting for 4 hours each on the N filled

and 4He filled gas cells. The counting was done at least
24 hrs after irradiation so that the background due to
annihilation 0.511 y's was low. The y-ray was identified
by its energy and by its 53 day half-life.

11C has a half-life of 20.5 min. An adequate irradiation

consisted of 500 namp of proton beam for a duration of

139

10 minutes. Beam intensity fluctuations can therefore
not be neglected. A chart recorder running at 3 in/min

was used to record the instantaneous beam intensity.

11

The C counting was started 3 minutes after irradiation.

Counting was continued for 3 hrs.; intervals were chosen
to be a 5 min. step followed by 10 min. steps. A pulser
with the frequency of 19.1 counts/sec was injected into the
detector preamplifier and was used to correct for deadtime
losses.
5.5 Data Reduction

The 0.511 MeV y-decay curves for (Kapton + 4He) and

1

(Kapton + 4N) show that besides the 20.5 minute component

there are shorter and longer half-lifes involved (see
Figure 15). Care had been taken during irradiation and

counting that both gas cells had received the same treatment.

Hence the decay curve for the 4He filled cell could be

14

subtracted point for point from the one for the N filled

cell. Since protons bombarding 4He do not lead to products

which 8+ decay, the difference curve for the two cells then

14

represents the contribution of N proton spallation products

to 8+ decay.

At 22 MeV bombarding energy the only relatively long

14N+p which contribute to

13

lived radioactive isotopes from

the 0.511 MeV annihilation radiation are N with a half-life

11c with a half-life of 20.5 minutes.

1

of 9.96 min and

1

150(1243), 40(713), oC(14s) are also produced but have

much shorter half-lifes. The decay curves and their

140

 

10“
.5113 DECRY CURVES

IJ III”

103

I I I J IIIII

H
O
M

I I lIlle
I

COUNT RRTEI COUNTS/PULSE I

 

 

 

 

_ -
101 E
E
10° 5 . .
10'! L I I I l
LIO 80 120 180 200

TIMEIMIN)

Figure 16. Data Points of 0-511Y Decay Curves for Nitrogen
and Helium Filled Gas Cells and the Curve Resulting
from Taking their Difference.

141

difference is shown in Figure 16. The line shown represents
a 20.5 min half-life and is only included as a reference.

It can be seen that shorter and longer half-lifes are present.
The shorter half-lifes can be understood since they may be
present as pointed out above. The longer half-life must
represent a difference in irradiation between the cells and
is not understood at present. The error introduced in
determining the 20.5 min half—life intensity is 10%. In
Figure 17 a number of fits to the difference curve are

shown with the fit parameters given for each curve. The
time scale is only valid for the left most data set.

Other curves were displaced to the right for display purposes.
The crosses in Figure 17 represent the data. We consider
half-lifes 10 min, 20.5 min and also a longer half-life,
either 41 min or 324 min. For a fit using two half-lifes

we select two data points; for three half-lifes we need
three data points. The selected points, boxed in Figure 61,
determine counting rate contributions of the different half-
life components. The solid line represents the calculated
counting rate. The contributions by the 20.5 min component
at 41 min after the end of irradiation to the fits shown in
Figure 61 are from left to right, 487, 460, 394, 430, and
435 counts/sec. We use the value 438i45 counts/sec in our
cross-section calculations.

11

5.6 Cross-Section Calculations for C
To calculate the 11C production cross-section from the
observed rate after irradiation, the decay of 11C during

142

 

 

 

 

 

0
LL] N
> m
a:
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(.1 o
co
>_ 00
C1:
LJ
LU 0
C3 :r
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Lu
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Z a
w :33
5 2:
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u.
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)0
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.—. N
Ln 0-0
L” o
I 00
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I’— o
:-
U7
'—
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u" 1-
JJLII’LL 1111 1 11111111 1 11111111 1
n N a. D a-s
o o b

Figure 17.

C) CD
IBSWDd/SINDOJJBLUH 1NDOJ

Sample Fits to the 0.511 V Difference Decay Curve.

143

irradiation has to be taken into account. A numerical
integration fortran program was written based on the
equation:

dN = :Efilgfla Z-At/H At + on

tAni

dN represents the net change in the number of 11C

nuclei during the time interval At.

N is the number of 11

C nuclei present at the beginning
of At.

H is the half-life;

o is the total cross-section for spallation production
of 11C.

nt is the number of target nuclei per cm2.

Ani is the total number of incident protons during the

time interval At.

The program is given an arbitrary value for 0 such as 1 mb,
and it starts by calculating dN for the first second of
irradiation. This becomes the value of N during the next
second after which the new dN is added to N. This is done
in one second time steps to the end of irradiation. The

Y counting rate at 2 half-lifes after the end of irradiation
is then calculated. The correct value for the cross-section
is then given by:

1 observed rate

0 = calculated rate

The irradiation histories for the 14N and the 4He activations

yield cross-sections which differ by only 0.37% justifying

the direct subtraction technique explained in section 5.5.

144

5.7 Cross-Section Calculations for 7Be.
The decay of a radioactive nucleus is governed by

the well known equation:

N = N z't/H
0

No is the number of radioactive nuclei present at time
t = 0.
H is the half-life of the nucleus considered.

The decay rate is then given by
dN__ _ 1092 -t/H
dt - H (N02 )
The initial number of nuclei N0 = ontni.
In our case 0 is the total cross-section for 7Be

production from 14N. The total number of incident protons,

n.

1, is related to the collected charge Q(coulombs) by

-19

ni = Q/(1.6021 x 10 coulombs)

14

and n the total number of target nuclei/cmz, for N gas

t!
is given by

19 -2

21%;1 (2)(2.687) x 10+ cm

nt = RP
The quantity P is the gas cell pressure in atmospheres,

T is the gas temperature in °K,

£(cm) is the total length of gas traversed by the beam.

we measured 2 by pressurizing the cell to 1 atmosphere
above atmospheric pressure and measuring the distance between
Kapton windows with a micrometer. P was the pressure of the
atmosphere at the time of filling the gas cell. This was

corrected for billowing of the windows when the cell is

placed in vacuum.

145

The rate measured by the counter for a y-ray from one

source is:

R = 1739-2— (Noz't/H) me = 3% ms

X is the number of y's per decay. For 7Be this is equal

to the branching ratio to the 0.477 MeV level in 7Li;

X = 0.103. e is the photopeak efficiency of the detector
for a point source at 25.6 cm, G is a geometric factor
taking account of the finite extent of the gas cell, No
is the number of radioactive nuclei present at time t=0
and H is the half—life of the nucleus considered.

a was found by counting y-rays from a N.B.S. calibrated
22Na source rated at 1.62 ucuries 15% on 11-11-70. The
efficiency measurement was performed on 3-21-71. The center
of the source was placed 25.6 cm from the Ge detector.
653500:2500 counts were accumulated in the 0.511 y-ray peak.
l62500i700 counts were accumulated in the 1.274 y-ray peak.

194200 counts were accumulated in a peak due to a pulser

running at 5 pulses/sec.

 

The error assignments are obtained from /counts in Peak+2Background
G=1 can be assumed for the source since it is quite small.
X=l.8 for the 0.511 y-ray and X=1.0 for the 1.274 y-ray.
From this data and the assumption that the logarithm
of the y-ray energy vs. the logarithm of the relative
efficiency traces out a straight line, e:=1.818x10-4 is
obtained for the absolute efficiency of the 0.477 y-ray

from 7Be.

146

The constants for the equation used to relate decay

rate to 11C cross-section are mostly the same as those

for 7Be. The photopeak efficiency for the 0.511 y-ray

4 11

is 1.714 x 10- . The half-life for C decay was taken

to be 20.5 min. X, the number of y's per decay, is equal

to 2.0.

5.8 Error Analysis
Table 11 summarizes error contributions to the cross-
section determination by radioactivation-decay measurements.

5.9 Cross-section Comparison

Table 12 compares our 21.7 MeV 11C and 7Be cross-section

measurements by the time-of-flight and y-counting methods,
as well as the recently published values (ES 71), (BCJR 71).

There is agreement within the quoted errors. From the

11

Epherre data it is also apparent that the C cross-section

falls rapidly with increasing proton beam energy near

11

21 MeV; hence, the marginal agreement for C is not

unexpected. Our 17 MeV llC time—of-flight data does not
agree with the Epherre data, but error bars almost meet

at 87 mb.

Table 11. Error Contributions to the Radioactivation-

Decay Measurements.

 

 

 

 

Error Source

Error in %

 

 

Comments

 

m

efficiency
pressure

temperature

0.18 'U

cell

1 distance beam travels in

14N

Q integrated charge

R decay rate after
llC
irradiation

R7 decay rate after
Be irradiation

X7 branching ratio
7 attenuation for C

Y attenuation for 7Be

distance of detector

6.0
0.5

1.5

From Lansing Weather
Bureau Station

Explained in
Section 5.4

Micrometer measure-

ment

(TM 62)

 

Added in quadrature the error for the

C cross-section is

then 13% and the error for the 7Be cross-section is 8%.

 

 

148

11

Table 12. C and 7Be Cross-section Measurement

Comparison.

 

11

Be

11

Be

:-
t "‘

Cross-sections at 21.7 MeV in mb

Radioactivation Time-of- Epherre et a1. Bodansky et a1.

 

Y counting Flight (ES 71) (BCJR 71)
Read from a 20 MeV
graph
36.2:4.5 39.5i10.1 50:12
49.0:3.8 41.2:7.2 45:8 46:5

Cross-sections at 17 MeV in mb
69:16 110:27
36.6:14 30:5

 

 

6. REVIEW OF PAPERS ON ASTROPHYSICAL THEORIES OF

LiBeB PRODUCTION

6.1 Introduction

A complete theory of LiBeB production has to explain
abundances and isotopic ratios encountered in nature. Table 13
is a short compilation of the presently available data of
importance to the theories on L(LiBeB) nuclei production.
The following pages give a short history of light element
synthesis theories by reviewing excerpts of papers on the
subject. The values used often vary somewhat from those in
Table 13, but the conclusions drawn in the various papers are

not sensitive to changes of that magnitude.

6.2 Early Theories of Nucleosynthesis of LiBeB

The early theories of nucleosynthesis recognized that
there was difficulty in producing the light elements even in
their comparatively low abundances. In 1955 Hayakawa (Ha 55)
and Fowler gt_§1. (FEB 55) proposed stellar surfaces as a
creation site with high energy protons causing spallation of
the heavier constituents of the stellar atmosphere. Fowler
gt_21, considered two possibilities. They envisioned hot
spots in magnetic spots where p = 10-8 -10‘-7 g/cm3 and
kT 2 SMeV and claimed under these conditions (Li, Be, B)/(C,N,0)=l,
the observed galactic cosmic ray ratio. They then weakened
this hypothesis by observing that in Apm stars, the proposed
site for the magnetic activity, the low Be abundance speaks

against this mechanism. The second possibility considered

was proton spallation of C,N,O at energies > 100 MeV in regions

‘40

 

Table 13. Abundances of Interest in LiBeB Production.

 

 

 

 

 

 

 

Abundances (H = Log EH = 12)
Element or Solar Sun Sun
Isotope System (MU 68)
(CA 67)
H 12.00 12
He 10.91
6Li 2.11 .29
7Li 3.21 < .9 {(913 68)
9Be 1.42 2.34
103 1.67
113 2.28 (3.6
C 8.72 8.51
N 7.97 8.06
0 8.96 8.83
Ne 7.96
Si 7.59 7.70.7.24
Ratios
In Cosmic Rays
LiBeB/nCNO = .24 (GMS 70)
Li:Be:B = .5:.45:l (FGS 68)
In Sun (MU 68)
Photosphere Corona UV Solar Cosmic Rays
C/N 2.8 10 ' 3.1
O/N 5.9 7.7 5.3

6Li/7Li 3 0.05

151

Table 13. (continued)

In Rocks (Earth) and Meteorites

7Li/6Li

12.5

11B 10B _

/

 

 

 

152

of p < 10.9 g/cm3. For either of these,Apm stars were found
to be too few in number to account for the cosmic abundance.

They then considered the possibility of this spallation
mechanism in M dwarfs being the source of the light elements.
They assumed M dwarfs contributed all of the LiBeB and 5x10'5
of the total cosmic abundance of matter in a time span of
109 years. To produce the observed abundance of LiBeB, the
ratio of (Li,Be,B)/(C,N,O) in the ejected material must be
in the range 10-3- 10-2. This represents 0.1 to 1 percent
efficiency assuming a ratio of one is the maximum possible
attainable by spallation of C,N,O in the gas. However since
the magnetic activity of M dwarfs is much less than that of
Apm stars the authors did not feel it was evident that this
ratio could be achieved in the ejected material.

In the classic paper on the synthesis of elements in stars
Burbidge, Burbidge, Fowler, and Hoyle (BBFH 57) still found
stellar atmospheres a possible synthesis site, but they also
considered gaseous nebulae and supernovae as possible candidates.
No calculation for the latter two were attempted. In this

paper there was also speculation that 7Li may be synthesized

in helium burning cores of late-type stars by

7 K captureg._7 7

3He(Ole) Be Li. The

 

Li can be brought to the
surface provided the hydrogen envelOpes only extend to depths
where the temperature is less than ”106 degrees.

In 1960 a paper by W. K. Bonsack and J. L. Greenstein
(BG 60) on the abundance of lithium in T-Tauri stars gave

new impetus to spallation-at-the-surface-of-stars theories.

153

They found that the Li abundance in T-Tauri stars is about 100
times the solar value or about the same as observed terresti-
ally. They also observed that the surrounding nebulae have
at least ten times less lithium per gram than the T-Tauri
atmosphere, which strongly suggests that Li is made in the
star. A number of calculations were performed in this paper.
To check whether cosmic ray Li could be the source of
stellar Li they started with the cosmic ray number ratio

-3, a cosmic ray energy density Ucr = 1 ev/cm3

9

Li _
(H—)cr _ 10

and a mean cosmic ray energy of E'= 10 ev, and the particle

density of hydrogen n = l/cm3. After condensation the Li/H

H
ratio due to cosmic ray Li abundance is then

. U
%i.: 10 3 _cr 5'10 12

EnH

which is compared to the approximate solar abundance ratio 10-11

and hence is found to be too low even for normal stars.
The authors also attempted to calculate the energy

required of each star to produce the observed high-abundance

of %E.= 10-9. They assume 100 MeV is needed per Li atom

synthesis. Assuming an efficiency factor B, the ratio of ELi'

the total energy needed for Li synthesis, to L the total

t!
stellar energy from hydrogen burning, is given by

 

which appears quite possible, but the authors do not postulate
a mechanism for actually bringing about the nucleosynthesis.
They also make a calculation for a spallation origin of

Li due to cosmic rays striking stationary heavy nuclei in the

154

atmosphere of a proto-star. The assumptions are: the cosmic
ray spectrum for protons is a delta function in proton energy

with Ep = 1 BeV; a target nucleus of atomic weight A, abundance

2/3

NA' will have a spallation cross-section of A in millibarns;

the efficiency a for producing Li per interaction is linear

A
between A=12 and A=20 with aA=0.l for A=12 and aA=l for A320.

The authors obtain the ratio

56
2/3
.L_i. = Uor 1 A§12 NAO‘AA 1
H E N2 '
P H

 

where Ucr is the cosmic ray energy density at the surface
of the star as it condenses. The term in brackets is estimated

to be 4 x 10-3. For UC = l ev/cm2 and Ep = 109 ev they then

r
obtain Li/H = 4 x 1012. This is low compared to 10-9.

The authors then point out that the observed Li abundance
in a star can be up to M/AM of the net abundance in the star,
where AM is the optically accessible mass of the star and
M is its total mass. This enrichment factor would imply
that the spallation process is due to a surface phenomenon,
concentrating cosmic ray or magnetic field energy at the
surface of a forming star. The authors claim trapped magnetic
field could supply the energy to produce the observed Li
abundance in T-Tauri stars, provided the energy is dissipated
near the stars' surface so AM/M is sufficiently small, where
AM now stands for the mass in the active region of the star.
In a volume of space containing one solar mass of gas and
initial magnetic field H the total magnetic energy stored is

estimated at 5 x 1055 H2 ergs. Assuming 250 BeV are needed

155

to create one Li nucleus (from the cosmic ray result cited
above) the observed abundance ratio becomes Li/H = .leM/AM.
Thus for an interstellar magnetic field of H = l x 10-5 gauss
and AM/M = 10-2; Li/H = 10—9 can be achieved.

Following the paper by Bonsack and Greenstein (BG 60),
T. Gold (G 60) pointed out that the surrounding nebulae of
T-Tauri stars could be gas remaining after star formation.
Spallation reactions in the surface at an early age of the
star (during strong magnetic activity) could then create Li
in a surface shell of the star. This could then be tied in
with a theory of the origin of the solar system in which the
shell is thrown off and most of the angular momentum of the
sun is transferred to it possibly by magnetic coupling. The
high lithium abundance in the earth and meteorites could thus
be explained.

In S. Bashkin and D. C. Peaslee (BP 61) the authors
come to the following conclusion with regard to light element
production: "L nuclei (Li,Be, and B) are produced by
spallation, most abundantly during the contraction stages of
a forming star. This qualitatively accounts for L abundances
in the solar system and T-Tauri stars. For the present sun
it is uncertain whether the L nuclei observed are currently
produced by flares or are the remains of an original stock."

The paper attempts an abundance calculation:

aF

Consider p(F)dF = aVe- dF

where p(F)dF is the number of flares per second containing

~

between F and F+dF fast protons (Ep Z ” 70 MeV), V is the

156

total rate of flare occurrence in the sun, and a is a parameter
specifying the distribution of sizes.

v 2 0.8 x 10’4/sec,

The rate of flares of size F0 or larger is P(FO) = Ve-aFo.

33, P(Fo) z 0.5/year; hence,a 3 8.5 x 10-33.

For F0 3 10
The authors then point out that half of the protons in a

flare will go into the sun's surface where they will cause
spallation reactions or, more likely, will be stopped by
protons. From the p-p cross-section for Ep = 0.1 - 0.3 BeV
they obtain a mean free path of 6 x 1025 protons/cmz. Given

a target nucleus, of abundance f relative to hydrogen which
has a cross-section for producing particle x of 0(x)mb for
fast protons, its probability of yielding a particle x per
fast proton is 0.06 fo(x). The production rate for a particu-
lar spallation product is then Y(x) = 6 x 1026 fo(x)/sec

where the total proton flux per second is given by

00

5:0 P(F)FdF = faVe-aFFdF =

m|<:

For the more numerous protons in the range 10-70 MeV the

28 fo'(x) where account

corresponding rate is Y'(x) = 2 x 10
has been taken of the shorter mean free path of protons in

this energy range. The authors then present a more or less
quantitative technique which results in an estimate of 80 mb
for light-isotope (L) production for the (C,N,O,Ne) targets;

26/sec. The authors

with f = 0.002 this leads to Y(L)310
then show that this production rate is too low to account

for even solar abundances:

157

Y(L)T

f(L)=———-23x10'
N
H

13

where f(L) is the abundance with respect to hydrogen in the

17

convective envelope of the sun; T =1.5x10 sec is the age

55 is the number of H atoms in the

of the sun, and NH=5x10
convective zone. They claim the observed L abundance in
the sun is about 103 greater than this.

It is also pointed out that the ratio %% 3 30 as observed
in the sun is difficult to understand, claiming preferential
loss of Li in photosphere or convective zone is not expected.

The series of papers: Fowler, Greenstein, and Hoyle
(FGH 61); Fowler, Greenstein, and Hoyle (FGH 62); Burnett,
Fowler, and Hoyle (BFH 65); concerns itself specifically with
an elaborate theory on the production of the light elements
in the spirit of the suggestion by Gold (1960). Mitler (1964)
also made detailed calculations based on this model.

The assumptions of the model are: planetary formation
has progressed to the point where solid bodies appear in
the gaseous disk surrounding the sun. Their composition
is 2 3/4 ice, 3 1/4 silicates and perhaps 5% carbon. A
proton flux with E'3 500 MeV impinges on the material in
the disk. In the absence of experimental production cross-
sections of the light elements from spallation of O, and Si,
the authors assumed production ratios 7Li/6Li = l and
inferred from the model that 11B/lOB = .3. The proton flux,

besides causing spallation of the target elements to form

Li, Be, B, also gives rise to a neutron flux which is

158

thermalized by the hydrogen present. The thermalized neutrons

then deplete 6Li and 10

B to yield the observed terrestial

. . . 7 . 6 . _ ll 10 _ .
isotopic ratios Li/ Li — 12.5 and B/ B — 4. To estimate
the energy needed to form the L nuclei in terrestial planets,
the authors assume one L nucleus is formed in nine proton
reactions. Assuming E? = 500 MeV they require[4.5GeV/L
nucleus producecfl. Assuming[50 L nuclei/10681] were produced

498i nuclei present in

43

by spallation, and taking 4.6 x 10

terrestial planets, implies 1.7 x 10 ergs is required.

They then consider an estimate by Hoyle according to which

45

5 x 10 ergs have to be dissipated in the transfer of the

angular momentum of the sun to the planets. If 4% of the
energy appears as high energy particles, they find only 10%

of the protons need to interact to produce the L nuclei.

118/10B

ratio. Based on the presently known cross-sections for 11B

10 12C and 16O, and assuming the

At present the weakest point of the theory is the
and B production from
contribution of Si spallation does not greatly affect the

net production, the 11B/loB spallation ratio is 2 for 500 MeV
protons. If lower energy protons are considered this ratio

10B by

can be greater than 4. Hence the depletion of
neutrons only increases this ratio above the terrestially

observed value.

6.3 Current Theories of Nucleosynthesis of LiBeB
Ideas present in the early theories combined with new

data resulted in a number of elaborate papers. The theories

159

proposed for light element production are quite distinct.
R. Bernas, E. Gradsztajn, H. Reeves, and E. Schatzman
(BGRS 67) attempt to identify the Li,Be,B production site
and mechanism as proton spallation of C,N,O,Ne in the solar
atmosphere before the Hayashi (fully convective) phase of

7Li/6Li ratio is then changed by 6Li(p,a)

the sun. The
reactions at temperatures between 2 and 4 million degrees
at the bottom of the surface convective zone during the
Hayashi phase. The material forming the planetary system
would still later have separated from the sun.

A number of spallation production cross-sections with

lSO-MeV protons on 12C and 16

0 had been measured by these
authors. They supplemented these with estimates based on
isospin formalism or with calculations based on the Serber
statistical method. Thus starting with a complete set of

cross-section values and a probable target mixture they

could calculate the formation rate of the light isotopes

from
dnL Z
———-= n f 0(M,L)¢(E )dE 6.31
where nL is the density of isotope L produced (nuclei/cm3),
nM is the density of target isotope M (nuclei/cm3),

0(M,L) is the cross-section for producing L from M by
protons of energy Ep,

QM,L is the threshold proton energy for producing

nucleus L from target M,

and ¢(Ep) is the proton flux.

160

3 -3

_ ' _ *4 _
The authors use nC/nH — 3 x 10 , nN/nH —.10 , nO/nH — 10 ,

3 for the isotopic target composition. They

nNe/nH = 3 x 10'
consider a probable average proton energy spectrum as observed
in solar flares and calculate isotopic spallation ratios
7Li/6Li = 2.5:1.0 and 11B/loB = 5:2.5. They compare these
with the terrestial-meteoritic values and find that the
11B/loB ratio requires no depletion mechanism while the
7Li/6Li spallation ratio’must be modified by the mechanism
outlined above. Of the light elements the energy requirement
for Be production is largest.

For stellar production the time integral of equation 6.31

yields for the production of the light nucleus L

5'5
53!?

/nH)X(t)dt 6.32

_<_ Mp (t) o (L) (“wane

where x(t) = Mi/Mc is a dilution factor; M1 is the mass in

which the spallation process occurs; MO is the total mass

of the convective zone on which Mi can be mixed. The possibility
of burn up at the bottom of the convective zone is allowed

for by the < sign. From the estimated average spallation
cross-sections leading to Be of 2 mb and the abundance of Be

in the sun the integral equation becomes

f¢P(E>4O MeV)X(t)dt = lOZO/cmz .

-8

For the present sun the authors estimate x(t) Z 10 and

the proton flux capable of spallation is ¢p(t)=107/cm2 sec.
Assuming the age of the sun is 5 x 109 years, the integral

yields 1.6 x 1016. The authors place the limits 7 x 1015

161

16

< f¢det<7x10 , and find the activity is too low by about

103. In the case of T-Tauri stars the authors estimate

the convective mass is 0.1 of the total mass hence

x(t) = 10-11; the period of the phase 3 106'5 years,so

20 16

to yield f¢det = 10 the particle flux must be 3 10

42

protons/cmz/sec or 10 erg/year. For a star the size of

the sun, this is a very:large energy requirement. The

authors then point out that the Herbig-Haro phase of a star,

before it becomes luminous, might also be the production site.
To estimate the production of light elements in galactic

cosmic rays the authors considered a proton flux above 100 MeV

4

of about 2 particles/cmz/sec. The ratio n = 3x10-

CNONe/n3
is taken as a time average over the age of the galaxy
10

(10 years).
nL
53': f¢p(nCNONe/nH)oLdt
~ . ~ -11 .
for UL ~ 30 mb this yields nLiBeB/nH ~ 1.6 x 10 , while

10“9 is found in several stars, the meteorites, and the earth.

H. E. Mitler (MI 67) wrote a critical review of theories
on the origin of the rare light nuclides. In particular he
made calculations on the energy requirement for producing
cosmic abundances by proton spallation of CNONe on the surface
of stars and compared the total energy to the energy available
from gravitational contraction. This is of interest for the
T-Tauri phase and the Herbig-Haro phase as considered in the
Bernas gt_al. model. The ratio is z 300 for the Herbig-Haro
phase hence eliminating it from consideration. For the

T-Tauri phase the ratio is 2 for the Bernas et a1. model.

162

These calculations are based on the Be abundance in the sun,
which represents the most severe energy requirement. Similar
calculations based on our measured cross-sections yield
almost identical results.

Mitler considers that the accelerating distance for a
proton may be 3 4 times its st0pping distance, hence the
irradiated material could be about 5 times as great as con-

sidered by Bernas, yielding a ratio of E = 0.4;

spal/Egrav
this puts the T-Tauri phase in the energetically just possible
range. Mitler then proposes an alternate theory where most of
the lithium (7Li) is made in a big bang and the remaining
light isotopes are produced by spallation during the T-Tauri

6 0 o a c a
Li and hence no miXing in a convective

phase. No burn up of
zone before ejection is required in this model. The energy
requirement then decreases by over a factor of 100, making
the process energetically quite possible.

The difficulties encountered in theories of autogenetic
origin of light elements in stars led H. Reeves, W. A. Fowler,
and F. Hoyle (RFH 70) to a theory which attempted to show
that the light elements were produced by galactic cosmic rays.
They divided the energy range of galactic cosmic rays into
three regions; E < 5 MeV/nucleon, 5<E<30 MeV/nucleon, and
E > 30 MeV/nucleon. They then considered the contribution
of p+C, N, O; a+C, N, O; p, a+Mg, Si, Fe; and a+a in the
middle and high energy region, where they assigned likely

mean cross-sections for the various production mechanisms.

163

For the case of spallation of heavy fast particles on residual
gas the escape form the galactic disk and the nuclear destruction
of the light elements produced were taken into consideration.

The generation rate of lithium per H atom was found to be
d Li 2 -28 -1

EE (fi—) 7 x 10 sec . To achieve a lithium abundance
of %5 " 10-9 a total time integrated flux of 5 x 10'8partic1es/cm2

is needed. For a galactic age of 1.2 x 1010

years this
represents an average flux of 12 particles/cm2 sec instead
of the present flux of 3.6 particles/cm2 sec.

It is instructive to compare this calculation with the

estimate in the paper by Bernas et a1. (BGRS 67), which

found the discrepancy to be a factor of 170.

Bernas et a1. ' Reeves et a1.

protons>100MeV:2/cmzsec protons>30MeV53.6/cmzsec
_ -4 _ -4

nCNONe/nH — 3x10 nCNO/nH - 15 x 10

time z loloyears time 3 1.2 x loloyears

+ equal production from heavy

4.5 cosmic ray spallation.

enhancement h+ 1/2 production from a
factor

spallation.

 

LT 2x production from a-a.

All together this yields a factor of 50. Thus some new data,
a new production mechanism plus some bias on either side can

make a significant change in the evaluation of a theory.

164

Better data especially in the low energy region of cosmic
rays and solar flares, as well as for abundance measurements
of light and medium heavy nuclei may very well lead to
revised theories.

From the low threshold of 14N+p + 11c + 113 and the

11 10

solar system ratio of B/ B, the authors find that the

11B from the flux in the medium energy region

contribution to
is low, and imply the flux at protons in the 5<E<30 MeV range
is §_5/cm2sec. The observed terrestial abundance of
deuterium cannot be accounted for by galactic cosmic rays.
The authors suggested big bang nucleosynthesis or neutron
capture in the atmosphere of neutron stars.

H. E. Mitler (MI 70) gave a detailed calculation of
light element production in galactic cosmic rays, using

12C and 16O and estimates

then available cross-sections for
for a+a reactions. He made a more or 1eSS arbitrary extrapo-
lation of the cosmic ray flux below 100 MeV/nucleon for his
calculations. The abundances obtained by Mitler, assuming
the galaxy is unchanged since its birth, were extremely close
to those observed in meteorites (Be and B especially). It
should be pointed out that absolute abundances are very
uncertain, values obtained for the crust of the earth, for
example, are about ten times higher than those obtained

for chondritic meteorites. Mitler then allowed for higher
production in the primitive galaxy as well as processing of

galactic material and found that at the time of solar genesis

the abundances of the first calculation would be increased

165

by a factor of 2.5. He concluded that he could not make
sufficient 7Li in galactic cosmic rays and suggests cosmo-
logical production as in Mitler (MI 67). There is also
difficulty with the 11B/loB ratio (too low) as well as with

7Li/6Li observed in stars. Mitler

low isotopic ratios
lists the usual palliatives plus the possibility of a
neighborhood supernova supplying thermonuclear lithium.

One additional observational asPect should be mentioned
because it has bearing on the question of light element
production in stars. Herbig (HE 65) pointed out an
interesting correlation of Li abundance and stellar age.
Young stars seem to have more lithium than older stars;
the usual explanation is that a slow destruction mechanism
such as (p,a) reactions at the bottom of a convective zone
is Operative. 7Li/6Li ratios are known for many stars
and vary from 2 to greater than 20. The lower ratio is
assumed to be the spallation ratio which will tend to
increase during depletion since the 6Li(p,a) rate is faster
than the 7Li(p,a) rate at the temperatures estimated.
However at present there is no correlation between high
7Li/6Li-ratios and stellar age. A good summary of light
element observations in stars is given by I.J. Danziger
(DA 67).

Cosmological production of the light elements has also

been investigated and may possibly account for 7Li production

as calculated by R. V. wagoner, W. A. Fowler, and F. Hoyle

(WFH 67). In a calculation for nucleosynthesis in exploding

objects (little bangs) R. wagoner (WA 69) finds that 7Li

166

and 9Be production would exceed and dominate the spallation
contributions as estimated in (BGRS 67), while 6Li and B

would be due to spallation production.

7. IMPACT OF NEW CROSS-SECTIONS

7.1 Introduction

Our cross-section measurements are particularly valuable
for model calculations of the type proposed in (BGRS 67).
The most significant calculations are based on the precise
isotopic ratios 7Li/6Li and llB/loB. Net abundances are
much more difficult to measure since chemical weathering
does separate elements but has no effect on the isotopic
composition of a particular element. It was found that the

7Li/GLi = 12.5 holds for chondritic meteorites and

ratio
for rock samples of the earth (KM 64). Similarly the
ratio 11B/lOB = 4.0 holds for meteorite (SH 63) and earth

rock samples (RA 63).

7.2 Isotopic Ratio Calculations

To calculate these ratios we consider the following
model for proton spallation in stellar atmosphere type
environments:

12C:14N:160 = 3:1:5 [This holds for

1) target mixture:
solar cosmic rays according to E.A. Muller (Mu 68).]

2) proton flux with spectrum E"Y [Solar flares usually
fit this (FW 65).]

The relative production of a particular isotOpe is then

given by:
= °° -Y
Ii E IE Oji(E)E xjdE , 7.21
3 o
Oji is the cross-section for producing isotope i from
target j,

167

168

Xj is the weighing factor for target j as given above,

E0 is the threshold energy of Oji#0.
To perform the integration we supplement the cross-section
measurements performed at this lab with other available
data summarized in Table 14. A linear interpolation
between data points is used. This is the cause of the
kinked curved lines in the logarithmic graphs of Figure 13
where all the Oji(E) used in the integration are shown.
Cases of conflicting data were resolved as follows: the
last published values by the same authors were preferred
over earlier data; emulsion data was given least credence;
final data were preferred over preliminary data. The high

12

energy region (>200 MeV) of mass 10 from C was based on

the cross-section for 10

account for 10B. The high energy region (>42 MeV) for

11

C at 1 GeV, which was doubled to
mass 11 from 14N is based on C cross-sections only; no
correction was attempted since the cross-section for mass 11

ll .
C cross-sections

measured at 42 MeV was comparable to
at higher proton energy and other spallation cross-section
'curves tend to slowly decrease towards higher energy.
Where data were available at closely spaced points (ES 71),
representative points were plotted.

we then calculated the ratios I7/I6 and Ill/I10 for
1.253y35.25. For y§2 there must be an energy cutoff
Emax<m since otherwise the average proton energy is not
finite. In the calculation for Ij this is not critical

however; the value Emax=3o GeV is taken for all integrations.

For a constant cross-section of a, Y = 1.25, and E0 = 10 MeV,

Table 14.

Spallation Data for C,

169

12 14

N and 160 Targets.

W
Cross-Sections in mb.

 

Source Ep Target Mass 6 Mass 7 Mass 9 Mass 10 Mass 11
GR 65 so 12c 9.2 32.7

GR 65 155 12c 9.8 19.9

GR 65 550 12c 7.4 16.6

AER 67 50 12c 11c 86.4
AER 67 150 12c >8.6 61
JD 70 125 12c 8.3

AER 67 980 12c 10c 3.3

AER 69 GeV 12c 8.3 18.7

FPLYB 71 150 12c 3.2

FPLYB 71 600 12c 5.3

JU 70 125 14R 12.7 11.1

AER 69 3000 14N 78e 12

AER 67 156 14R 11c 15
AER 67 522 14R 11c 22
AER 67 980 14R 11c 25.5
AER 67 5700 14N 7Ee8.6 11c 11
Es 71 4.5 14N 10
Es 71 5.5 14N 56
Es 71 6.5 14R 190
Es 71 8.5 14R 220
Es 71 10.5 14R 0.3 180
Es 71 14:5 14N 5.6 140
BCJR 71 14 14R 190

170

Table 14. (continued)

 

Source E Target Mass 6 Mass 7 Mass 9 Mass 10 Mass 11
YBDFGB 68 135 160 10. 13.4 1.7 11 25
GR 65 155 160 9.8 19 1.7

.AER 67 155 16o 13 11 25

YI 68 600 160 12.4 19.3 2.6 12 25
YI 68 19000 160 14.4 25.0 3.6 15 <45

171

 

IE: Nu.
(..—

 

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Oma o m z: UNH um H a scum Ha m: on m mm: D so A

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l>mzltm
mos ,oA moi Nos or

:2:- _ 52:. _ 5::— _ ::__H l m. _zlfififi q q

 

 

 

 

llllllll

 

 

lllllll

 

 

 

o“
.. m
:4 MW
.1 nd
I1 :1
m 8%.. m
A. 8%. um:
m $5.. 1
“NH emomae

mos

Figure 18.

172

(continued)

 

 

 

 

 

 

 

 

 

m
CD
.—.g

C) .4 _-
mm 5
U) 03 _.
GE CE
(.1 1:2: "‘
(\J o c: ‘7
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(BULO

105

2 3 '4
10EPIMEVJ10 10

10

173

(continued)

Figure 18.

A>mzsim
was .01 mos “or

 

ZZqfi fl :24_~__ 12.—#4 m :22.—

 

 

 

 

"Kb/

 

m mmczx
m. mmmzo

m mmc: 6

2.1 5.33...

 

 

 

I

lllJJJl l

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l

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ed

(QNLO

Nos

174

(continued)

Figure 18.

mos

A>mzlim

:01 mo_

Nos

0“

 

2A: _

a

_____d e _ #5 _q«__d5_1_ q

 

_____djfi«_

 

 

“a macro
OH mmczq

z: Hmomme

 

_aq~__ _

 

lllll l I_J___l 11]]! 1.1 1. I

L

[1.1 l l

 

 

o~

(EHJ)1>

175

(continued)

Figure 18.

l>wzlim

moi sol mos ~o_

OH

 

 

222‘. =:_:~ fl =::~__

  

 

   

 

 

.Ilt1!

IIAY\\\\1111

 

m mmczx
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m mmczp

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Jam—_—

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l

JIIIHJ l

l

l

llllil

1n11||1

 

 

ofi

(£fl4119

176

(continued)

Figure 18.

mos

A>mzllm
,o_ mos “oi

OH

 

_44—4 A.—

:_a_fia,_ q. ~:__dal_ «1 —:_fifi_ _‘

 

 

 

 

 

Z mmcz 6
OH mm¢24

owe hmomce

.24444 ~ ~

L

l

Ulllil

L

l

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1111]] J 1

 

 

OH

(QHLO

«or

177

Ij(Emax=30 GeV)/Ij(Emax= 0°) = 0.96; for y = 1.50 the ratio
is already 0.998. When no cross-section measurements are
available at this energy, the cross-section at the nearest
lower energy is assumed to be constant out to Emax' Figure
19 shows a bar graph which exhibits the net contribution

to isotope j by the different targets for two values of y.

It is evident that 14

N is the most important target in this
model in spite of its lower abundance.
Figure 20 and Table 15 summarize the calculated ratios.

7

Comparing the observed isotOpic ratios Li/GLi = 12.5

d 11B/loB = 4.0 to these values, one finds that the boron

an
ratio is matched only for y close to 1.25 and then increases
rapidly with increasing y, while the Li ratio is near 2 for
low values of Y and even for Y = 5.25 it only reaches the
value 6. There is hence no hope of attaining both observed
ratios with a proton spectrum of the pr0posed form and a

14N cross-sections it is

Specific Y- From Figure 10 for
evident that a Special proton spectrum, peaked below 30 MeV
but not rising as a high power of E to 10 MeV, can reproduce
the observed ratios (this type of argument was already
proposed in Bernas et al. (BGRS 67).). That this represents
a physical situation is not at all clear however. More
likely is some type of preferential depletion mechanism‘

for 6L1 or also cosmological 7Li production. Even the

boron ratio is not really satisfactory. Solar flares with

y 3 3 are what is actually observed. we get a ratio of

178

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mma:
: on m u m 2 o_ m m m
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J H. ... .1 8 ...... m
1.
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2 I
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z nu
o... z . .|:_ alum
iIJ o /
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0 .ul_ nu
m_1 Alx m—M
rmi T1 3
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w
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In
N

179

 

 

 

 

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»
..r . ...r . m1 1 m. . .
D
D D
a D ..
D
D 4 4
4 4 4 4 4 ..N
.0 .0 _M It
4 U 1. one.
4 I.
4 11:0
4 a ....m
4 .. 3
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4T
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Due :
7;
min qmeumam zoeoma moi e
m :3. Sm: 2254.565 3

‘Table 15.

 

g

180

Isotopic and Elemental Spallation Production Ratios

From a Target Mixture C:N:O (3:1:5) by Proton

Spectra E-Y.

7L1/6LI

 
 

 
  

____.._,___,___._ -____.__.—__ --.

118/108

LI/BE

 
 

BIBE

 
  
 

 

B/LI

'25 I7 307 902 2208 205
1050 108 “06 1000 32.4 302
1'75 108 508 1100 47.2 #03
2000 1.9 7.5 12.1 69.1 5.7
2085 201 908 1302 10107 707
2050 202 13.0 1903 150.9 10.6
2075 203 17.3 1504 22506 1406
3000 205 2303 1607 339.6 2003
3025 207 3105 1802 513.8 2803
3050 209 4206 1908 779.9 390“
3075 302 57.6 2106 1186.4 54.8
4000 305 7708 2308 180702 7600
4025 309 104.9 2603 2754.4 10409
4050 403 14102 2901 419905 14402
4075 408 18908 3204 640306 197'“
5000 503 25408 3603 9765.1 269.2
5025 600 34105 4007 1489305 36508

 

7i2=========================================L

181

11B 10B

3 20 in that case. Thermal neutrons would increase
10

/
this ratio (they deplete B preferentiallyh.thermal protons
decrease it only at a temperature which would lead to
complete destruction of Li. Hence a mechanism to alter

this ratio is difficult to come by.

Thus far we may draw the following conclusions:

14

While N dominates the light element production (eSpecially

for y‘: 3), we have not obtained results that differ greatly

14

from calculations based on guesses for the N cross-sections,

indicating these early results were rather fortuitously

correct. The 11B/10

B ratio suggests that the proton
spectrum causing spallation is rather flatter than what

is observed in solar flares.

7.3 Energy Requirement of (BGRS 67) Model

The energy requirement in the (BGRS 67) theory is
critical to its validity, we calculate it for the most
severe case, the gBe abundance in the sun. Starting
from equation 6.31 we find after integrating with respect
to energy and time that for a time integrated proton flux

f¢p(t)dt « E-Y, the minimum areal energy density

W(MeV/cm2) s f00

(E)EdE
EC ¢

9

required to produce all the Be in the sun is given by

(provided 7 > 2):
n -y+2
98e EC MC

..w ~
n
CNO ( y+2)(I9) Mi

 

EC is the low energy cutoff of the proton spectrum and to

 

182

obtain a lower limit on W this is chosen close to the 93e
production threshold. The other variables are defined in

section 6.3 and 7. For solar abundances from Table 13

 

 

M.
and for ii = 2 x 10 3 (MI 67):
C
10 E—Y+2
~ C
W “ (y—2 1.9 '
-29
For E = 30 MeV, y = 3, equation 7.21 yields I =0'llXIO cmz;
C 9 2
MeV
we obtain
w = 3 x 1029 MeV/cmz.
For the surface of the sun the total energy required is
then 3 x 1046 erg. For Y = 4, EC = 30 MeV, equation 7.21
-3l
yields 19 = 0.249xé0 cm2 so that
MeV
W = 2.2 x 1029 MeV/cm2 .

Both values are close to the estimates in (MI 67) and

(BGRS 67).

7.4 Observations

A reliable calculation of the net contribution of
various light element production mechanisms is at present
not possible. To repeat the calculations by H.E. Mitler
(MI 70) without measurements of (0+0) cross-sections or
better knowledge of the low energy cosmic ray flux would
be premature. The calculations for stellar production
depend critically on stellar models since mixing and
burnup in convective zones can cause large changes in
relative abundances. Cosmological contributions are the

most difficult to estimate since very little observational

183

evidence can be found which is directly related to this
mechanism. To all this is added the large uncertainty

in the actual net abundance measurements, so even if a
calculation is attempted, one does not really know with
what one should compare. It would be very interesting

to have boron isotopic ratios available from stars.
Unlike the range of lithium isotopic ratios observed,
from 2 (close to the spallation ratio for low 7) to over
20, which is usually explained by cosmological production
or differential depletion, the boron isotOpic ratio,
apparently not changed by either of these mechanisms, should
be the production ratio. Large fluctuation in the ratio
are not expected and any such fluctuations would provide

better insight into the production mechanism.

APPENDICE S

APPENDIX A
IONS TRAVERSING KAPTON

The manufacturer of Kapton does not reveal its exact
formula. However from the 21.65 MeV y-counting experiment
it is easily inferred that it is mostly carbon.

By weighing several pieces of 1 mil Kapton an average
areal density 3.8:0.1 mg/cm2 was found. The stopping

12

powers for protons on C as shown in Table 16 are taken

from (WBP 66).

Table 16. Proton energy loss in Kapton.

_T

 

Proton Stopping Power Proton energy loss(MeV)
Energy (MeV) (MeV cm /g) in 0.0005" Kapton

22 MeV 21.4 .081

42 MeV 12.7 .048

 

 

For the 21.65 MeV y-counting experiment it is important

11

to know whether 7Be and C are stopped by the Kapton.

The relations

Z
R=R.— (59’2
o
and
_ 1L
E — E0 (mo)
make it possible to use (WBP 66) to find the approximate

7 11

ranges for Be and C.

Ro is the range of the tabulated nucleus;

Z0 is its charge;

mo is its mass;

E0 is its energy.

184

185

R,Z,m, and E are the corresponding variables for the nucleus

of interest. In the energy range 1 MeV/nucleon and using

4He data, these formulas underestimate by a factor of 2
the 12C range in water and aluminum (see SE 68, Figures 25
and 26).

At 21.65 MeV the maximum energy for 7Be is 9.56 MeV;

the maximum energy for 11

C is 10.13 MeV. The lab angle
is of course 0° with respect to the beam for these cases.
To find the range for these particles one first calculates

the energy of the a particle given by the energy relation

7

E0Be = (9.56 MeV)(4/7) = 5.46 MeV for 78e
110 11

E0 = (10.13 MeV)(4/ll) = 3.48 MeV for C

The range of the a particle in 12C at a calculated energy
can now be looked up in (WBP 66).

7

R0Be = 4.7 x 10-3 g/cm2
11
R0 C = 2.4 x 10 3 g/cm2

The range can now be calculated using the first equation

.7
R Be

(4.7 x 10’3 g/cm2)(7/4)(2/4)2 = 2.05 x 10‘3g/cm2

11
R C

(2.4 x 10'3 g/cm2)(ll/4)(2/6)2 = 0.73 x 10’3g/cm2

Since these are underestimates by a factor of 2, it is

evident that while 0.0005" Kapton is thick enough to stop

11

the C; 0.001" Kapton is needed to stop all 7Be.

APPENDIX B

SLIT SYSTEM DESIGN CALCULATIONS

 

 

 

 

 

 

 

 

1“ 5—4 ”1
19 )r.(_ '32 ID .
H H - $1 -

Figure 21. Geometry of Slit System with Beam at 90°.
In Figure 21 S1 and 82 represent the back and front

slit respectively. D represents the part of the beam
trajectory visible to the detector for the beam at 90°

to the slit axis. The yield Y a 8182 should be maximized
for a given D. From Figure 21 the geometrical relation-

ships are evident:

S S

 

 

 

 

 

 

 

_2_._1 52. 9
2 2 = 2 = 2
H X X+R-H
These results then follow:
8
2
X = H
52+S1
S S +S (R-H)S
_ 2 _ 2 l _ 5| 1
D“(Hs+s+R H” H )‘H52+ H
2 1
To maximize Y set dY = 0 = Szdsl+slds2 subject to D = constant
R+R~H ds1=0
H H dS2
_R-H
dS2 — —§— dS1
H-R _
SZdSl + Sl( —§—'d31) - 0

186

 

187

The last formula has the following meaning. If HZR, that
is if the front slit is very close to the beam, then the
size of the back slit is only limited by the detector size.
The choice of the front slit opening is critical for beam
trajectories other than 90°. Then the range of possible
flight paths depends strongly on both beam width W and

front slit width 82. This is shown in Figure 22.

 

 

   

 

 

0:54

CASE I CASE 2

 

 

Figure 22. Approximate Range of Path Length Differences.
AR is the approximate range of path lengths. From Figure 22

it is seen that AR = a + 2b.

 

S2 w
case 1‘ “b = £2.30 b = 5156 ‘32”)
w 82
case 2‘ “b = 5166 b = 65.6 W52)
w 32
AR = m + tan8 for bOth cases.

This shows that for small angles 8, the beam spot size and
front slit width are equally critical as far as timing

resolution is concerned. Yield Y a W82. This is so because

188

in making the beam spot small, the beam intensity is cut
down proportionally. It is thus of advantage to have

'W 2 82. This maximizes yield for constant timing resolution
for small 0. Near 0 = 90°, AP 3 W and the front slit width

is not critical.

APPENDIX C
FORMVAR FILM THICKNESS MEASUREMENT

The stOpping power for a compound can be calculated

from the stopping power of constituent elements using the

 

formula.
STOPPING POWER = dE = 2 dB pc (1)
d(0CX) E d(pEX) (0E)

pc is the density Of the compound
DE is the density of an element
px is the areal density.

The formula Of formvar is H C 0 so

16 8 4
dB = dE pH dE pC dE Eg_ (2)
dlpr) ‘1sz"5 DE dxzpC “5 pE dZOOXS ”E

F = formvar, H = hydrogen, C = carbon, 0 = oxygen.
The stopping powers for 5.48 MeV a's were taken from

(WBP 66). One obtains from Eq. (2):

2

dB 2 MeV cm
ETBEET" [(21. .82)176 + 7. 463(— 96) + 6. .892(l76)] x 10 ___§___

(3)

2 MeV cm2

9

= 8.565 x 10

It was found that 5.48 MeV particles lost 0.089:.009 MeV

in traversing 44 double layers Of formvar.

 

dE _ 2 2
dpr — 8.565 x 10 MeV cm /g
dE = 0.089 MeV

189

190

x) = 0'089 2 g/cm2 = 1.04 x 10—4 g/cm2 .
8.565X10

d(

 

F

1 double layer = 2.36 ug/cm2 = 2.4:0.2 ug/cmz,

APPENDIX D
GAS HEATING MODEL

TO estimate the instantaneous heating of the gas a
calculation with the model given below is carried out.

When an Object Of cross-section A moves with uniform
velocity v through a gas, it will displace a volume Avt
in time t. The minimum velocity that must be imparted
to the volume Avt is v. This way the gas in front of the
Object is transported just behind the Object in time t.
The work done in moving this amount of gas must be supplied
by the Object.

Suppose the proton beam traversing the gas heats a
volume element Of height h, width w and length 2 to a
temperature Tf. Due to buoyancy the volume element will

rise, its terminal velocity should satisfy the equation
VT 2

vt(pV - ofgi)g = 0(vtlw)§--

V is the volume element = ihw:

T1 is the temperature Of the surrounding gas;

Tf is the temperature Of the heated gas;

v is the terminal velocity;

0 is the surrounding gas density;

9 is the acceleration due to gravity.
The left side represents the change in potential energy
when the heated volume rises the distance vt. The right
side represents the energy needed to move the gas of

volume vtiw out Of the way.
191

192

One Obtains for the terminal velocity:
2(T -T.)
_ f i 5
V - [ -—T;———'hg]
Assume the total amount of energy E deposited in volume

V is equal to the energy deposited in the gas during time

so E = tipSI
S is the stopping power Of the gas for protons of the
energy under consideration. I is the proton current.
The temperature rise of volume element V is then
given by
E/(pVK) = Tf - Ti'
where K is the specific heat of the bombarded gas.
Substituting for E, V, and t one obtains:

Tf - Ti = (hplSI)/(vp£th) = SI/(va)

2 = 2

(Tf-Ti)2v (Tf-Ti)32hg/Tf = SZIZ/(sz )

(Tf-Ti)3 = TfSZIZ/(Zhwngz)

This last equation can be easily solved by iteration.
Chosen units are:

S in (MeV cm2)/9

I in u coulombs/sec

K in cal/(g C°)

 

 

 

 

(SI 2 = [MeV cm2 1.60x10-6erg cal ‘yf lO—6coul/sec
K 9 MeV 4.184x107erg 1.60x1019cou1/proton
LE ‘
x cal 1
4
_ 1 2 . 2 cm
‘ ( 4.f84 ) (C ) 2

sec

193

Tf(C°)2cm4 2 2

(4.184)25ec2 K 2hwzg

3 _
(Tf-Ti) "'

 

For the experiment on 20Ne gas the values are I =0.5 and
0.1 respectively.
w =0.063 cm, h =0.ll4 cm
S = 13.9
K =0.246
For these values I find Tf(I=.5) = 321°K and Tf(I=.l) = 304°K.
A 22 MeV proton loses .081 MeV in a 1 mil Kapton window.
The stOpping power of 22 MeV protons in nitrogen is
20.88 MeV cmz/g. When the gas pressure is 30 cm (Oil) the

energy deposited in the cell per proton is then:

2
AB = (4.75)(2.54cm) 289 3 3 30 cm 20.88cm MeV
22.4x10 cm 13.8x76cm 9

=0.9 x 10.2 MeV

SO the total energy loss in gas and Kapton is 0.09 MeV

per proton. The usual beam intensity was 0.5uamp.

(0.09MeV)(0.5x10“6coul/sec)(l/l.6xlO—19

2.8 x 1011MeV/sec 20.01 calories/sec.

Power coul)

The gas cell body is made of brass and weighs 1450 9. Take

the specific heat Of brass at 0.09 cal/g, then the rate of

temperature rise of the cell is

0.01 c0 _ _4 o
(1450)(.09) sec - 0.8 x 10 c /sec

Since the gas cell is in metal contact with the scattering

chamber, no long term heating of the cell is expected to

194

result. The above assumes efficient cooling of the gas

by the brass body of the cell.

APPENDIX E
CALCULATIONS FOR BEAM DEGRADER

Energy straggling for a beam Of particles with nuclear
charge 2 passing through a target Of nuclear charge Z,

atomic number A and density 0 is given by (EV 55):

W2 = ”2264 WA) (0X)N (1)
‘where X is the distance of target traversed, N is Avagadro's
number.

Suppose a proton beam with energy 21.65 MeV is to
be degraded to 17 MeV. In (WBP 66) one finds the range Of
21.65 MeV protons and 17 MeV protons in Al. The difference
in range is the desired aluminum thickness; 0.2307 g/cmz.
For lead one Obtains 0.414 g/cmz.

TO compare the energy spread from formula (1) above,

consider
5 (px) = (13/17)(0.2307-E§) =0.111 g/cm2 for aluminum,
A cm
a (ox) = (82/207)(0.414—3§) =0.164 g/cm2 for lead.
A cm

Hence, aluminum is the better degrader. The actual energy

spread for aluminum is:

IE2 = 1.565 x 10’1 g-(pX) Mev2

KEQ

0.132 MeV .

A 0.035" thick aluminum plate was used as degrader.

The 6061 aluminum alloy has the composition:

195

196

98.0 % A1
1.0 % Mg
0.6 % Si
0.20% Cr
0.25% Cu

0.05% impurities.
It is thus safe to use the ranges for protons in pure
aluminum to calculate the expected energy loss using (WBP 66).

0.035" aluminum represents an areal density pX:

pX = (2.7g/cm3)(.035)(2.54) =0.240 g/cm3.
From (WBP 66) a 21.65 MeV proton has a range 0.6610 g/cm2
in aluminum. The range 0.421 g/cm2 corresponds to a proton
beam of 16.8 MeV.

The angular beam spread is given by

8 = 21(MeV) L
2E(MeV) “L(rad)

 

L = length in scatterer =0.035"
E = proton energy
L(rad) = radiation length Of aluminum = 8.9 cm

..° 6 = 303°.

APPENDIX F
BAND RESOLUTION CALCULATIONS

TOOTSIE plots a number proportional to Et2 against
a number proportional to E where E is the energy of the

particle and t is the flight time. One may rewrite:

8t2 = ( l mvz) (d/v)2 =

2 md2 (1)

NIH

where d is the flight path. Hence the plot by TOOTSIE
should be a set Of straight bands, parallel to the x-axis,
each band representing a mass. The width Of the bands
depends on energy resolution Of the detector, time resolution
of the beam pulse, flight path range, and time resolution

of the electronics. The last can be ignored except for very

low energy pulses, where it is extremely difficult to

 

estimate.
2 _ 0 2 6 2 _ 2
AEt - 'S—E- (Et )AE+F‘E (Et )At — t AE+2EtAt (2)
2
AB; = 9% + 2 9% (3)
Et

At has two contributing sources, 6t the beam pulse width,
and Ad/v from the range Of flight paths. Since t = d/v,

Eq. (3) can be written
2

—7AEt=%+2(5—:+9§) (4)
Et

The three contributions limiting the mass resolution
are independent Of each other, so for a comparison with data

the square root of the sum of their squares is apprOpriate.

197

198

AF was always 40 keV or better as measured from the
FWHM Of the 5.48 MeV alpha peak from an americium source.
The percent error then varies inversely with E.

The average beam pulse width was 0.5nsec. The percent-

age error varies inversely with flight time, hence with

energy:
d mc2
t=d/V=— -E—
c/2
maximum E 3 20 MeV, minimum mc2 Of interest is 6 x 938 MeV;
d 3 30 cm.
. 'tmin ~ 12 nsec.
t = 12 nsec + RF 2 65 to 84.
max 2
Hence the percent error contribution to éi§%—l- varies from
Et
8% to 1.2%.

The error due to path length variation is largest at
small forward angles. The following calculation is for a
0.040" beam width (horizontal dimension) and a 0.040" wide
front slit with the detector at 15° to the beam. The range
Of flight path distance is calculated for 90% of the particles

reaching the detector.

 

 

.“ '
$2 ...\\\\\\\ I

Figure 23. Range of Flight-Distance for 90% of Particles

Reaching the Detector.

199

*
Total area = 8—2—3
Sine
Shaded area = xztane
For shaded area to be 10% Of total area requires:

82*w l 2

 

-'—_Sln6 _6- = X tane
52*wcose
X ‘ 2
10 sin 8
2 = V + 52 - 2x

 

 

Sine tane

where 2 is the range of path lengths desired. For 8 = 15°,
S = 0.040", W== 0.040", I find 2 = 0.0256" = .65cm.

For a flight distance of 26 cm, the percent contribution

AEt2 .
to 13 then 2(0.65/26.0)100% = 5%.
Et2

APPENDIX G

TIME-OF-FLIGHT CROSS-SECTION INTEGRATION RELATED FORMULAS

Some details for calculating cross-sections from
angular distributions.

Below are tabulated a few fortran statements representing
equations used in the cross-section calculations.

The equation to calculate the number of channels
corresponding to energy loss in gas and window:

ECHC=((RA(L)-H)*P*2./7.6/.2241+2.0)*2.335/10.**2*Zl(M3)**

1.207*ZZ/(Zl(M3)**.6667+ZZ**.6667)**1.5*ECAL

(RA(L)-H) is the average distance the reaction product
travels in the gas; this varies with angle.

P is the gas pressure in cm Hg.

Zl(M3) is the charge of the reaction product, the
average for the expected products for a
particular mass band is used.

22 is the charge Of the target gas.

ECAL is the number Of channels per MeV Of particle

energy from the energy calibration curve.

An integration factor:
F(L) = (COSD((A(L-1)+A(L))/2.)-COSD((A(L)+A(L+1))/2.))/NM(L)
A(I) are angles at which data was taken.
NM(L) is the number of monitor counts for data taken
at angle A(L).

200

201

The factor combining most constants and geometric

variables:

G(L)=(CNM/Q)*(H/B1)((R/P)*(SIND(BA)/Z)*(.2241/.17854)

CNM

Bl

BA

Z

/273.1)

*(.76/.6452)*(.1602/.15625)*(.6283/.6025)*((T+273.1)

is the number Of monitor counts for the
calibration run.

is the total collected charge for the
calibration run in 10.8 coulombs.

is the pressure in inches Hg for the
calibration run.

is the gas temperature in °C assumed to

be equal to room temperature.

is the distance from S1 to 82 (see Figure 70)
in inches.

is the mean flight path length to S1 in inches.
is the width of S2 in inches.

is the angle at which data is taken, hence
this is A(L).

is the number of atoms per target molecule.

The number (.15625)(.l7854)(6.452) represents the area of

. 2
S1 in cm‘.

The quantity F(L)*G(L)*NSY is then the contribution to

the total cross-section for data taken at
angle A(L). NSY is the number of counts in
a specific energy spectrum corrected for the

low energy cutoff.

APPENDIX H

SETUP PROCEDURE

To set up the electronics systems a pulser is used to
simulate detector pulses at the preamplifier input. First
the time-pickoff control logic pulse output is monitored
with a cathode ray oscilloscope; and its sensitivity is
set so that it just does not free run and triggers only
'Occasionally on random noise. After this adjustment the
pulser is turned on and the fast timing logic is checked
out. The fast discriminators are checked for multiple
triggering. The delays for the RF stop pulse and the start
pulse to the TAC are adjusted so that pulses which arrive
simultaneously at the fast anticoincidence circuit also
would arrive simultaneously at the TAC (if the 25 nsec
anticoincidence requirement would not be in effect). The
TAC pulses generated by the pulser are monitored with a
ND 160 multichannel analyzer. A flat, continuous random
time spectrum should be Observed. The single channel
analyzer pulses to the slow coincidence module have to
arrive at the same time. This is done by turning the delay
knob on a SCA module while monitoring with the scope. The
veto pulse is similarly adjusted, choosing pulse length and
delay on the gate and delay generator module. The output
of the Universal Coincidence is checked next. It should
give logic pulses if the veto is disabled, and should have

202

203

no output if the pulser is also connected to the veto
preamplifier. The logic pulse from the slow coincidence
gates the energy and TAC pulses. The linear signals have
to have the correct delay to be passed by the linear gate
and stretchers. The amplifier provides a properly delayed
unipolar linear signal. The TAC pulse is delayed with a
427A delay amplifier (not shown in the electronics diagram).
The linear gate and stretcher controls are adjusted so
linear signals are 3 usec long and arrive at the same time

at the ADC's.

BIBLIOGRAPHY

AC 60

AC 70

AER 67

AER 69

BA 71

BBFH 57

BCJR 71

BFH 65

BG 60

BGRS 67

BP 61

CA 67

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