ABSTRACT
. . , 20. -
PROTON INDUCED SPALLATION OF me AND THE

ASTROPHYSICAL PRODUCTION OF THE
LITHIUM ISOTOPES

BY

Lolo Marangkup Panggabean

Cross sections for production of masses 6 and 7
in the proton induced spallation of 20Ne have been mea-
sured at the proton bombarding energies 30, 35, 40, and
42 MeV. The magnitudes of the mass 6 and mass 7 cross
sections at each energy are equal within the experimental
uncertainties, both rising from 1.5 mb at 30 MeV to 4 mb
at 42 MeV. ‘The angular distributions for both masses at
all energies are very similar} they go down monotonically
at back angles.

The measurements employed the time-of-flight (ETZ)
technique for particle identification. The energy E was
measured by stopping the particles in a surface barrier
Si-detector and the time-of-flight-T was measured by mea-
suring the time interval between the time the particles
were created and the time of their arrival at the detector.

1

Lolo Marangkup Panggabean

The time width of the proton beam bursts (0.4 nsec to
0.6 nsec) from the Michigan State University Cyclotron
yielded a mass resolution that was sufficient for this
experiment.

The 20Ne target gas of 99.66% purity was contained
in a cylindrical gas cell, 1.25 in. high and 4.75 in. in
diameter, which was equipped with kapton window for the
proton beam and a thin formvar window as an exit window
for the reaction products. The pressure of the target gas
varied from 21 to 43 torr.

Together with the cross sections for mass 6 and
mass 7 that are available in the literature, the cross
sections measured in this laboratory were used to calcu-
late the ratio of the production rate of 7Li to that of
6Li by the protons in stellar flares, assuming a spectrum

Y, where y is a constant. It was found

of the form E-
-7.1 .

that a spectrum E was required to produce the exper-

imentally observed abundance ratio of 12.5. The steepest

spectrum observed in solar flares has E-S’G. It is sug-

gested that one must include the a + a reactions as addi-

. 7 .
tional sources of Ll.

2
PROTON INDUCED SPALLATION OF ONe AND
THE ASTROPHYSICAL PRODUCTION OF THE

LITHIUM ISOTOPES

BY

Lolo Marangkup Panggabean

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Physics

1972

If

cm

.14 0"?

ACKNOWLEDGEMENTS

I sincerely would like to thank Prof. S. M. Austin
for introducing the tOpic of research and his guidance and
enduring patience from the beginning of the experiment to
the end of the final analysis of the experimental results.

I would also like to thank Dr. H. W. Laumer for
the valuable discussions that we had about the detail of
the experimental technique and his assistance in collect-
ing the data each day during the experiment.

I would like to thank Dr. R. A. Hinrich who was
willing to take the place of Prof. S. M. Austin during his
leave of absence and Mr. S. H. Fox and D. Larson who were
willing to assist in data collection when called upon.

Help from Mr. N. Mercer and his staff from the
machine shop and the staff of the Cyclotron Laboratory are
greatly appreciated.

I would like to thank the National Science Founda-

tion and Michigan State University for their support

during the research.

ii

Last but not least, I would like to thank the
Ford Motor Co. who provided the support during my first

year of study at Michigan State University.

iii

LIST OF TABLES.

LIST OF FIGURES

TABLE OF

LIST OF APPENDICES. . .

Chapter

I. INTRODUCTION. .

1.1

1.3

1.4

II. EXPERIMENTAL APPARATUS AND PROCEDURES

II.l

II.2

II.3

II.4

IIOS

II.6

II.7

II.8

CONTENTS

Astrophysical Problem

Calculations of Cross

Sections.

Importance of Low Energy Region

Cross Section Measurement for

Cyclotron Facilities.

Scattering Chamber.

Target.

Gas Cell and Slit System. .

Pressure Measurement.

The Thin Formvar Window . .

Main Detectors.

Monitor Detector.

iv

20

Page

vi

vii

ix

10
10
l3
14
15
19
20
22

23

TABLE OF CONTENTS (cont.)

Chapter qu0

11.9 Electronics for Time of Flight

Measurement . . . . . . . . .~. . 23

11.10 Accumulation of Data. . . . . . . . 31

III. DATA ANALYSIS . . . . . . . . . . . . . . . 35
III.1 Normalization of Data . . . . . . . 35

111.; Mass Spread . . . . . . . . . . . . 36

III.3 Yields Extraction . . . . . . . . . 42

III.4 Differential Cross Section. . . . . 91

111.5 Total Cross Section . . . . . . . . 101

IV. CALCULATION OF THE PRODUCTION OF LI, BE,
AND B IN THE SOLAR SYSTEM . . . . . . . . 106

IV.1 -Previous Calculations . . . . . . . 106
IV.2 Calculation of the Relative
Production Rate of 6Li and 7Li

Associated with Solar Flares. . . 108

V. SUMMARY AND CONCLUSIONS . . . . . . . . . . 140

APPENDIX. 0 O O I O O O O O O I O O O I O O O I O O 142

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . 151

LIST OF TABLES

Table Page
III.l Mass Resolution for 5.5 MeV Particles. . . . 39
111.2 Observed Mass Resolutions for Mass-6 and

Mass-7 at 5.5 MeV. . . . . . . . . . . . . 4o
III.3 Parameters Used for Extrapolation. . . . . . 33
III.4 Various Slit Sizes Used in the Experiments . 92
III.5 Differential Cross Sections. . . . . . . . . 94

III.6 Integrated Cross Sections. . . . . . . . . . 102
III.7 Systematic Error in Percent. . . . . . . . . 104

IV.1 Average Cross Sections for the Production
of Li, Be, B by Spallation of CNONe. . . . 127

IV.2 Proton Spallation Cross Sections . . . . . . 128

IV.3 Production Rate Ratio of 7Li and 6Li
(PR(7)/PR(6)) as a Function of y . . . . . 139

vi

11.1

11.2

II.3

II.4

11.5

11.6

II.7

III.l

III.2

III.3

III.4

III.5a

III.5b

III.5c

LIST OF FIGURES

Curve of Relative Abundance From (BBFH 57)
Based on Suess and Urey. . . . . . . . . .

Schematic Diagram of Time of Flight
Technique. . . . . . . . . . . . . . . . .

Schematic Drawing of the Beam Transport and
Analyzing System . . . . . . . . . . . . .

Horizontal Cross Section of the Gas Cell,
Slits and Detectors. . . . . . . . . . . .

Block Diagram of Monitor Electronics . . . .
Block Diagram of Time-of-Flight Electronics.

Electronics Used to Avoid the Non-linear
Region of the TAC. . . . . . . . . . . . .

Time-signal vs. Energy displays. . . . . . .
Mass bands display . . . . . . . . . . . . .
Schematic Drawing of Different Path Lengths.

Time Shift of the TPU Output as a Function
of Energy. . . . . . . . . . . . . . . . .

Representative Spectra . . . . . . . . . . .
Energy Spectra for Net Yields. . . . . . . .
Angular Distributions for Mass—6 . . . . . .
Angular Distributions for Mass-7 . . . . .

Angular Distribution for Mass-10 . . . . . .

vii’

Page

11

16
24

26

29
34

34

38
43
46
98
99

100

LIST OF FIGURES (cont.)

Figure Page

III.6 Production Cross Sections for Mass-6, 7 and

10 from Proton Spallation of 2ONe in the

Energy Range Ep = 30 to 42 MeV . . . . . . 103
IV.1 Production Cross Sections as a Function of

Energy 0 O O O O O C I O 0 O O O O O O O O 112

IV.2 Production Cross Sections Used for the
Calculation of the Production Rate of
Lithium. O O O C O O O O O I O O O O O O O 117

Bl Schematic Diagram Showing the Minimum and
the Maximum Time Signals . . . . . . . . . 146

BZ Schematic Diagram Showing the Time Signal
2 - . o o o o o o o o 146
TRF Tflight + constant

B3 Schematic Diagram of the Choice of the

Stop Pulse and the Corresponding Time
Signal 0 O O O O O I O O O O O O O O O O O 147

viii'

LIST OF APPENDICES

Appendix Page

A. FORMULA TO ESTIMATE THE RANGE OF 6LI

IN SI. 0 O O O O O O O O O O O O O O O O O 142

B. SELECTION OF STOP PULSE AND ITS
CONSEQUENCES o o I o o o o o o o o o o o o 144

C. NOWIZATION OF DATA. 0 C O O O O O O O O I 148

D. DERIVATION OF MASS RESOLUTION FORMULA. . . . 150

ix

Chapter I

INTRODUCTION ‘

I.l AstroPhysical Problem

Whileathe thermonuclear reactions in the interior
of the stars can eXplain the abundances Of many of the
light elements (A.< 60) as the result of a series of
fusions of lighter elements into heavier ones (BBFH 57,

Ba 71), one does not expect the isotopes of the elements

D, Li, Be,and B to be formed by the same mechanism. The
origin of this expectation is found in Figure 1.1 (BBFH 57)
where the measured abundances of the elements in the solar
system are plotted as a function of the mass number A.

It is seen that Li, Be, and B lie well below the general
curve, being a factor of 107 to 109 less abundant than

He. The reason for this low abundance is found in the
nuclear physics of these nuclei.

Isobars with A = s (5He and 5Li) and A = a (8Li,

8 .
Be, and 8B) are not stable and hence are not found in

nature. The isobars A = 6, 7, 9, 10, and ll do have

stable isotopes (6Li, 7Li, 9Be, 10B, and 11B) but are not

5

      
   

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IRON GROUP

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Fig. I.1.——Curve of Relative Abundances From
(BBFH 57) Based on Suess and Urey.

expected to survive due to (p, a) reactions on these iso—
topes in the interior of the stars at any temperature
above 106 0K (BGRS 67). Thermonuclear reactions proceed
at a non-negligible rate only at temperatures a factor of
ten higher than this, so these isotOpes will not be pres-
ent in significant amounts in the ashes of a thermonuclear
process. Thu;*we require a methanism for the formation
of Li, Be, and B in a region of low temperature, i.e. a
process which is not thermonuclear in nature.

W. A. Fowler, G. R. Burbidge, E. M. Burbidge, and
F. Hoyle (FEB 55, BBFH 57) first suggested such a mechanism,
namely proton or alpha induced spallatiOn reactions on
suitable targets found at the surface of the stars or in
the interstellar medium. Taking into consideration the
threshold energy and the abundances of elements in the

solar system the most important targets appear to be 12C,

14N, 16O, and 20Ne and the incident particles are protons

and alphas from solar flares and/or cosmic rays.

1.2 Calculations of
Cross Sections

 

 

To calculate the amount of Li, Be, and B produced

in the proton or alpha induced reaction one needs the

Spallation cross section for each element from each target
in addition to the flux of the incoming protons or alphas
and the abundances of the target elements. .

There have been many attempts to calculate these
crdss sections. The calculations are based on the Serber
model (Se 47), i.e. a fast nucleon cascade followed by a
slow evaporation according to Weisskopf (We 37), or a fast
nucleon cascade followed by a fast breakup according to
Fermi (Fe 50). Dostrovsky and several other collaborators
have done a series of calculations on different targets
at various energies (Do 65, Do 68). They applied the
Monte Carlo calculation technique for the fast cascade
as prescribed by MetrOpolis et al. (Me 58) and another
Monte Carlo calculation for the evaporation part following
the methods of their previous work (Do 58, Do 59, Do 60,
Do 61). They also included the effects of a diffuse
nuclear surface as initiated by Chen et a1. (Ch 68).

N. T. Porile and S. Tanaka (Po 64), R. G. Korteling and
A. A. Caretto Jr. (Ko 70a, Ko 70b) have also applied a
similar approach in their papers. The results of these

calculations are fairly good, only about 20 to 30% of the

calculations deviating from the experimental values by

more than a factor of two. These calculations are for

heavy targets (except Do 68) and high energies.

O

For lighter targets as 12C, 14N, 16O, and 20Ne

where the evaporation model is probably not suitable, the
Fermi break up model has been applied by R. Bernas and

E. Gradsztajn (BGRS 67)to follow the nuclear cascade. For
the energies considered in this paper (70, 100,-156, and
200 Mev) the results are, for Li, Be, and B, in good
agreement with the experimental values except for simple
reactions like pick up of a few nucleons. Unfortunately
these simple processes sometimes dominate the total pro-
duction cross section.

G. Rudstam (Ru 55, Ru 66) has devised a semi-
empirical formula which predicts the cross sections for
heavy targets (Ca) and R. Silberberg and C. H. Tsao have
extended the formula to include light targets (Si 72).
While each of the methods predicts, one way or another,
the approximately correct cross sections at high energies
none of them gives reliable information for the energy
region from the threshold up to about 100 MeV where the
cross section rises very rapidly reaching its maximum

value (see Figure IV.1). In this energy region then, one

has no option but to measure the cross sections.

I.3 Importance of Low
Energy Region

All proton spectra that have.been observed decrease

rapidly with energy E . The importance of the cross sec-

tions in the low energy region then depends on their slope.

For some models the low energy cross sections are extremely

'0

important, even dominant (see Section IV.2).

1.4 Cross Section Measurement
for 20Ne

 

While fairly complete measurements have been made
for targets of 12C, 14N, and 160 (see Chapter IV) the
production cross sections for 20Ne targets had not been
measured at any energy.

In this thesis I describe the cross section mea-
surements of the production of the isobars A = 6 and A = 7.
An attempt to measure the cross sections for A = 10 and
A = 11 was hampered by the available mass resolution and
hence the values of the cross sections for A = 10 only
are reported.

The technique is based on the kinetic energy

formula for a particle with a constant velocity V, i.e.

E = 1/2 MV2 where E and M are the kinetic energy and the

mass respectively. Also V = D/T where D and T are the
distance traveled and the time of flight over the dis-
tance D (see Figure 1.2). By rearranging it one can

write:

ETZ = M(l/2 D2) (1.1)

i.e. ET2 is pTOportional only to the particle mass and
other constants. Both the energy E and the time of flight
T of the reaction products can be measured and with the
help of the computer the product ET2 can be computed on-
line, displayed and stored; thereby the measurement of

the mass M is made possible.

A weakness of the time-of-flight technique is that
it does not separate the members of an isobar from each
other. For the purpose of astrOphysics, however, it is
sufficient to measure the cross section of an isobar since
there is only one member of each isobar A = 6, 7, 9, 10,
and 11 which is stable. The rest have short half lives
compared to an astrophysical time scale and 8-decay to
the stable member. The one exception is loBe with a half
life of 2.7 X 106 years. For the energies considered in

this thesis (30 to 42 MeV), however, it is not a serious

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problem since the threshold energy for 10Be is high
(37.8 MeV).

The measurement technique uses time of flight
for particle identification and has been described in
a paper by Davids et a1. (Da 70). Here it is modified
for use with a gas target, as is discussed in detail,
together with the experimental procedures, in Chapter II.

The variable energy proton beam from the Michigan
State University Cyclotron has a burst width of 4 0.3 nsec
insuring a small time spread for the reaction products
and hence a good mass resolution.

The angular distributions 0(8, Ep) were obtained
for A = 6 and A = 7 at 30, 35, 40, and 42 MeV proton bom-
barding energies. Integrating 0(8, Ep) over the angle 6
the cross section 0(Ep) is obtained. The analysis neces-
sary to obtain these cross sections is presented in
Chapter III.

Together with the cross sections that are avail-
able (see Table IV.2) and predictions from isospin sys-
tematics (valid at high energies) these cross sections
will be used to calculate the ratio of the production rate

of the isobars A = 6 and A = 7. This is presented in

Chapter IV.

Chapter II

EXPERIMENTAL APPARATUS AND PROCEDURES

II.l Cyclotron Facilities

 

The Michigan State University sector-focused
Cyclotron is used to accelerate protons up to 30, 35, 40,
and 42 MeV in conducting this experiment. The layout of
the machine, the beam line that leads to the 40 inch
scattering chamber in which the experiments were carried

out and the focusing elements are shown in Figure II.1.

Q Q Q

l' 2' ° ° °

10 are the magnetic quadrupole focusing

elements and M M M are beam alignment, analyz-

l, 2’ O O O 5

ing and beam switching dipole magnets.

When properly run the cyclotron can produce an
analyzed proton beam with an energy resolution < 0.1%.
The energy analysis slits at boxes 3 and 5 were set for
energy resolution of 0.07%. The careful design of the
central region makes it possible to select a narrow phase
group. A time width At of the proton beam burst of < 0.3
nsec FWHM has been obtained. In this experiment At varied
from 0.4 to 0.6 nsec FWHM. This time resolution is

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sufficient for our needs. For the present experimental
setup, the fastest particle of interest (i.e. 20 MeV
6Li ion) has a time of flight of 12 nsec, so the width
of the beam corresponds to only a spread of 3.5% in time
or less than 7% in mass since the contribution of the
time spread to the spread in mass is twice the percentage
spread in time (see Section III.2). The neighboring
isobars are separated by (7-6)/7 = 14%.

In most cases 3 to 4 u amps of protons are ex-
tracted with 100% efficiency and a current of 300 to 800
n amps is incident on the target in a beam 0.03 to 0.05
in.wide and less than 0.1 in. high. The proton beam is
collected in a Faraday cup which is 57 in. long and 4 in.
in diameter and integrated by a current integrator (ELCOR
Model A3lOB). The Faraday cup was isolated from the
scattering chamber by'a 1.5 in. plastic ring and was
surrounded with a water-filled fifty-eight-gallon barrel

to shield the detectors from radiation produced by the

stOpping beam.

l3
II.2 Scattering Chamber

The scattering chamber1 is located in the experi—
mental vault no. 2 (see Figure 11.1). Its inside diameter
is 40 in. and the height provides 13.5 in. of working space
above the beam line. The chamber is provided with a ro—
tatable tableaand a monitor arm. The beam line is 4.985
in. above the table and 2.625 in. above the arm. Both
the table and the arm are equipped with radial groves
and dowel pin holes along the sides of the groves at the
radii of 6 in. to 18 in. separated by 2 in.

During these experiments the proton monitor counter
was positioned on the table and the detectors and the
target were positioned on the arm; the table was kept in
position while the arm was rotated to the desired angle.
The position of the arm was read through a digital read-
out with an accuracy of 0.01° least count. The chamber

was evacuated down to 7 X 10”6 torr.

 

1Manufactured by William M. Brobeck & Associates,
Berkeley, California.

14

II.3 Target

A gas target of 20Ne, isotopically enriched to
99.66 Mol % with a gross composition of 99.71 Mol % Ne,l
is used. The main contaminantsinthe target are hydrogen
(0.22 M01 %), helium (0.07 M01 %), nitrogen (< 0.01 M01 %)
and carbon dioxide (< 0.01 M01 %). Other contaminants
are 21Ne (0.05 M01 %) and 22Ne (< 0.01 M01 %).

Since the contaminants make up only a very small
percentage of the target (0.34 M01 %) their presence has
been ignored in the measurement of the pressure in the
gas target. For the same reason the contributions to the
cross section of productions of Li, Be, and B by C, 0,
21Ne, and 22Ne have been ignored.

The data at 42 MeV was taken with pressure of
20.8 torr Hg while the rest were taken at various pres-
sure ranging from24.2 to 43.3 torr. For the slit system
used this correSponds to a target thickness of 22.2 ug/cm2

at 20.8 torr and 46.21 ug/cm2 at 43.3 torr assuming the

temperature of the target is the room temperature (300° K).

 

1Manufactured by Monsanto Research Corporation,
Miamisburg, Ohio.

15
11.4 Gas Cell and Slit System

The gas is contained in a gas cell with a diameter
of 4.75 in. and a height of 1.25 in. It essentially con-
sists of two pieces of circular plates, made of brass,
connected by a spacer that makes up one-sixth of the wall
of the cell (See Figure II.2). The rest of the wall is
made up of 0.0005 in. Kaptonl through which the proton
beam can go without losing a significant amount of energy
(a 30 MeV proton loses 0.030 MeV in 0.0005 in. Kapton).
The construction of the cell has been described in detail
elsewhere (La 71).

A shell whose design is explained in (La 71) can
be positioned through the spacer so as to function as an
exit slit for the reaction products. The slit is covered
with 16 double-layers of formvar films that, on the aver—
age, corresponds to 38 pg/sz. Earlier experiences proved
that the formvar film might break so one needed several
slits (see Section II.6). The width of the slit ranges
from 0.0425 to 0.0435 in. and they are 0.75 in. high.

The height and the rear end of the shell are large

 

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compared to the dimensions of the rear aperture (0.125 in.
by 0.25 in.) which is positioned at a distance of 9.6
inches from the front slit; hence, it is treated as a
two-slit system with a rectangular rear aperture accord-
ing to the description of Silverstein (Si 59).

The gas cell with the shell, the rear aperture,
and the detectors are fixed in their position on a steel
rail that is mounted on the arm of the scattering cham-
ber. The whole system moves with the arm of the scatter-
ing chamber as a unit (see Figure II.2).

The shield in Figure II.2 is made of lucite,

4.5 in. thick on the side facing the port and l in. on
the other side. It is used to protect the detectors
from neutrons.

From Figure II.2 it is seen that the reaction
products have to traverse a certain distance through the
gas before they reach the formvar window. This distance
depends on the angle between the beam and the detector
and on the position of the shell. The gas cell itself is
positioned off the center of the scattering chamber by
0.021 in. in a direction perpendicular to the radial

grove of the arm Of the scattering chamber and 0.25 in.

18

in the direction parallel to the grove, away from the
center of the chamber. This allows the shell to be posi-
tioned such that at 15° angle of detection the distance
between the beam and the front slit is about 1 in. and
with the same setting at 90° the distance will be about
0.25 in. Both distances are small enough so there is no
need for a regdjustment of the position of the shell when
the angle of detection is changed.

There are both disadvantages and advantages asso-
ciated with the use of a gas target. One disadvantage
is that the exit areal density and hence a correction for
spectrum cutoff (see Section III.3) is angular dependent.
With a pressure of 43.3 torr at 15° the exit areal density
is 118 ug/cm2 gas and at 90° it is 29 ug/cm2 of gas. To
this, 38 ug/cm2 formvar window is to be added. In addi-
tion to that there is an imbedded disadvantage in the
use of a gas cell with a time of flight technique, i.e.
the difference in the flight distance for particles
created at various points along the passage of the proton
beam causes a spread in the flight time. The advan-

tages are the accuracy of the measurement of target

thickness and that it is possible to obtain a very pure

l9

. 2
and thin target. Of course for ONe, there are essen-

tially no other Options available.

II.5 Pressure Measurement

 

The pressure of the gas target is measured with
an oil manometer connected to the gas cell during the
experiment. This manometer was designed for the measure—
ment of the low pressures-involved in this experiment. It
has a range of 135 cm of oil and the meniscus can be read
to within 0.5 mm; hence, the pressure can be read to
within 1 1 mm of oil or, for most cases, i 0.17% of the
pressure.

Octoil-S pump fluid1 is used in the manometer;
it has a low viscosity that provides a quick reading and
a very low vapor pressure (2.7 x 10-7 torr at 25° C)
compared to the gas pressure which, in most cases, was
approximately 40 torr. In these experiments the vapor
pressure was ignored since the error associated with it

is very small (6.8 X 10-8%). Its density at 25°C is

0.9812 g/cm3.

 

1Manufactured by Consolidated Vacuum Corpora-
tion. - '

20

A manifold interconnects the manometer, scatter-
ing chamber, gas cell, and the gas cylinder containing
the target gas.

To check the local heating by the proton beam in
the gas both the elastically and inelastically scattered
(leaving 20Ne in its first excited state) protons were
counted and cOmpared at two experimental cases. In the
first case a lOO-namp. beam was sent through the target
for 100 sec. while in the second case a 500-namp. was
sent for 600 sec. The ratio of the number of protons
per coulomb in both cases was 1.004 while the ratio of

the pressure readings was 1.004. This indicates that

the beam heating by the proton beam is negligible.

II.6 The Thin Formvar Window

The formvar window is prepared in a simplified
version of the method of Hoogenboom (Ho 61). Formvar—E
(C4Hl608) is available in the powder form.1 A certain
amount of formvar is diluted in 1-2 dichloroethane to

obtain a 2% (by weight) solution. A film is obtained

by dipping the tip of a piece of wire (14 8.5. gauge)

 

1Available from Shawinigan Resins Corporation,
Springfield 1, Massachusetts.

21

into the formvar solution and then drawing a line on the
surface of distilled water contained in a glass beaker
thereby forming a thin layer of formvar solutiOn on the
surface of the water. Within a few seconds the 1-2
dichloroethane evaporates leaving a formvar film.

The film is lifted from underneath with the help
of a square ldOp somewhere in the middle of the film.

One double-layer film is then obtained and directly ap-
plied on to the shell. In this work a 16-double-layer
formvar window has been used.

The performance of the formvar window prepared
this way has been very satisfactory. Its durability
seems to lessen in the case of a repeated pumping down of
the gas cell and-letting itrup to atmospheric pressure.

The thickness of the film was measured by measur-
ing the energy loss of a 5.48 MeV alphas from an Am-source.
The result is that each double layer, on the average, has
a thickness of 2.4 i 0.2 ug/cm2 (La 71). The total

thickness of the window used here is thus 38 i 3 ug/cmz.

22

II.7 Main Detectors

A silicon surface barrier detector, called the
E detector (see Figure II.2) is used to measure the energy
of the particles. The thickness of this detector is so
chosen that the most energetic particle produced in the
reaction, that is 6Li in the ground state, is just
stopped in the detector. At 30 and 35 MeV a 86 u-detector
is used (needed 64 u) while at 40 and 42 MeV a 150 u-
detector is used (see Appendix A).

The detector was cooled by circulation of alcohol
at -78.5°C and was overbiased by a faCtor of two to de-
crease the detector risetime and increase the sensitivity
of the time pickoff unit (see Section III.3).

A second detector, called the veto detector, is
used to detect particles that pass through the E detector.
These are lighter particles which are not of interest.

For all runs the thickness of the veto detector is 260 u.
The purpose of the veto detector is to avoid the dead-
time of the analog-to-digital-converter associated with
processing the large number of detected protons and alpha

particles.

23

II.8 Monitor Detector

To monitor the elastically scattered protons a NaI(T1)
detector is used (see Figure II.3). The discriminator level
of the monitor single-channel-analyzer was adjusted to ac-
cept both elastically scattered protons and inelastically
scattered protons leaving 20Ne in its first excited state.
The logic signal from the single-channel-analyzer was sent
to a scaler and to channel zero. The total proton spectrum

was also recorded with a multi-channel-analyzer (ND 160).

II.9 Electronics for Time
of Flight Measurement

 

In this section (and hereafter) the electronic
modules used during the experiments will be frequently men-
tioned. For simplicity the names of the modules will be
abbreviated. Below is the list of the modules together

with their descriptions and models.

 

MODULE DESCRIPTION MODEL
1. Fast Discriminator (FD) ORTEC 417
2. Delay (DELAY) ORTEC 425
3. Dual Coincidence (DUCO) ClOZB/N, EG&G
4. Dual Discriminator (LRS) Model 121 Discriminator

LeCroy Research System
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25

5. Time Pickoff Control (TPC) ORTEC 403A
6. Time Pickoff Unit (TPU) ORTEC 260
7. Time to Amplitude Converter (TAC) ORTEC 437

8. Timing Single Channel Analyzer

(SCA) ORTEC 420
9. Linear Gate and Stretcher

(LINGATE) ORTEC 442
10. Preamplifier (PRAMP) ORTEC 109A
11. Selective Active Filter

Amplifier (AMP) ORTEC 440
12. Gate and Delay Generator ORTEC 416
13. Universal.Coincidence (UCOIN) ORTEC 418

14. Analog to Digital Converter (ADC) NORTHERN SCI

NS-629
15. NaI(Tl) Detector MSU—L. LEARN
16. Multichannel Analyzer ND 160
17. Sealer ORTEC 430
18. Computer XDS 7

The block diagram for the electronic setup is

shown in Figure II.4. The upper row is for the energy
pulses, the middle row is for the veto pulses, and the
lower row is for the time pulses.

The energy pulse goes through the TPU (thereby gen-

erating a pulse that-serves as a start pulse for the TAC) and

 

 

 

 

26

 

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27

is then amplified. The prompt output goes to a SCA to
generate a logic pulse that goes to a UCOIN module in a
coinCidence mode.

Pulses from the cyclotron RF system were used as
stop pulses for the TAC, the output of which is the time
signal. One of the TAC output.pulseSgoes to another SCA
to generate afilogic pulse that goes to the UCOIN module
in coinCidence mode. This means the UCOIN module will
output a pulse if there is a coincidence between the
energy and the time signal in which case the gate in each
of the linear<qatesfor the energy and time signals are
Open and letting the other half of the energy and time
signals go through; they are adjusted so they enter the
ABC's at the same time. The ABC's were set in a synchronous
mode.

The pulse from the veto detector, after amplifi-
cation, goes to a SCA, then to a Gate Generator and fi-
nally to the UCOIN module in anti-coincidence mode. This
veto pulse will inhibit an output of the UCOIN even if
the energy and the time signal are in coincidence in
which case there is no pulses entering the ADC's. This

case corresponds to a particle passing through the E

detector which is not of interest.

The rest of the modules in the lower row are used
to avoid the non—linear region of the TAC (15% of the
range setting). They are shown in Figure 11.5.

The non-linear region can be avoided by a proper
delay of the stOp pulses. If, however, every stop pulse is
accepted the range of time that can be measured is 15 nsec.
less than the period of the RF. The setup shown in Figure
11.5 allows one to reject or to accept a stop pulse if it
arrives before or after a certain period of time which in
this experiment was 25 nsec. with a range setting of 100
nsec. The entire RF period is then available for analysis
of pulses.

The signal from the TPC is fed into a PD, the out-
puts of which are fed into the LRS module and, after proper
delay, into the START terminal of the TAC. Upon arrival of
the input pulse at the LRS module it generates a positive
going pulse the length of which is adjustable; in this
experiment it was chosen to be 25 nsec. long (the non-linear
region was 15 nsec.). Pulses from the RF system are fed
into another FD whose outputs are used to select the stop
pulse and as a stOp pulse for the TAC.

The selection of the stop pulse is done by feeding

one of the stop pulses and the positive going pulse from the

29

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30

LRS module into a DUCO module operated in anti-coincidence
mode. The DUCO module gives an output which is fed into the
other half of the LRS module which will generate a negative
going pulse. This negative going pulse, together with the
other stop pulse, properly delayed, are fed into the other
half of the DUCO module operated in coincidence mode. The
final output Of the DUCO module serves as the selected stop
pulse and is fed into the TAC. The start pulse then is de-
layed by the amount of time necessary to carry out this logic.
The net result is that only stop pulses which arrive
25 nsec. after the start pulse are recorded. Long flight
times correspond to small TAC pulses, the lowest energy
identifiable particle yielding a 25 nsec. pulse while
short flight times give large TAC pulses, the fastest par-
ticle identified yielding a 25 nsec. + 1 RF period pulse.
A more detailed explanation appears in Appendix B.
With the time-of-flight technique it is clear that
there is a low energy limit for each mass such that it
can be unambiguously assigned to a mass band (see Ap-
pendix B). From the kinematics of the reaction the
kinetic energy of the most energetic particle, which is
6Li in the ground state, is known and the time of flight

of the slowest particle that can be unambiguously assigned

31

is equal to the time of flight of 6Li (g.s.) plus one

RF period, hence depends on the bombarding energy of the
protons and the flight distance. Increasing the flight
distance will increase the low energy cutoff while de-
creasing the flight distance will decrease the low energy
cutoff but worsen the time of flight resolution and hence
the mass resqution. For this experiment the flight dis-
tance at 15 degrees laboratory angle is 28 cm. With this

setup the low energy cutoff is about 0.6 to 1 MeV for

mass 6, 7, and 10.

II.lO Accumulation of Data

At the beginning of every experiment the resolu-
tion of the electronic system was measured. It was always
better than 40 Kev FWHM for 5.48 MeV alphas from an 241Am
source. Then a random time spectrum was taken-..This
is done by using the pulser (ORTEC 204) to simulate par-
ticle pulses and the RF pulses as the stop pulses. Since
the frequencies of the RF and the pulser are so different
then the time length measured are essentially randomly

distributed on the nanosecond scale from the minimum

length (25 ns) to the_maximum (1 RF period + 25 ns). A

32

random time spectrum assures that the TAC is Operating
beyond its non-linear region which is 15% of the range
setting. ‘

Next the width of the proton beam burst was mea-
sured. It was found to vary from one experiment to
another in a range from 0.4 to 0.6 nsec. FWHM.

Now the beam is sent to the target and the mass
spectrum is studied by displaying the mass bands on Time-
Energy axes using the EDE routine of the program TOOTSIE
(Ba 70). Energy gain is adjusted to make sure that all
particles are detected by positioning the 6Li ground state
peak to the most right side of the energy axis. Also the
discriminator level of the TPC is adjusted to insure that
it triggers for every energy pulse detected. Then the
delay of the RF pulse train is adjusted such that the
fastest particle of interest (6Li) corresponds to the
longest time signal since TS = TRF - Tflight + constant.
This can be checked by looking at the spectrum (see
Figure II.6).

The last step is to switch to the ET2 routine of
TOOTSIE which will calculate M = A + E(Ts — TO)2/NORM

where A, NORM, and T0 are constants to be input to the

program. The constants were so chosen that the mass

33

bands are as straight as possible. The display is on
M - E energy axes (See Figure II.7).

The two-dimensional spectrum in Figure II.7 was
taken at 15° with 40 MeV proton bombarding energy. The
low energy cutoff here is a straight line, it corresponds
to a constant time signal-~the minimum time signal.

At every angle where a measurement was taken a
background run was also taken. The background was mea-
sured by evacuating the gas cell and sending the beam
through it. The amount of beam used was, in most cases,
25% of the integrated charge used to measure the fore-
ground.

The data were collected and stored on both cards

and magnetic tapes for further analysis.

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Chapter III

DATA ANALYSIS

III.l Normalization of Data

The raw data is corrected for the dead time of the
ADC's during which the ADC's do not accept pulses. This
is done by sending one of the pulses coming from the mon-
itor detector to a scaler and on to channel zero of the
ADC's. The ratio between the count in channel zero and
the scaler gives the fraction of the time during which
the ABC's are accepting the data. The background data
have been multiplied by the ratio of the integrated charges
during the data taking and the background run.

The area under the elastic peak of the monitor
Spectrum has been found by using the program SAMPO.
TOgether with the integrated charge of each run during
the data taking and the pressure of the gas target mea-
sured during the run the ratio of the counts in the peak
to the product of the pressure and the integrated charge

for each run agrees to within 3 to 4% as is shown in

Appendix C.

35-

36

III.2 Mass Spread

Each mass band is comprised of particles distri-
buted along the mass axis at various energies. At each
energy a mass resolution can be assigned.

From the two dimensional spectrum it is seen that
the mass resorution(%%) for each band is worse in the low
energy region. The band of lighter mass is better re-
solved than the ones for heavier masses. This is prob-
ably due to the poorer energy resolution for heavy par-
ticles in that energy region and the time width of the
beam burst.

Energy E and the time of flight T are the two
parameters measured. TOOTSIE calculates the product ET2
(in arbitrary units which is prOportional to the mass M
of the particle.

A spread in E and T will then determine the spread

of M as follows:
1/2
A(ET2) = [AE2(T2) + 432T2(AT)2]

2 1/2
AM_A(ET2_) E AT :]
M _ "EH +4(T)

AE: being the energy resolution of the detecting system

AT: is the time resolution for the time length corre-
sponding to the time of flight of particles within
' 1 "AE ‘ “FAB.
the energy range E 7? to E

37

The time spread AT is primarily due to the time

shifts for the start pulses associated with a group of

A . .
energy pulses (E — %g) to (E + 7;) coming from different

points in the targets. There are three contributing

causes:

1. Pulses associated with particles of the same mass
and energy traveling through different path

lengths.

2. Pulses associated with particles of the same mass
but slightly different energies that cause time

shifts in the output of the time pickoff unit.

3. Time Spread due to the finite width of the proton

beam bursts.

The first contribution can be calculated from the

energy formula, where

"— = '—D- (D : flight path),

where AD depends on angle as is seen in Figure III.1.

At 17° scattering angle the length ACD is 0.19 in.

NSEC

 

 

B

Fig. III.1.--Schematic Drawing of Different Path
Lengths. FS = Front Slit, BE = Rear Aperture; a = 1°.

 

 

 

 

3.0 i
2.7 " °
0

2.6 - 0

o
LO "

c 1 1 1 1 1
0.5 LO 2.0 3.0 ' 4.0 5.0
E(MeV)

Fig. III.2.-—Time Shift.(nsec.) of the TPU Output
as a Function of Energy.

39

The second contribution is important only for
energies lower than 5 MeV (see Figure III.2), while the
third contribution is measured and its value ranges from
0.4 nsec. to 0.6 nsec. FWHM.

Adding these contributions in quadrature the band

resolution at energy E is calculated according to:

. 1/2
[303112) = (A302 + 4(A_D_)2 + 4(EPEiM.)2 + 4(331129.)2
2 B D T T

.ET

(see Appendix D), the result of which for 5.5 MeV particles

at 17° scattering angle are tabulated in Table III.1.

TABLE III.l.--Mass Resolution for 5.5 MeV Particles; E = 40 MeV,
D = 28 cm, Scattering Angle = 17°, Front Slit =
0.425 in., Beam Width = 0.5 nsec.

 

 

 

2 2 AT 2 2
AB 2 AD 2 BEAM 2 A ET
Particles ("9 (%) 4(——0 (%) 4(-——-——0 (%) ‘i———L(%)
E D T 2
ET
6 .
L1 0.53 11.7 22.5 5.9
7.

L1 0.53 11.7 19.3 5.6
lOB 0.53 11.7 13.5 5.1
11B 0.53 11.7 12.3 5.0
12C 0.53 11.7 11.2 4.8

 

40

As expected the mass resolution for high energy
particles is largely determined by the time resolution;
for lower energy particles it would be determined by the
energy resolution. Geometry affects all particles in the

same way.

For comparison the observed mass resolutions for

mass 6 and 7 mentioned in Table III.1 are shown in

Table III.2. The observed and the calculated mass reso-

lutions agree to within 1%.

TABLE III.2.--Observed Mass Resolutions for Mass-6 and Mass-7 at
5.5 MeV; EP = 40 MeV, Scattering Angle = 17°,
D = 28 cm; Beam Width = 0.5 nsec.

 

 

Observed Mass Scale = 0.16 mass unit/channel.
Mass Resolution (FWHM) for:

Mass-6 = 2.5 channels
= 6.7%
Mass-7 = 2.5 channels

= 6.9%

 

Comparing the band separation for mass-6 and
mass-7 which is (7-6)/7 or 14% with the calculated mass
resolution from Table III.1 which are 6%, one expects that

mass-6 and mass-7 should be well separated down to low

41

energy region. Experimentally, however, it is not so.
For mass-6 and mass-7 the separation is good down to

4 MeV while from there on to lower energy region it is
smeared almost uniformly. After a thorough investigation
it was concluded that it was due to the background events
that covered the low mass region up to about mass-8 or
mass-9 (therefore the background was subtracted). From
the data at 17° scattering angle mentioned above it was
found that the yield for mass-8 was only 3% of the yield
for mass-7. Since there is no stable isotope with A = 8,
it is not expected to have a large yield for mass-8, as
it is the case with the data, and therefore the above
conclusion is made.

In the higher mass region the bands are not well
separated even as high as 5 MeV. In addition the bands
seem to bend down in the very low energy part. The reason
for it is not clearly understood but it is probably due
to the incomplete charge collection in the E-detector

that will cause a too-small energy signal, hence a too-

small mass.

 

42

III.3 Yields Extraction

The 2-dimensional spectrum (ET2 vs E) displaying
the bands of masses detected during each run was read
from tape and either diSplayed on the storage scope using
the code TOOTSIE or was printed, giving the number of
counts with a~given set of values of E and ET2,-for closer
inspection.

Starting from the high energy region the mass-6
or mass-7 band is chosen by tracing the position of Li
and 7Li ground state that comes from the 2-body break-ups
using their energies as identifications as are predicted
by the program FASTKINE (written by Dr. R. A. Paddock
in this laboratory). The upper and lower limits of each
band are determined by drawing a straight line from the
high energy region, then identified, to the low energy
region.

By projecting each band on the energy axis, the
energy distribution for each mass is obtained. Then the
entire procedure is repeated to obtain the energy spectra
for the background runs. The background spectrum is then
normalized to the foreground spectrum and subtracted from

it to form the net spectrum (see Figure III.3 and III.4).

43

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.Fig. III.4.--(cont;) . . . (0.18 MeV/channel).

CH

CH
C)

COUNTS/CHEN

(fl
(3

COUNTS/CHEN

54

EP= 39.9 namema =30 °. THRGET NEED

 

COUNTS/CHEN

0
r HESS 8

fl * 1114M! . n .-

 

 

flHSS 7

 

 

 

HESS 10

“I! ‘.. mm .

 

lfimwahmk. 1

 

 

 

 

so 100
CHRNNEL NUHBER :

Fig. III 4.-e(cont.) . . . (0.18 MeV/channel).

100$ 5
H955 S .
g ..
'—
I:
:3
$3 ’ .
I .‘L i
100
"885 7
g ..
F-
2:
g; 5
4 L i L Lfi - :l L J a 1
10°F:
HESS 10
E _
£5
5 _.
'—
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L L L
50 100

5?: Lt0.1 HEU. eLaB=90 PTHRGET N520

55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

’CHRNNEL NUNBER,

Fig. III.4.--(cont.) . . .

(0.18 MeV/channel).

56

5P= L*0.0 NEU. sum-=37 2 THRGET N520

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50
“95$ 6
g all
g ..
p—
2 -.
:3
$3 I_ _ n
L— L... L JUJ _ 1
505
HESS 7
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g ..
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50:2 ' 5
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g .
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L :' 77.Lfi A L L
50 100

ICHaNNEL NUNBER

. Fig. III.4.--(cont.) . ; . (0.18 MeV/channel).

S7

5P: Lr0.1 r150. eLHB=L+S 9 TRRGET N520

 

 

 

 

 

 

 

 

 

 

 

 

 

50v
”955 8
3!
GE
5
5..
E 2
:J i ,
CD
° H
50
HESS 7
g.
.—
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SO .
1195310
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L)
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I 50 100

' ‘CHHNNEL NUHBEB

-Fig. III.4.--(cont.) . . . (0.18 MeV/channel).

(n
O
T

58

5P= 39.9 NEMLRB =50 °. TFIRGET N520

 

 

 

 

 

 

 

 

 

 

 

 

 

N955 S

:2
CE
5
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[195510
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5
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50 100

 

 

CHRNNEL NUHBER

'Fig. III.4.--(cont.) . .'. (0.18 MeV/channel).

S9

5.: 90.1 r150. emB=90 Mensa N520

 

mass 9

 

 

 

 

 

 

 

HHSS 10

 

 

 

 

 

2
$5
9
E.
:3 L
O
U
‘ J l. L
50 100

CHRNNEL NUMBER

Fig. III.4.--(cont.) . .-. (0.18 MeV/channel).

60

5.: 39.9 "EU-9mg =70 °. TERGE'I: N520

 

 

 

 

 

 

 

 

 

 

 

 

 

50 ’
HESS S

E
5
h
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9 l
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k
r:-
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x S l 1
50

F HESS 10
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50 100

'CHENNEL NUHBEE

Fig. III.4.--(cont.) . . . (0.18 MeV/channel).

 

61

EP= H04 HEU. emf-‘80 PTEEGET NEED

 

 

 

 

 

 

 

 

 

7S .
Ff HESS 6
Q.
3
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35
5
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50 100

 

 

 

 

CHENNEL NLIHBEE

Fig. III.4.--(cont.) . ... (0.18 MeV/channel).

00
(fl

coums/ CHEN coums/ CHEN

COUNT S/ CHEN

62

5P: 90.0 HEU. ema=90 2 TEEGET N520

 

HESS S L

 

 

“D
(n
7&7

 

31 l 1

 

“ g ‘ HESS 10

 

 

 

 

bJflAMLAn—d ' . I

 

 

 

50 100
CHENNEL NUHBEE

_Fig. III.4.-—(cont.) . .'. (0.18 MeV/channel).

63

5P: 90.0 HEU. eLHB=100.°TEEGET.NE80

 

 

 

 

 

 

 

 

HESS S
L l l
HESS 7
l L
HESS 10
E
g...
2
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t.)
M1 1 l 1
~ 50 100

 

 

CHENNEL NUHBEE_

.Fig. III.4.--(cont.) . .'. (0.18 MeV/channel).

64

5?: 39.9 momma =100.° TEEGET N520

 

ED
(0

COUNTS/ CHEN

 

 

mass 9

 

 

“0
(fl_

; COUNTS/ CHEN

 

HESS 7

l

 

 

“D
(n_

COUNTS/ CHEN

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l

 

 

Fig.

VLnr-Ll 11!

50

100

CHENNEL NUHBEE

III.4.--(cont.) . . .

(0.18 MeV/Channel).

 

65

% 5P= 90.1 HEU. BLRB=110.°TEEGET N520

 

 

 

 

 

 

 

 

 

 

 

 

50
Ft HESS S
h
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50%
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50 ' 2
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5
5 .
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50 100

,CHENNEL NUHBEE

.Fig. III.4.--(cont.) . .-. (0.18 MeV/channel).

66

5P= 90.1 1150.0LRB=125.° 13111351 N520

 

 

 

 

 

 

 

 

 

253
HESS S
5 1
P-
3
L1. 1 IL L L
25:
HESS 7
h
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25% ‘
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5
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WM 1 1 1 1

50 A 100
‘CHENNEL NUHBEE ‘

.Fig. III.4.--(cont.) . . a (0.17 MeV/channel).

67

... .. 0 I .
EP— 35.7 1150.555B ~15 . 1919951 N520

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1001:
HESS 8
21.
G:
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L)
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P
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LL LL L a L
100 2 '0
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EE b
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100
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21-
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§
0L
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l L
50 100

CHENNEL NUHBEE

Fig; III.4.--(cont.) . . . (0.17 MeV/channel).

68

.. _ 0 '
EP- 35.0 "EU’BLEB -20 . TEEGET NEED

w L

 

ID
U"

COUNTS/ CHEN

HESS S

 

 

 

 

n0

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s}

 

 

 

 

m.
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1

J

 

 

 

 

 

mass 10
:2
(I
It
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9
P-
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L W L
100

-CHENNEL NUHBEE _

.Fig. III.4.—-(cont.) . . . (0.14 MeV/channel).

69

5P: 35.7 ”EU-91.113“ 30’. 19191351 N520

 

Ln

0

COUNTS/ CHEN

HESS S

 

 

11L. 1 h. .

 

 

01
C3_

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c:

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50 ' 100
CHENNEL NUHBEE

.Fig. III.4.——(cont.) . .'. (0.17 MeV/channel).

7O

5 = 35.0 1150. 01.93" 95. 191-1951 N520

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2‘ .
HESS S

2'
c1:
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' 50 , 100

CHENNEL NUHBEE'.

Fig. III.4.--(cont.) . . .I(O.l4 MeV/channel).

 

71

_. ~ _. 0 '
EP~ 35.7 1150.11.58 -50 . 1913951 N520

 

 

 

 

 

 

 

 

7S
HESS S
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50 100

CHENNEL NUHBEE _

Fig. III.4.—-(cont.) . . . (0.17 MeV/channel).

 

5 = 35.0 1150,1598: 60‘: 1919951 N520

 

 

 

 

 

 

 

 

P
e .
HESS 8
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COUNTS/ CHEN

 

 

 

 

f“

 

COUN TS/ CHEN

 

 

 

 

 

100
CHENNEL NUHBEE
Fig. III.4.-—(cont.) . . . (0.14 MeV/channel).

72

5,,= 35.0 1150. 91.93: 90‘: 11911951 N520

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e.
HESS 8
z I
CE
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1195510
2
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5
1....
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50 100

 

 

CHENNEL NUHBER
51g. III.4.-—(cont.) . . . (0.14 MeV/channel).

__ ... 0
EP— 35.7 HEU’BLEB —-75 . TEEGET NEED
50 ‘ ,
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2
a:
I
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50 100

 

 

 

 

 

 

 

 

 

 

Fig.

CHENNEL NUHBEE

III.4.——(cont.) . . .

(0.17 MeV/channel).

 

74

5?: 35.0 1150. 51.193 =90 ‘2 11919951 N520

 

 

 

 

 

 

 

 

 

85
T mass 5
3
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:3
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100 ‘

 

CHENNEL NUHBEE

Rig. III.4.--(cont.) . . . (0.14 MeV/channel).

5 = 29.9 1150,6158: 15°. 1913951 N520

 

....
\l

HE S

COUNT s/ CHEN
I

 

mnnan -ffLJLLA ..LILL L

 

 

a...
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COUNTS/CHEN
1

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17
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50 100

' CHENNEL NUHBEE

. Fig. III.4.—-(cont.) . ... (0.13 MeV/channel).

7Sr
HESS 8
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HESS 7
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50 100

76

.. ‘ .. 0 I

 

 

 

 

 

 

 

 

 

 

CHENNEL NUHBEE‘

Rig. III.4.—-(cont.) . . . (0.13 MeV/channel).

77

_. _. 0

 

00

. H

HESS S

COUNT 8/ CHEN
1

 

 

 

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COUN TS/ CHEN
1

 

 

 

0 - . . ' “.799

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(COUNTS/CHEN
l

 

 

 

[Lme L - 1.

50* 100’
CHANNEL NUHBEE-

. Fig. III.4.-—(cont.) . ... (0.13 MeV/channel).

78

.. ‘ _. O
5P-— 30.1 1150. 61.113" 35. 1911951 N520

 

\l
n

COUNTS/CHEN

HESS S

 

LLLV L

 

 

\l
n

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\l

COUNTS/ CHEN

 

HESS 10

LLMHJLILEMJLL5.‘A,A.5. _ L ' 1

 

 

 

50 100
CHENNEL NUHBEE .

.Fig. III.4.--(cont.) . . . (0.11 MeV/channel).

79

5?: 30.0 HEU. 31.113" 952 11319951 N520

 

0!
c3

HESS S

 

 

 

 

 

 

 

 

 

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r-
2
=
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50 100
CHENNEL NUHBEE

° Fig. III.4.--(cont.) . .'. (0.11 MeV/channel).

EP= 29.6 nememf 53. Tansy NEED

80

 

 

 

 

 

 

 

 

 

2
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° [l

h“; 11 l 1 ll ..
50 100
CHRNNEL NUHBEH
- Fig. III.4.--(cont.) . J . (0.13 MeV/channel).

 

f0

COUNTS/(MEN

'0

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81

EP= 30.0 new. eLfi8= 55°. TRRGET {qt-:20

 

 

 

HESS 6

ARRAL n 1

 

. COUNTS/CHIN

 

'nass 7

flfllnflnnl

 

 

 

7 Fig. III.4.--(Cont.) . .

HESS 10
1 nfll‘l rm; 4 L . I
50 100

CHENNEL NUflBER

 

. (0.11 MeV/channel).

 

 

82

EP= 30.1 new. em: 85? THRGET. N520

 

' m

COUNTS/CHEN

n)

n)

[185$ 6

 

 

 

 

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50 100
. CHRNNEL NUHBER‘

' Fig. III.4.——(cont.) . . . (0.11 MeV/channel).

 

83

5?: 29.6 115mm = 75‘: THRGET‘NEE’O

 

 

 

 

 

 

 

 

2
HESS S
E
5
h
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2
3
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3
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0
11111 1 1 1 1
50 100
CHHHNEL ~unszn 
Fig. III.4.-—(cont.) . . . (0.13 MeV/channel).

84

5?: 30.0 MEU. ems: 752 TRRGET NEED

 

 

 

 

 

 

 

 

 

 

 

 

so
HESS 6
E
g NM 1 .. .11.
C3
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, f l 1
50
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50 100

 

.Fig.

CHHNNEL NUHBER -

III.4.-—(cont.) . ... (0.13 MeV/channel).

 

85

5?: 29.8 Mmema =1oo.° THRGET NEE-20

 

 

 

 

 

 

 

P. 1
H955 8
i
3
r- V
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§
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1111 n 111 ‘ 1 L .fi 1
50 100
CHENNEL NUHBER
.Fig. III.4.--(cont.) . .-. (0.13 MeV/Channel).

 

86

The spectra are then integrated over energy to
obtain the total yield. Since the spectra cut off at an

energy ELO of about 0.8 MeV because of the limiting sensi-
tivity of the time-pickoff unit or because of the limit
due to the finite size of the time interval between two
beam bursts, these spectra must then be extrapolated to
zero energy to obtain the total yield at a given angle.
Since the reaction products lose energy in going
’through the gas of the target and the formvar window, ELO
for each mass was corrected to be equal to the energies
of these particles at the time they were created. The
energy loss in the gold layer in front of the surface
barrier Si-detector (40 ug/cmz) was ignored since it was
only 0.02 MeV for a 1 MeV 7Li (No 70) (the energy scale
is always larger than 0.1 MeV/channel), and of course it
is not expected to be much different for 6Li, compared
to 0.43 MeV and 0.08 MeV for 20Ne at 15° and 90° scat-
tering angle respectively. These corrections were made
by integrating the stopping power formula:

2
dB Zr (E)

= 0.30711 x --—-§—— In A(E)
d(pX) . W 8 [l-esp(-AI/D(E))]D

 

 

~82 (MeV cmZ/g)

(A(E) and p are explained in the (Wi 66)),

87

to find the energy E of a particle whose energy loss is

I

such that after traversing the total exit areal density
(gas + formvar) its energy is equal to ELO' This formula
has been translated into FORTRAN IV language in the MSU
Cyclotron Laboratory by Dr. P. S. Miller. The range in
20Ne given by this program and the table by Northcliffe
et al. (No 703 for 1.4 MeV 7Li agree to within 8% (1.4
MeV is chosen just for convenience in reading the table,
although it is very close to the value of BI in most
cases, see Table III.3). A table of initial energy, and
the corresponding energy loss for every run is generated
and the energy after traversing the exit areal window is
matched to ELO and thereby EI is chosen. ELO is found
from the energy calibrations for each run based on the
position of 6Li ground state group. BI found this way
is the energy at creation of the particle with energy BLO'
Since no particles formed with energy less than
EI are detected one has to add to the yield that is found
from the net Spectrum the estimated yield of the unob-

served region. This is done by multiplying the number of

<2hannels corresponding to E by the average number of

I

<:ounts per channel over the first five channels in the

Iiet energy spectrum and adding this to the yield.

88

 

O OOH.O mam.~ «.mm OOH.OH mm0.0 mOn.v~ OO sea
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90

Table III.3 shows the energy cutoff for 6Li at different
angles for different bombarding energies together with the
number of channels to be extrapolated, which number depends
in general on the angles. This averaged extrapolation is
reasonable since there is no indication of a strong peak-
ing in the low energy region and the spectrum also has to
go to zero at zero energy in the laboratory system because
the Jacobian of the transformation of the cross section

from the center of mass system to the laboratory system

is zero (J = pLhB/pcm) (St 63). Fifty percent of this
extrapolating yield is assigned as the uncertainty in the
extrapolation and is added in quadrature to the statis-
tical error associatedeith the net yield to result in
the error reported in Table III.

Since the mass resolution is worse for mass-10
than for mass-6 and mass-7, one cannot separate mass-10
from mass-ll at low energy and extrapolation has to be
done from higher channels. Even though the energy cutoff
for this mass is experimentally about 1.7 MeV the extrap-
olations have been started from the 3.4 MeV region. This

large extrapolation introduces a substantial uncertainty

into our measurements of the mass-10 cross sections. In

91

addition it is impossible to reliably separate mass-11
from the large mass-12 yield, even at 3.4 MeV. For‘this

reason we have been unable to obtain an estimate of the

mass 11 cross section.

III.4 Differential Cross Section

90

The differential cross section of production is
calculated by using the formula (Si 59, W0 53):

Y sin 6

0(6) = nNG

where: Y = yield for each mass at the laboratory
angle 0 as described above

n = number of target per cm
N = number of the incident protons

G = G-factor of the two-slit-system with
rectangular aperture

and are calculated as follows:

 

 

n _ 6.023 X 1023 x P X p x E1. atoms
22.414 X 103 13.6 x 76 T

P being the pressure of the gas target in cm oil and p

the density of the oil in g/cm3 (= 0.9812 g/cm3).

92

N = QFC protons

1.6021 x 10*19
QFC being the integrated charge collected in the Faraday

Cup in Coulombs.

4blb21
= -————— -+
G Rh (1 A0) (cm)
where: bl = the half width of the front slit (cm)
h§ = the half width of the rear slit
1 = the height of the rear slit (cm)
R = the distance between the beam and the
rear slit (cm)
h : the distance between the front and rear
slits (cm)
A0 = slope non-dependent term (Si 59).

Table III.4 lists the various front slits used in the

experiments.

TABLE III.4.--Various slit sizes (in in.) used in the experiments.

 

 

Front Slits Rear Aperture

 

 

 

Width Height Width Height
0.0425 0.75 0.125 0.25
0.0430 0.75

0.0435 0.75

 

93

Table III.5 lists the differential cross sections
for mass-6 and mass-7 and lower limits for mass—10 mea-
sured at different angles and bombarding energies while
Figure III.S shows the angular distributions. For mass-6
and mass-7, at the same bombarding energy, the angular
distributions turn out to be similar both in the form !“

and magnitude, generally monotomically decreasing with

increasing angle.

 

Differential cross sections obtained this way
agree with the cross sections given by the program Gas
Cell (written by Dr. R. A. Paddock in this laboratory)

to within 1.4%.

94

TABLE III.5a.--Differential Cross Sections (MB/SR) (Ep = 42 MeV).

 

41

 

LabkeAngle 3%10) ' Error (%)
Mass 6: 15.0 0.40374 19.4
30.0 0.78126 14.2
45.0 0.51040 23.1
65.0 0.58811 15.3
90.0 0.16257 70.0
Mass 7: 15.0 0.58397 13.7
30.0 0.47423 24.7
45.0 0.32170 ' 33.6
65.0 0.41696 22.6
90.0 0.23884 40.8
Mass 10: 15.0 0.31275 16.5
30.0 0.17936 65.3
45.0 0.31810 32.1
65.0 0.21667 43.6
90.0 0.08831 88.1

 

Mass 6: 10.0 0.56932 9.7
17.0 0.42410 5.5
17.0 0.44788 6.4
30.0 0.48506 8.8
30.0 0.40964 9.0
37.0 0.38636 9.1
45.0 0.24482 23.2
50.0 0.33637 11.3
60.0 0.29054 17.5
70.0 0.21264 18.1
80.0 0.23568 16.4
90.0 0.15871 26.3

100.0 0.14693 28.9
100.0 ' 0.11306 33
110.0 0.11272 43.5

125.0 0.05453 73.2

TABLE III.5b.--Cont.

 

 

Lab.(81)\ngle %(9) 1 Error (9.4)
Mass 7: ‘ 10.0 0.77269 6.4
17.0 0.45030 8.1
17.0 0.51125 4.8
30.0 0.42168 9.6
30.0 0.35882 9.4
37.0 0.26535 13.1
“ 45.0 0.34236 12.9
50.0 0.27076 16.1
60.0 0.25229 17.9
70.0 0.16078 24.8
80.0 0.21552 18.0
90.0 0.02897 77.4
100.0 0.06905 59.5
110.0 0.04196 11.7
125.0 0.02994 32.8
Mass 10: 10.0 0.59674 5.7
17.0 0.42534 3.0
17.0 0.42232 4.2
30.0 0.39365 4.6
30.0 0.41657 5.0
37.0 0.50122 5.1
45.0 0.40889 6.4
50.0 0.38812 7.4
60.0 0.33612 9.8
70.0 0.24168 12.4
80.0 0.26782 9.1
90.0 0.20784 17.5
100.0 0.08522 19.4
100.0 0.06338 43.2
110.0 0.07240 10.1
125.0 ' 0.02780 37.9

96

 

 

TABLE III.5c.--Differential Cross Sections (MB/SR) (Ep = 35 MeV).
LabkeAngle ggKe) ' Error (%)
Mass 6: 15.0 0.66974 7.1
20.0 0.25473 13.9
30.0 0.28732 8.5
45.0 0.17209 13.2
60.0 0.13990 22.7
60.0 0.14335 16.5
75.0 0.18407 15.9
90.0 0.06882 26.6
Mass 7: 15.0 0.62895 7.3
20.0 0.21001 16.2
30.0 0.15788 14.8
45.0 0.18122 10.7
60.0 0.10836 27.3
60.0 0.07949 25
75.0 0.15408 18.9
90.0 0.06423 26.3
Mass 10: 15.0 0.48208 3.7
20.0 0.25084 12.2
30.0 0.12720 10.4
45.0 0.13697 14.9
60.0 0.16578 6.2
‘60.0 0.15082 11.8
75.0 0.10237 11.9
90.0 0.06817 18.1
= 30 MeV)

TABLE III.5d.--Differentia1 Cross Sections (MB/SR) (Ep

__

Mass 6:

15.0
25.0
25.0
35.0
45.0
55.0
55.0
65.0
75.0
75.0
100.0

0.32729
0.22388
0.22293
0.15373
0.10010
0.11815
0.13333
0.05769
0.17192
0.17627
0.10285

...-
1.0

1...;

H
w

H
O

1...:
J)

b

TABLE III . 5d . --Cont .

9 7’

 

 

Labzejmgle %(9) ‘ Error (15)

Mass 7: 15.0 0.25274 4.6
25.0 0.18287 8.7
25.0 0.16530 4.6
35.0 0.11733 6.2
45.0 0.08997 5.4
55.0 0.09240 21.9
55.0 0.11707 14.0
65.0 0.04447 18.8
75.0 0.09670 21.9
75.0 0.12647 13.3
100.0 0.07640 16.7
Mass 10: 15.0 0.52923 2.4
25.0 0.12976 11.9
25.0 0.10905 5.7
35.0 0.05532 11.6
45.0 0.04758 7.8
55.0 0.03787 30.6
55.0 0.04878 33.6
65.0 0.02925 16.9
75.0 0.07880 19.4
75.0 0.06267 18.4
100.0 0.01469 52.4

 

 

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Fig.
Bombarding Energy.

98

 

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LHBBNGLEIDEGREES]

III.5a.—-Angular Distributions for Mass—6.

 

1TIIIITIIIflfF

 

 

 

 

 

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Q 1., d-i
E P 1 '1
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99

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Fig. III.5b.—-Angular Distributions for Mass-7.

£9 = Bombarding Energy.

DIFF. COS.

DIF F. 0.3.

(ma/SR)

10

1119/88)

10

I
5...

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L10 80 120
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Fig.

Ep = Bombarding Energy.

100

 

 

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L10 80 120
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III.5c.--Angular Distributions for Mass-10.

lOl

III.5 Total Cross Section

For each mass and bombarding energy the total
cross section is calculated by summing the areas of the
trapezoids under the straight lines connecting the points
of the measured cross sections in the 0(6) - cos (6)

plane. ACCording to the formula

180
0T(B) = f 0(6) sin 6d6d¢
o
180
= 2n f 0(6) sin ads
0
o (E) - 2n 1
T _ f 0(6) d(cos 6)
-1

where 0(6) is the average value of both cross Sections de-
fining a trapezoid. For the backward angles for which
there is no data taken it is assumed that the cross sec-
tion is the same as the cross section at the largest
angle where measurement is made. For 30 MeV it is 100
degrees in the laboratory system, for 35 and 42 MeV it
is 90 degrees while for 40 MeV it is 125 degrees. It is
also assumed that the cross section at 0 degrees is the
same as it is at the smallest angle where the cross sec-
tion is measured which is 10 degrees for 40 MeV and 15
degrees for the rest. Results of this calculation is

listed in Table III.6 and plotted in Figure III.6.

102

TABLE III.5.--Integrated Cross Sections.

 

 

Contribution from

 

 

Tot.
E M V M mb
p( e ) ass 0( ) Error Frontl Back
(5") 1%) 1%)
42 6 . 4.1031 $28.8 2.1 24.9
7 3.8861 $36.6 3.2 38.6
10 1.9075 $46.0 3.5 29.1
40 6 2.4485 $21.2 2.2 6.0
7 1.9142 $20.1 3.9 4.2
10 2.5356 $11.4 2.2 2.9
35 6 1.6411 $24.8 3.9 26.3
'7 1.4017 $27.9 4.3 28.8
10 1.3364 $24.5 3.4 32.1
30 6 1.5882 $25.1 4.4 33.6
7 1.2156 $25.9 4.6 32.6

10 0.65995 $25.7 17.2 11.6

 

IPront = Area in the 0(6) - 6 between 6 = 0° and the smallest angle

Where measurement is made.
BC“iczk = Area between the largest angle (where measurement is made)

and 8 = 180°.

TOTRL CROSS SECTION [MB]

103

 

 

 

 

s
D MESS E3
" A mass 7
=1? M98810
9.—
a...
f
1 0 l 1 l
20 HO
E ( MEU 3

Fig. III.6.--Production Cross Sections for Mass 6,
7, and 10 from Proton Spallation of 2ONe in the Energy

Range E = 30 to 42 MeV.
P

104

To estimate the error in the integrated cross
sections 50% of the contribution from front and back
angles where there is no measurement made hawe been
assigned as an error and included in the error tabulated
in Table III.6 after combining it with the error of the

differential cross sections. Systematic errors are

listed in Table III.7.

TABLE III.7.--Systematic error in percent.

 

 

 

Source of Error » Error (%) Measuring apparatus
Area of rear aperture 0.39 Traveling microscope
Front slit width 1.2 to 1.7 Peeler gauge
R distance between Steel rule and

beam and Rear Aperture 1.0 micrometer
h distance between front Steel rule and
and rear slit . 0.3 micrometer
T temperature 1.5
P gas pressure‘ 0.17 Oil manometer
QPC integrated charge 3.0 Elcor A3103

current integrator

 

Added in quadrature these errors contributions yield:

3.9%. This error is small compared to error due to the

105

extrapolation of the cross sections to front and back
angle (see Table III.6). The total error in Table III.6
includes both the statistical and the extrapolation error.
If these error combined with the systematic error it is
clear that latter is negligible. Due to the extrapola-
tion procedure that was applied to the yield of mass-10,
the numbers listed in Table III.6 for mass-10 are probably

less reliable than the other results.

Chapter IV -
CALCULATION OF THE PRODUCTION OF LI,

BE, AND E IN THE SOLAR SYSTEM

IV.1 Previous Calculations

Even in the absence of the experimental cross
section from 20Ne H. E. Miller (Mi 70) and R. Bernas
et.al. (BGRSG7) have-attempted to calculate the production
of Li, Be, and B by Spallation reactions.

H. E. Mitler assumes the galactic cosmic-ray
particles coming on the CNONe targets in the inter-
stellar medium to initiate nuclear reactions thereby
producing Li, Be, and B. The contributions both from
the reaction of protons on CNONe and from CNONe ions on
hydrogen are taken into consideration. The production
cross sectionsused in the calculation are mostly from
the compilation by Audouze (AERS 67). Recently Epherre
and Seide (ES 71) have published the cross section for
7 14

Be of N from 13 through 40 MeV. It peaks to 40. mb at

20 MeV, contrary to the cross section used by Mitler

106‘

‘which is a smoothly rising curve reaching the value of
10 mb at 10 GeV. Mitler attempted to account for the
contribution from the a-reactions using cross sec-

tion estimates based on the cross sections measured from

12C, 14N at 90 MeV (Jung 69) and at 100 through 137 MeV

(E0 71). The cross sections for. a-reactions on 16O
and 2ONe have been assumed to be equal to the correspond-
ing cross section from 14N. The reaction products are
assumed to have a maximum path length of 4 g/cmz. This
reflects the fact that Li with energy greater than
120 MeV/nucleon (and hence range > 4g/cm2) will escape
the galactic disk and will not contribute to the abun—
dance of lithium in the solar system. Taking into account
also the possibility of an interchange between the inter-
stellar medium and the material of the star as a function
of time Mitler concludes that 6Li, 9Be, 10B, and 11B may
be produced by Spallation reactions initiated by the
galactic cosmic ray particles on 12C,.14N, 16O, and ZONe
in the interstellar medium, but that the abundance of
Li remains unexplained.

Bernas et al. (BGRS 67)have examined a rather dif-

ferent mechanism. They assume that the protons in the solar

cosmic rays are the bombarding particles and that the

108

C, N, O, and Ne in the photosphere are the targets. They

assume the energy spectrum of the solar particle_as being

E-Y, where E is the kinetic energy and y is a constant

taken to have a value that ranges from 3 to 5 according
to the measurements of Freier and Webber (Fr 63). The
cross section is assumed to be zero at energies lower

than Q the threshold energy for the production of

eff'

the maximum number of a particles, and equal to 5, whose
values are tabulated in Table IV.1, p. 127, for energy

above Q They find that the production ratio for

eff'

nll/nlO agrees with the observed solar system abundance
ratio (4.0), while n7/n6 (2.5) is much too small compared

to the observed ratio (12.5).

IV.2 Calculation of the
Relative Production Rate
of 6Li and 7Li Associated
with Solar Flares

 

 

The production rate of a light element L (L rep-

resents 6’7Li, 6He, 7Be) by the solar protons bombarding

the target M (M represents 12C, 14N 160, 20Ne) in the

I

SOlar surroundings can be expressed as follows:

109
Emax -l
= dE
PR(L) 4n g nM f ¢p(E) OL’M(E) (sec )
Ethres
where: PR(L) = production rate of the element L
n = relative abundance of the element M
M .
in the solar system
¢ (E) = proton flux in the solar cosmic rays
p (sec-cm2«-ster--MeV/sec)'l
o (E) . .
L,M = production cross section of the element
L by proton bombardment of the target M
at bombarding energy E(cm2)
E = threshold energy for the nuclear reac-
thres .
tion M(p, )L
Emax = maximum value for the energy used in

the integration

The values for nM are available in the literature.

Bernas et al. (BGRS 67) used the ratios ncanmoznNe

30:1:10:30, while Mitler (Mi 70) used another set of

values, i.e. = 3.7:l:6.5:0.78. The abun-

nC:nN:nO:nNe
dance of these elements in the solar cosmic rays has
also been measured. Bertsch et a1. (Be 72) reported the

abundances of the same elements in the solar cosmic rays

as = 2.95:1:S.26:0.84. In this section the

ncanznO:nNe

calculation is carried out for the values of both Mitler

and Bertsch et al.

110

The flux of solar protons has also been measured.
The variation of flux with energy can be expressed in
several ways. In the early work it was represented as
an exponential function of the rigidity R (the momentum
per unit charge) of the proton, exp(-R/Ro(t)).where R is
the rigidity of the proton and Ro(t) is the character-
istic rigidity. The value of R0 depends on time, i.e.
on the age of the flare activity and seems to vary from
one flare to another (Fr 63). The characteristic rigidity
gets smaller as the flare activity gets older, i.e. the
rigidity spectrum peaks more strongly to the low energy
region as the flare activity progresses (Fr 63).

More recently, it has become common to describe
the spectrum by a power law EDY (Fr 63, Hs 70, Be 72)
where E is the energy of the proton and y is a constant
whose value differs from one event to another. Simpson
(Si 70) has observed proton spectra over the period of
June 1966 to January 1967 with values for y that range
from 1.6 to 5.6.

The production cross sections for the isobars

A = 6, A = 7, A 10, and A = 11 have been collected.

They are tabulated in Table IV.2, p. 128, and plotted

111

in Figure IV.1. Out of this collection I have chosen a
set of cross sections for each of the isobars A = 6 and
A = 7 to be used in this calculation (see Figure IV.2).

The procedure followed in choosing the cross
section has been to compare with the rest of the data
over a wide energy range. Data that follow the general
trend are favored over those which do not. The latest
data by the same author are favored over his old ones.
Where there is no data available I either have consulted
the calculated value by Bernas et al. (for the high
energy region E > 150 MeV) or made an interpolation.
In either case a fifty percent error is assigned.

In the low energy region, from the threshold to
42 or 44 MeV, data are available in the form of isobaric
cross sections. (The data of Epherre et al. (ES 71) on 14N
was actually measured for 7Be only, but other mass-7 produc-
ing reactions are not energetically allowed below 30 MeV.)

For 12C, the 0(6He + 6Li) data of Davids et al.
are used below 50 MeV (Da 70). At higher energies 0(6Li)
is taken from Table IV.2 and 0(6He) is taken to be 0.5 mb
(BGRS 67). For A = 7 there are isobaric yield data

available for the energy range 28 to 44 MeV (Da 70) and

tOgether with 0(7Be) from Table IV.2 0(7Li) is

112

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tau) N011033 55011:) 10101

m8

-..... .

-

0H

omwm+mw¢3
mmwm+kam
okDUm+okmwmjj

p..r..t. .

. 3m: 1m
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—1:#.a . .

mmmw

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Hkmw

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—..:_ PL

...uaoocau.a.>H

OH

 

1.1%. 1.

rum. .ariz

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(011) 11011333 88083 510101

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Aidfifid q a

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ADM—Lam

to. mo. mo.
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kmwmmc ZH mwjo a

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mo. so. mg + m8 1 S . .
E:— .J a 1 1144 q a 4 fl 113 .J 4 . 1:: . a A I.
n . m A a . ea .1.
n. mwm .....om
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117

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H 3w: 1 w
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r $ 1
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r. .r.. . . h...P.P P . b...F. . . . ...PP. . . P 1

 

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{011) N011038 88063 10101

119

m2

 

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1 3w: 1 m
m2

1.»:ooc1a.m.>H .mam

no.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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120

 

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H 3m: 1 w

:4.fi4 fi 4 144444 4 a 1.11:...4 A a 11411.4 - 4
T 1
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1

T ... p p 1? LLF7.FL » . [Tbbbb _ _ 1F bbprbb . b 1

 

 

 

 

 

C)
(811) Mamas 85083 "111101

 

 

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O
H

122

 

AOuQOOVLttmo>H omflm

H 3m: H w

...._.. . 1...... . 1...... . 1...... .

 

J

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[11111 1

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Emww % %

 

 

l

I

[811] NOILDBS 88083 “111101

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aku¢.n30wu a

J:r_.. _ _:.b_ . b _ _.:._L H . .....b.L »

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123

constructed by subtracting 0(7Be) from 0(7Li + 7Be). For

energy higher than 155 MeV 0(7Li) = (7 i 1.5) mb (BGRS 67)

while for energy between 44 and 155 MeV I assume the

cross sections follows a straight line in a log-log scale.

Table IV.2 supplies 0(7Be). These chosen cross sections

. are plotted in Figure IV.2. fl

with the similar procedure the cross sections from

14N are construCted. The data by Laumer (La 71) and i

2.7“

Epherre et a1. (ES 71) are used to construct 0(7Li). At
high energy the estimated values for C(6Li), C(7Li), and
0(7Be) are all 10 mb (BGRS 67) but the measured value
for 0(7Be) at 2200 MeV is (8.6 i 0.8) mb (see Table IV.2,
p. 128) and hence I have assumed that 0(6Li) = 0(7Li) =
0(7Be) = (8.6 t 0.8) mb. The maximum value of the cross
sections for 6Li and 7Li have been assumed to be equal to
1.5 times the value of the cross section at high energy,
and the value of 0(6He) is taken to be 0.8 mb (BGRS 67).
In the calculation by Mitler (Mi 70) the cross
sections for 6Li, 7Li, and 7Be from 16O are plotted. They
are taken from the compilations by Audouze (see Table IV.2,
p. 128). His extrapolation to lower energy is comparable

to the data by Laumer (La 71) and hence I have used those

124

values in this calculation and taken o(6He)to be 0.6 mb
(BGRS 67).

The cross sections from 20Ne and 160 between
30 and 42 MeV are comparable. Furthermore there is no
known resonance in the proton reactions on both 160 and
20Ne that lead to the production of any of these isobars
and hence it“is expected that the excitation function
for such isobars,in both cases, will be smooth and sim-
ilar. Based on these considerations I have assumed for
the purpose of this calculation that the cross section
from 20Ne and 16O are equal.

The integration is carried out from the threshold
energy up to 100 BeV (contributions from higher energies
are negligible) and the ratio of the produCtion rate is
calculated for y = 1.5 to 7.2 for the solar abundances by
Bertsch (Be 72) and up to 7.4 for the abundances of
Mitler (Mi 70).

The ratio of the production rate for the isobar
A = 7 and A = 6, PR(7)/PR(6), rises from 1.6 for y = 1.5
in both cases to 14 for y = 7.2 or 7.4 respectively. The

value l2.5 for the production rate is obtained for

y 7.l with Bertsch's solar abundance data and for

7.2 with Mitler's solar abundance data (see

Y

125

Table IV.3, p. 139). This value is comparable to the
value for chondritic meteorites which is 12.2.

This value of 7 seems to be high compared to the
highest observed value of 5.6 (Si 70). It is somewhat
premature, however, to make any strong comment on the
value Y = 7.2 without knowing more about the cross sec- ”a
tions from the relevant targets at higher energy.

Table IV.3, p. 139, shows that the production rate

ratio increases as the value of 7 increases which behavior

 

 

has also been shown byLaumer (La 71) where the contributions
of 20Ne to the production rate was ignored, the difference
being the slower rate of increase of the ratio in this
calculation.

According to the model of Wagoner, Fowler, and
Hoyle (WFH 67) a certain amount of Li can also be pro-
duced in the primeval big-bangs. This will decrease the
production ratio PR(7)/PR(6) required from the Spallation
reactions and will permit production at a lower y.

Regardless of the value of y that will lead to the
correct production ratio, however, it is clearly seen

that the later stage of the flare activity is very impor-

tant in the matter of production ratio, so it is important

126

to know the value of y as a function of time, and do the
calculation of the production rate as an average over

time.

'0

TABLE IV.l.-—Average Cross Section (in mb) for the Production of Li,

127

Be, B by Spallation of CNONe.

 

 

 

6 , 7 , 7 9 ‘ 1o 11 11
L1 L1 Be Be C
12 -
c o 10 7 12 2 10 16 so
14 -
N o 10 10 10 2 10 10 30
16 —
o . o 10 12 4 2 10 10 15
20 —
Ne o 8 8 8 2 12 12 12

 

Taken from

(BGRS 67).

128

 

 

 

 

.Hmm so. mcHEEdU ma m UmNHHmEHocwH coon w>mn mama "mcwoaya
momomom» m H OH mma
: w.m H ¢.va oooma
: v.m H v.mH 000
mm mm» m.H H OH mma
: H.vH oooma
ho Hy v.~a com
mm mm N H OH mmH
: m H ma 000
mm H» m H OH mmH 0
ma
Ohmmmhh m.v H >.NH omH zva
: m.H H v.5 ooo
Humrqmm o.H H m.m OmH
Ohmmmoo H.N H m.m oma
no fix N.H H m.m ooom
.Hm um musooc<
xn coHuowm mmouo :oHumHHmmm wo >o>Hsm :0 muonooum : m.H H m.h 0mm
.Hm um musoocd
>n coHuoom mmouu coHumaammm mo %o>Hzm co musnooum .2 : m H OH mma
.Hm um musoocm
>3 :oHuoom mmouu :oHumHHQO mo >0>Hsm :0 musnooum .2 : N H o Om
. .Hm um onsopc¢
xn coHuoom mmouu coHHmHHmmm mo >m>usm :0 ousnooum .*H mm mm m H Ha vv UmH
"mxumfimm .Hmmom Hquvo H>ozv2 uoouoe

 

 

. HA...

MOM Hmzv mcoHuoom mmOHU coHuoHHon :0uoum11.dm.>H mum<b

129

 

 

 

 

 

 

mmmwmomw m.N H o.m mma
: N.N H N.vH oooma
: N.N H m.HH oom
mm mm» N.H H m.m mma
. : m.MH oooma
: m.HH com
mm H» m N + m m mma o0H
ohmmmmw m.v H m.m omH ZHH
= H.H H o.m ooo
Huqumm o.H H m.h oma
onmmmon m.H H m.m oNH
.Hm um
onsoocc an :oHuomm mmouo coHumHHmmm mo >m>u9m co musnooum no ax v.H H H.m ooom
. .Hm um
mm50©:¢ >2 coHuomm mmOHU coHumHHmmm mo >m>usm :0 musnooum : N.H H m.m 0mm
.Hm um
mmsoocm >n coHuomm mmOHU COHumHHmmm mo >m>usm :o oussooum : N.H H m mmH
.Hm um
musowc4 >Q COHuomm mmOHU :oHumHHmmm mo No>H5m co musnooum : m.H H n om
.Hm um
masoccd >2 :oHuomm mmOHU :oHumHHmmm mo >o>usm co musnooum mm mm N H HH vv UNH
"mmeEom .Howom HHA Ho H>mzvm Homuwe
... Hod Hmz. coHuoom mmouo :oHBBHHcam couonmun. m.>H mum<a

130

, 7
TABLE IV.2c.--Proton Spallation Cross Sections (MB) for Be.

 

 

 

Target E(MeV) 0(7Be) Refer. Remarks:
12C 35 10.4 i l AERS 67 *, from Br 62
40 15 i 1.5 " *, from Br 62
45 22 i 2 " *, from Br 62
50 25.5 i 2.6 Cu 63
60 24.3 i 2.4 AERS 67
80 20.5 i 2.1 "
100 17.5 i 1.8 "
150 12.1 i 1.2 "
200 10.2 i 1.0 "
300 10.0 t 1.0 "
400 10.5 t 1.1 "
600 11.0 i 1.1 "
1000 10.8 i 1.1 "
2000 10.5 t 1.1 "
3000 10.3 i 1.0 "
6000 10.0 i 1.0 "
10000 9.7 t 1.0 "
28000 9.2 i .9 "
3100 9.6 i .8 ST 68
4100 9.65 "
6700 9.35 "
8100 9.3 "
10300 9.3 "
11500 9.1 "
12500 9.2 "
126 4.0 i 1.7 JJBSB70
150 12.1 i 1.2 FPLYB7l
600 11.0 i 1.1 "
155.0 9.5 Wi 67
150.3 9.4 "
145.3 8.9 "
139.6 9.9 "
134.0 10.3 "
128.2 10.8 "
122.3 10.8 "
116.0 10.8 "
109.6 11.6 "
102.9 11.4 "

95.7 11.6 "

,- 7
~:—'-.—-~

131

TABLE IV.2c.--Cont.

 

 

Target E(MeV) 0(7Be) Refer. Remarks:
88.0 11.7 Wi 67
80.0 12.7 "
71.2 13.9 "
61.5 14.6 "
60.0 15.5 "
59.0 16.0 "
56.0 16.3 "
53.3 18.5 "
53.1 16.9 "
50.5 17.3 "
47.0 19.1 "
47.0 18.0 "
44.6 18.5 "
41.5 18.9 "
39.5 19.2 "
37.5 19.3 "
35.8 18.2 "
34.0 16.3 "
31.9 11.1 "
29.8 3.4 "

27 4 0.42 "
24.5 0.05 "
14N 21 50 BCJ 7O

50 12.4 Bi 67

100 6.4 Bi 67

2200 8.6 t .8 Re 65

126 1.6 i 1.6 JJBSB70
13 .32: .08 ES 71 Read from a graph
14 2.3 i .5 " ‘
15 6.6 i 1.4 "
16 15.0 i 3.0 "
17 23.5 i 5.5 "
18 33.0 i 6.5 "
19 41.5 ;I: 9.5 ' "
20 50.0 110.0 "
22 46.0 :10.0 "
24 41.0 1 9.0 "
26 32.0 i 6.0 "
28 27.0 i 5.0 "
30 20.0 i 4.0 "

132

TABLE IV.2c.--Cont.

' 7
Target E(MeV) 0( Be) Refer. Reparks:

 

32 16.0 ES 71
34 14.5
36 12.5
38 11.5

40 10.0

|+ I+ |+ |+ H-
M w 0.: La) b
0 U! U! U1 O

16O 55

63

70

85
110
120
130
130
140
150
155
155
208
297
396
600
5700
155
600
19000
30

45

60

70

85
2200
19000
135
600
19000

From AERS 67

O
n:
m a)
y
H
'<m
n:

 

(11wa

0100010)
U!
3’
...:
0"
N

O 0
U1

0
WWO‘N

" *, From AERS 67

U100

b»h‘id F'PJIH horava n>+a1~ P'PHO“

Be 60 *, From AERS 67

I 0....
mObooooouwxowsommc-m

H
o\Imommwwmwmmmmuqmbmbbbqwmmmhww

l+|+ H H-r+l+t+ H H-h+|+l+ H H-h+|+l+ H H-r+l+ H H-h+l+l+ H H-b+l+

...:

 

132

TABLE IV.2c.--Cont.

 

7
Target E(MeV) 0( Be) Refer. Remarks:

 

ES 71

32 16.0
34 14.5

36 12.5

38 11.5

40 10.0 " run
160 55 From AERS 67 ? ~~i
63 "

70

85
110
120
130
130
140
150
155
155
208
297
396
600
5700
155
600
19000
30

45

60

70

85
2200
19000
135
600
19000

H- |+ H- H- H-
M w w w b-
0 U1 UT U1 0

m a:
:u
...:

‘(h
N

o
N

. i
n u _ i
. .

U. rl
' K

0..
UlblUN

 

A1 62 "

Va 63 "

Be 65 "

Ra 64 "

" *, From ABRS 67
Be 65 " .
Be 60 *, From AERS 67

U1

0100mm

1+ H H-r+I+I+ H H-r+r+l+l+ H H-h+l+l+ H H-r+r+n+|+ H H H-P+I+I+ H

0
U1

0..
U‘kOO‘M

.b P‘rd P‘F‘lfl harata n>rala P'F4+4

 

O 0..
mOmeOOU'IQUSDUIU‘bU‘

mmmwmwmmmmqubmhanmmmmbuw
U|\D\O

[—1 H
O \1 U1 0
0 0 o o o

 

 

133

TABLE IV.2d.--Proton Spallation Cross Sections

9
(MB) for Be.

 

 

 

 

 

 

 

 

Target E(MeV) 0(9Be) Refer:
12
C 126 2.5 t 1.0 JJBSB 70
150 3.2 i 0.4 FPLYB 71
600 5.3 i 0.7 "
14 ‘
N 126 4.8 i 2.8 JJBSB 70
160 “155 1.7 i 0.5 Yi 68
600 2.4 i 1.2 "
19000 2.2 i 1.1 "
135 1.9 i 0.6 YBDFGB 68
135 1.7 i 0.5 "
600 2.4 i 1.2 "
19000 2.2 i 1.1 "
135 1.7 i 0.4 YSB 69
600 2.6 i 0.9 "
1000 3.6 t 1.0 "
1 . . 10
TABLE IV.2e.--Proton Spallation Cross Sections (BM) for Be.
10
Target E(MeV) 0( Be) Refer. Remarks
12
C 220 2.2 i 0.8 Ho 64 *, AERS 67
’ 126 <0.4 JJBSB 70
150 1.1 i 0.1 FPLYB 71
600 2.8 i 0.4 "
14
N 126 1.6 t 1.6 JJBSB 70
16 .
O 155 0.37 i 0.20 Y1 68
600 0.6 i 0.4 "
19000 0.64 i 0.50 "
135 0.35 t 0.20 YBDFGB 68
600 0.60 i 0.40 "
19000 0.64 t 0.50 "

 

133

9
TABLE IV.2d.--Proton Spallation Cross Sections (MB) for Be.

 

 

 

Target E(MeV) 0(9Be) Refer: Remarks
120 126 2.5 i 1.0 JJBSB 70
150 3.2 i 0.4 FPLYB 71
600 5.3 i 0.7 "
14 ‘
N 126 4.8 i 2 8 JJBSB 70 .1.
160 “155 1.7 t 0.5 Yi 68
600 2.4 i 1.2 "
19000 2.2 i 1.1 " 9
135 1.9 i 0.6 YBDFGB 68 Q
135 1.7 t 0.5 " y
600 2.4 i 1.2 "
19000 2.2 i 1.1 "
135 1.7 1 0.4 YSB 69
600 2.6 i 0.9 "
1000 3.6 t 1.0 "

 

. 10
TABLE IV.2e.--Proton Spallation Cross Sect1ons (BM) for Be.

 

 

 

Target E(MeV) 0(lOBe) Refer. Remarks
12
C 220 2.2 i 0.8 Ho 64 *, AERS 67
126 <0.4 JJBSB 70
150 1.1 t 0.1 FPLYB 71
600 2 8 i 0.4 "
14
N 126 1.6 i 1.6 JJBSB 70
16 .
O 155 0.37 i 0.20 Y1 68
600 0.6 i 0.4 "
19000 0.64 i 0.50 "
135 0.35 i 0.20 YBDFGB 68
600 0.60 i 0.40 "
19000 0.64 t 0.50 "

 

134

10
TABLE Iv.2f.--Proton Spallation Cross Sections (MB) for B.

 

 

 

0
Target E(MeV) o(1 B) Refer.. Remarks
12C 150 > 6 Cl 61
14M 150 > 3 C1 61
160 155 11 r 3 Yi 68
600 12 z 5 "
2.146 > 12 F0 62
135 11 r 3 YBDFGB 68
600 12 r 5 "

 

10
TABLE IV.2g.--Proton Spallation Cross Sections (MB) for C.

 

 

 

 

Target E(MeV) 0(10C) Refer. Remarks
12
C 143 2.8 t 1.3 C1 61 AERS 67,
156 2.6 r 0.3 Va 63 " ,
365 3.7 i 0.4 Sy S7 ” ,
420 3.5 r 0.3 " " ,
522 3.3 r 0.3 " " .
648 3.2 i 0.3 " " ,
832 2.9 t 0.2 " " .
980; 3.3 i 0.3 " " ,
14N 156 1.6 t 0.3 Va 63 "
16O 155 1 t 0.2 " "
420 6 r 2 Sy S7 " ,
980 4 i 0.2 " " ,

 

135

. 11
TABLE IV.2h.--Proton Spallation Cross Sections (MB) for B.

 

 

 

1
Target E(MeV) o( 1B) Refer. Remarks: ‘
12C 153 16 r 4 Go 60
120-150 2.8 t 1.1 Au 62
660 <28 r 2 Zh 60 From the Supplement of Survey
of C.S. by Audouze et al. I
160 155 25 r 8 Y1 68 e
.600 “ 25 t 12 " *
135 25 i 8 YBDFGB 68 3
600 25 t 8 " I
. F.

 

. . . 11
TABLE IV.21.-—Proton Spallation Cross Sections (MB) for C.

*-

 

—.

Remarks:

Refer.

0 (11¢)

E(MeV)

'Target

 

from Wh 58

Cu 63a

1.1
.3.0

32.9

21.1

12

89.1

30.1

3.1

92.5

33.3

3.0
4.3

89.4

42.0
50
60
80
100

Cu 63 from AERS 67

86.4

4.6

81.1

3.6
3.1

+5

70.5

61.3

2.3

45.0

150

136

2.0

39.0

200
300
400
600
1000
2000
3000
6000
10000

1.8

35.8

33.6 t 1.2

1.5

30.8

1.4

H

28.5

1.4

+|

27.2

1.4
1.4

27.1

27.0

1.4

26.8 t 1.3
85.2

44

26.9

28000

Me 66

3.0

50.7

2.8
2.4

80.3

59.5

H

80.6

64.7

2.3
72.6 i 2.2
68.2 i 2.0

75.6
67.2

69.7

79.2

82.7

2.0
1.9

88.2

4*!

62.7

98.5

137

 

= = cm 8 0mm 6
= = om u owe o
= = o.vH H 0.6m m
nmmum m Eoum pmcwmuno mosam> an mm mv.m H mo.oa v
= mm mm v a HH oonm
.1 s = : v.0 H m.mN 0mm
4 . = = «.6 A m.m~ mmm
. . z = 8.8 8 m.mH can
. . . = = m H on 886
. . = = m 8 ma mum
4 . = am am o.m H v.m~ cmv
= me 8> H 8 ma mma
. . = Ho Ho m.a H 6.6 mva
s s I
oaaaa me 28H . = mm 62 ma + mm .m3
= = = mm m m
= . = = 08 m
= h a. .. om mnm
nmmum m Eouu pmcflmuno mmsam> .Hm mmmd Hm Hm 0H m zv.H
= ¢.H H 8.68 m.mma
= m.H a 6.0m «.mva
= m.a H m.Hm «.mqa
= m.H a m.~m m.mm~
= o.H H m.vm h.m~H
= 6.H H m.mm m.v~H
= 6.~ A 8.6m «.maa
. = m.H A m.om m.mo~
66.02 8.3 H m.Ho m.moH
“mxumsmm .ummmm 10 so “>6zvm 068668

HA

 

.ucounl.flm.>H mqmmb

138

 

 

4 66 66 6 H OH 6666
4 . 4 4 6 H H.6H 666
4 . 4 4 H 6 H 6.6 666
4 . 4 4 6 m H 6H 666
4 . 4 66 66 H 6 H 6.6 666
4 66 6: 6 H H6 666
. 4 66 66 v H H 6.6H 666
4 66 6> H H HH 66H
4 66 66 6 H 6.6H 66H
4 . 4 4 H H 6H 66H
4 . 4 4 H H 6H 66
4 . 4 4 H H 6H 66
4 . 4 4 H H OH 66
4 . 4 4 H H 6.6 66
ammHm 6 EOHH 66¢HmHno 665H6> .66 6666 66 6> H H 6.6 mm 06H
4 4 6 H 66 66 .
4 4 6H H 66 66
4 .. 66 H 66 66
4 4 66 H 66H 6H
4 4 66 H 66H 6H
4 4 66 H 66H 6H
4 4 66 H 66H 6H
4 4 66 H 66H 6H
. 4 4 66 H 66H 6
nmmum 6 soHH 666Hmuno 666H6> H6 66 66 H 666 6
u mxumsmm ..Hmmmm Sat 6 :65 m ”6053.

 

. HCOUII . Hm .>H mqmgh

139

7 6
TABLE IV.3.--Production Rate Ratio of Li and Li (PR(7)/PR(6)) as a
Function of y.

 

 

 

 

PR(7)/PR(6)

Y Solar Abundance Data

Bertsch et a1. Mitler
1.5 1.62 1.60
2.0 9 1.73 1.72
2.5 1.95 1.78
3.0 2.27 2.21
3.5 2.68 2.58
4.0 3.23 3.07
4.5 3.95 3.72
5.0 4.90 4.59
5.5 6.12 5.62
6.0 7.68 7.18
6.5 9.67 . 9.04
7.0 12.15 11.41
7.1 12.72 11.95

7.2 14.17 12.52

 

Chapter V

SUMMARY AND CONCLUSIONS

Production cross sections of 20Ne for mass-6 and
mass-7 have been measured at 30, 35, 40, and 42 MeV proton
bombarding energies. At each energy the cross sections
for mass-6 and mass-7 are, within the experimental uncer-
tainties, equal, and rise from about 1.5 mb at 30 MeV
to 4 mb at 42 MeV (see Table III.6 and Figure III.6).

Together with.the cross sections of 12C, 14N,
and 160 measured in this laboratory and the cross sec-
tions compiled in Table IV.2, the ratios of the produc-
tion rate of 7Li and 6L1 by protons in the stellar cosmic
rays were calculated. The proton flux was assumed to be

Y and calculations were made for var-

prOportional to E-
ious values of y. The observed abundance ratio

n7/n6 = 12.5 can be achieved only for a y = 7.1, while
the steepest proton flux that so farghas been observed
for the sun is E-s°6 (Si 70). This means that for this

model to be correct there need to be other sources of

Li or selective depletion of 6L1.

140

141

Possible additional sources amenable to laboratory

4

study are the a + a reactions 4He(a,p)7Li and He(a,d)6Li

which favor the production of 7L1 over 6Li according to
Mitler's estimate (Mi 70) based on the inverse reactions
7 . 4 6 . 4 . . . .
Li(p,a) He and L1(d,a) He. Taking into conSideration
the abundance of 4He in the surface of the stars (for
the sun it is 21ordersof magnitude more abundant than

1 . . .
2C) the contribution from the a + a reactions.can be

significant.

APPENDICES

 

APPENDIX A

FORMULA TO ESTIMATE RANGE OF 6L1 IN Si

To estimate the range of 6Li ground state in Si,

the following formula was used:

-.

M
_ .21 .3L. 2
RLi(E)a- R (13.) ( ) ( )

0.
Ma zLi
Mm.
where E = Ea (E;—)

The energy E of 6L1 is known from the kinematics
of a twoFbody final state reaction and hence Ed can be
calculated and then Rd is read from the graph (see In-
struction Manual for Surface Barrier Detector, ORTEC).

The formula is based on the assumption that the
relative stopping of two materials is independent of
ion identity at a given velocity i.e. a given value of
E/M (No 70). Explicity, if A and B are two different
materials and p and q are two different ions, then at

the same velocity:

E E
J3. =- .51
M M
P g
or E = E E2-
P qM‘q

142'

 

143

(dE/dx)p,A _ (dE/dx)q!A

 

 

 

and (dE/dx)p,B " (dE/dx)q,B
Z 2
where (dE/dx)p,B m.fiE_ zB (Wi 66)’
P Z 2
(dE/dx)q,B m {494— zB
q
_ (dB/dX)p.B
z 2 M .
(dE/dx)p,A = (dE/dx)q,A.(§E) (i3)
. q p
z 2 M
R (E ) 4 R (E ) (—39 (—29
P P q q Z M
P g
M
where E = E —E
P q M
q
R.p = range of ion p with energy E?
Rq = range ion q with energy Eq

atomic number of the ion

N
II

mass of the ion

2
ll

 

APPENDIX B
SELECTION OF STOP PULSE AND

ITS CONSEQUENCES

Let at t = O a start pulse arrives at the FD.
Assume that the time needed to travel from FD to LRS to

DUCO is tl nsec. and from there to LRS and back to DUCO

and on to TAC is t2 nsec. (tl + t2 z 18 nsec.) (see

Figure II.5). Delay is then set to t1 + t2 hence at

t = t1 + t2 TAC will be started.

From t = t1 through t = (t1 + 25) nsec. DUCO will
be closed and no step pulse is accepted. The first stOp
pulse to be accepted is the one that arrives at DUCO
(coincidence mode) just after t = (t1 + 25) nsec. and it

will arrive at TAC at t = H: + 25 + t2) nsec. Hence the

1
length of the time signal by TAC is (tl + 25 + t2) nsec.
- (tl + t2) nsec. = 25 nsec.

A stop pulse that arrives just before t = (t1 + 25)
nsec. will be rejected and the succeeding st0p pulse will

be accepted. This corresponds to the maximum TAC signal,

equal to 25 nsec. plus TRF (see Figure 8.1).

144'

145

Since the TAC is started by the pulse from the
detector and stopped by the RF pulse its output is equal
to a TRF-related-constant minus time—of-flight (see
Figure 8.2). The time interval 011 is adjusted such that
the fastest particle corresponds to the maximum TAC out-
put signal as depicted by case I in Figure B.3. The time
signals corresponding to slow particles can be obtained
by moving the t = 0 position in the direction of increas-
ing time (case II and III) while keeping the positions of
the stop pulses the same. Case IV the minimum TAC signal
for the slowest of the four particles. The next slower
particle, that is with a time of flight difference just

greater than T from the fastest particle, will have a

RF
TAC signal equal to Tmax' This case will cause an error
since E(T - To)2 for this particle will be too small due
to a too-small value of (T—To)2. In general every two

particles whose time of flights differ by one period of

the RF have the same time signal T.

146

(ESTOP PULSES STOP PULSES ACCEPTEO____I_€”
1 REJECT60__4,I

' 'v..._._..(1)._._.._‘v

Le__25ns___,l l
VI ...... _ (11:).___v{

PULSE PULSE

1L 1 l A
U 11

STOP(I) ‘ STOP(H)

l
START ‘ START
1 i
f

0 TI ”1' :t 12 I T w i
“T FD AT TAC : I
:é——TI = 25ns_,| :

'6 T1: = 2505 + TR; _____;.

 

Fig. Bl.--Schematic Diagram showing the minimum
(TI) and the maximum (TII) time signals.

 

 

 

STOP PULSE STOP PULSE
(TAC) (TAC)
lk-AT|_i< TRF )|
I I I
BEAM. 1 DET BEAM I TIME A
T r T T . __,
0N TARGET I ON TARGET ' AXIS
I

¥--—”}nghc ““*913ré

k—TIME SIGNAL __,|

START PULSE
(TAC)

Fig. BZ.--T = T

8 RF ' Tflight + (ATi’AT2)‘

147
@ REJECTED ACCEPTED

 

 

 

 

 

 

 

 

 

STOP PULSE—9 VI IV
[(— 25m —9l I
I START I I STOP
r r r I ;
I==O for : I 1 : f
fastest particle
K I Tmax I >1
1 I
l
CID ' I
l l lR‘STeT ! L STOIP\
F [ fi l t y r
l= O for I I 1 : I
slow particlel !< T I )7;
I I
l I
' '
I I
K— 25ns ——)|
, I . I START I I STOLP‘
I I V r I I
II = O for I I I I
slower particle I I
I I<— T —I——->I
I I
I I
@ I I
K'— 2508
. I 1 WEST TI 379‘”-
I I l I T l I
l= O for I I I I

slowest particle I T , I
K— mm -->I

Fig. B3.--Schematic Diagram of the Choice of the
Stop Pulse and the Corresponding Time Signal (T).

148

 

 

 

APPENDIX C
Run E Charge Pressure , 1 Percent
No. Thata Proton (10**-6C) (MM 011) M°nlt°r C°n3ta“t Error
77.0 15.0 42.1 2092.60 28.80 28708 .476 3.7
78.0 30.0 42.1 1991.70 28.80 27289 .475 3.7
79.0 45.0 42.1 2663.60 28.80 36986 .482 3.7
80.0 65.0 42.1 3333.40 28.80 46365 .482 3.6
81.0 90.0 42.1 3304.80 28.80 46281 .486 3.7
92.0 17.0 40.1 4172.99 58.40 101568 .416 3.2
93.0 30.0 40.1 3969.30 58.10 95928 .415 3.2
94.0 45.0 40.1 3692.20 57.80 90423 .423 3.1
95.0 60.0 40.1 3558.60 57.50 86340 .421 3.1
96.0 80.0 40.1 5183.50 57.40 123170 .413 3.0
97.0 110.0 40.1 3802.80 57.00 48322 .2222 3.2
98.0 125.0 40.1 2568.50 56.90 14522 .0992 3.4
99.0 10.0 40.1 957.90 56.60 22014 .406 3.2
108.0 17.0 39.9 2000.10 55.11 42375 .384 3.4
109.0 30.0 39.9 2535.20 49.90 45816 .362 3.8
110.0 50.0 39.9 3104.40 51.10 61845 .389 3.4
111.0 70.0 39.9 3076.90 55.80 64877 .377 4.0
189.0 100.0 39.9 3725.60 33.55 51008 .408 3.6
123.0 15.0 29.6 1757.60 50.10 148234 1.683 3.3
124.0 25.0 29.6 2508.30 50.00 202688 1.616 3.8
125.0 55.0 29.6 2096.40 50.00 175851 13677 3.4
126.0 75.0 29.6 2085.30 49.70 174653 1€685 3.4
127.0 100.0 29.6 1674.80 49.80 137604 1.649 3.5
128.0 37.0 40.0 3216.30 60.00 83327 .431 3.9
129.0 90.0 40.0 2557.20 59.52 67548 .443 3.9
130.0 100.0 40.0 1861.30 59.00 48950 .445 4.0

1

Constant = Monitor/(Pressure x Charge).
Error assigned to Constant; it includes error in the
integrated charge (3%), fit error and statistical error to the fitted

Percent Error

peak returned by SAMPO which are added in quadratures.

2 , . .
Monitor counter was pos1tioned at 60° for the runs no. 92 through 99,

except for runs no. 96 and 97 where it was positioned at 50°.

 

149

Appendix C.--Cont.

 

Run E Charge Pressure _ , Percent
Theta , Monitor Constant
No. Proton (10**-6C) (MM 011) Error
134.0 15.0 35.7 2295.30 54.35 86640 .694 3.6
135.0 30.0 35.7 2457.10 54.00 94081 .709 3.9
136.0 60.0 35.7 3865.30 53.75 137160 .660 4.0
137.0 75.0 35.7 3375.40 53.35 129147 .717 3.8
144.0 20.0 “35.0 595.80 59.70 28302 .795 3.2
145.0 60.0 35.0 4135.60 59.70 199394 .807 3.1
146.0 45.0 35.0 3355.80 58.60 154933 .787 3.2
147.0 90.0 35.0 5000.40 58.40 246441 .843 3.1
152.0 55.0 30.0 3259.58 58.80 240563 1.255 3.3
153.0 45.0 30.0 3791.20 58.70 282206 1.268 3.2
154.0 75.0 30.0 5601.70 58.10 415454 1.276 3.4
155.0 25.0 30.1 3028.40 118.51 382353 1.065 3.2
156.0 35.0 30.1 3227.60 117.82 412493 1.084 3.1
157.0 65.0 30.1 3634.70 117.82 477620 1.115 3.1

 

APPENDIX D

DERIVATION OF MASS RESOLUTION FORMULA

The time-of-flight of a particle is the sum of the
time the particle needs to travel over the specified dis-
tance D plus the electronic delay and the finite time

width of the proton beam burst:

= + +
T TD TBEAM TTPU (1)

(see Section III.2).

2 2 2 ' 2 2
[A(ET2)] = (AE)2[§_('P£—)J + (ATDIZ 3.93.2.1. +

3E aTD
2' 2 2 2
2 3(ET ) 2 3(ET I
(AT ). (—-—- + (AT ) (—
BEAM aTBEAM TPU BTTPU
1/2
2 AT AT AT
A(ET ) _ Ag 2 D 2 BEAM 2 TPUZ] (2)
—-——-2 - (E) + 4 [(_T ) + (-——-—T ) + (——-T )

ET

150

 

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AERS 67

Al 62

Au 62

Ba 71

Ba 70

BBFH 57

BCJ 70

Be 72

Be 65

Be 60

Be 59

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IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

IIIIIIIIIIIIIIIIIIIIIIIIIIIIII

2