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THESIS

 

 

W 3//

ABSTRACT

ACTIVATION ANALYSIS OF THE 209131 (p,2n) REACTION

By

Erederick G. Krauss

The excitation function and absolute cross section of
the 209Bi’(p,2n) 208Po reaction has been measured from
threshold to 27 Mev in approximately 1 Mev intervals. The.
27 Mev proton beam from the Michigan State University
cyclotron was used to activate a set of bismuth targets
using the stacked foil technique. The a-particles from the
208Po reaction product were detected using a silicon surface
' barrier detector with an overall energy spread of 105 Kev and
were observed to have an energy of 5.08 i 0.053 Mev. Using‘
the data of Andre et al (Phys. Rev. 101, 6#5 (1956) ) an
extrapolation method was deve10ped to determine the energy

of the cyclotron beam. This resulted in a determination of
the beam energy to within * 500 Kev.

ACTIVATION ANALYSIS OF THE 209131 (b.2n) REACTION

By

Frederick G. Krauss

A THESIS

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

MASTER OF SCIENCE.

Department of Physics and Astronomy

1966

Approved by

ACKNOWLEDGEMENTS

Sincere appreciation for making it possible to do
this research and thesis must go to Dr. Charles R. Gruhn,
Dr. William H. Kelly, Dr. Morton M. Gordon and
Dr. Sherwood K. Haynes. The author would also like to
express appreciation for the help given by the staff of
the MSU Cyclotron Laboratory in fabricating parts for the
apparatus and keeping the electronics equipment in top
notch condition. Finally, thanks must go to the fellow
graduate students Dave Cluxton, Merrit Mallory and

Jim Kolata for the constant help and encouragement.

I.
II.

. III.

IV.

V.

TABLE OF CONTENTS

Introduction
Theory
A. Excitation function

B. Determination of cyclotron beam energy

.Experimental Apparatus

A. Targets

B. Degraders

C. Target mount

D. Cyclotron beam

E. Activity measuring apparatus

0

Experimental Results

'A. Excitation function and absolute

cross section

. . o
B. Discussion of error
Conclusion

Bibliography

.Page

«0 «a (m 0‘ 4r no ID er

MMHH
'0me

30
32
33

Table

GUI-FLOR)!“

LIST OF TABLES

Page

Mylar thickness uniformity check - 8
-Bismuth thickness uniformity Check

Aluminum foil uniformity check 10

Experimental results. ‘ . 26

Andre data 27

Experimental errors 31

Figure

LIST OF FIGURES

Schematic diagram of experimental set-up '
Surface barrier detector apparatus

aas flow-type proportional counting chamber
Typical proportional counter Spectrum
Typical surface barrier spectrum
Excitation function

Beam energy determination

Beam energy determination

Page

11}
16
2O
21
23
25
28

I. INTRODUCTION

This thesis represents the results of an experimental
Study at the Michigan State University Cyclotron Laboratory.
The purpose of this experiment was to obtain the excitation

208Po reaction. ‘Bismuth'

function of the 20931 (p,2n)
targets were prepared, bombarded in a proton beam from

the cyclotron, and the polonium reaction produCt measured
by its a-particle activity with a silicon surface barrier _
detector and a gas flow type proportional counter. Results
were in partial agreement with those of Kelly, done in 1950,
and published by Bell and Skarsgard in 1956.1'2 Using the ,

'data of Andre et a1, an extrapolation method was developed

to determine the energy of the cyclotron beam.3

II. THEORY

A. Excitation function. The excitation function is

 

defined as the functional dependence of the cross section.
of a particular reaction Oi on the energy of the incoming
particle. This function has several characteristics. It
is zero below a certain threshold energy, where it is.
energetically impossible for the reaction to occur. As

the energy of the incoming particle rises, the probability
for the reaction to occur increases, depending primarily on
two factors, namely the ratio of the coulomb barrier to the
energy of the incoming proton, and the competition from
those reactions having lower threshold energies. The first
'factor places an approximate limit on the total compound
nucleus cross section a and is computed as follows:

c om

acorn a file (1 .. 313.1),

E .

P

where R defines the interaction radius at a sharp nuclear
surface, V(R) is the coulomb potential at R, and ED is the
incident proton energy in the center of mass system. In a
semi-classical calculation Dostrovsky et a1 multiply V(R) by
.a constant smaller than one, effectively lowering the coulomb
barrier.” Competition from reactions having lower threshold

energies tends to lower the excitation function in a ratio

that keeps the sum Of the cross sections of the individual

\

~

reactionsc1 equal to the total compound nucleus cross

section, i.e.,

As the energy of the incoming particle rises further,
additional reactions become energetically possible. The
cross sections of these reactions increase, and since the
sum of the individual reaction cross sections must equal .
the total compound nucleus cross section, the cross section

of the individual reaction under consideration reaches a
maximum and then starts to drOp off. Competition at higher
energies is strong, and the excitation function for this
reaction becomes small, but never drops to'zero because this
,reaction is always energetically posSible.

In this experiment, the stacked foil technique was used .
to study the 20931 (p,2n) 208Po process. A number of bismuth
targets were bombarded with a proton beam so that each target _
,received protons of a different energy. A measurement of the
number of activated atoms on each target gave the excitation
function.

Since 208

Po decays by emission of 5.11 Mev a-particles,
a measurement of the decay rate on each foil determined the
number of activated atoms. Other reactions producing unstable
'polonium nuclei do not interfere with the a—activity
measurement for a number of reasons. The products of the
(p,3n) and higher processes decay mainly by electron capture

and are short-lived. The (p,n) process produces 209Po,

\

'3

‘\

,which deCays by a-particle emission, but this a has an energy
Of n.88 Mev, which is far enough'away from the 5.11 Mev a of
2OBPO to be differentiated with high-resolution detectors.
Furthermore, the reaction cross section Of the (p,n) process
is down byua factor of about 10, and, due to the difference
in half-lives (103 years versus 2.9 years), the maximum
activity of 209P0 from a bombardment is only about 2.8% of

the activity of 208Po. Thus the (p,2n) process is very

Clean on both sides of the excitation function.

The threshold energy for this reaction is calculated
to be 9.63 Mev and is measured to be 9.65 i 0.08 by C. 0. Andre
et al.5’3 The threshold energy for the 209Bi (p,3n) 207Po
reaction is 9.4 Mev higher than this; so that to study the

.complete (p,2n) excitation function: it is necessary to have
proton energies varying from.9 to well over 20 Mev.

B. Determination of Cyclotron Beam Energy. In order tO'
plot the excitation function, the energy at each of the bismuth
targets.had to be known. In the stacked foil technique, the
targets are arranged in a target pack with energy degraders
placed between them to reduce the proton beam energy in
approximate 1 Mev steps. The required thicknesses of the
degraders can be calculated according to formula for energy
loss per unit path length of heavy charged particles passing

through a homogeneous absorbing medium,

GE , Are 2 N2 in ° - in (1 ~ (g) ) ' (g) !

I
m'o

 

O

where me is the charge of the heavy incident particle, m0
.is the rest mass of the electron, V'is the velocity of the
incident particle, I is an empirical constant dependent on
the atomic number 2 of the absorber, and N is the number in
atoms/cm3 of the absorber.7 A computer program called "Foil",
available in the laboratory, takes a bombarding particle of
a given energy through a set of targets and degraders, and
calculates the energy of the particle at each of the targets
using the above formula. ‘
Thecbeam energy of the cyclotron, however, was known
only to within 1 or:2 Mev. In order to plot the excitation
function, a method of successive approximation was used to
find the beam energy knowing the threshold energy of the
_reaction. This method proved to be very sensitive with the
main limitation being the energy straggling, which amounted
to about 500 Kev at 10 Mev with a 27 Mev incident beam.

III. EXPERIMENTAL APPARATUS

A. Target. The bismuth foils used in this experiment
were made by evaporating bismuth, under vacuum, onto l/W mil
mylar film.. This was accomplished by taping a sheet of mylar
film of sufficient size to produce all the necessary targets
for a run to the top of a large bell Jar. Care was taken
so as to keep the mylar clean and free of hand oils. A .
tantalum boat filled with metallic bismuth was placed between'
the current terminals near the bottom of the evaporator, about
50 cm away from the mylar. After a vacuum on the order of

6 microns had been achieved, the boat was heated up to

10'
. evaporate the bismuth onto the mylar. Evaporation times of
‘15 and 30 minutes produced foils averaging 0.3 and 0.7 mg/bm2--
of bismuth, respectively. '

The foils were cut and weighed after evaporation. At
first it was attempted to cut the foils by using an x-acto
knife and a straight edge, cutting along the lines on
millhmeter graph paper placed on top of the foils. Because
of slippage and the thickness of the lines on the graph paper,
this resulted in errors on the order of one or two percent.
Foils used in the second run were cut by clamping the sheet
of bismuth-plated mylar between a very accurately machined
aluminum block and a cutting block with a small cam operated
clamp. Cutting around the aluminum block with the X-acto

knife resulted in very uniform cutting from foil to foil.

6

A size of 3 cm by 6 cm was chosen for the foils So that
they would be large enough to handle and yet small enough to
fit in a mount which would fit inside the Faraday cup.

‘ weighing was done on a Mettler type H16 balance. Two sources
of error appeared in the determination of the areal density

of the bismuth. One source came from the assumption that the
mylar foils were cut from the mylar sheet adjacent to the
mylar used in the plating process. When weighed, they agreed
to within 0.5% of their average weight, namely 0.92 mg/Cma.

. See Table 1. The other source of error came from the assumption
that the evaporation process yielded a uniform bismuth coating
on the mylar. Because there was about a 0.1 mg/Cm? deviation.
from the average weight, this could have resulted in up to a
"30% error in foil uniformity.‘ HOwever, a number of foils'
were cut into 0.9 cm dia. pieces which were then weighed._.
The result of this indicated that the error in bismuth.
non-uniformity on any one foil was less than 3%. See Table 2.
The fOils were conveniently stored in books made up Of file
cards both before and after the bombardment.

B. Degraders. The most convenient material to use

 

between the bismuth foils as preton beam energy degraders

was aluminum foil.' Being available only in 1 mil thicknesses
meant that many layers had to be used between the bismuth
targets. 0n the first run, strips of aluminum foil were
folded accordion-style to make degraders of the required

thicknesses.. This method did not allow the precise

Table 1. Mylar thickness uniformity check.
Weights of 3 cm by 6 cm foils.

"Table 2.

F011 weight (mg)

16.6u
16.26
16.49
15.70
16.57
15.86
17.08
17.35

Average weight
16.49

Greatest % variation

0.5 %

Bismuth thickness uniformity check.
Weights of 0.9 cm diameter pieces
of Bismuth plated mylar foil.

Foil weight (mg)

oooooooo
NNNNQNN

.4
-=~aowqo»=¢flm

Average weight
0.756

Greatest % variation_

3%

positioning of the bismuth foils and led to difficulties
explained below. In the second run; the aluminum foil was
cut in the same manner as the bismuth foils, except that
greater care had to be taken to assure a smooth cut. Even
when clamped.very tightly between the aluminum block and the
Cutting block, the aluminum foil had a tendency to tear.
These foils, together with the bismuth foils Could be
precisely positioned in the target mount. I

Some of the aluminum foils were weighed to determine
their uniformity, and the agreement was within 1%. See
Table 3. The stopping power calculations gave the number.
of aluminum foils necessary to degrade the beam in approximate
1 Mev steps between the successive bismuth foils. At 35 Mev
(bombarding energy, 10 one mil thicknesses were necessary .
behind the first few bismuth foils, and at 27 Mev, 9 one mil
’ thicknesses were needed. Target stacks were made up with
succeséively fewer aluminum foils between bismuth foils._

C. Target mount. The target mount for the first run '

 

consisted of two copper plates, slightly larger than the
. foils, one side having capper cooling tubing soldered to
it, and the otherside having a window machined into it to
allow the beam to pass through to the foils. The bismuth
foils, together with the aluminum energy degraders, were
inserted between the plates, and the entire sandwich was
clamped together. This mount worked quite well as far as

the bOmbardment was concerned, but led to difficulties when

Table 3. fAluminum foil uniformity check.
'Weights of 3 cm by 6 cm foils.

Foil weight (mg)

119.75
118.16
117.65
117.81
118.g0
117. 3
118.49
117.68

‘Average weight

118.21

Greatest % variation

1%

10

“it came to determining the source position on the foils.
Since the foils were not positioned accurately one behind
the other, a technique had to be develOped for locating
the activity.‘ The technique will be explained below.

The second target mount was machined out of a 1/2 inch
block of capper. A 3/8 inch deep, rectangular hole Just
large enough for the foils was milled into one side of the
block, and a loOp of copper cooling tubing was soldered to)
the other side. To hold the foils in place, a 1/1 inch
aluminum plate was milled to fit into the rectangular hole'
in the copper block so as to clamp the set of target foils
in firmly. A window was also milled into the aluminum plate.
The entire assembly was fastened together with four small.
-bolts. See Fig. l. . 0
Target cooling was necessary to prevent the bismuth
- from being evaporated and the mylar melted or weakened by
the heat created by dissipating the entire energy of the
beam in.the target. With ten nanoampere beam, about 0.3
watts must be dissipated at 30 Mev. Radiation to the walls
of the scattering chamber could not be relied upon to
dissipate this heat, since the beam dimensiOns were very
small and local heating intense. Hence the entire target
assembly was cooled. The existing dry ice-alcohol heat
exchanger usually used to cool detector mounts within the
scattering chamber was a very convenient means of roviding
the coolant. Connecting tubing was also available within
the scattering chamber.

11

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D. Cyclotron beam. The Michigan State University

 

Cyclotron was used in making the bombardment. This
isochronous cyclotron is a 6# inch, sector focused,‘
variable energy and multiple.particle machine, capable
of producing up to 55.3 Mev protons. (In this experiment,
H- ions were accelerated, and an aluminum stripper foil
was used to achieve single turn extraction ofOH‘+ ions. The
beam was passed thrOugh two quadrupole focusing magnets and
a bending magnet before reaching the collimator and target
in the scattering chamber. This is shown in Fig. 2. A
35 Mev beam was used for the first run, and a 27 Mev beam
was used for the second run.

Preparation for the run was facilitated by the large
'36 inch diameter scattering chamber. The target assembly,
mounted inside a short piece of beam pipe which acted as a
Faraday cup, was taped to the detector arm within the
scattering chamber. A lucite block was placed between the
.beam pipe and the detector arm so that the pipe was
electrically isolated from the arm. Thus the pipe was able
to collect the charge incident on the target.

The open end of the beam pipe was placed adjacent to
the incoming beam port of the scattering chamber, with a
collimator in the port. A pair of large horseshoe magnets
was placed straddling the beam pipe near the target assembly
to assure that no charge escaped from the Open end.

.Electrical connections from the Elcor model A3103 current

13

Stripping foil

Cyclotron

Beam pipe

 

- Quadrupole magnets

. Bending magnet

 

 

Collimator

 

 

Scattering chamber

 

Faraday cup and target

 

Fig. 2. Experimental set up
(Not to scale)

1h

‘\

integrater to the pipe inside the scattering chamber and
cooling lines from the heat exchanger to the target mount
completed preparations for the activation, ‘

E. Activity measuring apparatus. The a-particle
activity of the bismuth foils was measured with a Nuclear
Diode model SL 2-20-5 surface barrier detector placed 2.93 cm
away from the foil. The counting was done in'a small vacuum
chamber using a standard rotary pump capable of a'25 micron
vacuum. The foils were inserted, one at a time, into the
proper position with reSpect to the detector, and counted
until four or five hundred events were recorded. This
usually took two to three hours for the more active foils,
and overnight for the weaker ones. CThe apparatus is
-'diagrammed in Fig. 3.

The output pulse from the detector was preamplified
with a Tennelec model lOO-A preeamp, amplified with an
0rtec model #10 amplifier, and analyzed by a Nuclear Data
' series 120 five hundred twelve channel analyzer. An Amzul
a test source was used to calibrate the analyzer. 'The
Spectra were read out of the analyzer via typewriter readout.
The resolution of the apparatus was #0 Kev.

As mentioned before, the activity on the first set of
foils had to be located very precisely. A photographic’
technique was develOped for this. It was at first thought
that some kind of scintillator was necessary. Zinc sulphide

powder was mixed with styrene and benzine, and then painted

15

1/8" Lucite plate with graph paper
glued to top surface

Foil

 

 

PC/7CKZZ/ZSZ/C/72/)6/WCVJC/' xfl/AC//WC//U/VZ£/)’/7C//C/7q

 

Lucite cylinder,
machined as shown "—‘-—*'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4¥___Collimator
2::e2:::w for Kw - Surface barrier
\\\\\\\\ detector
I \\\\\\\ c Connector
U \\ '

 

 

 

Fig. 3. Surface barrier detector apparatus.
When used, this apparstus is placed in a
small vacuum chamber. (Scale - full size).

16

very evenly on glass slide plates. Standard Poloroid ASA

3000 film was exposed to an Ameul

test source with the zinc
. sulphide layer inbetween. The same process tried without
the zinc sulphide worked even better. Experiments with a
few of the foils showed that a white spot could be seen on
-the developed print after a few hours exposure.

Next, a technique had to be develOped to’very accurately
position the foils on the print, so that after processing;‘the
exact location of the foil on the print would be known. Once°
the outline of the foil was transferred to the print, the
location of the activity on the foil was known. In order to
accomplish this, a block of lucite was machined to hold the
film over three depressions, each of which held a foil. The
.metal tab on the end of the film was used to position it at
one end of the block, and the film was creased_over the edge
at the other end of the block. 'In this manner, the film was
exposed to three of the foils at a time. After processing
the film, both the film and the print were saved. Holes
drilled through the corners of the foil depression in the
lucite block allowed transferring the corners of the foil
(to the film by use of a pointed tool, and these were transferred
.to the.print with the same tool. A vernier caliper was then
(used to measure the position of the activity with respeCt
to the sides or the foil.

The surface barrier detector was mounted upside down with

'a collimator over it. A piece of graph paper was glued to

17

an eighth inch sheet of plastic with a hole centered 2.93 cm
above the detector. The entire assembly is shown in Fig. 2.
The foil was positioned on the graph paper, activity side down,
to within 1 mm. The apparatus was placed in the vacuum chamber
which was allowed to pump down for several minutes before
the count was started.

Another type of counter was built in order to count all
of the particles coming off the foil. This was a gas flow”
type proportional counter. For ease of construction cylindrical
geometry was chosen. The gas flow type of counter was chosen
because of the availability of the standard P-2 counting gas
(90% argon, 10% methane), and because of the necessity of
placing the foils inside the chamber. A five inch long, two
'inch diameter piece of copper tubing with a 1/16 inch wall
was used for the outside part of the chamber. The criterion
for the chamber length was that it be more than twice the
length of the foil so that the end effects could be ignored.
To create the neCessary field of 20 v/Cm at the outside and.

2 x 10“ v/Cm at.the center wire, the diameter of the center

wire needed to be about 1 mil.8 Some 1 mil tungsten was -
obtained as a gift from General Electric Company. Putting
the above dimensions into the formula,

. V's E1 r1 1n (b/a),
where a and b are the radii of the wire and the chamber,
reSpectively, and E1 is the field at radius r1, the voltage V

to be impressed on the chamber was calculated to be between

18

716 and 906 volts. Teflon ends for the chamber, a BNC connector

for the center wire at one end, a wire support at the other

end, gas inlet and outlet provisions and a bubbler type gas

flow measuring device completed the chamber. Foils were '

placed'on the inside wall of the chamber as shown in Fig. A.
The chamber worked very welf even at lower voltages

than those calculated. Counts were taken with 500 volts

on the center wire. The difficulty with the chamber was

the continuum of energies seen below the energy peak. A

typical spectrum is shown in Fig. 5. An explanation of

this was found in the calculation of the sensitive solid

angle of the chamber. The range of 5.11 Mev a—particles

in argon at atmospheric pressure was found to be #.3 cm,

(which gave the chamber approximately a 0.5m solid angle.

There were some a-particles, therefore, that left the foil,

lost only part Of their energy in the gas and then collided

with the wall of the chamber. These particles accounted

for the Continuum. Because of theSe problems, the proportional

counter was used only to provide a qualitative check on the'

data taken with the surface barrier detector.

19

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IV. EXPERIMENTAL RESULTS

A. Excitation function and absolute cross sectiOn.
The foils were analyzed using the two types of apparatus
already described. An energy spectrum of each foil was
printed out of the Nuclear Data analyzer in tabular form.
‘ Typical spectra from the surface barrier and proportional
chamber counters are shown in Figs. 5 and 6, reSpectively.
The counts in the channels corresponding to the 5.11 Mev
a-particle peaks were summed, divided by the counting time
and normalized to foil thickness. These numbers gave the
value of the excitation function on an arbitrary scale for
that particular foil. 8

The absolute cross section calculations gave the above
lthe excitation function the proper scale factor. The absolute

cross section is defined as,

N00

o e 'N_I ,
where “no is the original number of a-active nuclei formed

‘in the bombardment, N is the total number of bismuth atoms
per cm2 available for activation, and I is the number of
incident protons.9 The number "no is obtained from the

activity on the foils by differentiation of the decay formula,

N a N e'0’693t/T

a do
where N is the number of a—particles at any time, t and T >
is the halfflife. The activity in counts per minute is,

I dNa ‘ 0'6?3 N00 . 6—0.693t/T.
at‘“T(min) '

 

Counts

—I1

20_

 

AE=105 Kev ”-E

 

 

 

 

 

- A

 

T

I
325 350 535
Channel number

Fig. 6. Typical surface barrier Spectrum.
The tat—particle energy is 5.11 Mev.
Each channel represents 15 Kev. (Foil No. 6).

23

‘\

If the time between bombardment and measurement of activity'.
is short compared to the half-life, as was the case in this
experiment, "no is simply,

dNao

HE-

T

N » '3 m 0

GO

 

 

The number I is determined by dividing the total measured
Charge incident on the target by the charge per incident

particle. The areal density in grams per cm2

of the target,
when multiplied by Avagadro's number and divided by the atomic
weight in grams of the target material yields N, the number of
available target centers per cme. Results, together with error
bars are shown in Fig. 7 and are tabulated in Table 4. The
data of Andre et a1 is also included_in the figure and
'tabulated in Table 5. The difference between the beam energy
at the targets and the threshold energy, e, is plotted against
the cross section in Figs. 8 and 9. This data was used to find
the appropriate machine energy to insert in the computer
' program "Foil" which would give the proper threshold in Fig..6.
As can be seen from the graph, this method of determining the
machine energy was very sensitive. Slight deviations in
incident proton energy gave rise to large errors in the
threshold energy. Andre's data was of considerable help in
pinning down the proper machine energy. '

The fact that other activities were not present was borne

out in the observation that the centroid of the energy peak
shifted less than one channel (about 14 Kev) from foil to foil.

24

 

 

 

10 ,‘1
-1
10 ,
T .
.lo'?_
' ‘23 9"
b I
10 ‘2 l
I
O Present data.
I . Data of C.G. Andre et al.3.
1075
l
l
l
10'5 '
' F I r i T r I
0 5 . ' 10 15 20 25 5O

Ep (Mev)Lab

209

Fig. 7. -Excitation function of the B1 (13,31) process.

25

Table A. Experimental data from the 27 Mev run.

 

 

26

EpLab a “Statistical- e
(Mev) - (barns ) errors (Mev)
. (barns )
27.10 .135 ..010 _17.u5
‘ 26.15 .229 _.011 16.50
(3 24.16 . .342 .03 14.51
; ' 23.23 ‘ .395 .020 13.58
I 22.27 .811 .03 12.52
22.27 .73 .05 ' 12.52
20.38 .937 .06 10.73
20.38 .91 .06 10.73
19.44 .903 .06 9.79
19.44 .92 .05 9.79
18.61 1.07 .06 8.96
18.61 1.02 .03 8.96
17.75 .937 .05 8.10
16.85 .845 .05 7.20
16.06_ .750 .04. 6.41
16.06 .739 .05 6.41
_. 15.25 , .850 :05 5.60'
14.40 .462 .03 4.75
14.40 ' .499 .03 n.75 '
13.68 .3454 .03 1.03
12.9u .246 .01 3.29
12.16 .087 .006 2.51 '
11.53 .0367 .005 1.88)
10.89 .0107 .0022 1.21
9.72 5 x 10‘” .0005 .07
9.21 3.9 x 10‘“ .00108 .05

Table 5. 20931 (p,2n) data of c. 0. Andre et 31.3

'Ethreehold cm a 9.65 t 0.08

o(p,2n) Epcm - ' 6

(mb) (Mev) (Mev)

6.98 i .24 10.60 .95
4.75 f .16 10.48 .83
3.38- i .12 10.36 .71
2.12 i .08 10.23 .58
1.17' f .05 10.11 ~ .46
.62 t .03 ‘ , .9.99 .3A
.25 i .01 9.87 .22
.065 i .005 9.7u .09

100

10

61am)

.1

 

 

 

/'
A v
/
_7
t/ _
/
/
i
/
X E0 a 26.7 Mev
0 Ed I- 27.2 Mev
D Bo I 28.0 Mev
0 Data of 6.0. Andre et 9.13
6 s Ep - 9.70 Mev
I 8 I f I I
0.5 1.00 1.50 2.0 2.5 5.0

E (Meir)

Fig. 8. Bombarding energy determination
28

1000

  
     
   

 

 

1
x no - 26.7 Mev .
0 E0 :- 27.2 Mev
D 30 I- 28.0 Mev
0 Data of 0.0. Andre at 2.13
€-Ep - 9.70 Mev
100 _
13;
b
10 __
1!
1 I
i 10
0.1

6 (Mev)

' Fig. 9. Bombarding energy determination

v-o; -.. 4"“

29

Possible evidence of the 209Po a-activity was seen on several .
of the Spectra by a small number of counts in the channels
corresponding to its 4.88 Mev a—particle signature.

The flat-topped shape of the surface barrier detector
energy peak was attributed to the thickness of the foils.
The a~particles that originated within the foil traveled a
certain distance through the foil and hence lost some of their
energy before being counted. This energy loss per unit path
length was calculated for the foil in Fig. 4, and was found

to be in the neighborhood of 65 Kev.11

This compares with the
peak width of the spectrum, which is about 105 Kev.

B. Discussion of error. In the computation of the

 

absolute cross section errors appeared in each of the numbers
-N§o, N and I. These errors are tabulated in Table 6, and the
total error in each of the numbers was found by taking the .
square root of the sum of the squares of the individual errors.
The total error in the absolute cross section was similarly
.-calculated and found to be 8.7%. I

In the threshold method of detemmining the incident proton
beam energy, error was due mainly to energy straggling. This
placed a limit of about 500 Kev on the beam energy determination,
OOr a 1.9% error. Errors in the beam energy at each foil were
due mainly to the density determination of the degraders. This

amounted to 1.3% which raised the error in the incident beam

energy to 2.2%.

30

H

Table 6. Tabulation of errors contributing to the
total error in the absolute cross section

calculation.
. I
Error in Source of error Percent
N00 Statistical 6
Half-life12 1
Geometry 4
Analyzer dead time 0 .
Total 7.3
N. - Mass determination 1.5
Areal density 2
Uniformity 3
Total 3.9
.". I. ' Charge Collection I 2
(guess)
I
Integrator 1
Total 2.2

31

V. CONCLUSION.

The excitation function of the 209Bi (p,2n) process
.found in this experiment was in partial agreement with

that found by Kelly.1

The absolute cross section at the
peak of the excitation function checked to within 10 percent
of Kelly's. However, Kelly's threshold was down approximately
4 Mev from that given by Andre.3 The function exhibited all
the characteristics it should have according to theory.
An improvement on the experiment would be to include
more bismuth foils in the target pack with smaller beam
energy increments between them. This would give more data
points, and reduce the chance of losing important data points
due to bismuth coming off the foils.
The sensitivity of the threshold method of determining
the cyclotron beam energy suggeSts that this method be used
to calibrate the beam energy of the machine, eSpecially when~
-.the beam energy is near the threshold energy. The restriction
here is due to energy straggling in the degraders which becomes
significant as the beam energy gets much larger than the
threshold energy. However, at higher beam energies, the _
209Bi (p,3n) and (p,4n) processes might be used more accurately.-
In addition, the threshold method of beam energy determination

would be a very good method of checking relative beam energies.

: :32

10.

VI. BIBLIOGRAPHY

Kelly, B. L., UCRL - 1044 (unpublished), 1950.

Bell, R. E. and Skarsgard, H. M., Canadian Journal
of Physigs, Volume 34, 1956.

 

 

Andre, C. G., Huizenga, J. R., Mech, J. F.,
Ramler, w. J., Rauh, E. G. and Rocklin, S. R.,
Physical Review, 101, 645, 1956..

 

Dostrovsky, L., Fraenkel, Z. and Friedlander, G., °
Physical Review, 116, 683, 1959.

 

Ashby, V. J. and Catron, H. C., Tables of Nuclear
Reaction Q values, UCRL - 5419, 1959.

 

 

Evans, R. D., The Atomic Nucleus, 1955, Page 441.

 

Watt, D. E. and Ramsden, D., High Sensitivity Counting
Techniques, 1964, Pages 81-94.

 

 

Semat, H., Introduction to Atomic and Nuclear Physics,
1962, Page 109.

 

R102, M. and Muday, R., Range Energy Tables, UCRL - 2301,
195 . _ I

Templeton, D. H., Physical Review, 78, 312, 1950.

 

33