• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Theory
 Design and calibration of...
 Experiments and results
 Discussion of results, recommendations...
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: Neutron decay spectrometer.
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00091576/00001
 Material Information
Title: Neutron decay spectrometer.
Series Title: Neutron decay spectrometer.
Physical Description: Book
Creator: Karam, Ratib Abraham,
 Record Information
Bibliographic ID: UF00091576
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000558938
oclc - 13428162

Downloads

This item has the following downloads:

Binder1 ( PDF )


Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    List of Tables
        Page v
    List of Figures
        Page vi
        Page vii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Theory
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
    Design and calibration of apparatus
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
    Experiments and results
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
    Discussion of results, recommendations and conclusions
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
    Appendix
        Page 77
        Page 78
        Page 79
        Page 80
    Reference
        Page 81
        Page 82
        Page 83
    Biographical sketch
        Page 84
        Page 85
    Copyright
        Copyright
Full Text













NEUTRON DECAY SPECTROMETER













By

RATIB A. KARAM












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA
April, 1963














ACKNOWLEDGMENTS


The author wishes to acknowledge his gratitude

to his supervising committee. Special gratitude is

due Dr. T. F. Parkinson, chairman of the advisory com-

mittee, for his invaluable encouragement. It was a

pleasure to work with Dr. Parkinson.

Dr. G. R. Dalton, a member of the supervisory

committee, participated in many helpful discussions.

Dr. F. E. Dunnam, another member of the

supervisory committee, cheerfully loaned some of the

auxiliary equipment used in this work. Dr. Dunnam

also assisted generously in the preliminary calibration

problems.

Mr. D. F. Mooney of the Department of Nuclear

Engineering participated in many helpful discussions

associated with the electronic equipment. Mr. Mooney

also designed the power supply of the containment

magnet.

Mr. Robert Hartley assisted generously with the

low energy proton calibration of the detection system.

Mr. Henry Moos built the housing unit for the detection

system. Mr. L. D. Butterfield patiently operated the

University of Florida Training Reactor during the

experiments.















TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . ii


LIST OF TABLES . . . . . . . . v


LIST OF FIGURES . . . . . . . . vi


Chapter

I. INTRODUCTION . . . . . . 1

Slow Neutron Spectrometers . . 1
Intermediate Neutron Spectrometers 3
Fast Neutron Spectrometers . . 4
New Approach . . . . . . 7
Feasibility . . . . . . 9


II. THEORY .. . . . . . . . 12

xy- Plane . . . . . . 18
yz- Plane . . . . . . . 20
Transformation from CM to Lab
Coordinates . . . . . . 25
Resolution . . . . . . 30
Proton and Electron in Coincidence. 32


III. DESIGN AND CALIBRATION OF APPARATUS . 37

Apparatus .. . . . . . 37
Calibration . . . . . . 45


IV. EXPERIMENTS AND RESULTS . . . . 53

Experiments . . . . . . 53
Treatment of Data . . . . . 64


iii












TABLE OF CONTENTS (Cont'd)


Chapter

V. DISCUSSION OF RESULTS, RECOMMENDATIONS
AND CONCLUSIONS . . . . . .

Discussion . . . . . . .
Recommendations . ... . . . .
Conclusions . . . . . . .


APPENDIX

Comparison of Measured and Calculated
Proton Counting Rates . . . .


REFERENCES . . . . . . . . .


BIOGRAPHICAL SKETCH . . . . . . . .


Page











LIST OF TABLES


Table page

I. Summary of Neutron Spectrometry Methods . 8


II. Values of fp, ,/, and p)p for Given
Values of p in the xz plane, Given
S= 4.029797xl0-17, = 90 . . . 18


III. Values of /op, [ and Op for Given
Values of &y in the xy- plane, Given
P = 4.029727xl0-17, 6p = 0 . . . 19


IV. Values of qpp and 6 p as a Function of T
at e6 = 900 ( p = 4.475x10-17; P/
= 2.0287x10-17; EP = 400 Mev). . . 24


V. Velocity of Neutron as a Function of Energy 28


VI. Values of the Maximum and the Minimum
Velocity of the Proton as a Function of
the Neutron Energy in the Lab System . 29


VII. The Resolution, R, Based on the Maximum
Velocity in the CM System, as a Function
of Neutron Energy . . . . . . 31


VIII. Proton Counting Rate as a Function of
Magnetic Analyzer Current* [Beam of
Neutrons Not Collimated; Graphite Plug In]. 59


IX. Proton Counting Rate as a Function of
Magnetic Analyzer Current* [Beam of Neu-
trons Collimated and Graphite Plug Removed]. 61











LIST OF FIGURES


Figure Page

1. Number of Protons Emitted per Minute Along
a Path Length of 1 Meter versus Energy,
Based on a Neutron Beam of 1010 Neutrons
per cm2 per second . . . . . . . 11

2. Coordinate System for Decay of Neutrons . 14

3. Possible Orientation of /f/ with Respect
to 7 (E = 400 Kev) . . . . . . 21

4. Transformation of Velocity of Proton from
CM to Lab Coordinates . . . . . . 26

5. Angle of Proton in Lab System, versus
Angle in CM System, V for Constant
Neutron Energies . . . . . . . 34

6. Angle of Proton in Lab System, '^ versus
Angle in CM System, V/ for Higher
Constant Neutron Energies . . . . . 35

7. Frame for Containment Magnet . . . . 40

8. Schematic Diagram of Power Supply for
Containment Magnet . . . . . . . 41

9. Shape of Pole Piece . . . . . . 43

10. Assembly of Detection System . . . . 44

11. Calibration of Analyzing Magnet, Magnetic
Flux Density versus Current . . . . 46

12. Effect of Magnetic Field on Photomultiplier.. 48

13. Beta Spectrum of Cs137 as Measured by
Analyzing Magnet . . . . . . . 49

14. Spectrum of Monoenergetic Protons Produced
by the Texas Nuclear Accelerator and
Analyzed by the Analyzing Magnet . . . 51











LIST OF FIGURES (Cont'd)


Figure Page

15. Magnetic Field Required to Bend Protons
through a Radius of 3 Inches . . . 52

16. Sketch of Apparatus in Use . . . . 54

17. Radiation Detection versus Analyzing
Magnet Current in a Neutron-free Field . 56

18. Proton Counting Rate versus Analyzing
Magnet Current (No Collimation, Graphite
Plug In) . . . . . . . . 58

19. Proton Counting Rate versus Analyzing
Magnet Current (Collimated Beam, Graphite
Plug Removed, RUN A) . . . . . 62

20. Proton Counting Rate versus Analyzing
Magnet Current (Collimated Beam,
Graphite Plug Removed, RUN B) . . . 63

21. Arbitrary Proton Flux versus Energy
(Uncollimated Beam, Graphite Plug In) . 66

22. Arbitrary Proton Flux versus Energy
(Collimated Beam, Graphite Plug Removed) 67

23. Illustration for Coincidence Measurements. 72


vii














CHAPTER I


INTRODUCTION


Neutron spectrometry is usually classified into

three categories: slow, intermediate and fast neutron

spectrometry. The range of energy that each category

covers is arbitrary and not well defined. Generally,

however, slow neutron spectrometry indicates the energy

of the neutron to be less than 10 Kev. The range of

intermediate neutron spectrometry may arbitrarily be

specified to be from 10 Kev to 1 Mev. Fast neutrons may

be specified as those neutrons with energies above 1 Mev.


Slow Neutron Spectrometers

The instruments that are generally used for slow

neutron spectrometry are the crystal spectrometer and the

time-of-flight spectrometer. The range of energy over

which the crystal spectrometer is useful is from 0.02 ev

to 10 ev. In some cases (1, 2)* the upper limit of 10

ev was extended to 50 ev. The resolution of this spec-

trometer is good in the thermal range of energy; however,

it has a very low efficiency (see Table I).

*
Underlined numbers in parentheses refer to the
list of references.









2

The most widely used time-of-flight spectrometer

is the "chopper." The neutron burst for the time-of-

flight method is produced by a rotating mechanical

shutter. The choppers which can be used for thermal

neutrons only are called slow choppers and those which

can be used for neutrons of energies up to about 20 Kev

are called fast choppers. There is no difference in

the basic design of either chopper. The mechanical

shutter in the fast chopper can acquire greater speed

than that in the slow chopper.

From the relationship, E = mv2, and that between
2
time and velocity, the energy resolution of a chopper is


E = 0.028E 3/2 R (1)


where AE is the spread in electron volts of the neutron

energy and R is the resolution in microseconds per

meter. If R is taken as 0.01 microseconds per meter, it

is seen that the resolution at 100 ev is 0.28 percent,

at 10 Kev is 2.8 percent, and at 1 Mev is 28 percent.

This deterioration in resolution as a function of the

neutron energy limits the usefulness of the chopper as

a spectrometer for measuring cross sections to energies of

less than 20 Kev. In measuring resonance structure of

nuclei whose widths of resonances are approximately 0.1 ev,

the chopper usefulness is further limited to about 40 ev

(3).









3

Another type of time-of-flight spectrometer is

that which is associated with particle accelerators.

The particle accelerator is used to produce bursts of

neutrons for spectral analysis. The width of the burst

of neutrons produced by a pulsed accelerator is usually

about one-tenth that of the chopper (4, 5). This is an

important advantage with respect to the ultimate attain-

able resolution; however, the narrowness of the burst

creates the problem of timing in detectors.


Intermediate Neutron Spectrometers

For the intermediate neutron energy, 20 Kev to

1 Mev, there is no adequate spectrometer. An attempt

to use gas recoil counters (6) as neutron spectrometers

for the energy range, 20 Kev to 3 Mev, was only parti-

ally successful. The pulse-height distribution for

monoenergetic neutrons obtained by a gas recoil counter

was successfully accounted for theoretically (7, 8);

however, for a complex neutron spectrum the gas recoil

counter is of little use because monoenergetic neutrons

give rise to a pulse-height spectrum extending from

zero pulse height to a maximum equivalent to the neutron

energy.

Another type of a gas counter which is based on

the detection of reaction products produced by the









4

neutrons is the He3-Counter. The performance of the He3-

Counter depends on the properties of the reaction


n + He3 -- P + T + 0.77 Mev.


If the range of the proton and the range of the triton

produced by this reaction do not extend beyond the sensi-

tive volume of the counter, a proton whose pulse height

is proportional to the energy of the neutron plus the Q

of the reaction, 0.77 Mev, is produced. Pulses produced

by elastic recoils impose a limit on the usefulness of

the reaction. When these pulses correspond to an energy

in excess of 0.77 Mev the interpretation of the pulse-

height spectrum in terms of a neutron energy spectrum

is no longer straightforward. Therefore, the range of

this type of spectrometer is from a few Key to about 1.5

Mev (9).


Fast Neutron Spectrometers

A variety of spectrometers has been developed for

fast neutron spectrometry. Only a few of these spectrom-

eters will be reviewed here.

Proton Recoil Spectrometer. The principle

involved in this spectrometer is that neutrons incident

on a hydrogenous target (radiator) knock off protons and

the proton recoils are detected by means of a









5

scintillation spectrometer. The proton recoils from the

radiator are strongly dependent on the angle of observa-

tion so that the angle subtended by the spectrometer at

the radiator severely reduces the number of recoils

received by the spectrometer. It is estimated that this

spectrometer works adequately if a resolution less than

10 percent is not required (9).

Another spectrometer that operates on the proton

recoil principle is the stilbene scintillation crystal

built by H. W. Brock and C. E. Anderson (10). In this

spectrometer the proton recoils produced in the crystal

give up their energy in the crystal also. Thus, in

principle, all of the proton recoils can be analyzed.

The resolution of this spectrometer is limited to the

intrinsic resolution of the crystal (approximately 10

percent). Another undesirable feature of this spec-

trometer is the conversion of pulse-height spectra to

energy spectra. Discrimination between gamma-ray pulses

and neutron pulses is achieved by special circuits based

on the difference in shape of the two pulses. The lower

limit of the range of this spectrometer is set by the

minimum energy of the neutron for which proton recoils

take place (a few tenths of a Mev). The upper limit can.

conceivably be as high as 40 Mev (11).









6

Other spectrometers. There are several other types

of spectrometers that have been used in neutron spectrom-

etry, e.g., the LiI(Eu) scintillation spectrometer, counter

telescope, bubble chambers, and nuclear emulsions. A

brief summary about the features of these spectrometers

is given in reference (9). All of these spectrometers

have serious limitations. There is one other spectrometer,

developed by Temple Love and R. B. Murray (12), which

acquired a certain amount of success. This spectrometer

consists of a thin layer of Li6F sandwiched between two

solid state detectors. Fast neutrons incident on the

assembly give rise to Li6(n,CX)T events releasing a total

energy equal to the neutron energy plus the Q of the

reaction, 4.78 Mev. The alpha and the triton. are de-

tected by the two detectors in coincidence and the total

energy shared by these particles is indicated by summing

the output pulses of the two detectors. The amplitude

of the summed pulses is proportional to the energy of

the incident neutron. The resolution of the spectrom-

eter is about 10 percent for 3-4 Mev neutrons and the

efficiency is 10-6 10-7 in this energy range. The

lower limit of the neutron energy at which this spec-

trometer becomes useful is about 1 Mev. No upper limit

was given.









7

Pertinent features of the various neutron

spectrometry methods are shown in Table I.

To sum up this discussion, the statement made by

W. H. Jordan (13) of Oak Ridge National Laboratory is

quoted, "The world still needs a good neutron spectrom-

eter." The following discussion is concerned with a

new approach to neutron spectrometry.


New Approach

The new approach to neutron spectrometry is based

on the decay of the neutron into a beta, a neutrino and

a proton; hence the name, Neutron Decay Spectrometry, was

adopted. To obtain the neutron spectrum from the decay

products of the neutron, one can either measure the

energy of the emitted proton alone or measure the energy

of the proton in coincidence with the beta. Both types

of measurements have their advantages and disadvantages.

By measuring the energy of the proton alone, one can

obtain a relatively high counting rate at the expense of

resolution for neutrons below 100 Kev. The resolution

obtainable by this method is limited by the fact that

emission of protons in the center of mass coordinates

(henceforth referred to as CM) is isotropic and there-

fore the velocity vector of the proton in the laboratory

coordinates (henceforth referred to as Lab) will exhibit









8

TABLE I
SUMMARY OF NEUTRON SPECTROMETRY METHODS

Resolu- Range of Energy
En;ev Method tion Efficiency Where Method
(Percent) (Percent) Applies

0.019 Crystal(a) 0.8 10-6-10-7(b) 0.02 50 ev

1.8 Crystal 7.5 10-6-10-7 0.02 50 ev

29 Crystal 26.0 10-6-10-7 0.02 50 ev

ixl02 Chopper 0.28(c) reasonably 0 20 Kev

ixl04 Chopper 2.8 high(d) 0 20 Key

ixl06 Chopper 28.0 high 0 20 Kev

Proton
xl106 Recoil 10.0(e) 10-6 0.5 40 Mev

ixl06 He3 Counter 12.4(16) 4xl0-5(16) 0.5 1.5 Mev

ixl06 Stilbene 10.0 1-10 1 10 Mev
Crystal

3x106 Li6F(f) 10.0 10-6-10-7 > 1.0 Mev

(a) Based on data given in reference (1).

(b) Based on calculations given by Goldberg and Seitz (14).

(c) Based on Equation (1) with R=0.01 microseconds per
meter.

(d) Efficiency depends on the detector used. Seidl et al.
reports an efficiency of 0.3 percent for 1 Key neutrons
reaching the sensitive volume of their BF3 detector (15).

(e) Resolution and efficiency are related in such a way
that if the resolution improves the efficiency decreases
(f) Li6F sandwiched between two solid state detectors).

(f) Li6F sandwiched between two solid state detectors.









9

a maximum and a minimum for monoenergetic neutrons. For

high energy neutrons the variation in the velocity vector

of the proton in the Lab system becomes unimportant and

a 5 percent resolution for 1 Mev neutrons is attainable.

By measuring the proton and the beta in

coincidence, one can obtain very good resolution for low

energy neutrons at the expense of the counting rate which

is severely reduced. For this work the former method was

used.


Feasibility

The half-life of a neutron was measured by J. M.

Robson (17) to be 12.8 minutes. The neutron density from

a beam of ixl010 thermal neutrons per cm2 per sec is

4.55xl04 neutrons per cm3. The decay constant of a

neutron is 9.023x10-4 disintegrations per sec. The num-

ber of disintegrations in one minute is


(Io I) = I(l e-9023x10-4(60))

= 4.55xl04(l 0.947)

= 2420 disintegrations/min/cm3.


This decay rate is not very high; however, if all the

protons decaying from a 1010 n per cm2 per sec beam of

neutrons are magnetically confined and collected along a









10

one meter path length, one can see that the count rate

becomes appreciable. It should be noted that for high

energy neutrons the decay rate will be very small. The

relativistic velocity of a 2 Mev neutron is 1.38xl09 cm

per sec and therefore the neutron density of a 1010 n

per cm2 per sec beam is only 7.2 neutrons per cm3 per sec.

This number of decays per cm3 is very small indeed and

unless one confines the protons along a very long path

length, spectrometry based on the decay of neutrons

becomes impractical. Figure 1 shows the total number of

protons emitted per minute along a path length of one

meter as a function of neutron energy. Figure 1 indicates

that enough decays will take place to warrant measurements.

















105






E-



z 104
0 '

Q
H -












103
10 100 1000

ENERGY, EV

Figure 1. Number of Protons Emitted Per Minute Along a Path Length of 1 Meter
versus Energy, Based on a Neutron Beam of 1010 Neutrons per cm2 per Second














CHAPTER II


THEORY


The formulation by which one can relate the energy

of the decayed proton to the energy of its parent, the

neutron, is developed in this chapter. A method for

solving the three-body problem for the decay of neutrons

in the CM coordinates is developed in the first section.

This method is based on arbitrary specification of the

momentum vector of the beta particle and then solving

for the momentum vectors of the proton and the neutrino.

The second section deals with the transformation

from the CM to the Lab coordinates. The maximum velocity

of the proton in the CM coordinates is used to calculate

the maximum and minimum velocities of the proton in the

Lab coordinates as a function of neutron energy. It is

shown that the average velocity of the proton is equal

to the velocity of the neutron. The theoretical resolu-

tion attainable from measuring the proton energy

distribution is based on the possible maximum and mini-

mum energy of the proton associated with a single neutron.

The third section deals with the detection of

the decay proton and electron in coincidence. The









13 '

directions of emissions of the proton relative to the

direction of motion of the neutron are calculated in the

Lab system as a function of the angle in the CM system

for various neutron energies.

The neutron decays as follows


n -- P+ + + V + Q. (2)


In the CM coordinates the sum of the moment of the

proton, the beta and the neutrino is



+ + = 0. (3)


where f is a momentum vector. The decay in Cartesian

coordinates can be represented as shown in Figure 2.

The momentum vector of the beta particle is

shown along the x-axis for clarity. In this coordinate

system the sum of the three moment along the x-axis,

y-axis and z-axis is


x: PPsinp cos p + / sin c Goso


+ (Vsin q/ cosev, = 0, (4)


y: 1psin pp sin 9p + 1 sin 3 sin6)

+ f/sin ( sin,/G = 0, (5)


















































S/ 9

y---P


N
N
N


/

I /
I /
N N //
N


Coordinate System for Decay of Neutrons


Figure 2.











and,

z: fpcos q p + cos + f cosp = 0, (6)


where is the magnitude of the vector f .


Conservation of energy requires that the sum of the

kinetic energies of the proton, the beta and the neutrino

be equal to the energy equivalence of the difference

between the mass of the neutron and the sum of the masses

of the beta and proton. That difference is


c2 mn (mp + m/ ) = 780 Kev, (7)


where,


c = the speed of light (2.99793xl010 cm/sec),

mn = the rest mass of the neutron,

mp = the rest mass of the proton,

and mp = the rest mass of the beta.


In Equations (4-7) there are nine unknowns and there are

only four equations. In order to solve this system of

equations one may specify P Pg and OA and may

furthermore limit the solution to the xz- plane, xy-

plane or the yz- plane. After obtaining all possible

values that each variable can take on in each plane,

one can combine these solutions together and thus obtain

the complete picture.








16
The beta particle is arbitrarily chosen to be
emitted along the x-axis. This choice of direction for
the beta sets P = 90 degrees and Op = 0 degrees. If
the directions of the protons and the neutrino are
limited to the xz- plane, then @p and 6/V must be 180
or 0 degrees. Under these conditions Equations (4) and
(6) become

x: in + + sin + ( + ,sin = 0, (8)

and
z: /pcos p + /cos .V = 0. (9)


The sum of the squares of Equations (8) and (9) gives

(/p (2 2 + 2 sin (10)


The beta spectrum emitted from thermal neutron
decay is known (17) to vary between 0 ev and 780 Kev.
The most probable emission takes place at an energy of
about 400 Kev. The relativistic mass of the beta
particle at 400 Kev is 1.623618xlO-27 grams (18) and
the value of the momentum, ( is




= (1.623618x10-27gm)(2.481986xl010 cm/sec)


= 4.029797xl0-17gm-cm/sec.


(11)









17

Since the energy of the beta particle was arbitrarily

chosen as 400 Key then the kinetic energies of the

proton and the neutrino are related as follows:


Ep + Ev = 780 400 = 380 Kev, (12)


where Ep is the kinetic energy of the proton and E ) is

the kinetic energy of the neutrino. If the mass of the

neutrino is considered to be zero then the energy and

the momentum of the neutrino obey the relation


E = = fc. (13)


If one treats the energy and momentum of the proton

non-relativistically then by Equation (12) and Equation

(13) the momentum of the proton is related to the

momentum of the neutrino as follows:


P 2 = 2mp(6.087866xl0-7 c)


= 2.036306xlO-30 1.002765x0-1310 (14)


Combining Equations (10) and (14) yields


[)P2 + (8.059591xl0-17 sin ) + 1.002765xl0-13)


- 2.034682xl0-30 = 0.


(15)









18

One can calculate f as a function of ,/,by Equation

(15). Knowing p and 9 one can calculate rp and

(p by using Equations (14) and (9) respectively. Table

II summarizes the possible values that p, )p and

TV can have in the xz- plane.


TABLE II

VALUES OF fp, JV AND pp FOR GIVEN VALUES OF IN THE
xz- PLANE, GIVEN = 4.029797xl0-17, = 90o





0 2.0287xl0-17 4.475xl0-17 1160:57'

+3 2.0285x10-17 4.680xl0-17 115:39'
-3 2.0288xl0-17 4.520xl0-17 116:45'


*Counterclockwise direction is taken as positive
and clockwise as negative.
**
Units in gm-cm per sec.


In order to conserve momentum, pq must remain in the

range, -3O0_ z 30; otherwise momentum can not be

conserved. It should be pointed out that the value of

fp is very sensitive to slight variations in / .

xy- Plane

The equations that govern the emission of the

beta, the proton and the neutrino in the xy- plane are










x: /p cos 60p + + cos e7 = 0, (16)

y: fp sin G p + r sin 0,/ = 0. (17)


The sum of the squares of Equations (16) and (17) gives


P 2 f2 2 + 2 cos &,
(18)

Again, by substituting for P from Equation (14) into
Equation (13) one gets

2 + (8.059591 cos ~ + 1.002765xl0-13)

2.034682xl0-30 = 0. (19)

Equations (19) and (15) are similar except for the term
cos 8 which appears in Equation (19), whereas the
term sin p appears in Equation (15). Table III sum-
marizes the possible values that /p, / &, pp, and
can take on in the xy- plane.

TABLE III
VALUES OF %p, f/l and Op FOR GIVEN VALUES OF 6P, IN THE
xy-PLANE, GIVEN / = 4.029727xl0-17, OR = 0o



870 2.0285x10-17 4.680xl0-17 2050:39'
900 2.0287xlC-17 4.447xl0-17 2050:09'
930 2.0288xl0-17 4.520x10-17 2060:38'
Units in gm-cm per sec.









20

Again in order for momentum to be conserved eQ must

remain within the angle 870 Z L 93.

It is seen from Tables II and III that in the

xz- plane the values of /p and are the same as in

the xy- plane. This agreement was anticipated. The

difference in the values of p and eOl and 9 p and & p

is due to the difference in orientation of the vectors

op and P with respect to the z-axis or the x-axis.


yz Plane

It was shown above that the angle between the

neutrino and the beta particle (400 Kev) can not be less

than 87 degrees nor more than 93 degrees in the xy-

plane. Similarly p must remain in the range -36 (p9,

! 30 in the xz- plane. Thus if the direction of the beta

particle is arbitrarily kept along the x-axis, then the

direction of the neutrino can vary in the yz- plane be-

tween 0 and 360 degrees and the momentum will be con-

served. In Figure 3 the possible angles that the neutrino

can take on are shown in the yz- plane. If the "wedge-

shaped" volume in Figure 3 is rotated through 270 degrees

in the yz- plane, all possible directions that can

take on would be generated. The magnitude of the possible

values of in the xz- or the xy- planes does not change






































X









Figure 3. Possible Orientation of 9 with Respect
to (E = 400 Kev)







22
by this rotation; only the directions are changed. The
change in these directions is governed by the relations

x: fpsin q pcos p +. sin 9 /cos &V + r = 0,

(20)
y: 10pSin 4 psin p + sin p qsin &/ = 0, (21)
and
z: /Opcos pp + icos qp2 = 0. (22)

An expression for sin q p is obtained from Equation (22)
as


sin p 2- 2( COS 2 (23)


An expression for cos q) p is obtained from Equation (21)
as


cos q p = 2

p 2- cos 9i t (24)

4cos h,,) 2 (/ sin sin 2J .

Substituting Equations (23) and (24) into Equation (20)
one gets

P2 cos 2 sin p,/sin 2'

= sin Pcose + (25)







23
Squaring both sides of Equation (25) one gets


( p2 ( cos q 2 / ( sin sin ,) 2

(92 + sin i sin ) + 2 sin sin2 .

(26)

Equation (26) relates to ) and
Since there are only limited values that OZ/ can take on,
viz., 870 9 : 930, then one takes the special case,
9/ = 90 degrees. Under this condition Equation (26)
becomes


p2 ( 12 + t2. (27)

By varying p 2 in Equation (22) in the y-z plane one can
calculate qp p as a function of f. Knowing I p then
one can calculate G p by Equation (3). Table IV sum-
marizes the results. In a similar way one can vary Q1
and compute P p and 9 p.
One concludes from the above treatment that by
fixing one parameter, namely the kinetic energy of the
beta particle, one can solve a three-body problem. It
was shown what values the momentum of the neutrino can
have and within what angles with respect to the beta
particle axis the direction of the momentum can vary.












TABLE IV

VALUES OF p AND 9 p AS A FUNCTION OF AT Z = 900

( p = 4.475xl0-17 = 2.0287x1017; E = 400 Kev)





00 116 :57' 1800:00,

100 116:31' 1850:02'

200 115:13' 1890:52'

30 1130:07' 1940:16-

45 1080:481 1990:486

600 103:06' 2030:46'

800 940:31' 2060:361

90 900:00' 2060:57'



Furthermore, the allowed maximum and minimum moment of

the proton were calculated. Since the kinetic energy of

the beta particle can vary between zero and about 780

Kev, one can repeat the above calculations for several

values of the kinetic energy of the beta particle.

Associated with the energy distribution of the betas,

there is an energy distribution of the protons. The

proton carries away maximum energy when the energy of

the neutrino is minimum, i.e., when the emission is

reduced to a two-body system comprising the beta particle









25

and the proton. Thus for a two-body problem the

momentum of the beta particle is related to the momentum

of the proton as


mp vP = mpVp (28)


where v is the velocity of the particle in cm per sec.

Energy conservation requires that


Eg + Ep = 780 Kev. (29)


By using Equations (28) and (29), it was found that the

velocity of the proton, Vp, in the CM coordinates is

4.45 x 107 cm per sec. In the calculation, the energy

of the beta particle was treated relativistically and

the energy of the proton was treated classically. This

maximum velocity of the proton was used to calculate

the maximum and minimum velocity of the proton in the

Lab coordinates.


Transformation from CM to Lab Coordinates

In order to relate the velocity of the proton to

the velocity of the parent neutron, one should make a

transformation from the CM coordinates to the Lab

coordinates. This transformation is readily understood

with the aid of Figure 4.






















Direction

of Neutron


vn


Figure 4. Transformation of Velocity of Proton from
CM to Lab Coordinates


In Figure 4 the symbols are defined as follows


Vp = velocity of proton in CM system,

VL = velocity of proton in Lab system,

9 = the angle between the vectors, vp
and vn in the CM system, and

= the angle between v-' and vn in the
L n
Lab system.


It should be noted that j can vary between zero and 180

degrees. Thus vL will be a maximum if 4' is zero and a

minimum if 41 is 180 degrees. This variation in Vj is

due to the fact that the beta particle can be emitted in

any direction in the CM system with respect to the

direction of the beam of neutrons. Thus for monoenergetic








27
neutrons there will be a distribution of protons bounded
by the maximum and the minimum vL.
The velocity of the proton in the Lab system is
related to that in the CM system by the relation


S= n + (Vp) + 2vn Vp cos (30)

Since 4 varies between zero and 180 degrees, then the
maximum vL can be expressed as

2 2 2
vL) = (Vn) + (vp~ + 2vn vp, (31)
max

and the minimum vL can be expressed as


L)in n + (Vp) 2vn Vp. (32)


It was shown earlier that the maximum possible
velocity of the proton, Vp, in the CM system is
4.45 x 107 cm per sec. If the maximum velocity is used
in Equations (31) and (32) it is seen that the range
between (vL)max and (vL)min will include all values of
VL calculated with smaller Vp. The relativistic rela-
tionship between the velocity and the energy of the
neutron is


E = moc2 {-l 12 1 (33)

[ c2)











where


mo = rest mass of the neutron,

E = kinetic energy of the neutron,

v = velocity of the neutron,

and c = velocity of light.

Equation (33) can be rearranged as follows


moc
Vn = c2 -
E + m c2


(34)


The velocity of the neutron was calculated as a function

of neutron energy by Equation (34). Table V shows the

results.


TABLE V
VELOCITY OF NEUTRON AS A FUNCTION


E ; ergs

1.60207x10-10

1.60207x10-9

1.60207x10-8

1.60207xl0-7

8.01035x10-7

1.60207x10-6

3.20410xl0-6

8.01035xl0-6


OF ENERGY


Vn ; cm/sec

1.34x107

4.34x107

1.44x108

4.39x108

9.78x108

1.38x109

1.95x109

3.08x109


E ; ev

102

103

104
105

5x105

106

2x106

5xl06









29

By using the values of vn given in Table V in

Equations (31) and (32), (vL)max and (VL)min were

calculated as a function of neutron energy. Table VI

shows the results.


TABLE VI

VALUES OF THE MAXIMUM AND THE MINIMUM VELOCITY OF THE PROTON
AS A FUNCTION OF THE NEUTRON ENERGY IN THE LAB SYSTEM


E; ev (vL)max;cm/sec (vL)min;cm/sec (VL)Ave;cm/sec


102 6.04x107 3.11xl07 4.57xl07

103 8.79x107 3.15x106 4.36xl07

104 1.83x108 1.06x108 1.44x108

105 4.77x108 4.01xl08 4.39x108

5x105 1.02x109 9.38x108 9.77x108

106 1.42xl09 1.34xl09 1.38x109

2x106 1.99x109 1.91x109 1.95x109

5x106 3.12x109 3.04x109 3.08x109



Comparison of the third column of Table V with the fourth

column of Table VI reveals that the velocity of the neutron

is almost identical to the average velocity of the proton

in the Lab system. The only exception to that is at a

neutron energy of 100 ev. The deviation of the proton

velocity from the neutron velocity at low energy is due to

the kinetic energy that the proton receives from a zero ev









30

neutron. This energy results from the difference between

the neutron mass and the sum of the proton and electron

masses.

Since the average velocity of the proton emitted

from the decay of any neutron is nearly the same as the

velocity of the parent neutron, then the energy of the

neutron is related to the energy of the proton as follows:



En m Ave



= 1.0014 (EP)Ave. (35)


For all practical purposes, it is seen that measuring

the energy of the decay proton yields the energy of the

neutron.


Resolution

Even though the average velocity of the proton

is almost the same as that of the parent neutron, the

difference between (vL)max and (vL)min is a measure of

the resolution attainable. If one defines the resolu-

tion as

(Ep) Ave (E) min
R =
(Ep)Ave











then


(EP)max (EP)min

(Ep) + (Ep)
R = (36)

(Ep)max (Ep) min

The resolution as a function of neutron energy is

calculated in Table VII.


TABLE VII

THE RESOLUTION,R, BASED ON THE MAXIMUM VELOCITY IN
THE CM SYSTEM, AS A FUNCTION OF NEUTRON ENERGY


E ; ev (Ep)max; ev (EP)min; ev R; %


102 1,754 507 55.2

103 4,041 5 99.7

104 18,529 5,140 30.6

105 122,034 81,164 20.2

5x105 545,760 454,783 9.1

106 1,063,752 935,194 6.4

2x106 2,077,397 1,903,219 4.3

5xl06 5,099,540 4,822,696 2.7


It should be emphasized that the resolution as defined

here means the half width at the base instead of the

usual definition of half width at half maximum. Thus

the values for the resolution shown in Table VII would

be better if the usual definition were employed.









32

Nevertheless, one can see that resolution for neutrons

below 100 Kev is poor. In order to obtain better resolu-

tion at lower energy one must count the decay proton and

electron in coincidence.


Proton and Electron in Coincidence

The relationship between V the angle in the CM

system, and & the angle in the Lab system, can be

derived from the law of sines. From Figure 4 one obtains

the following relations


a Vp
a- (37)

sin( -') sin c'

and
b Vn
= (38)
sin /Y sin c


Since a = b, then


vn sinj = vp sin(Y/-A). (39)


Upon rearranging Equation (39), one gets

vn
cotr = cot 4 + csc (40)
vp


Equation (40) allows one to calculate 4\ for any value

of 4 The value for Vp used in Equation (40) was











4.45 x 107 cm per sec as calculated from the two-body

problem. Figures 5 and 6 show 4 as a function of 4) for

constant neutron energies. It is seen from Figures 5

and 6 that for a neutron energy below 1003 ev, AI varies

between zero and 180 degrees. At higher energies A/ will

be restricted to smaller values. At a neutron energy

of one Mev the maximum deviation of the proton from the

axis along which the neutron travels is slightly below

two degrees. If the decay proton and electron from the

parent neutron are measured in coincidence, one is

essentially fixing the angle 14 to one value. Further-

more, since the velocity of the decay electron is nearly

the same in the CM and the Lab systems for neutrons

below one Mev then by measuring the decay protons as

a function of rq in coincidence with the decay electrons

one would get the spectrum of the neutrons. The improve-

ment in resolution that one gets will be limited only

by the size of the increments that r can take on. The-

oretically, these increments can be very small and thus

one can obtain very good resolution in the low energy

region.

As an example, A was calculated for neutrons

with energies of 100 and 110 ev for a fixed W of 90

degrees. The values of A were found to be 730:15' and

72:14' respectively. Thus a change in I of one degree











Vp = 4.45xl07 cm/sec
(Two-body Problem)


20 40 60 80 100 120 140 160


Figure 5. Angle


of Proton in Lab System, Y \, versus Angle in CM System, p ,
for Constant Neutron Energies


120


100



80



60




40



20


V DEGREES


180












6


5


4 100 Kev


g 3 500 Kev


2

1
1 1 Mev L\



20 40 60 80 100 120 140 160 180

S, DEGREES

Figure 6. Angle of Proton in Lab System, versus Angle in CM System, / ,
for Higher Constant Neutron Energies









36

will give a resolution of 10 percent at 100 ev. These

calculations are based on the maximum possible velocity

of the proton in the CM system. The probability of

emission of protons with such a velocity is of course

very small. A better basis for the calculation would

be that which is associated with the most probable

emission (the case considered with the three-body

problem, E P = 400 Kev). Thus a better resolution

would have been obtained had the most probable emission

been considered.

If 1 is varied in increments of less than one

degree, the resolution will of course improve. At this

point, one may point out that the size of the increment

in i will be affected by the available neutron

intensity; very intense beams of neutrons will be

required for small increments in 4(. With coincidence

measurements one is restricted to a small volume from

which protons and electrons can be detected (see Sec-

tion 2 of Chapter V).














CHAPTER III


DESIGN AND CALIBRATION OF APPARATUS


Apparatus

The equipment used in this work consisted of

(1) a containment magnet, (2) a magnetic analyzer and

(3) a detection system. Details about each unit follow.


Containment Magnet

The containment magnet was designed to contain

protons with maximum velocity of 3.66x107 cm per sec.

This velocity is higher than the velocity of the proton

with the most probable emission in the CM coordinates.

The equation relating the magnetic flux density to the

velocity of the proton and the radius of the cylindri-

cal solenoid, "containment magnet," is


m v
B = -- (41)
e R


where B = magnetic flux density in webers/m2,

m = mass of proton in kg,

v = velocity of proton in m/sec

e = electrostatic charge (1.6xl0-19 coulomb),

and R = radius of cylindrical solenoid in meters.

37









38

If R is assumed to be 0.0254 meters, then it is seen by

Equation (41) that the magnetic flux density required

for containing protons with velocity of 3.66xl05 meters

per sec is 0.15 webers per square meter.

For long solenoids Boast (19) gives the follow-

ing formula relating the magnetic flux density, the

current, the length of the solenoid and the number of

turns.


B /oN I
B = / (42)
S


where /,o = the absolute permeability of free space,

(47Wxl0-7 weber/m-amp),

N = the number of turns,

I = the current in amps,

and S = the length of the solenoid.


If one arbitrarily chooses S to be one meter and chooses

to use wire gauge number 14 (diameter = 0.06408 in.),

then the maximum current, I, that one can use without

excessive heating is set at 5.87 amps (20). Thus by

Equation (42) the magnetic flux density that is obtained

by winding one layer of wire, gauge number 14, is

4.53x10-3 webers per square meter. Previously it was

shown that the total flux density required to contain









39

protons with velocity of 3.66x107 cm per sec was 0.15

webers per square meter. Thus the number of layers needed

on the containment magnet is 33 layers.

Figure 7 shows the frame of the containment magnet.

The number 14 gauge wire was wound around the aluminum

tube in Figure 7. The steel rods between the two end

steel plates served two purposes: (1). a support for the

coiled wire and a means for preventing the aluminum tube

from being bent by the weight of the wire, and (2) a

means by which a more uniform magnetic field throughout

the aluminum tube was achieved.

In order to minimize the power requirement of

the containment magnet and thus eliminate the necessity

of an elaborate power supply, the containment magnet

was wound into two sections which were connected in

parallel. The power supply was designed by Donald F.

Mooney of the Department of Nuclear Engineering at the

University of Florida. Figure 8 shows the schematic

diagram of the power supply.


Magnetic Analyzer

The magnetic analyzer used in this work was

available at the Department of Nuclear Engineering. This

analyzer was designed and built by Elliott Kurzman (21)

as part of the 10 Mev Electron Linear Accelerator project









1/4 di o
1/4" STL.ROD





-l"I.D. AL. TUBING



END PLUGGED
WITH 1/32" 0 O
AL PLATE 1/4"STL. PLATE


39.37"


Figure 7. Frame for Containment Magnet













FUSE


ml = 0 50 Amp

m2 = 0 100 Volts

DI-D5 = IN 1203 A


Figure 8. Schematic Diagram of Power Supply for Containment Magnet.











at the University of Florida. The shape of the pole

pieces is shown in Figure 9. The gap between the pole

pieces was 5/8 in. and the maximum attainable magnetic

flux density was 3500 gausses at full current.


Detection System

The detection system consisted of a 0.006 in.

thick by 2 in. in diameter CSI(Tl) crystal mounted on a

2 in. in diameter by 18 in. long lucite light pipe. An

RCA 6342 A photomultiplier was coupled to the light

pipe with silicone grease. The output of the photo-

multiplier was fed into a preamplifier, RCL model 20200,

and then into an RCL linear amplifier, model 20100. The

output of the amplifier was connected to an RCL scaler,

model 20302.

The light pipe was wrapped with aluminum for

maximum transmission of light. The length of the light

pipe, 18 in., was necessary in order to eliminate the

effect of the magnetic field in the photomultiplier.

Some improvement in light transmission might have been

obtained with a logarithmic spiral light pipe as was

done 'a Argonne National Laboratory by W. C. Kaiser et

al. (22).

The detector assembly is shown in Figure 10.

The chamber which has the shape of the pole pieces,




















d 4.08"


Figure 9. Shape of Pole Piece










4.08" L


d


KEY :8)
1 Photomultiplier (6342 A)
2 Light Pipe
3 CsI(Tl) Crystal /
4.- Hollowed Chamber
5-6 Collimating Arms 7
7-8 Leads to Vacuum
System
Entire shell made of aluminum


3.00 Dia


Figure 10. Assembly of Detection System










45

shown in Figure 10, was inserted between the two pole

pieces and the open end at the left side of this chamber

was tightly connected to the containment magnet by a

rubber stopper slipped over this collimating arm. ,The

detector assembly as well as the containment magnet

was evacuated by a Veeco type RG-3A vacuum system.

Experiments were conducted with a pressure of 10-6 mm

of mercury. The curvature of the analyzing magnet was

set at 3.0 in. The width of the collimating arms on

both sides of the chamber positioned between the two

pole pieces was 3/8 in.


Calibration

The containment magnet was calibrated with a

Dyna-Empire, Inc. gaussmeter, model D-855. It was found

that this magnet becomes quite hot at full current of

12 amperes. Thus it was decided to operate the contain-

ment magnet at a current of 8 amperes. The magnetic

flux density at this current was approximately 1000

gausses.

The analyzing magnet was also calibrated with

the Dyna-Empire, Inc. gaussmeter. Figure 11 shows the

calibration curve. The uncertainty in each reading is

well within the circle around each point. The effect

of the magnetic field from the analyzing magnet on the

photomultiplier which was mounted on the 18 in. light











3500 -




3100




2700




2300




S1900
H


1500 -



H 1100




700



300 .


10 30 50 70 90 110 130

CURRENT, MA

Figure 11. Calibration of Analyzing Magnet, Magnetic Flux
Density versus Current









47

pipe was studied as a function of the current to the

analyzing magnet. The detector used in this study was

a 1/4 in. thick by 2 in. in diameter anthracene crystal.

Figure 12 shows the results. The fluctuation is no

more than the statistics associated with the counting

rate.

A check on the performance of the analyzing

magnet and the detection system was made with beta

particles from Cs37. The cesium source was a Tracerlab,

Inc. type R-34 disk source. This source was encased in

a thin plastic housing. The detector used with the

detection system was the anthracene crystal. Figure 13

shows the counting rate versus current to the analyzing

magnet. The uncertainty in each reading was taken as

the square root of the reading.

Since the beta particles from Cs137 are quite

energetic (0.51 Mev) (23), the range of these betas is

considerably longer than the range of 1 Key protons.

Thus it was decided to check the detection system with

protons in the energy range that would be encountered

from the decay of neutrons. The detector used in this

check was the 0.006 in. thick by 2 in. in diameter

CsI(Tl) crystal. The Texas Nuclear, model HV-150,

neutron generator was modified to accelerate protons.

























Source Cs137


I I I I I I I I I k


100


140


180


CURRENT, MA


Figure 12. Effect of Magnetic Field on Photomultiplier



















1300 -



1200 -



1100 -




1000 -



900 -
BACKGROUND


800


10 15 20 25

CURRENT, MA






Figure 13. Beta Spectrum of Cs137 as Measured by
Analyzing Magnet









50

The modification consisted of replacing the deuterium

bottle with a hydrogen bottle and eliminating the tri-

tium target altogether. The energy of the protons was

varied by varying the high voltage on the Texas Nuclear.

Figure 14 shows the counting rate as a function of the

current to the analyzing magnet for 5 Kev, 10 Kev and

20 Kev protons. The scatter of some of the points was

caused by fluctuation of the Texas Nuclear machine.

The spread in each peak might be attributed to scatter-

ing of the protons before arriving at the chamber between

the two pole pieces. The uncertainty in each reading

was again taken as the square root of the reading.

The magnetic field required to bend various

energy protons was calculated by Equation (41) and the

results are shown in Figure 15. Using the results shown

in Figure 15 and those in Figure 11 the currents to the

magnetic analyzer required to bend 5 Kev, 10 Kev and 20

Kev protons were calculated and shown in Figure 14 as a

function of energy. It is seen that calculated and

experimental currents do not agree. This disagreement

could be caused by either inaccurate calibration of the

accelerated protons or inaccurate calibration of the

magnetic field (Figure 11) or both. It is noted from

Figure 14 that for the energy range considered the

energy of the proton is related to the current of the

magnetic analyzer linearly.










6.0


10 Kev --U Calculated 20

5.5 + -+Experimental

-I
S5 Kev 15
S5.0 _
5.0 20 Kev 0


S 4.5 -10



4.0
H -- 5




I I I I I I I I I I I I I I I
10 30 50 70 90 110 130 150

CURRENT, MA


Figure 14. Spectrum of Monoenergetic Protons Produced by the Texas Nuclear
Accelerator and Analyzed by the Analyzing Magnet









4.8


4.0




S 3.2


H
S2.4


H

S1.6 -U




0.8 -





5 10 15 20 25 30 40 50 60 70 80 90

PROTON ENERGY, KEV

Figure 15. Magnetic Field Required to Bend Protons through a Radius of 3 Inches













CHAPTER IV


EXPERIMENTS AND RESULTS


Experiments

All experiments were performed at the south beam

port of the University of Florida Training Reactor (24).

This beam port is 6 in. in diameter on the outside of

the shield and tapers down in one step to 4 in. The

exterior of the port is about 6 feet from the center

of the core. In all experiments the containment magnet

was placed in a horizontal position against this port

and the rest of the equipment was attached to the

containment magnet, as is shown in Figure 16. In these

experiments the CsI(Tl) crystal was used with the

detection system. The crystal was about 4 inches away

from the axis of the beam of neutrons and gamma rays.

A sheet of lead 1 in. thick was wrapped around the

crystal. The reactor was operated at 10 kilowatts,

the maximum permissible power level.

Experiment 1. The first experiment served two

purposes: (1) the counting rate was obtained as a

function of current to the analyzing magnet with the

neutrons shut off by two 4 in. in diameter by 5 in. long

53







1 Fuel Box
2 Graphite Plug
3 Neutron Beam
4 Reactor Shielding
5 Containment Magnet
6 Magnetic Analyzer
7 Detection System


0


Figure 16. Sketch of Apparatus in Use


3
( T> lo


]


1Y









55

boron-loaded paraffin plugs and 0.035 in. thick sheet of

cadmium placed between the containment magnet and the

paraffin plugs, (2) the effect of the magnetic field

produced by the containment magnet on the photomulti-

plier was checked. The effect of the magnetic field

was checked by rersing the polarity of the field and

repeating the experiment. Figure 17 shows the experi-

mental results. It is seen from Figure 17 that the

magnetic field of the containment magnet does affect the

photomultiplier; however, the magnetic field of the

analyzing magnet has no effect. Furthermore, the effect

of the magnetic field of the containment magnet gave a

constant displacement between curves 1 and 2 in Figure

17. The increase in the counting rate (curve 1) caused

by the magnetic field of the containment magnet over the

correct counting rate obtained without the magnetic

field was about 7 percent. The decrease in the counting

rate when the magnetic field was reversed was about 19

percent. The uncertainty in each reading was taken as

the square root of the reading and this uncertainty is

within the circle around each point. In Experiment 1

there was no guarantee that the radiation field was free

of neutrons. Thus Experiment 1 was repeated with a Co60

source with the reactor shut down. Results similar to

those shown in Figure 17 were obtained.
















0 Field Direction
Radiation Direction

E Field Direction
Radiation Direction




EOp poEKD 0 0


I I I 1 1 1 1


I I I I I I 1 1


100


CURRENT, MA







Figure 1I. Radiation Detection versus Analyzing Magnet
Current in a Neutron-free Field


105


I I











Experiment 2. The experimental arrangement of

this experiment was similar to that in Figure 16. The

graphite plug between the containment magnet and the fuel

element was kept in place. The thermal neutron flux at

the end of the containment magnet was measured to be

4.46xl06 neutrons per sec per cm2. The magnetic field

of the containment magnet was oriented in the manner which

enhanced the photomultiplier output (see Figure 16).

Readings were taken after turning on the current to the

containment magnet and waiting until the temperature

of the coils reached equilibrium.

The readings taken with no current to the

analyzing magnet were considered as gamma background

because under such conditions protons could not be bent

into the detector. Thus the differences in counts per

unit time between the readings taken with and without

magnetic field in the analyzing magnet were considered

as counts per unit time caused by protons emitted from

the decay of neutrons. Figure 18 shows the proton

counting rate as a function of current to the analyzing

magnet and Table VIII shows the data. The background

was averaged over nine readings and it was found that

the maximum deviation from the average was 1.2 percent.

Each reading that appears in Table VIII was the average

of at least three readings. The uncertainty in each

reading was simply the maximum deviation from the mean.





















104


p


'pc


I I I I I


I I I I 11111


10 100
CURRENT, MA




Figure 18. Proton Counting Rate versus Analyzing Magnet
Current (No Collimation, Graphite Plug In)












TABLE VIII

PROTON COUNTING RATE AS A FUNCTION OF MAGNETIC
ANALYZER CURRENT*



Current; MA Counts/min; Ave


3

6

9

11

15

18

20

21

26

40

50

70

100

120

150


13,580

14,691

12,092

11,771

8,748

10,260

13,461

13,394

15,073

13,808

14,457

7,164

9,016

9,119

11,682


300

1,000

1,600

1,000

2,500

1,500

1,100

1,300

1,900

1,000

1,700

1,100

1,000

1,320

1,300


Average background = 234,929 2,800 counts/min.

Beam of neutrons not collimated; graphite plug
in.









60

Experiment 3. The experimental conditions of

Experiment 3 were similar to those of Experiment 2

except that the neutron beam was collimated and the

graphite plug between the middle fuel element and the

containment magnet was removed. The-diameter of the

collimated beam was 1 in. The collimator was built by

welding two iron pipes concentrically and filling the

region between the two pipes with heavy concrete. The

purpose of the collimator was to reduce the gamma ray

background to a minimum. Unfortunately a reduction in

the neutron beam was also experienced. The results are

shown in Table IX and in Figure 19 and are designated as

Run A. This same experiment was repeated under the same

conditions except the pulse-height selector was lowered

from 60 to 50 units. During this run the detection system

was drifting. In order to compensate for the drift a

background was taken before and after each reading. The

average of the two was subtracted from the reading to

give the counting rate of the protons. The results of

this run are also summarized in Table -IX and shown in

Figure 20 and designated as Run B. The increase in

background in Run B was caused by lowering the pulse-

height selector thus allowing more noise to be regis-

tered. The uncertainty in the readings in Run A was

taken to be the same as the square root of the average











TABLE IX
PROTON COUNTING RATE AS A FUNCTION OF
MAGNETIC ANALYZER CURRENT*


Current; MA Counts/10 min

RUN A
21 5,150 806

30 7,340 t 806

50 12,300 t 806

80 3,150 t 806

150 100 t 806
RUN B

10 8,028 1,030

20 5,354 1,030

30 4,670 + 1,030

40 7,796 1 1,030

50 11,074 1,030

60 5,378 + 1,030

80 6,903 1,030

100 5,310 1,030

150 1,020 + 1,030
Average background = 649,540 806/10 min.
(Run A)
Average background = 1,053,879 1,030/10 min.
(Run B)
*Beam of neutrons collimated and graphite plug
removed.






























.1


I I I II III,


g g I a a am,


I--I aI I I A I A I I I I I I I i


20 100
CURRENT, MA
Figure 19. Proton Counting Rate versus Analyzing Magnet Current
(Collimated Beam, Graphite Plug Removed, RUN A)


104











103


!


I
























103


'I i


100


CURRENT, MA

Figure 20. Proton Counting Rate versus Analyzing Magnet
Current (Collimated Beam, Graphite Plug Re-
moved, RUN B)


I j









64

of two background readings. The general agreement

between Run A and Run B indicates that the drift effect

was negligible.

Experiment 4. In this experiment it was

attempted to measure the pulse-height distribution of

the protons. The output of the RCL linear amplifier

was fed into a Nuclear Data 256-Channel Analyzer, model

100. The rest of the detector system was the same as

that previously described.

Because of the high gamma background and the

low proton energy, it was not possible to get the

pulse-height spectrum of the protons.


Treatment of Data

The counting rate of the protons shown as

ordinates in Figures 18, 19 and 20 is actually the num-

ber of events per unit time per unit volume in a

velocity incrementA v about v, the velocity of the

proton. The increment of velocity is related to the

radius of curvature by the relation (25)


S = AR (43)
v R


where

AR = the width of the collimating arm (3/8 in.),

and R = the radius of curvature required for the
protons to get to the detector (3 in.).











Thus Av = 0.125 or 12.5 percent. The number of protons
v
per unit velocity, N(v), is equal to the counting rate of a

of a particular proton velocity range, A> v, divided by 0.125 v.

This operation is essentially a transformation of the

data in Figures 18, 19 and 20 to histograms. The width

of each element in the histogram is & v. By joining

the midpoints of each element one gets N(v) versus v.

The number N(v) is related to the flux 0 (v) as


(v) = N(v) v (44)


where 4 (v) is the flux per unit velocity per unit time

per unit area. The flux per unit velocity is related

to the flux per unit energy as


4(E)dE = 0(v)dv


or (E) = v N(v)
mv

or '(E) = N(v), (45)


where (E) is an arbitrary flux and is equal to

m (E).

By applying the above techniques to the data

presented in Figures 18, 19 and 20 the data shown in

Figures 21 and 22 were obtained.




















0 Experimental Data

O Experimental Data
divided by Collec-
S 100 '. tion Efficiency
(0.308)

--*MAGNUM GNU II
Calculation



O r 2


n 10

E-4





I . I I ..I .. 1.. I 1. t i | ..
0.3 1.0 10
ENERGY, KEV

Figure 21. Arbitrary Proton Flux versus Energy
(Uncollimated Beam, Graphite Plug In)


20














0 RUN A (Figure 19)

O RUN B (Figure 20)


l/E


1 10


ENERGY, KEV



Figure 22. Arbitrary Proton Flux versus Energy (Collimated
Beam, Graphite Plug Removed)


100















10


H
-0


>4

H


100














CHAPTER V


DISCUSSION OF RESULTS, RBOMMENDAT-IONS
AND CONCLUSIONS


Discussion

Figure 21, Chapter IV, shows that the spectrum

appears to be l/E in two regions, 0.3 0.7 Kev and

2.0 20 Kev. The velocity of 0.7 Kev protons is

3.6xl07 cm per sec. The containment magnet was

designed to contain protons with maximum velocity of

3.66x107 cm per sec. Thus the discontinuity in Figure

21 at about 0.7 Kev can be explained by the fact that

beyond this energy the containment magnet was not con-

fining all of the protons. As the energy of the neu-

tron increases, the direction of motion of the proton

approaches more and more the direction of motion of

the neutron. This fact is illustrated in Figures 5 and

6, Chapter II. Thus the forward motion of the higher

energy protons plus the effect of the magnetic field

from the containment magnet seems to contain the higher

energy protons effectively. This is seen in the second

region (2 20 Kev) where the flux is again l/E. In the









69

energy region (2.0 < En / 20 Kev) the loss in decay

protons that are not contained in the solenoid is being

compensated by the decrease in the allowed angular

distribution of decay protons.

The displacement between the two l/E regions

in Figure 21 is explained as follows. When neutrons

decay, the emission of protons and electrons is nearly

isotropic in the CM system. Unless the kinetic energy

of the neutron exceeds the kinetic energy of the pro-

ton, the direction of motion of the proton will vary

between 0 and 180 degrees with respect to the direction

of the motion of the neutron. In other words, at least

half of the protons that were emitted from low energy

neutrons were traveling in the opposite direction from

that of the neutrons. If the over-all efficiency of

collecting the low energy protons is assumed to be

0.308, then by multiplying the low l/E region in Figure

21 by 3.25 the two regions join smoothly. For higher

energy neutron decay, the "preferred" angle of the

proton in the Lab system approaches the direction of

motion of the neutron.

The Appendix shows a comparison of the measured

and expected proton counting rate. It was found that

the measured counting rate was 1.2 times the expected

counting rate.









70

A possible source of error in the measurements

is the production of protons by the (n,P) interactions

in nitrogen and aluminum. The production of protons

by the (n,P) reaction in nitrogen was calculated to

be 5.7 per minute in the entire length of the contain-

ment magnet for a pressure of 10-6 mm of Hg, as

compared to 2.42x105 protons produced by the decay of

thermal neutrons. Furthermore, the energy of the

protons produced by the (n,P) reaction in nitrogen was

calculated on the basis of mass differences being 1.06

Mev. Thus it is seen that the protons produced by the

(n,P) reaction in nitrogen could not have affected the

measured proton counting rate because of the energy dif-

ference. The other possible source for the production

of protons was the (n,P) reaction in the aluminum in

the containment magnet. The threshold for this reaction

is about 1.7 Mev and the cross section is 0.025 barns

(26) at 2 Mev. The neutron flux at 1.7 Mev that was

available was about 3 neutrons per cm2 per sec, assum-

ing l/E distribution for this energy region, and thus

it appears that the (n,P) reaction in aluminum was

unimportant.

There are no available neutron spectrum

measurements for the University of Florida Training









71

Reactor for comparison with the data shown in Figure 21.

However, C. A. Thompson (27) calculated the spectrum of

the UFTR using MAGNUM GNU II (28) and the results showed

that the spectrum is l/E in the graphite, the fuel and

in the center of the core for the energy region con-

sidered.

The results in Figure 22 show that the spectrum

when the graphite plug between the middle fuel element

and the containment magnet was removed tends to decrease

faster than l/E.


Recommendations

It is felt that the gamma-ray background was too

high and its elimination should improve the performance

of the Neutron Decay Spectrometer considerably. There

are two methods by which one can practically eliminate

the gamma background. The first method is the use of

solid state detectors. Presently available solid state

detectors, however, can not be used for the detection

of charged particles below about 10 Kev. Thus the use

of the solid state detectors is limited to energies

above 10 Kev.

The second method is the use of electron

multipliers that are insensitive to gamma rays. Elec-

tron multipliers have been used to detect very low ion









72

currents in mass spectrometers. D. B. McCulloch (29)

states that an electron multiplier when used with a

vibrating-reed electrometer can detect a current as low

as lxlO-19 amps or approximately 1 event per second.

This sensitivity is extremely useful for this type of

work and could possibly warrant successful results using

electron-proton coincidence measurements. The coinci-

dence measurements can be done as shown in Figure 23.


15 arm


Direction of neutron


1960


P+ arm


Figure 23. Illustration for Coincidence Measurements









73

In Figure 23 the angle between the proton and the beta

arms should be adjustable. When a neutron with zero

energy decays in the middle chamber, the angle between

the beta and the proton is (as determined in Table I)

about 196 degrees. If the beta arm is kept in position

and the proton arm is moved in small increments toward

the direction of motion of the neutron, then one would

be counting the decay products of higher energy neutrons.

This arrangement corresponds to having a proton detector

placed in such a way that Y = 90 degrees and 1 = 90

degrees in Figures 5 and 6. As the proton arm is moved

in small increments, ^% is decreased while / stays

constant. It can be seen from Figures 5 and 6 that by

this operation one would start measuring low energy

neutrons and then proceed to the higher energies. The

reason for keeping the beta arm fixed in its position

is that when low energy neutrons decay, the velocity

vector of the electron is essentially the same in the

CM and Lab systems.

Besides giving better resolution for neutron

spectrum measurements, the coincidence decay spectrometer

can be used to measure the effective mass of the neutrino.

This can be done by measuring the energy of the beta as

well as the energy of the proton in coincidence. From









74

knowledge of the angle between the beta and the proton,

the mass of the neutrino can be deduced.

The magnetic field density of the containment

magnet should be increased by at least a factor of 5.

This increase in the magnetic field will result in

better confinement for all the protons. At the same

time this increase in the magnetic field will affect

the photomultiplier or the electron multiplier. Thus a

compromise between the effect of the field on the photo-

multiplier and the better confinement that would result

from an increase in the field should be made. Another

improvement in the design of the containment magnet

would be to make the dimensions such that the contain-

ment magnet could be inserted in one of the beam ports

in the UFTR.

The design of the analyzing magnet could be

improved by either of two methods. The first method

would be to increase the magnetic field density so that

higher energy protons could be analyzed. The second

method would be to increase the dimensions of the pole

pieces so that a larger radius of curvature could be

used. Inherent in the second method would be a required

increase in the magnetic field so that the magnetic

field density would stay constant.

In order to analyze protons of 1 Mev or above,

one must take precautions to eliminate the nitrogen









75

atmosphere in the system because the (n,P) reaction in

nitrogen produces 1 Mev protons. A suitable substitute

for nitrogen would be oxygen. The threshold for the

(n,P) reaction in oxygen is above 10 Mev.


Conclusions

It was demonstrated in this work that neutron

spectrometry can be done on the basis of the decay of

neutrons and subsequent analysis of the resultant pro-

tons. Figures 21 and 22 show the results of such

measurements.

The efficiency of the Neutron Decay Spectrometer

for thermal neutrons is about 3.3xi0-7 percent. This

value of the efficiency is based on the number of pro-

tons emitted per cm2 per second divided by the number of

neutrons per cm2 per second. The efficiency decreases

exponentially with increasing neutron energy. The

efficiency is increased by a factor of 100 for a 100 cm

path length.

The resolution of the Neutron Decay Spectrometer,

as can be seen from Table VII, is poor for low energy

neutrons but improves as the energy of the neutron

increases. This improvement of resolution with increas-

ing energy is a unique characteristic of this type of

spectrometer. The resolution of the usual neutron











spectrometers such as choppers and other time-of-flight

spectrometers decreases with increasing neutron energies.

An improvement in resolution for low energy

neutrons could be achieved if the decay proton and elec-

tron were measured in coincidence. The coincidence

measurements, however, would require higher neutron

fluxes. The use of an electron multiplier along with a

vibrating-reed electrometer whereby one could measure a

current of ixl0-19 amps should make the coincidence

measurement feasible.

The Neutron Decay Spectrometer is a very

inexpensive instrument in comparison with other appara-

tus used to measure neutron spectra in the Kev range.

The most severe limitation of the Neutron Decay

Spectrometer is its low efficiency and the world may

still need a better neutron spectrometer.


































APPENDIX


COMPARISON OF MEASURED AND CALCULATED
PROTON COUNTING RATES








78

The energy of the proton in ev is related to its

velocity in cm/sec as


1.6xl0-12 E = 1 m v2 ,
2


(46)


where the 1.6xl0-12 is a conversion factor from ergs to

ev. From Equation (46) one obtains


d v 1.6xl0-12
dE mv


(47)


Combining Equation (44) and Equation (45) of Chapter IV,

one gets


N (v)xl.6xl0-12

m
m


(48)


It was stated in Chapter V that the proton counting rate

was N(v) v. The counting rate at a current of 3 ma

(Table VIII) was 13,580 counts per minute. This count-

ing rate corresponds to a velocity of 1.9x107 cm per sec

and a v is 0.238x107 cm per sec. Thus N(v) = 9.5xl0-5

counts per unit velocity per sec per 71 cm3. The 71 cm3

correspond to the volume of a cylinder 100 cm long by

3/8_in. (0.952 cm) in diameter, the collimating opening.

Substituting the above value for N(v) in Equation (48),

one gets


n[ E












9.5xl0-5 x 1.6x10-12

1.67xl0-24 (71)


(j(E) = 1.28x106 protons per ev per
cm2 per sec.


But O(E) = vN(E), thus


N(v) = l.28x106
1.9x107


= 6.75xl0-2 protons per ev per cm3 per sec


= 4.05 protons per ev per cm3 per min.


It was estimated from Figure 21 that the efficiency of

collecting these protons was about 0.308. Thus the total

number of protons that should have been collected should

be 13.1 per ev per cm3 per minute.

The thermal flux as measured by gold foil

activation at the entrance of the containment magnet was

4.46x106 neutrons per cm2 per sec. The thermal neutron

flux is usually defined to cover an energy range of

about 0 0.1 ev. Thus


4.46x106
(E) =-
0.1


= 4.46x107 neutrons per ev
per cm2 per sec.









80


The number of protons emitted from a thermal flux of

1010 neutrons per cm2 per sec is shown in Figure 1,

Chapter 14 to be 2.42x103 per ev per cm3 per minute.

Thus for a flux of 4.46x107 it is found that the

expected N(E) = 10.8 protons per ev per cm3 per minute.

The experimental N(E) and the calculated N(E) seem to

agree rather well.














REFERENCES


1. D. J. Hurst, A. J. Pressesky and P. R. Tunnicliffe,
Rev. Sci. Instr. 21, 705 (1950).

2. W. H. Zinn, Phys. Rev. 71, 705 (1947).

3. J. A. Harvey, "Nuclear Science Technology," M. L.
Yeater Ed., p. 67, Academic Press, New York (1962).

4. L. M. Bollinger, "Nuclear Spectroscopy," Fay
Ajzenberg-Selove Ed., Part A, p. 342, Academic
Press, New York (1960).

5. W. W. Havens, Jr., "Nuclear Science Technology,"
M. L. Yeater Ed., p. 91, Academic'Press, New York
(1962).

6. A. T. G. Ferguson, "Fast Neutron Physics," J. B.
Marion and J. L. Fowler Ed., Part I, p. 179,
Interscience Pub. Inc., New York (1960).

7. W. D. Allen, A. T. G. Ferguson and N. Roberts,
Proc. Phys. Soc. (London) 68 A, 650 (1955).

8. W. D. Allen and A. T. G. Ferguson, Proc. Phys. Soc.
(London) 70 A, 639 (1957).

9. L. Cranberg and L. Rosen, "Nuclear Spectroscopy,"
Fay Ajzenberg-Selove Ed., Part A, p. 358, Academic
Press, New York (1960).

10. H. W. Brock and C. E. Anderson, Rev. Sci. Instr.
3J1, 1063 (1960).

11. C. H. Johnson, "Fast Neutron Physics," J. B. Marion
and J. L. Fowler Ed., p. 247, Interscience Pub.
Inc., New York (1960).

12. Temple Love and R. B. Murray, IRE. Trans. Nuclear
Sci., NS-8, 91 (1961).












REFERENCES (Cont'd)


13. W. H. Jordan, Nucleonics 20, 50 (1962).

14. M. L. Goldberger and F. Seitz, Phys. Rev. 71,
294 (1947).

15. F. G. P. Seidl, D. J. Hughes, H. Palevsky, J. S.
Levin, W. Y. Kato and N. G. Sjostrand, Phys. Rev.
95, 476 (1954).

16. R. Batchelor and C. C. Morrison, "Fast Neutron
Physics," J. B. Marion and J. L. Fowler Ed., p.
413, Interscience Pub. Inc., New York (1960).

L 17. J. M. Robson, Phys. Rev. 83, 349 (1951).

-.18. National Bureau of Standards, "Tables for the
Analysis of Beta Spectra," Appl. Math. Ser. 13,
(1952).

I19. Warren B. Boast, "Principles of Electric and
Magnetic Fields," Harper and Brothers, New York
(1948).

20. The Radio Amateur's Handbook, 32 ed., West
Hartford, Conn., (1955).

(21. Elliott Kurzman, "An Energy Analyzer for a Linear
Electron Accelerator," Thesis, University of
Florida, June (1959).

22. W. C. Kaiser, A. J. Mackay and W. W. Managan,
"Logarithmic Spiral Light Pipe for Scintillators,"
ANL-6196, August (1960).

23. J. M. Hollander, I. Perlman and G. T. Seaborg, Rev.
Mod. Phys. 25, 613 (1953).

p 24. J. M. Duncan, "University of Florida Training
Reactor Hazard Summary Report," Florida Engineer-
ing and Industrial Experiment Station, Gainesville,
October (1958).

r 2-25 W. E. Stephens, Phys. Rev. 45, 513 (1934).












REFERENCES (Cont'd)

26. R. J. Howerton, "Tabulated Neutron Cross Sections,"
UCRL-5226, May (1958).

< 27. C. A. Thompson, "Neutron Flux Calculations for a
Graphite Moderated Twenty Percent Enriched Reactor,"
Thesis, University of Florida, Gainesville, January
(1961).

28. C. B. Leffert, "Instruction Manual for the Nuclear
Reactor Codes System MAGNUM," General Motors
Research Staff Report.

29. D. B. McCulloch, "The Application of 'End-on Input'
Electron Multipliers to Ion Beam Detection in the
Mass Spectrometer," AERE GP/R 2279, Harwell, Berk-
shire, England (1957).














BIOGRAPHICAL SKETCH


Ratib A. Karam was born in Minyara, Akkar,

Lebanon, on March 8, 1934. In January, 1954, he came

to the United States, and in February of the same year

he started attending Jacksonville University. At

Jacksonville University he received the Freshman

Chemistry Achievement Award. In June, 1955, he came

to the University of Florida and in June, 1958, he

was granted the degree of Bachelor of Science in

Chemical Engineering. In September, 1958, he started

his graduate work at the Nuclear Engineering Depart-

ment of the University of Florida and in January, 1960,

he received the degree of Master of Science in

Engineering. From January, 1960, until the present he

worked at the Nuclear Engineering Department as an

Assistant in Research part of the time and as a gradu-

ate student the rest of the time.

Mr. Karam is married to the former Bobbie

Epting and they have one son, Ratib A. Karam, Jr. He

is an associate member of the Sigma Xi Society and a

member of the student branch of the American Nuclear

Society.









This dissertation was prepared under the direction
of the chairman of the candidate's supervisory committee
and has been approved by all members of that committee.
It was submitted to the Dean of the College of Engineering
and to the Graduate Council, and was approved as partial
fulfillment of the requirements for the degree of Doctor
of Philosophy.


April 20, 1963




Dean Col6Yge of Engineering




Dean, Graduate School


Supervisory Committee:




Chairman



^S7I& ^U^t


N










Internet Distribution Consent Agreement


In reference to the following dissertation:

AUTHOR: Karam, Ratib
TITLE: Neutron decay spectrometer. (record number: 558938)
PUBLICATION DATE: 1963


I, I&t -fr[' /[ 4/, as copyright holder for the
aforementioned dissertation,\hereby grant specific and limited archive and distribution rights to
the Board of Trustees of the University of Florida and its agents. I authorize the University of
Florida to digitize and distribute the dissertation described above for nonprofit, educational
purposes via the Internet or successive technologies.

This is a non-exclusive grant of permissions for specific off-line and on-line uses for an
indefinite term. Off-line uses shall be limited to those specifically allowed by "Fair Use" as
prescribed by the terms of United States copyright legislation (cf, Title 17, U.S. Code) as well as
to the maintenance and preservation of a digital archive copy. Digitization allows the University
of Florida or its scanning vendor to generate image- and text-based versions as appropriate and
to provide and enhance access using search software.

This grant of permissions prohibits use of the digitized versions for commercial use or profit.


Signature of CopyrigHt Holder


Pointed or Typed Name of Copyright Holder/Licensee


-eronal information blurred



Date of Signature

Please print, sign and return to:
Cathleen Martyniak-C
UF Dissertation Project
Preservation Department
University of Florida Libraries
P.O. Box 117008
Gainesville, FL 32611-7008




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs