A 0-60 ampere current supply and the beta-gamma angular correlation of arsenic-74.

Scholarship at UWindsor

Scholarship at UWindsor

Electronic Theses and Dissertations Theses, Dissertations, and Major Papers

1-1-1963

A 0-60 ampere current supply and the beta-gamma angular

A 0-60 ampere current supply and the beta-gamma angular

correlation of arsenic-74.

correlation of arsenic-74.

University of Windsor

Follow this and additional works at: https://scholar.uwindsor.ca/etd

Recommended Citation Recommended Citation

Colclough, John Delbert, "A 0-60 ampere current supply and the beta-gamma angular correlation of arsenic-74." (1963). Electronic Theses and Dissertations. 6327.

https://scholar.uwindsor.ca/etd/6327

This online database contains the full-text of PhD dissertations and Masters’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license—CC BY-NC-ND (Attribution, Non-Commercial, No Derivative Works). Under this license, works must always be attributed to the copyright holder (original author), cannot be used for any commercial purposes, and may not be altered. Any other use would require the permission of the copyright holder. Students may inquire about withdrawing their dissertation and/or thesis from this database. For additional inquiries, please contact the repository administrator via email

A 0 - 6 0 AMPERE CURRENT SUPPLY

AND THE p - X ANGULAR CORRELATION

OF As

74

BY

JOHN DELBERT COLCLOUGH

A T h e s i s

S u b m i t t e d t o t h e F a c u l t y o f G r a d u a t e S t u d i e s t h r o u g h t h e D e p a r tm e n t o f P h y s i c s i n P a r t i a l F u l f i l l m e n t

o f t h e R e q u i r e m e n t s f o r t h e D e g re e o f M a s t e r o f S c i e n c e a t

A s s u m p tio n U n i v e r s i t y o f W in d so r

W in d s o r , O n t a r i o

1963

INFORMATION TO USERS

The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction.

In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

®

UMI

UMI Microform EC52506 Copyright 2008 by ProQuest LLC.

All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

ProQuest LLC 789 E. Eisenhower Parkway

PO Box 1346 Ann Arbor, Ml 48106-1346

APPROVED:

E. E. H a b ib

F . H o l u j_{u j}

K - . £ : x % $ k S ~ .

R. J . T h i b e r t

7 f > '

ABSTRACT

A 0 - 6 0 amp. c u r r e n t s u p p l y i s d e s c r i b e d . The r a t i o o f t h e

o u t p u t r m s . r i p p l e c u r r e n t t o t h e d c . o u t p u t c u r r e n t i s o f t h e o r d e r o f

10" L. The o u t p u t c u r r e n t d o e s n o t d r i f t f o r a l l p r a c t i c a l p u r p o s e s and

c h a n g e s l e s s t h a n

0

01

1

0

t h e room t e m p e r a t u r e c h a n g e s by 10 C°. A " f a s t - s l o w " B e l l , Graham and

P e t c h c o i n c i d e n c e c i r c u i t i s d e s c r i b e d and c i r c u i t d i a g r a m s a r e g i v e n

f o r t h e t r a n s i s t o r i z e d " f a s t " u n i t . T h i s e q u ip m e n t was u s e d i n c o n ­

j u n c t i o n w i t h t h e G erholm c o i n c i d e n c e s p e c t r o m e t e r t o s t u d y t h e

a n g u l a r c o r r e l a t i o n b e tw e e n t h e 0 . 9 3 mev. p o s i t r o n g r o u p and t h e s u b s e q u e n t

600 k e v . gamma r a y o f t h e d e c a y A s ^ ---= t»G e^. The m e a s u r e d ^

c o e f f i c i e n t s a t e n e r g i e s o f W = 1 . 8 , 2 . 0 , 2 . 2 , 2 . 4 and 2 . 6 ( r e l a t i v i s t i c

u n i t s ) a r e :

w A

1 . 8 0 . 0 4 3 7 0 . 0 0 5 5

2 . 0 0 . 0 0 4 5 0 . 0 0 0 5 1

2 . 2 - 0 . 0 3 6 5 0 . 0 0 7 2

2 . 4 - 0 . 0 2 4 0 . 0 0 9 2

2 . 6 - 0 . 1 6 8 0 . 1 2 3

C o r r e c t i o n s w e r e made f o r s c a t t e r i n g o f t h e 511 k e v . a n n i h i l a t i o n gammas

a n d f o r t h e c h a n g e i n t h e 511 p e a k h e i g h t w i t h r e s p e c t t o t h e 600 k e v .

p e a k h e i g h t when t h e s c i n t i l l a t i o n s p e c t r o m e t e r was r o t a t e d . The s m a l l

a n i s o t r o p y i n d i c a t e s t h a t t h e r e i s no s t r o n g K o f j s e l e c t i o n r u l e t o

r e d u c e t h e c o n t r i b u t i o n f o r m a t r i x e l e m e n t s o t h e r t h a n B i j .

l i

ACKNOWLEDGEMENTS

I would lik e to express my appreciation to Dr. E.E. Habib

for h is guidance and in stru ctio n throughout th is work.

My thanks goes to Mr. W. Grewe for the part he played in

the construction of the current supply.

The a ssista n c e o f Mr. R.H. Young

in preparing the source and recording the data is a lso acknowledged.

I

would lik e to thank Miss Lee Latter for typing the manuscript.

1 am

indebted to the National Research Council for fin a n c ia l support in the

form of a bursary.

ABSTRACT

i i

ACKNOWLEDGEMENTS

i i i

CHAPTER I BETA RAY SPECTROMETERS

i)

Introduction

i

i i )

General P roperties of Magnetic Spectrometers

2

i i i )

Ring Focus and B a ffle s

3

iv )

Response of a Spectrometer to a Monoergic Beam

4

v)

Response of a Spectrometer to a Continuous D istrib u tio n

6

v i)

Lens Spectrometers

6

v i i )

The Gerholm Instrument

9

CHAPTER II

^ ANGULAR CORRELATIONS

i )

Introduction

13

i i )

S e le c tio n Rule E ffect

15

i i i )

R elations Between X and Y under the m odified B ij

20

Approximation

\

iv )

C alculation of

( ^

)

23

CHAPTER I I I THE CURRENT SUPPLIES

i)

Introduction

25

i i )

The Reference Supplies

25

i i i )

The Fast Feedback System

30

iv )

The Servo System

30

v)

The Drive Mechanism

32

v i)

The Local Power Supplies

33

v i i )

Construction of the Current Supply

35

v i i i )

T ests on the Current Supply

36

CHAPTER IV THE COINCIDENCE METHOD

i)

Introduction

40

i i )

e-

Coincidences

40

i i i )

e -e Coincidences

42

iv )

Coincidences

46

v ) D e s c r i p t i o n o f o u r F a s t C o i n c i d e n c e C i r c u i t

46

v i)

Adjustment of the "Fast-Slow" Coincidence C ircu it

47

CHAPTER V THE As74 EXPERIMENT

i )

Introduction

49

i i )

Procedure

49

iv

I l l )

I n te r p r e t a t i o n o f R e su lts

52

CONCLUSION

55

BIBLIOGRAPHY

57

v

TABLE NO.

PAGE NO.

I

F i r s t Forbidden M atrix Elements

18

I I

The A

C o e f f ic ie n ts

54

v i

L I S T OF ILLUSTRATIONS

l . l

A Response Curve

3

1.2

Lens Spectrom eter B a ffle s

4

1.3

Short Lens F ie ld Form

9

1.4a

Angular C o rre la tio n Spectrom eter

11

1.4b

E le c tro n -E le c tro n Spectrom eter

11

1.5

F ie ld Form of th e Gerholm Spectrom eter

12

2.1

2 " ( ^ ) 2 + ( ^ ) O f Decay Scheme

21

3.1

Block Diagram of Power Supply

26

3.2

R eference S upplies

27

3.3

Power B ooster

28

3 .4

Servo 8ystam

31

3.5

Schematic of Scanning Mechanism

33

3 .6

Local Power S upplies

34

3.7

n Ganged Zener Diodes

29

3.8

Thorium Lines

37

3.9

Log

v s. D ial

38

4.1

Simple Decay Scheme

40

4 .2

Complex Decay Scheme

41

4.3

B e ll, Graham and P atch "Fast-Slow " Coincidence C ir c u it

43

4 .4

The F a st C irc u it

44

4.5

Prompt Coincidence Curve

45

4.6

Diode Bias Curve

48

5.1

Decay Scheme of A s ^

50

5.2

The 511 kev. and 600 kev, Photopeake

51

v i i

BETA RAY SPECTROMETERS

(1) In tro d u c tio n

Magnetic beta ray spectrometers are used e x te n siv e ly to

analyse complex nuclear sp ectra .

They may be c la s s i f i e d in to two basic

ty p es, the f l a t and the h e lic a l spectrom eter.

In the f l a t type the

magnetic lin e s of force are mainly in the d ir e c tio n perpendicular to

the e lectro n paths whereas in the h e lic a l instrument the lin e s of force

are mainly in the same d ir e c tio n as the e lectro n paths.

t h is type.

One wishes to have a maximum lum inosity (source area x

transm ission) w hile at the same time achieve a maximum energy

r e so lu tio n .

These are, however, m utually c o n flic tin g requirements.

Increasing the lum inosity u su a lly r e s u lts in a decrease of the

r e so lu tio n and v ic e versa.

Problems a lso a r ise regarding d etector

V

d esig n , f ie ld shapes and power requirements.

O rig in a lly the f l a t spectrometers focussed electro n s only

in one plane w hile the len s spectrom eters were space fo cu ssin g .

Today,

however, nearly a l l f l a t types being used are space fo cu ssin g .

This is

^

is the d istan ce to the a x is of symmetry.

This f l a t spectrometer

is easy to construct and to adjust to a high r e so lu tio n .

The

trans-There a re many problems involved w ith sp ectro m eters of

achieved by shaping the transverse f i e l d to vary as

where

m ission can be made high (

) and the source and d etecto r

problems are easy to s o lv e .

1

2

( i i ) G e n e r a l P r o p e r t i e s o f M a g n e t i c S p e c t r o m e t e r s

The e q u a t i o n o f m o t i o n o f an e l e c t r o n m oving i n a p l a n e

p e r p e n d i c u l a r t o a u n i f o r m m a g n e t i c f i e l d i s g i v e n b y :

w h e r e

=r r e s t m ass o f t h e e l e c t r o n

\ / .= v e l o c i t y o f t h e e l e c t r o n

^ 22. r a d i u s o f e l e c t r o n o r b i t

The momentum c a n be e x p r e s s e d , u s i n g ( 1 ) , a s :

I p = j w \ \J “

^

C

^

I t i s t h e r e f o r e c o n v e n i e n t i n e x p e r i m e n t a l w o rk t o e x p r e s s

t h e momentum i n t e r m s o f i t s f t ^ ( g a u s s - c m . ) v a l u e . The

c o r r e s p o n d i n g e n e r g i e s c a n be c a l c u l a t e d d i r e c t l y o r o b t a i n e d fro m

t a b l e s . The r e l a t i o n ( 2 ) i n d i c a t e s t h a t i n t h e f l a t s p e c t r o m e t e r ,

w h e r e ^ i s c o n s t a n t f o r a l l e n e r g i e s a n d t h e f i e l d u n i f o r m ,

t h e r e i s a l i n e a r r e l a t i o n s h i p b e tw e e n t h e momentum f o c u s s e d a n d t h e

a n a l y s i n g f i e l d . A l t h o u g h m o s t o t h e r s p e c t r o m e t e r s do n o t h a v e c o n s t a n t

f i e l d s o v e r t h e e n t i r e t r a j e c t o r y , t h e y d o , h o w e v e r , u n d e r t h e

c o n d i t i o n s o f f i x e d s o u r c e , d e t e c t o r a n d b a f f l e p o s i t i o n s , e x h i b i t a

l i n e a r r e l a t i o n s h i p b e tw e e n t h e f i e l d a t a n y one p o i n t a n d t h e

momentum of the electro n s focussed.

This is a lso co n d itio n a l upon the

shape of the f i e l d remaining the same as the f ie ld B v a r ie s.

The transm ission

i*)

of a spectrometer is defined as the

fr a c tio n of the electro n s of momentum

p

em itted from the source

which arrive at the d etecto r when the instrument is focussed on

.

The r e so lu tio n of a spectrometer is defined with resp ect to i t s response

to a source of monoergic e le c tr o n s .

Response curves of Figure 1.1 are

obtained.

Figure 1.1

where A p

The r e so lu tio n

^

is defined as

is the momentum spread at h a lf maximum and

is the momentum at

the peak counting r a te .

Since A ^

^ P®

where K is a con stan t,

R is independent of PD the r a tio R/u) is c a lle d the figu re of m erit and

va ries from 20 in the older instruments to

. I

for many of the

v

b est modern ones.

( i i i ) Ring Focus and B a ffle s

In a h e lic a l (le n s ) type spectrometer the e le c tr o n image

o f the source at the d etecto r has u su a lly a large sph erical aberration.

A p o sitio n of minimum sp h erica l aberration g en erally occurs before the

electro n s cross the symmetry a x is .

This is c a lle d the ring focus and

a great improvement in performance is obtained by p lacing d efin in g

b a ffle s at t h is point rather than at the d e te c to r .

Hubert(1952) has

4

shown the combination of b a f f le s , as shown by the s o lid lin e s of

Figure 1 .2 , leads to an improvement in r e so lu tio n while r eta in in g the

same transm ission as other b a ffle systems represented by the dotted

lin e s in Figure 1 .2 .

The combination of diaphrams

, D

,

d efin e both

the s o lid angle and the momentum band.

The diaphrams

can be

replaced by a s in g le co n ica l b a ffle and Dg by a moveable b a f f le .

The

gap between th e moveable b a f f le and th e c o n ic a l b a f f le d e fin e s both

th e tra n sm issio n and r e s o lu tio n of th e in stru m en t.

This lead s to a

s im p lifie d adjustm ent over o th e r systems and is th e type used in the

f i r s t Gerholm in stru m e n ts .

(iv ) Response of a Spectrometer to a Monoeraic Beam

d eductions as th e q u a n tity

)r\

to be d e fin e d in t h i s s e c tio n .

We s t a r t

w ith a monoergic e le c tr o n beam of f i n i t e an g u lar w idth emerging from

a f i n i t e s o u rc e .

We wish to d e s c rib e th e response of a sp e c tro m e te r to

F igure 1.2

Lens S pectrom eter B a ffle s

The r e s o lu tio n

R i s not

as convenient fo r making q u a l i t a t i v e

t h i s beam.

According to Gerholm (1956) th e fu n c tio n

^ ( , jji * ^ Y is

p r o b a b ility of rec o rd in g an e le c tr o n of momentum

^

when th e instrum ent

is s e t to focus e le c tr o n s of momentum p .

I f

^

p

then

It can

be

shown th at

is independent

o f

and

P

W elting

jm

we have:

V = , u .

P

o o

f l C t . r W = =

d - I

This d e fin e s

which Is c o n s ta n t f o r a given sp ectro m eter depending

only on th e so u rc e , d e te c to r and b a f f l e geometry.

I f

is th e i n t e n s i t y o f th e monoergic source o f mean momentum

^ th en th e co u n tin g r a t e

a t a momentum s e t t i n g o f ^

w i l l

• » V I C p ) =

The peak co u n tin g r a t e is

^

‘

I f a p ^o t i s mac*e °*

V)(P) VS.

P

th e a re a under th e peak i s ;

-= w a *

Now

van ish es U nless p ^

and th u s th e e f f e c tiv e

range of in te g r a tio n is sm a ll. T h erefo re

p

remains roughly c o n sta n t

and may be moved o u tsid e th e in te g r a l s ig n .

T h e re fo re

:-oo

W I

Area under

peak

p

Thus:

s

Area under peak

Peak cou n tin g r a t e

In sp e c tro m e ters where th e peak p r o f i l e is sym m etric, Y\ w i l l be very

n e a rly equal to th e r e s o lu tio n ^ .

This c o n d itio n i s s a t i s f i e d fo r

th e Gerholm Instrum ent u sin g th e Hubert b a f f l e system .

( v ) R e s p o n s e o f a S p e c t r o m e t e r t o a C o n t i n u o u s D i s t r i b u t i o n

6

F o r a beam o f e l e c t r o n s o f c o n t i n u o u s d i s t r i b u t i o n we

i n t r o d u c e a s h a p e f a c t o r w h ic h i s t h e p r o b a b i l i t y p e r

e l e c t r o n , t h a t t h e momentum w i l l l i e i n a u n i t i n t e r v a l o f momentum

a b o u t ^

W ith t h e s p e c t r o m e t e r f o c u s s e d a t t h e c o u n t i n g r a t e

60

i s

\

Hi)

M

i>

S i n c e 4 ( ^ v a r i e s s l o w l y w i t h r e s p e c t t o J ^

p u t < H

0

Then t h e c o u n t i n g r a t e becomes r. 60

6

P l o t t i n g v s t h e a r e a u n d e r t h e c u r v e i s

T h e s e f o r m u l a s w i l l e n a b l e u s t o make q u a n t i t a t i v e a n a l y s i s on t h e

o b s e r v e d s p e c t r a .

( v i ) Lens S p e c t r o m e t e r s

I t i s e a s i l y s e e n t h a t a n e l e c t r o n m oving i n a u n i f o r m

m a g n e t i c f i e l d p e r p e n d i c u l a r t o i t w i l l d e s c r i b e a c i r c u l a r o r b i t . I f

i t a l s o h a s a v e l o c i t y com p o n e n t i n t h e d i r e c t i o n o f t h e f i e l d , t h e n

i t w i l l d e s c r i b e a h e l i c a l p a t h . Such i s t h e s i t u a t i o n i n a l o n g l e n s

s p e c t r o m e t e r . The e l e c t r o n r o t a t e s t h r o u g h a n a n g l e o f 3 6 0 ° b e f o r e

r e t u r n i n g t o t h e sym m etry a x i s w h e re t h e d e t e c t o r i s p l a c e d . T h i s i s

t h e s i m p l e s t s i t u a t i o n t o v i s u a l i z e a s f a r a s l e n s s p e c t r o m e t e r s a r e

c o n c e r n e d . The e q u a t i o n s o f m o t i o n s f o r a hom ogeneous f i e l d a r e

a c c o r d i n g t o S i e g b a h n ( 1 9 5 5 ) :

z

HUTW

The

s o lu t i o n f o r

r ( z \ is

t " z s |^ ) S U \a- b t *5 U a. §>

where

^

b *

^

is th e angle of emission of the e l e c t r o n w ith r e s p e c t

t o the

5? a x i s .

When the p aths are drawn in the

2 plan© i t is

found t h a t

the

paths i n t e r s e c t each o th er r a t h e r c l o s e ly w ith in a

c e r t a i n re g io n ,

The c o n d itio n f o r such a r in g focus is given by

A r

M W

• t i t i # 4 4 f “ 4 r t i - i ^

This leads to th e c o n d itio n

= ***“ ^ o c \

To c a l c u l a t e the r e s o lv in g power the width of th e image a t

the

r in g focus is expressed in terms of i t s

a y

v alu e .

The f i r s t

o rd e r e f f e c t is gsero

we have p laced the rin g focus a t the p o in t where

=

&

The second o rder c o n t r ib u t i o n is

A

-Z i v

*ss,

■+«

o th er te rm s ,

fcx

o c

h a l f the opening angle a t the source,

S u b s t i t u t i n g

& r s r b { & < ) $ V a a ^ I B 4 c & a V 4 ' Su a o t \

in we get

% W \

The r e s o lv in g power is

8

Since

'

»>.

t

.

A r _ 1 L M b ?

/ B « )

then

V

J

k _ ^

1

S u b stitu tin g in we get

* — & * “

( 3 -4 e.o

S ^

R

The term in brackets has a broad minimum at 45 .

However,

due to p r a c tic a l con siderations such as source dimensions and c o i l s iz e

o

i t is found the optimum o v e r a ll angle of em ission is 30 .

The main

disadvantage with the long lens uniform f ie ld spectrometer is due to the

spreading of the e lectro n beam a fte r passing the b a f f le s .

This requires

a rather large d etecto r thereby introducing a high background count r a te .

An Improved design due to Siegbahn (1946) uses a fieldform which is con­

cave upwards.

S la t is and Siegbahn (1949) experimented with d iffe r e n t

f i e l d gradients and found a pronounced increase in transm ission at a

ce r ta in strong f ie ld grad ien t.

In th is type the electro n rays cross

each other at the centre and gather again at the d etecto r.

This allows

a sm aller counter to be used while achieving a 3 per cent transm ission.

The short len s was developed before the long le n s.

Busch

(1927) pointed out the analogy between e le c tr o n op tics of magnetic

len ses and ordinary lig h t o p tic s .

He ca lcu la ted the fo c a l length for

•t <»

a b o rt lenaes

(

_

*

C

J ,

T “ q I * * ) ' L 2

where

> °) *-s the f i e l d component perpendicular to the len s along

the a x is .

The f ie ld form of the short len s is drawn in Figure 1 .3 .

Typical p h y sica l dimensions would be 15 cm long and 15 cm diameter.

Resolving powers of 2 .5 per cent and transm issions of 0.5% are u su a lly

obtained.

3 o

* \ s * \ o

o

i

F i g u r e 1 . 3 S h o r t Lens F i e l d Form

( v i i ) The G erholm I n s t r u m e n t

I n t h i s i n s t r u m e n t t h e two h a l v e s ( s e e F i g u r e 1 . 4 b ) a r e

m a g n e t i c a l l y i n d e p e n d e n t o f e a c h o t h e r . T h e r e f o r e , m a g n e t i c f i e l d s

o f d i f f e r e n t s t r e n g t h s c a n be u s e d i n e a c h h a l f , t h u s p r o v i d i n g t h e

o p p o r t u n i t y t o f o c u s s i m u l t a n e o u s l y e l e c t r o n s o f two d i f f e r e n t e n e r g i e s .

The f i e l d f o r m , a s shown i n F i g u r e 1 . 5 m e a s u r e d a l o n g t h e a x i s i n c r e a s e s

r o u g h l y l i n e a r l y w i t h i n c r e a s i n g d i s t a n c e . T h e o r e t i c a l ( L i n d g r e n ) a s

w e l l a s e x p e r i m e n t a l s t u d i e s o f t h e t r i a n g u l a r f i e l d s h a p e show t h a t

i t g i v e s a f a v o u r a b l e h i g h l u m i n o s i t y ( s o u r c e a r e a x t r a n s m i s s i o n ) w h ic h

c o m p e n s a t e s f o r t h e s m a l l g e o m e t r i c a l d i m e n s i o n s o f t h e i n s t r u m e n t s . A

h i g h t r a n s m i s s i o n i s v e r y i m p o r t a n t i n c o i n c i d e n c e e x p e r i m e n t s . S o u r c e s

up t o 5 mm i n d i a m e t e r c a n be u s e d w i t h o u t s a c r i f i c e i n r e s o l u t i o n w h ic h

i s 3 p e r c e n t a t a n e f f e c t i v e s o l i d a n g l e o f 3 p e r c e n t . I f i t i s a l s o

p o s s i b l e t o c o n v e r t t h e i n s t r u m e n t i n t o an e l e c t r o n - g a m m a a n g u l a r

c o r r e l a t i o n s p e c t r o m e t e r . I n t h i s s e t ( F i g u r e 1 . 4 a ) up t h e a v e r a g e a n g l e

10

of em ission is reduced to reduce the co rrectio n factor for f i n i t e aperture

angle.

This r e s u lts in a lower transm ission.

Typical fig u res for a 5 mm

source a r e :r e so lu tio n 3 per ce n t, transm ission 1.8 per cen t.

The gamma spectrometer may be rotated between the 90° and the

270° p o s itio n s .

Adjustments are provided so that the axis of ro ta tio n

p asses through the source p o s itio n .

The gain of the p h otom u ltip lier is

a ffe c te d by the extern al magnetic f ie ld of the beta le n s.

The peak

p o sitio n of the 511 kev. a n n ih ila tio n gamma decreases 2 .5 channels (25

k ev .) on the k ick sorter when the spectrometer is rotated from the 180°

to the 90° p o sitio n .

S ‘ SOURCE C -C R Y ST A L L C - U O T C U GHT COLLECTOR P M -F H O T O M U .T n .IE R

B i-C N T « M C £ M F f l t 8 ,'E X IT B A FFLE

F i g u r e l . i i b E l e c t r o n - E l e c t r o n S p e c t r o m e t e r

270*

PH

F i g u r e 1 An g u l a r C o r r e l a t i o n S p e c t r o m e t e r

FIELD STRENGTH

ARBITRARY UNITS

500-1

aooH

300

200

100H

SOURCE

40 cm

■

H

F i g u r e 1 . 5 F i e l d Form o f t h e G e rh o lm I n s t r u m e n t

p - )f ANGULAR CORRELATIONS

( i ) I n t r o d u c t i o n

p - ^ a n g u l a r c o r r e l a t i o n s h a v e two m a in a r e a s o f a p p l i c a t i o n .

One i s t o t e s t t h e f u n d a m e n t a l law s o f n a t u r e s u c h a s p a r i t y n o n c o n s e r v a ­

t i o n and t h e o t h e r i s t o s t u d y n u c l e a r s t r u c t u r e . The f o r m u l a s f o r t h e

p - ^ a n g u l a r c o r r e l a t i o n a r e e x p r e s s e d i n t e r m s o f c e r t a i n n u c l e a r m a t r i x

e l e m e n t s . We g a i n i n s i g h t i n t o t h e n u c l e a r s t r u c t u r e by kno w in g t h e

r e l a t i v e m a g n i t u d e s o f t h e n u c l e a r m a t r i x e l e m e n t s r e s p o n s i b l e f o r t h e

b e t a t r a n s i t i o n .

The f i r s t a r t i c l e on J3- ^ a n g u l a r c o r r e l a t i o n t h e o r y was

p u b l i s h e d by F a l k o f f a n d U h l e n b e c k ( 1 9 5 0 ) . S i n c e t h e n a g r e a t many

e x p e r i m e n t a l a n d t h e o r e t i c a l w orks h a v e b e e n p e r f o r m e d . N o t a b l e

a c c o m p l i s h m e n t s a r e t h e a n a l y s i s o f S b l 2 4 ( H a r t w i g a n d S c h o p p e r ) a n d P r * ^

( S t e f f e n ) . K o n o p i n s k i ( 1 9 5 9 ) h a s w r i t t e n a r e v i e w a r t i c l e on a l l o w e d

t r a n s i t i o n s a n d W e i d e n m u l l e r ( 1 9 6 1 ) h a s p u b l i s h e d an a r t i c l e on f i r s t

f o r b i d d e n t r a n s i t i o n s . An e x c e l l e n t s u r v e y o f t h e l i t e r a t u r e may b e f o u n d

i n h i s p a p e r . K o t a n i ( 1 9 5 9 ) h a s a l s o w r i t t e n a n a r t i c l e on t h e d e v i a t i o n s

fro m t h e ^ a p p r o x i m a t i o n .

When two p a r t i c l e s a r e e m i t t e d s i m u l t a n e o u s l y fro m a n u c l e u s

a n a n g u l a r c o r r e l a t i o n b e tw e e n t h e i r d i r e c t i o n s o f e m i s s i o n c a n i n

p r i n c i p l e be o b t a i n e d . The fo rm o f t h e c o r r e l a t i o n f u n c t i o n W ( © )

d e p e n d s o n l y on t h e a n g u l a r momenta o f t h e n u c l e a r s t a t e s i n v o l v e d and

o f t h e o u t g o i n g p a r t i c l e s . I t i s o f t h e form W ( & ) = l+AgP^COS

13

14

f o r f i r s t fo rb id d en t r a n s i t i o n s .

To determ ine

t h e o r e t i c a l l y

requires

more d e ta ile d in fo rm atio n concerning th e in te r a c tio n s d es­

c r ib in g th e decay p ro c e s s .

A ll allow ed t r a n s i t i o n s have is o tr o p ic

B- a n g u la r d i s t r i b u t i o n s and i f th e shape o f an energy spectrum is

s t r i c t l y id e n t i c a l to t h a t f o r an allow ed case then th e d i s t r i b u t i o n w ill

be a ls o i s o t r o p i c .

Many nonunique f i r s t fo rb id d en t r a n s i t i o n s , A3* ^ ®

j

have allow ed shape b e ta ra y energy s p e c tr a . The

^

approxim ation is a p p lic a b le to t h i s c a s e .

In t h i s approxim ation

th e coulomb energy o f th e e le c tr o n a t th e n u c le a r ra d iu s is la r g e r than

th e t o t a l energy o f th e e le c tr o n . M athem atically we have

where

Wft ■ m ax.^ - r a y energy

R a n u c le a r ra d iu s

oL * f in e s tr u c t u r e c o n sta n t

2

* no. o f p ro to n s

The m easurable q u a n titie s in th e

^

approxim ation do n o t

g iv e us enough in fo rm atio n t o determ ine th e n u c le a r m a trix elem ents

u n iq u e ly .

He f in d , however, th a t v a lu a b le r e la tio n s , among th e n u c le a r

m a trix elem ents may be gain ed by c o n sid e rin g nonunique f i r s t fo rb id d en

t r a n s i t i o n s which show d e v ia tio n s from th e ^ approxim ation.

The unique

f i r s t fo rb id d en t r a n s i t i o n s , ^ A T

s .

JL ^ have a unique energy spectrum .

T here i s only one nuclear matrix element contributing to the transition

i . e . th e B*. term .

In t h i s case both th e energy and an g u la r dependence

•*)

<

o f a l l aieasurable q u a n titie s a re determ ined.

In the nonunique t r a n s i ­

t io n s showing d e v ia tio n s from th e ^ approxim ation th e re is a p o s s i b i l i t y

t h a t th e c o n tr ib u tio n from m a trix elem ents o th e r than th e B ; *

term is

s m a l l . I n t h i s c a s e we e x p e c t t h e n o n u n i q u e t r a n s i t i o n s t o b e h a v e

s i m i l a r l y t o t h e u n i q u e t r a n s i t i o n s . To e x p l a i n t h i s s i t u a t i o n a

s e l e c t i o n r u l e i s i n t r o d u c e d w h ic h i n h i b i t s c o n t r i b u t i o n s fro m m a t r i x

e l e m e n t s o t h e r t h a n \ © » ' .

J

( i i ) S e l e c t i o n R u le E f f e c t

The H a m i l t o n i a n d e s c r i b i n g t h e weak i n t e r a c t i o n i n ^ d e c a y

i s o f t h e fo rm

= ^OOl T+ < +

o ' o t

T . T - l U F - r ^

w h e r e a n d a r e t h e n u c l e o n a n d l e p t o n p o s i t i o n v e c t o r s . i s

t h e o p e r a t o r i n i s p i n s p a c e w h ic h t r a n s f o r m s a n e u t r o n t o a p r o t o n and

„ L.

H r . i s t h e o p e r a t o r , i n i s p i n s p a c e f o r l e p t o n s , w h ic h t r a n s f o r m s

+

a n e u t r i n o i n t o a n e g a t r o n . The H e r m i t i a n c o n j u g a t e s 'X a n d T _

make t h e r e v e r s e t r a n s f o r m a t i o n s . O a n d O . ^ a r e o p e r a t o r s w h ic h

a c t on t h e n u c l e o n and l e p t o n wave f u n c t i o n s r e s p e c t i v e l y . We w o u ld

l i k e t o know t h e fo rm o f O a n d C)^_ .

The H a m i l t o n i a n , , m u s t be i n v a r i a n t u n d e r L o r e n t z

t r a n s f o r m a t i o n s , i n c l u d i n g r o t a t i o n s a n d t r a n s l a t i o n s o f t h e a x e s .

C o n s e r v a t i o n o f a n g u l a r momentum i s a l s o r e q u i r e d . T h e s e r e s t r i c t i o n s

i n d i c a t e t h a t t h e H a m i l t o n i a n m u s t b e a l i n e a r c o m b i n a t i o n o f s c a l a r s

a n d p s e u d o s c a l a r s . The s c a l a r s a n d p s e u d o s c a l a r s c a n be c o n s t r u c t e d

fro m t h e l e p t o n a n d n u c l e o n wave f u n c t i o n s i n f i v e d i f f e r e n t w a y s . The

wave f u n c t i o n s a r e m u l t i p l i e d by 4 4 m a t r i c i e s w h ic h a r e c o n s t r u c t e d

from five independent matricies. There are two sets in common use. One

s e t i s oC cL k ? ^ and t h e o t h e r

c o r r e s p o n d i n g s e t i s An i m p o r t a n t p r o d u c t

m a t r i x i s K ^ Z — X ^ i

*^3

T h e r e a r e a l s o t h r e e p r o d u c t s ~ QC sr . As a n e x a m p le c o n s i d e r

16

t h e v e c t o r i n t e r a c t i o n . The f o u r q u a n t i t i e s ( 4 > ^ h ’Cm H- V . , „

^

f o rm a f o u r - v e c t o r . The s c a l a r p r o d u c t o f two s u c h v e c t o r s i s i n v a r i a n t

I

^

a n d h e n c e a p o s s i b l e c o m b i n a t i o n o f O s a n d O t S l e a d s t o

( . 3 *

w h ic h i s a s c a l a r m a t r i x e l e m e n t .

4

a n d i n i t i a l n u c l e o n wave f u n c t i o n s r e s p e c t i v e l y w h i l e a n d

d e n o t e t h e i n i t i a l a n d f i n a l l e p t o n wave f u n c t i o n s r e s p e c t i v e l y . A

p s e u d o s c a l a r i s t h e " s c a l a r " p r o d u c t o f a v e c t o r a n d a p s e u d o v e c t o r . A

s u i t a b l e p s e u d o v e c t o r i s ^ if . Hence a

p o s s i b l e i n t e r a c t i o n m a t r i x i s

£ (.a* K*Mi€cK‘h*',

t* < c , I is)

T h i s i s c a l l e d t h e v e c t o r i n t e r a c t i o n . The p s e u d o v e c t o r i n t e r a c t i o n i s

g i v e n by

£ ( i t

c ' £ / i )

(

The C a n d C a r e c o u p l i n g c o n s t a n t s .

The f i v e p o s s i b l e f o rm s o f i n t e r a c t i o n s a r e known a s t h e

s c a l a r , t h e p s e u d o s c a l a r , t h e v e c t o r , t h e a x i a l - v e c t o r , a n d t h e t e n s o r

i n t e r a c t i o n . I t h a s b e e n e s t a b l i s h e d ( W e i d e n m u l l e r ) t h a t t h e v e c t o r and

a x i a l - v e c t o r i n t e r a c t i o n s a r e r e s p o n s i b l e f o r t h e b e t a d e c a y .

F o l l o w i n g W e id e n m u l l e r (1 9 6 1 ) t h e H a m i l t o n i a n f o r t h e V-A

( v e c t o r - - a x i a l - v e c t o r ) i n t e r a c t i o n i s

U r “ ?

^

v

^

r

~A

\

* r * t ' y

The v a r i o u s f o r b i d d e n m a t r i x e l e m e n t s a r e f o u n d by e x p a n d i n g t h e s e c o n d

s q u a r e b r a c k e t a n d t a k i n g i n t o a c c o u n t n u c l e a r m a t r i x e l e m e n t s o f t h e

o r d e r v / c .

F o r t h e v e c t o r i n t e r a c t i o n t h e f i r s t s q u a r e b r a c k e t g i v e s

r i s e t o m a t r i x e l e m e n t s ^ I a n d ^ oC . H e re oC i s o f t h e o r d e r

o f v / c a n d h a s t h e s e l e c t i o n r u l e A 3 r o I ( h a o -~t> c> ) ^ / ,

w h i c h i s f o r b i d d e n w h i l e § I i s an a l l o w e d m a t r i x e l e m e n t . I n t h e

e x p a n s i o n o f t h e s e c o n d b r a c k e t we k e e p t e r m s o f t h e o r d e r

gF

kF

w h e re g a n d k a r e t h e n e u t r i n o a n d e l e c t r o n momentum r e s p e c t i v e l y . T h u s ,

t h e m a t r i x e l e m e n t I becom es w h ic h o b e y s t h e s e l e c t i o n r u l e f o r

f i r s t f o r b i d d e n d e c a y . C o r r e s p o n d i n g t e r m s o f o r d e r

F

e l e m e n t §o(. w o u ld l e a d t o s e c o n d f o r b i d d e n m a t r i x e l e m e n t s . T h u s ,

t h e two f o r b i d d e n m a t r i x e l e m e n t s o r i g i n a t i n g from t h e v e c t o r i n t e r a c t i o n

a r e a n d § h .

The a x i a l v e c t o r i n t e r a c t i o n c o n s i s t s o f two p a r t s ,

^ 6

The <> i s a n a l l o w e d m a t r i x e l e m e n t . K e e p in g t e r m s o f t h e

o r d e r g r a n d k r i n t h e s e c o n d b r a c k e t l e a d s t o t h r e e f i r s t f o r b i d d e n

m a t r i x e l e m e n t s fro m t h e J 6> m a t r i x .

T h e s e a r e :

j

S c * * ? ]

a n d

S

=

S

£ ^

^

"

" S* i U ' ?^ l

^ i s a l r e a d y f i r s t f o r b i d d e n b e i n g o f o r d e r v / c . T h u s , t h e a x i a l

v e c t o r i n t e r a c t i o n g i v e s r i s e t o f o u r f i r s t f o r b i d d e n m a t r i x e l e m e n t s .

The s i x f i r s t f o r b i d d e n m a t r i x e l e m e n t s , w i t h t h e i r s e l e c t i o n r u l e s and

common n o t a t i o n s , a r e g i v e n i n T a b l e 1.

The r a n k

X

TABLE 1

F i r s t F o r b i d d e n M a t r i x E l e m e n ts

Symbol M a t r i x E le m e n t

A

T

AT T

C * \ f c - l r

- \

\ x

- C v \ \r

M ‘ y

•A

- C v U < x .

a

\ * A 6 X *■

-

I

A a

w

W

h A .

C - n \ B : :

O , * \

2.

OWo (_ 0 — * • )

V/*.© ^ V —

1

1 ^ 1 ~

C R U i

e a c h ^ d e c a y h a s t o s a t i s f y

| 3 , , - 3 , |

5 . * 3 ,

- C M

w h e re J

0

d e c a y . I t i s c o n v e n i e n t t o i n t r o d u c e two p a r a m e t e r s i a n d ' Y t

T h e s e a r e d e f i n e d a s f o l l o w s :

y 4

v -V ^ VO

\ o r X - *

VJ ^ ' Sj ^ l U 4 > \ r X - V

T h e s e r e p l a c e t h e r e l a t i v i s t i c n u c l e a r m a t r i x e l e m e n t s ^ a n d >j

Xj l

,

v

=%

> ' X ,

y —

v " f ,

I n t h e ^ a p p r o x i m a t i o n t h e f o l l o w i n g r e l a t i o n i s s a t i s i f e d :

| * . | - | V , | t

> > I w I H

? t ■

U n d e r t h e s e l e c t i o n r u l e e f f e c t we a s k t h a t t h e p a r a m e t e r become o f

t h e same o r d e r a s , o r l a r g e r t h a n , ^ ( a n d ^ . T h i s may b e u n d e r ­

s t o o d i n tw o p o s s i b l e ways d e p e n d i n g on w h ic h n u c l e a r m o d e l i s a p p l i c a b l e .

One i s known a s t h e "K s e l e c t i o n r u l e " w h i l e t h e o t h e r i s t h e " j

s e l e c t i o n r u l e . "

The K f o r b i d d e n n e s s was i n t r o d u c e d b y A l a g a , A l d e r , B ohr and

M o t t e l s o n ( 1 9 5 5 ) . K i s t h e com p o n e n t o f t h e n u c l e a r t o t a l a n g u l a r

momentum J on t h e n u c l e a r a x i s o f s y m m e tr y . The r a n k X m u s t s a t i s f y

r e l a t i o n ( 2 ) a b o v e a s w e l l a s ( 3 ) b e lo w

|

- w , I

fc>\< ^ V i-

K -V v<*

f o r a t r a n s i t i o n

I * . ,

>■"*' ^

20

The r e g i o n s o f a p p l i c a t i o n w h ic h h a v e b e e n e s t a b l i s h e d f o r t h i s m o d el

a r e 150 < A < 1 9 0 a n d A > 2 2 5 .

The j s e l e c t i o n r u l e i s due t o t h e c o n f i g u r a t i o n c h a r a c t e r

o f t h e M a y e r - J e n s e n s h e l l m o d e l . H e re j i s t h e t o t a l a n g u l a r momentum

o f a n u c l e o n i n a s h e l l . F o r j f o r b i d d e n n e s s one c o n s i d e r s n u c l e i i n

t h e r e g i o n 50 - j? ; N ^ 8 2 . I n t h e M a y e r - J e n s e n m o d el n u c l e o n s o u t s i d e

t h e c l o s e d s h e l l ? = N»50 b e l o n g t o t h e h , g , d , d a n d s

s t a t e s . Among t h e s e o n l y t h e h s t a t e h a s odd p a r i t y . S i n c e t h e

f i r s t f o r b i d d e n t r a n s i t i o n s c h a n g e p a r i t y t h e number o f n u c l e o n s w h ic h

o c c u p y t h e h s t a t e h a s t o b e c h a n g e d by one u n i t d u r i n g t h e d e c a y .

T h e r e f o r e , we m u st h a v e a ^ ^ 2 2 . and t h e a v a i l a b l e n u c l e a r m a t r i x

e l e m e n t w i t h N m akes t h e m a j o r c o n t r i b u t i o n . T h u s , i n j

f o r b i d d e n n e s s we h a v e t h e r e l a t i o n s

j f o r b i d d e n n e s s c a n n o t be a p p l i e d w h e re N and Z b e l o n g t o d i f f e r e n t

m a j o r s h e l l s .

M a tu m o to , M o r i t a a n d Yamada ( 1 9 5 5 ; 1958) h a v e s u g g e s t e d

e x a m i n i n g t h e c a s e w h e r e

2

T h i s i s c a l l e d t h e m o d i f i e d a p p r o x i m a t i o n .

( i i i ) R e l a t i o n s B e tw e e n X a n d V u n d e r t h e M o d i f i e d A p p r o x i m a t i o n

We w i l l i n t h i s s e c t i o n c o n s i d e r r e s u l t s o n l y f o r a d e c a y

schem e o f t h e t y p e shown i n F i g u r e 2 . 1 .

I n t h e m o d i f i e d B « * a p p r o x i m a t i o n we n e e d o n l y two p a r a -

m e t e r s . T hey a r e a s f o l l o w s :

X

■v

j L L

j

,

%

R

a n d

^ and a r e s i m i l a r t o a n d '"j d e f i n e d p r e v i o u s l y a n d a r e

t h e r e l a t i v e m a g n i t u d e o f t h e c o n t r i b u t i o n s fro m m a t r i c e s o f r a n k z e r o

a n d one w i t h r e s p e c t t o I n t h e d e c a y schem e o f F i g u r e 2 . 1

o d d - o d d

e v e n - e v e n

F i g u r e 2 . 1 2 " ( ^ ) 2 + ( ^ { ) 0 + D ecay Scheme

t h e b e ta -g a m m a d i r e c t i o n a l c o r r e l a t i o n i s g i v e n a s i n e q u a t i o n (

1

a n i s o t r o p y (M atum oto e t a l . 1 9 6 3 ) .

22

_

[-U V t * +

A l ' w [ i f + Y % M i i i f e V

+

* i ^ » ' }

I f we m e a s u r e 14 ^ a t a c e r t a i n e n e r g y a n d i n s e r t t h i s i n t h e a b o v e

e q u a t i o n we w i l l o b t a i n a r e l a t i o n b e t w e e n

X

^

c i r c l e i n t h e Y p l a n e . I t i s

( x - v . V

+

“ o

.

=

^

Where

v'A,

T

—

_

-^5 ^ 3 -i- ft 4 ^

Y ~ v t /v a . i ; VAJ V_ * _J

\ - - ( r X f . f X

we We w o u ld l i k e t o o b t a i n v a l u e s f o r X an<* ^ • *n p r i n c i p l e

c o u l d o b t a i n X a n d ^ e x p e r i m e n t a l l y fro m two d i f f e r e n t

e x p e r i m e n t s a n d c o m p a re t h e r e s u l t s w i t h t h e o r e t i c a l c a l c u l a t i o n s . The

l a t t e r c a l c u l a t i o n s d o , h o w e v e r , r e q u i r e m ore p r e c i s e k n o w le d g e o f t h e

n u c l e a r r a d i a l wave f u n c t i o n t h a n we h a v e a v a i l a b l e . I n s t e a d we c a n

g e t a s e c o n d r e l a t i o n b e t w e e n X a n d ^ w h ic h i s d e p e n d e n t on t h e

b r a n c h i n g r a t i o (w h ic h c a n b e d e t e r m i n e d e x p e r i m e n t a l l y ) a n d t h e r a t i o

I S

T h i s r a t i o i s d e p e n d e n t on t h e n u c l e a r m o d e l a s su m e d . The s e c o n d r e l a t i o n

i s a g a i n a c i r c l e i n t h e p l a n e a n d i s g i v e n by

R:'

w h e re

<=».

t .

5 a , $c.

( W i ) .

a | a n d a ^ a r e t h e b r a n c h i n g r a t i o s f o r t h e ^ and ^ t r a n s i t i o n s w h i l e

f ^ , ffc , a n d f t ^ a r e t h e i n t e g r a t e d F e rm i f u n c t i o n s f o r ^ d e c a y a n d

t h e c o r r e c t e d i n t e g r a t e d f e r m i f u n c t i o n s f o r ^ a n d ^ d e c a y

r e s p e c t i v e l y . T h e s e a r e g i v e n b y M atum oto e t a l . ( 1 9 6 3 ) . I f X and

h a v e s o l u t i o n s , i . e . i f t h e two c i r c l e s c r o s s e a c h o t h e r , t h e n t h e

a ssu m e d n u c l e a r m o d e l i s r e a l i z e d . I n t h i s w ay, we c a n t e s t e a c h n u c l e a r

s t a t e s , m o d e l t o f i n d t h e c o n f i g u r a t i o n o f t h e ^

c W )

( i v ) C a l c u l a t i o n o f

F o r r o t a t i o n a l e x c i t a t i o n o f t h e c o l l e c t i v e m o d e l ( K s e l e c t i o n

r u l e ) t h e r a t i o i s :

-^ = 1 1 ) 1

T h i s i s c o n s t a n t f o r a l l n u c l e i h a v i n g d e c a y schem es o f F i g u r e 2 . 5

F o r t h e j - j c o u p l i n g s h e l l m o d e l ( j s e l e c t i o n r u l e ) t h e

c a l c u l a t i o n o f M i s m ore d i f f i c u l t . R e s u l t s a r e g i v e n b y M atum oto e t a l .

( 1 9 6 3 ) .

T hey a r e a s f o l l o w s ;

( i ) f o r p r o t o n s e x c i t e d :

(ii) for neutrons excited:

^ V v O ^ 4 - 1 ^ i w , 2 ^ p )

( i ) I n t r o d u c t i o n

Two s o l i d s t a t e 0 - 6 0 amp. c u r r e n t s u p p l i e s h a v e b e e n b u i l t

i n t h i s l a b o r a t o r y t o p r o v i d e c u r r e n t f o r t h e G erholm c o i n c i d e n c e

s p e c t r o m e t e r . The r a t i o o f t h e r m s . r i p p l e c u r r e n t on t h e o u t p u t t o t h e

d c . o u t p u t c u r r e n t i s o f t h e o r d e r o f 10*"*%. The o u t p u t c u r r e n t d o e s n o t

d r i f t f o r a l l p r a c t i c a l p u r p o s e s and c h a n g e s l e s s t h a n

0

01

t h e l i n e v o l t a g e c h a n g e s by 10% o r t h e room t e m p e r a t u r e c h a n g e s by 10

C°

The b l o c k d i a g r a m o f t h e s u p p l y i s shown i n F i g u r e 3 . 1 . T h e r e

a r e two f e e d b a c k s y s t e m s , - t h e f a s t f e e d b a c k s y s t e m , w h ic h c o n t r o l s t h e

c u r r e n t , a n d t h e s e r v o s y s t e m w h ic h c o n t r o l s t h e v a r i a c s s o t h a t t h e r e i s

a lw a y s 3 v o l t s a c r o s s t h e 2N278 s e r i e s r e g u l a t i n g pow er t r a n s i s t o r s .

T h r e e p h a s e 117 v o l t 60 c y c l e p o w e r i s f e d t o t h r e e g a n g e d G e n e r a l R a d io

V a r i a c s . The o u t p u t fro m t h e v a r i a c s g o e s t o a t h r e e p h a s e f u l l wave

r e c t i f i e r . The r e c t i f i e r o u t p u t i s f i l t e r e d by a 1 0 ,0 0 0 u f . c a p a c i t o r .

C u r r e n t p a s s e s fro m t h e p o s i t i v e t o n e g a t i v e t e r m i n a l s o f t h e f i l t e r

t h r o u g h a s e r i e s c o n n e c t e d r e s i s t o r c h a i n c o n s i s t i n g o f t h e s p e c t r o m e t e r

c o i l s , t h e 0 . 1 5 ohm s t a n d a r d r e s i s t o r , a n d t h e 10 2N278 p o w e r t r a n s i s t o r s .

O v e r l o a d p r o t e c t i o n f o r t h e 10 p a r a l l e l c o n n e c t e d 2 N 2 7 8 's i s p r o v i d e d by

a n

8

( i i ) The R e f e r e n c e S u p p l i e s

The 9 . 3 v o l t o u t p u t fro m t h e r e f e r e n c e s u p p l i e s c h a n g e s l e s s

t h a n 0.01% when t h e i n p u t r m s . v o l t a g e i s c h a n g e d fro m e i t h e r 117 t o 128

25

'

75528

u n i v e r s i t y

m m n m m i m m m

F

IG

U

R

E

3

1

B

L

O

C

K

D

IA

G

R

A

M

C

U

R

R

E

N

T

S

U

P

P

L

Y

G J ■v

R e p r o d u c e d with p erm ission of th e copyright owner. F urther reproduction prohibited without perm ission.

S

E

R

V

II7V:

r m s . :

4 4 V. rms.

t

8 4 V- r

: 9 0 V. r m f t s / i

^ JL

. ■© * 3 0

Ca

r s c t i f i e r s a n d f i l t e r s

Cg f o r l o c a l p o w e r s u p p l i e s .

* + 3 0

o - 9. 3

V-L o g . P o t .

R e f e r e n c e

■»- 9 . 3 V.

Li n. Pot .

Z\

R e f e r e n c e

■o ♦

C, » I 0 0 ut *. 1 5 0 VDC.

C2 - 3 0 0 0 u t . , 5 0 VDC.

C3 * I 5 0 0 u f . , 5 0 VDC.

D| * I 0 J 2 D i o d e

D2 ■ F 2 D i o d e

Z ( * I N 2 6 2 3 9 - 3 V t e m p , c o m p e n s a t e d

z e n e r

d i o d e *

Z 2 - 2XI N262I * 18V

"

"

"

"

Z4 * I N 2 8 3 6

8 2 V, 5 0 WAT T

z e t i e r

d i o d e .

Z3 « I N2 8 3 3 B

6 2 V , "

"

"

"

R, ■ 9 0 0 ohms , R2 - 2 2 K , R3 » 6 8 0 ohms, R4» 3-3 K

R E F E R E N C E

S U P P L I E S

F I G U R E

3 - 2

F

I

G

U

R

E

<

m

jo

m

o

o

0 )

m

O

$

m

JO

cr

8

.

<o

’ Z V

*

55

\

CM CO (ft ®

2 <

1

(b •>»

o

z

7 w ° u i 3 <

(ft |A N

£ 5

7. (ft

<

(B a (A -■

O

2. M

m -*■

-# o

CL

Cl

(ft

“» O (ft t * o

-4> OJ

5 ^

5 =

(0 (ft

(ft

o

a.

(ft

o r from 117 t o 106. T h i s i s a c c o m p l i s h e d by u s i n g " g a n g e d " z e n e r d i o d e

c o n s t r u c t i o n a s shown i n F i g u r e 3 . 2 . T e m p e r a t u r e s t a b i l i t y i s o b t a i n e d

by u s i n g t e m p e r a t u r e c o m p e n s a te d z e n e r d i o d e s i n t h e l a s t two s t a g e s .

Z , and Z ^ h a v e t e m p e r a t u r e c o e f f i c i e n t s o f 0.0 0 1 % /C ° a n d 0 .0 0 5 % /C °

r e s p e c t i v e l y .

F i g u r e 3 .7 n Ganged Z e n e r D io d e s

The r e g u l a t i o n f o r n g a n g e d z e n e r d i o d e s ( F i g u r e 3 . 7 ) i s

e a s i l y c a l c u l a t e d fro m t h e e x p r e s s i o n

a r e t h e d r o p p i n g r e s i s t o r s shown i n F i g u r e 3 . 7 .

U s i n g t h i s e x p r e s s i o n two a n d t h r e e s t a g e r e f e r e n c e s u p p l i e s

w e r e c o m p a r e d . I t was f o u n d t h a t s u f f i c i e n t r e g u l a t i o n c o u l d o n l y b e

a c h i e v e d w i t h a t h r e e s t a g e s u p p l y . T e m p e r a t u r e c o m p e n s a t i o n was r e q u i r e d

i n t h e s e c o n d s t a g e s i n c e t h e r e g u l a t i o n f a c t o r ( r ^ / R ^ f o r t h e o u t p u t

s t a g e was n o t s u f f i c i e n t t o c o m p e n s a te f o r t h e t h e r m a l d r i f t s o f an

" u n c o m p e n s a t e d " s e c o n d s t a g e z e n e r d i o d e .

R |

r 2

Rn

w h e r e A V 0 i s t h e o u t p u t v o l t a g e c h a n g e c o r r e s p o n d i n g t o a n i n p p t

v o l t a g e c h a n g e o f 'I*W a r e t h e dynam ic

im p e d e n c e s o f t h e z e n e r d i o d e s Z ^ , Z ^, «. « .

2

30

( i i i ) The F a s t F e e d b a c k S y s te m

As shown i n F i g u r e 3 . 1 t h e o u t p u t fro m t h e r e f e r e n c e s u p p l y

i s c o n n e c t e d a c r o s s a 10 t u r n , 1001c l o g a r i t h m i c p o t e n t i o m e t e r . A B u r r -

Brown 1 6 0 2 / 0 4 c h o p p e r s t a b i l i z e d o p e r a t i o n a l a m p l i f i e r c o m p a r e s t h e

v o l t a g e a c r o s s t h e s t a n d a r d r e s i s t o r (Vba) w i t h t h e v o l t a g e p i c k e d o f f

f ro m t h e l o g a r i t h m i c p o t e n t i o m e t e r ( V b c ) . The a m p l i f i e d d i f f e r e n c e

s i g n a l (V ba-V bc) i s i n v e r t e d a n d f e d t o a pow er b o o s t e r s t a g e ( F i g u r e

3 . 3 ) . The o u t p u t o f t h e p o w e r s t a g e i s c o n n e c t e d t o t h e 10 p a r a l l e l

c o n n e c t e d 2N278 s e r i e s r e g u l a t i n g t r a n s i s t o r s ( F i g u r e 3 . 3 ) . The p h a s e

o f t h e f e e d b a c k s i g n a l i s s u c h a s t o r e d u c e t h e d i f f e r e n c e (V ba-V bc) t o

z e r o .

The s y s t e m w i l l e x h i b i t h i g h f r e q u e n c y o s c i l l a t i o n s u n l e s s

a c . f e e d b a c k i s u s e d t o d r o p t h e g a i n o f t h e o p e r a t i o n a l a m p l i f i e r a t

h i g h f r e q u e n c i e s . A N y q u i s t d i a g r a m c o u l d h a v e b e e n p l o t t e d t o d e t e r m i n e

t h e f e e d b a c k e l e m e n t s r e q u i r e d f o r s t a b i l i t y , b u t s i n c e a maximum r i p p l e

r e d u c t i o n a n d a low t i m e c o n s t a n t w e re a l s o r e q u i r e d i t was e a s i e r t o

s e t up t h e c i r c u i t a n d d e t e r m i n e t h e f e e d b a c k e l e m e n t s e x p e r i m e n t a l l y .

The s t a n d a r d r e s i s t o r i s made from c o n s t a n t a n s t r i p , wound

n o n - i n d u c t i v e l y and i s c o o l e d by a 10 i n c h f a n . The f a n a l s o p r o v i d e s

c o o l i n g f o r t h e v a r i a c s , t h e r e c t i f i e r s and t h e v a r i o u s p o w e r t r a n s i s t o r s .

( i v ) The S e r v o S y s te m

The s e r v o f e e d b a c k s y s t e m c o m p a r e s t h e v o l t a g e V ah, w h ic h

i s k e p t a t 3 v o l t s ( F i g u r e 3 . 4 ) and t h e v o l t a g e Vag, a c r o s s t h e p o w e r

t r a n s i s t o r s . The d i f f e r e n c e i s c h o p p e d by t h e 60 c y c l e c h o p p e r and

a m p l i f i e d ( F i g u r e 3 . 4 ) a n d t h e n f e d t o t h e s e r v o m o to r w h ic h c o n t r o l s

t h e a n g u l a r p o s i t i o n o f t h e t h r e e g a n g e d v a r i a c s .

The a m p l i f i e r c o n s i s t s o f a d i f f e r e n c e a m p l i f i e r T ^ , T

2

2 N 5 2 7

TO COLLECTO!

OF 2 N 2 7 8 ' S

10 K 5 6 K■

2 N I7 2 8

(c le v ite )

2 N I67

2N5I I

I-5V. rm s - I

6 8 0

|K 60*'v^P

ohm

.. 2 N I6 7

IK

10 ohm s'

10 Out

10 Out

2 2 K ±

2 7 K

TR A N SISTO R

TRANSFORMER

2N 5II

2 N I 7 2 8

(clevite)

12 V O L T S

-ioOO

10 K 5-6K

TO

S E R V O

^ 1-4 u f • M O T O R

— o

HAMMOND I 6 7 D

F I LAMENT TRANS.

F I G U R E 3 4

THE S E R V O S Y S T E M