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DISTRIBUTION IN ANGI$.
211&
FROM BORON BOHBARDJSD BY PROTONS
by
WILLIAM L* WHITSON
A dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy,
In the Department of Physics, in the Graduate College
of the State University of lo^a
A u g u st 1340
ProQuest N um ber: 10984099
All rights reserved
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a n o te will ind ica te the deletion.
uest
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Published by ProQuest LLC(2018). C opyright of the Dissertation is held by the Author.
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\ \0 ^ 0
l o fo O -3
C o p , 2-
A-KfJOV'LEIXr iSflT
The a u t h o r w i s h e s t o a c k n o w le d g e t h e
a d v i c e and e n c o u ra g e m e n t o f P r o f e s s o r A. E l i e t t
tin d e r w hose d i r e c t i o n t h e work trhs c a r r i e d o u t*
He w i s h e s a l s o t o e x p r e s s a p p r e c i a t i o n o f t h e
v a l u a b l e a s s i s t a n c e o f Dr* V^.B* Mckean# Dr* J . G .
P l a i n # and M e s s r s . y .JV io u n g # J . A # J a c o b s , A .S .
A t c h i s o n and t o a c k n o w le d g e t h e w ork o f Mr. J*G .
S e n tin e lla in c o n s tru c tin g th e p r e c is io n p a rts o f
t h e ^ a fc p a ra tu s .
512519
iii
TABLE OF JOiiTEiMTB
Acknowledgm ent
Page
ii
In tro d u c tio n
1
A p p a ratu s
3
R e so n a n c e o f C o n tin u o u s and
Long Range A lp h a s
9
D i s t r i b u t i o n i n A n g le
12
D isc u ss io n
19
A p p e n d ix I
21
A p p e n d ix I I
23
1
m m o m z tio R
B oron b om barded by p r o t o n s g i v e s two g r o u p s o f
a l p h a - p a r t i c l e s , an a p p a r e n t l y hom ogeneous g ro u p o f r a n g e
4*4 cm a n d a c o n t i n u o u s g ro u p w i t h a maximum r a n g e o f
a b o u t 5#7 cm*
S u g g e s t e d r e a c t i o n s a re *
11
1
8
4
B
+ H — HBe ♦ Be
(1 )
f o r t h e hom ogeneous g r o u p , and
B11 + H -— *-Z He4
(2)
f o r th e c o n tin u o u s g ro u p .
T h e re i s a r e s o n a n c e i n t h e e x c i t a t i o n o f
r e a c t i o n (1 ) f o r a b o m b a rd in g e n e r g y v a r i o u s l y r e p o r t e d
1 ,2 ,3
from 159 t o 172 Kev i n r e c e n t w o rk .
A l l e n , Haxby
mwm.im mn**
*B .7Faldem an,R .W addel,D . 3 a l l l h a n , F . S c n e i d e r , P h y s . Hev.
2
M i 545 (1958)
J . S *A l l e n j R . O . B a x b y , J . B * W i l l i a m s , P h y s . Rev* 5 5 . 525
8R.B.Bowers<MC, P h y s . R e v . , £ 5 , 322 (1 9 3 9 )
Itm+mwrnwrnmmmmmmmm**
m m m mmmm mm —
—
mtrn mmmm mm ■ » — » —
«■» mm « » — <*»«— — »«■»<»» —
i
g
an d W illia m s
r e p o r t t h e h a l f - w i d t n , m e a su re d u s i n g a
9
t h i n s o l i d t a r g e t t o be 10 Kev. Bowersox f i n d s t h e
y i e l d f o r t h e hom ogeneous g ro u p o f r e a c t i o n (1 ) t o i n ­
c r e a s e e x p o n e n t i a l l y b e tw e e n 200 and 400 K ev.
Bo r e s o n a n c e h a s h i t h e r t o b e en o b s e r v e d f o r t h e
c o n t i n u o u s g ro u p o f r e a c t i o n ( 2 ) j i t s e x c i t a t i o n c u r v e
was n e v e r shown t o b e o t h e r t h a n a n o rm a l e x p o n e n t i a l
r i s e i n t h e e n e r g y r a n g e 1 0 0 -4 0 0 Kev.
The p r e s e n t w ork ,
u s i n g t h i n t a r g e t s , shows a s t r o n g r e s o n a n c e i n t h e
1
in m o m itm a
B oron bom barded by p r o t o n s g i v e s two g r o u p s o f
a l p h a - p a r t i c l e s , an a p p a r e n t l y hom ogeneous g ro u p o f r a n g e
4*4 cm an d a c o n t i n u o u s g ro u p w i t h a maximum r a n g e o f
a b o u t 3#7 cm*
S u g g e s te d r e a c t i o n s a re #
11
1
8
4
B + H — HBe + Be
(1)
f o r t h e homogeneous g r o u p , and
11
1
4
B ♦ fl— ^ 3 He
(2 )
f o r th e c o n tin u o u s g ro u p .
T h e re i s a r e s o n a n c e i n t h e e x c i t a t i o n o f
r e a c t i o n (1 ) f o r a b o m b a rd in g e n e r g y v a r i o u s l y r e p o r t e d
1 ,2 * 3
from 159 t o 172 Kev i n r e c e n t w o rk,
A l l e n , Haxby
w
m
w
o
m
WI n il H> mm............................ .................................. ■ i iiin n n i n
iiji i* i im
ai .m
m
imii
m tm m m tim
m i ■■ m w i r n o » i
m n* ■■■ ■■
mm
* B .W a l d e m a n ,R ,W a d d e l ,D * l a l l lh a n ,W .S c u e i d e r , P h y s , Rev.
2
5 i * 543 (1938)
J * S * A ll© n ,R ,0 ,H & x b y ,J ,H ,W illia m s , P h y s , Rev, 5 3 . 325
(1 9 3 8 )
R ,B *B ow ersox, P h y s . R e v . , 5 5 ,
(1 9 3 9 )
and w i l l i a m s
2
r e p o r t t h e h a l f - w i d t n , m ea su re d u s i n g a
t h i n s o l i d t a r g e t t o b e 10 K ev.
Bower*sox
f in d s th e
y i e l d f o r t h e hom ogeneous g ro u p o f r e a c t i o n ( 1 ) t o i n ­
c r e a s e e x p o n e n t i a l l y b e tw e e n 200 and 400 Kev.
Ho r e s o n a n c e h a s h i t h e r t o b e en o b s e r v e d f o r t h e
c o n t i n u o u s g ro u p o f r e a c t i o n ( 2 ) j i t s e x c i t a t i o n c u r v e
was n e v e r shown t o b e o t h e r t h a n a n o rm a l e x p o n e n t i a l
r i s e i n t h e e n e r g y r a n g e 1 0 0 -4 0 0 K ev.
The p r e s e n t work,
u s i n g t h i n t a r g e t s , shows a s t r o n g r e s o n a n c e i n t h e
2
c o n t i n u o u s g ro u p a t t h e s a me e n e r g y a s t h e r e s o n a n c e o f
t h e hom ogeneous g r o u p .
A sym m etric a n g u l a r d i s t r i b u t i o n s o f t h e fo rm
2
1 ♦ Acos a , w here a i s t h e a n g l e t h e e m e r g e n t a l p h a p a r t i c l e iaakes w i t h t h e beam, h a v e b e e n r e p o r t e d f o r
r e a c t i o n (1 ) by N e u e r t ^ and f o r b o t h r e a c t i o n s (1 ) and
( 2 ) by H axby, A l l e n and W i l l i a m s .
4
-H .H e u e rt, P h y sik . Z e i t s .
618 (1 8 5 7 )
°R«0 * H a x b y , J . S . A l l e n , J * H . W i l l i a m s , P h y s . Rev* JJJ, 140
(1 9 5 9 )
I n t h e p r e s e n t w o rk , f o r t h e f i r s t t i m e , r a n g e num ber c u r v e s h a v e b e e n t a k e n f o r a l p h a - p a r t i c l e s e m i t t e d
a t v a r i o u s a n g l e s w i t h r e s p e c t t o t h e p r o t o n beam.
d a ta i s ta k e n u sin g t h i n ta r g e ts *
A ll
we f i n d s p h e r i c a l
sym m etry f o r a l l r a n g e s b o t h a t r e s o n a n c e and a t 200 Kev.
3
im s /a s s .
H u n to o n , B l l e t t , B a y le y and tTan A l i e n
m m ■* w
6
in i mi m itm mmi imu — m> Mmmv m t'im mm m \ ......
»■* m i» n»
m
h w w w K ii k
wi mi #
6
>w w i i i i >» w < im
w o rd in g
iiwmin
wi
w !H» ww
R .H u n t o o n ,A # E l le t t,D * B a y l e y ,J * V a n A l l e n ( i n p r o c e s s o f
p u b lic a tio n )
i n t h i s l a b o r a t o r y h a v e d e m o n s t r a t e d t h e f e a s i b i l i t y and
2
2
a d v a n t a g e s o f u s i n g t h i n g a s t a r g e t s on t h e H ♦ H —
3
1
H 4*-:H r e a c t i o n . T h is t e c h n i q u e i s a p p l i e d t o t h e b o r o n p r o t o n r e a c t i o n a n d , s i n c e t h e e q u ip m e n t i s i n m ost r e s p e c t s
i d e n t i c a l w i t h t h a t u s e d i n t h e p r e v i o u s v orfc, o n ly a
b r i e f d e s c r i p t i o n o f a p p a r a t u s w i l l be g i v e n .
The p o t e n t i a l s o u r c e f o r a c c e l e r a t i n g t h e p r o t o n s
i s a C o c k c r o f t —W&lton t y p e t r a n s f o n a e r - r e c t i f i e r - q u a d r u p l e r g i v i n g e n e r g i e s up t o 500 Kev*
I o n s p ro d u c e d i n a
lo w v o l t a g e a r c a r e a c c e l e r a t e d i n a f i v e f o o t , e i g h t
se c tio n tu b e .
A m ain beam o f 250 m ic r o a m p e re s i s m ag n e t­
i c a l l y a n a l y z e d a n d , a f t e r p a s s i n g t h r o u g h a d ia p h ra g m
s y s te m , g i v e s a w o rk in g c u r r e n t o f . 5 t o 2 m ic ro a m p e re s i n
t h e t a r g e t cham ber*
The t a r g e t a s s e m b ly i s shown s c h e m a t i c a l l y i n
F ig * 1 .
F o r a l i g n m e n t p u r p o s e s t h e d i f f e r e n t i a l pumping
s y s te m ( t u b e , c a p i l l a r i e s , pum ps, h e a t i n g c o i l s , e t c . )
i s c o u n t e r p o i s e d and c o n n e c te d a t one end t o t h e a c c e l ­
e r a t i n g t u b e and q t t h e o t h e r t o t h e t a r g e t cham ber by
m ovab le f l a n g e d j o i n t s , A and B, s e a l e d w i t h s t o p c o c k
4
To Aceii.mAToi)T«ii
G R C A tE J o i n t
[T arobt C h a m W R
F ig ,l
T a r g e t A ssem bly
5
grease*
The t a r g e t cham ber i s a l s o sup o r t e d in d e p e n d e n t-*
l y and a s y l p h o n s w i v e l j o i n t a t 2 w i t h a d j u s t i n g s c re w s
a t -B .a llo w s r o t a t i o n o f t h e t a r g e t cham ber a b o u t Z a s a
c e n te r*
B oron t r i f l u o r i d e *
t h e g a s used* i s i n t r o d u c e d
fro m a s u p p l y t a n k t h r o u g h a n e e d l e v a l v e i n t o t h e t a r g e t
cham ber w here i t s
p r e s s u r e i s m a i n t a i n e d a t 2 ram o f fig*
The g a s i s pumped o u t t h r o u g h t h e d i f f e r e n t i a l pumping
s y s te m t o m a i n t a i n t h e vacuum i n t h e a c c e l e r a t o r tube*
The beam* th e n * i n g o in g from th© a c c e l e r a t o r t u b e t o
t h e t a r g e t cham b er p a s s e s t h r o u g h a r e g i o n o f i n c r e a s i n g
gas d e n sity *
The d e t a i l s o f t h e t a r g e t cham ber a r e shown i n
F ig * 2m
A l p h a - p a r t i d e s from t h e t a r g e t volume* G* p a s s
t h r o u g h 1 / 8 i n c h c i r c u l a r a p e r t u r e s * H* and f i n a l l y
t h r o u g h 1 / 4 i n c h h o l e s * I* o v e r w h ich a r e p l a c e d aluminum
f o i l s o f 1*85 cm a i r e q u i v a l e n t s t o p p i n g power#
B esid es
t h e s e windows p l a c e d a t f i v e a n g l e s (50* 60* 90* 120*
a n d 150 d e g r e e s ) w i t h r e s p e c t t o t h e beam* a s i x t h window
i s p l a c e d a t 90 d e g r e e s i n a d i r e c t i o n p e r p e n d i c u l a r t o
t h e p l a n e o f F ig # 2 and p a s s i n g th r o u g h t h e c e n t e r o f t h e
t a r g e t volume* G.
B o re a g a i n a r e d e f i n i n g c i r c u l a r
a p e r t u r e s o f 1 / 8 and 1 / 4 i n c h and a 1*85 cm f o i l window*
Two i o n i z a t i o n cham b ers a r e used#
One i s f i x e d
a t t h e 90 d e g r e e window and t h e o t h e r * J* F ig# 8* can be
r o t a t e d i n f r o n t o f any one o f t h e o t h e r f i v e windows*
The i o n i z a t i o n cham ber f i x e d a t 90 d e g r e e s i s u s e d a s a
m o n i t o r a s w i l l be d e s c r i b e d l a t e r .
ro ta tin g s tru c tu re
e
Ambsr
F^saoay Case
4.5®
.or®
G u a r d ftm<s
C ollector
0
----------------- r—
z
I
(
3
y —AlvtBER
nches
• P a b a d a y Ca g e
F ig * 2
T a r g e t 3ha.\ber
7
o f t h e m o v a b le i o n i z a t i o n cham ber i s r i g i d l y c o n n e c t e d t o
t h e t a r g e t cham ber and i t s p o s i t i o n s a c c u r a t e l y d e t e r m i n e d
by s t o p s «
The ch am b ers a r e c a p a b l e o f m o tio n r a d i a l l y
w i t h r e s p e c t t o t h e c e n t e r o f t h e t a r g e t cham ber end a r e
fix e d , i n p l a c e ?rt.th s e t sc re w s*
The t o t a l r a d i a l m o tio n
i s 1 . 5 cm w h ic h t o g e t h e r w i t h t h e i n i t i a l f o i l o f 1 . 8 5 cm
s t o p p i n g pow er and two a u x i l i a r y f o i l s o f .9 3 and 1*85 cm
s t o p p i n g pow er c h an g e t h e amount o f a b s o r b i n g m a t e r i a l i n
t h e p a t h o f t h e e m e rg in g a l p h a - p a r t i c l e c o n t i n u o u s l y fro m
1 . 8 5 t o 5*8 cm a i r e q u i v a l e n t .
The f r o n t o p e n in g o f e a c h
i o n i z a t i o n cham ber i s 5 / 8 i n c h i n d i a m e t e r and a c o l l e c t o r
p l a t e 1 / 8 i n c h i n d i a m e t e r i s s e t 1 / 4 i n c h from i t .
It
h a s b e en d e te r m i n e d fro m p o lo n iu m a l p h a s t h a t p a r t i c l e s musk
e n t e r *1 cm i n t o t h e cham ber i n o r d e r t o g i v e p u l s e s i n
t h e a m p l i f i e r ( s e e A p p e n d ix I ) .
by l u c i t e .
M e ta l p a r t s a r e i n s u l a t e d
The g e o m e try i s su c h t h a t t h e s e n s i t i v e volum e
o f t h e i o n i z a t i o n c h a m b e rs , s e t a t t h e i r l a r g e s t r a d i i ,
c o u ld s e e t h e e f f e c t i v e t a r g e t volume w i t h c l e a r a n c e .
A bout 1000 v o l t s I s a p p l i e d t o t h e a n o d e , and s m a ll w i r e
g r i d s s p a c e d 1 mm a p a r t a r e s o l d e r e d a c r o s s t h e p l a n e o f
t h e o p e n in g #
The p u l s e s i n t h e i o n i z a t i o n cham bers a r e
a m p l i f i e d s e p a r a t e l y i n l i n e a r a m p l i f i e r s and r e c o r d e d on
len co m ec h an ica l c o u n te rs*
A l l f o i l t h i c k n e s s e s '-e re d e te r m i n e d by a
p o lo n iu m a l p h a s o u r c e i n c o n j u n c t i o n w i t h a t h i n i o n i z a t i o n
cham ber*
B om barding e n e r g i e s v e r s d e te r m in e d u s i n g t h e
330 Kev f l u o r i n e gamma~ray r e s o n a n c e and c h e e k e d w i t h a
8
r e s i s t a n c e v o l t m e t e r (55 0 10 megohm IR3 r e s i s t o r s ) «
r i p p l e i n t h e beam on t h e t a r g e t i s l e s s t h a n 8 K ev.
The
The
s t o p p i n g power o f b o r o n t r i f l u o r i d e a t 8 ma o f fig f o r
160 Kev p r o t o n s i s a b o u t 2 Kev p e r cm w h ich g i v e s a n e n e r g y
l o s s o f t h e beam i n e n t e r i n g t h e t a r g e t cham ber o f 10 Kev.
The s t r a g g l i n g i n t h e beam i s * t h e n , l e s s t h a n 1 K ev.
ftflSQfljJMg.Qg o o m a q o u s ..amp
low
ramgjs a l e b a e .
I n t h e f i r s t p a r t o f t h e w o rk, a y i e l d - e n e r g y
c u r v e was t a k e n t o d e t e r m i n e t h e p o s i t i o n o f r e s o n a n c e anct
th e shape o f th e cu rv e in th e v i c i n i t y o f resonance*
T h is
was d one u s i n g o n l y t h e m o n i t o r i o n i s a t i o n cham b er f i x e d
a t 2 . 4 cm.
The e f f e c t i v e t a r g e t t h i c k n e s s was 1 Kev*
The o r d i n a t e o f Fig* 3 shows t h e num ber o f a l p h a -
p a r t i c l e s c o u n te d a t v a r i o u s v o l t a g e s f o r a d e f i n i t e amount
o f c h a r g e c o l l e c t e d a t t h e b o tto m F a r a d a y cup a s r e a d by
a c u rre n t in te g ra to r*
The h a l f - w i d t h o f t h e r e s o n a n c e
a p p e a r i n g a t 16Q±5 Kev i s 6 Kev*
Fig* 4 , t a k e n f o r a
t a r g e t t h i c k n e s s o f 5 K ev, shows a h a l f - w i d t h o f 7 Kev*
The h a l f - w i d t h o f t h e r e s o n a n c e may be much l e s s t h a n t h a t
o b s e r v e d s i n c e t h e i n d e t e r m i n a c y i n t h e b o m b a rd in g e n e rg y
i s t h e same o r d e r o f m ag n itu d e*
To d e t e r m i n e w h e th e r any f l u o r i n e a l p h a - p a r t i c l e s
a r e p r e s e n t when b o r o n f l u o r i d e i s used., m e th y l b o r a t e was
s u b s t i t u t e d a s a t a r g e t b u t no m e a s u r a b le d i f f e r e n c e i n
t h e s h a p e o f t h e y i e l d c u r v e , F i g . 3 , was o b s e r v e d .
The c u r v e s i n F i g . 5 show how t h e y i e l d c h an g e s
when t h e s h o r t e r ra n g e a l p h a - p a r t i c l e s a r e s t o p p e d b e f o r e
r e a c h i n g t h e i o n i z a t i o n c h a m b e r.
They show t h e y i e l d a t
r e s o n a n c e t o b e composed o n ly 8 p e r c e n t o f a l p h a - p a r t i c l e s
h a v i n g ra n g e g r e a t e r t h a n 3*9 cm*
I f t h e r a t i o o f d ie
num ber o f a l p h a - p a r t i c l e s a t r e s o n a n c e t o t h e num ber a t
some h i g h e r e n e r g y l i k e 200 Kev i s c a l l e d R, F i g . 5 shows
t h a t R I n c r e a s e s w i t h range#
200
U-
KV]
£ loo
200
150
ENERGY IN KILOVOLTS
F ig * 5
Y ie ld -e n e rg y cu rv e f o r
t a r g e t t h i c k n e s s o f 1 Kev
600
2.5 CM. BF, GAS AT 2 MM. PRESSURE
400
KV
U_
150
200
ENERGY IN KILOVOLTS
Fig# 4
Y ie ld -e n e rg y cu rv e f o r
t a r g e t t h i c k n e s s o f 5 Kev
11
ALPHA PARTICLES FROM BORON PLUS PROTONS
AT 90r TO SEAM
RANGE
500
500
cn
Iz
o 100
o
Li-
> 2.4 CM.
RANGE >2.1 CIA
100
150
200
200
ISO
160
160
LLl
RANGE > 3 .0 CM.
3
RANGE > 3.9 CM.
120
120
80
80
40
40
ISO
F ig . 5
150
200
ENERGY
IN
200
KILOVOLTS
V a ria tio n of y ie ld r l t h
ra n g e
12
DISTRIBUTION IB ANGLE
A n g u l a r d i s t r i b u t i o n d a t a were t a k e n a t r e s o n ­
a n c e and a l s o a t 200 Kev u s i n g a t a r g e t o f 2 Kev maximum
th ic k n e ss*
For each d a y f s run th e p o s itio n o f th e reso n ­
a n c e was d e t e r m i n e d by t h e m o n i t o r i o n i z a t i o n cham ber and
cu rren t in te g ra to r.
In a l l subsequent re a d in g s th e c u rre n t
i n t e g r a t o r was u se d t o c h e c k t h e y i e l d t o rem ove t h e
p o s s i b i l i t y t h a t a c c i d e n t a l s h i f t s i n a l i g n m e n t had
o ccured,
W ith t h i s c h e c k on t h e r e s o n a n c e p o s i t i o n , r a n g e s num ber c u r v e s w e re t a k e n by c o m p a rin g c o u n ts o b s e r v e d a t
t h e v a r i o u s a n g l e s t o t h o s e c o l l e c t e d s i m u l t a n e o u s l y by
t h e m o n ito r a t d0 d e g re e s *
The m o n i t o r i o n i z a t i o n cham ber
was s e t t o c o u n t a l l p a r t i c l e s o f r a n g e g r e a t e r t h a n 2 . 1
cm a n d t h e m o v ab le i o n i z a t i o n cham ber s e t a s d e s i r e d *
An
o s c i l l o s c o p e showed by v i s u a l c h e c k t h a t a l l p u l s e s v e r e
r e c o r d e d * and r e p e t i t i o n o f a t l e a s t one o f t h e p r e v i o u s
day*s a n g le -m o n ito r r a t i o s d e te rm in e d t h a t a m p l i f i e r
c h a r a c t e r i s t i c s re m a in e d c o n s t a n t .
F i g . 6 g i v e s t h e d a t a t a k e n a t reson a n c e a s i t
was t a k e n i n t h e l a b o r a t o r y .
The o r d i n a t e
i s th e
r a t i o o f c o u n t s r e c o r d e d a t a n g l e a t o t h o s e r e c o r d e d on
t h e m o n ito r*
S e v e r a l c o r r e c t i o n s m ust be a p p l i e d t o
t h e s e d a t a b e f o r e t h e y i e l d a t d i f f e r e n t a n g l e s c an be
c om pared and t h e d i s t r i b u t i o n i n a n g l e d e t e r m i n e d .
G eom etry o f t h e t a r g e t cham ber shows t h e
30
1ZCf
60*
ISO
90'
Cm
of
« ig . 6
A ir
C m o f A ir
rtange-nuraber cu rves a t reson ance
b efore c o r r e c tio n
14
------ 5
-------------------------------------------------------------------------------------------------------------
"
e f f e c t i v e t a r g e t volum e t o p r o p o r t i o n a l t o i / s l n a , w i t h
n e g l i g i b l e e r r o r , w h e re a i s t h e a n g l e b e tw e e n t h e e j^ e r g i n g a l p h a and t h e d i r e c t i o n o f t h e beam i n t h e l a b o r a t o r y
system *
Then
N (a) * 1 ( a ) s i n a
(A)
w h e re 1 ( a ) i s t h e o b s e r v e d number o f c o u n t s and ft ( « )
r e l a t e s c o u n t s f o r e q u a l t a r g e t vo lu m es t r a v e r s e d by t h e
beam.
In in q u ir in g a b o u t th e a n g u la r d i s t r i b u t i o n o f
a l p h a - p a r t i c l e s h a v in g a g i v e n e n e r g y , i t i s n e c e s s a r y t o
com pare p a r t i c l e s , e m e rg in g a t d i f f e r e n t a n g l e s , ,vh l c h h a v e
e q u a l e n e r g i e s I n a s y s te m a t r e s t w i t h r e s p e c t t o t h e
c e n t e r o f m ass o f i n c i d e n t , t a r g e t and p r o d u c t p a r t i c l e s *
A p u r e l y g e o m e t r i c a l c o n s i d e r a t i o n ’- i l l r e l a t e E , t h e
e n e r g y i n t h e c e n t e r '.of mass s y s t e n , t o
i n t h e l a b o r a t o r y sy stem *
its
en erg y
A n o th e r p a r t i c l e h a v in g t h e
same e n e r g y E b u t e m e rg in g a t d i f f e r e n t a w i l l h a v e e n e r g y
E(<&«g) *
e q u a tio n r e l a t i n g p a r t i c l e s o b serv ed In th e
l a b o r a t o r y s y s te m an*' hwving e q u a l e n e r g y i n t h e c e n t e r o f
mass s y s te m (w here
d eg rees) i s
h a s b e en a r b i t r a r i l y s e l e c t e d a s 30
( s e e A p p e n d ix I I )
E9Q * s a ~ £ ^Ea EpMa Mp/M2 «cos
w here Ma *
a
(B)
m ass o f a l p h a p a r t i c l e
Mp * m ass o f i n c i d e n t p r o t o n
M »
m ass o f compound n u c l e u s ( b o r o n
4* p r o t o n )
Ep « e n e rg y o f p r o t o n
C o r r e s p o n d i n g r a n g e s f o r t h e s e e n e r g i e s w ere o b t a i n e d
7
fro m L i v i n g s t o n and B ethe* T r a n s f o r m a t i o n s c o r r e c t i n g a ,
15
f
It, L i v i n g s t o n and H .A .B e t h e , Rev, Mod, P h y s , S-l, 266
(1 9 3 7 )
th© o b s e r v e d a n g l e , t o t h e a n g l e 0 i n t h e c e n t e r o f m ass
5
s y s te m h a v e n o t b e e n e f f e c t e d h e r e s i n c e t h e c h a n g e i s
slig h t*
I n F ig * 7 , u s i n g r e l a t i o n s
(A) and ( B ) , p a r t i c l e s
a r e c o m p a re d , t h e n , w h ic h h a v e e q u a l e n e r g i e s i n t h e c e n t e r
o f m ass s y s te m and a r e p l o t t e d a t t h e r a n g e t h e y w ould
h a v e i f t h e y came o f f a t 90 d e g re e s *
s ta tis tic a l flu c t­
com puted from y[W/#$ w here ft i s
u a tio n s o f th e r a tio I
t h e t o t a l num ber o f c o u n t s o b s e r v e d a t t h e a n g l e , a r e l e s s
th a n £ .0 0 5 .
The d i s t r i b u t i o n i n a n g l e i s s p h e r i c a l l y
sy m m etric*
F ig * & shows t h e u n c o r r e c t eel c c*.t a ta k e n a t
200 ftev*
The r a t i o l e v e l s o f f t o a v a l u e o f *05 p a s t
a s t o p p i n g pow er o f 4*0 cm b u t a l t h o u g h . t h i s p a r t o f t h e
c u r v e was c h e c k e d v e r y c a r e f u l l y i t f a i l s
a t 4*4 cm f o r th© hom ogeneous group*
to drop a g a in
The c o u n t i n g r a t e
i s much l o w e r a t SCO Fev t h a n a t t h e r e s o n a n c e and t h e
i n h e r e n t b a c k g ro u n d o f t h e i o n i z a t i o n c h a m b e r - a m p l l f i e r
sy s te m i s a b o u t 75 p e r c e n t o f t h e r a t i o o b s e r v e d p a s t
4*0 cm*
The e r a I s :I o n o f 6*95 cm a l p h a - p a r t i d e s from
f l u o r i n e in th e t a r g e t gas e x p la in s th e r e s t o f th e c o u n ts
o b s e rv e d *
A c c o r d i n g l y *05 was s u b t r a c t e d
fcata a l l r a t i o s
b e f o r e c o r r e c t i o n , u s i n g (A) and (B ), t o F ig * 9*
Bee©
a l s o s t a t i s t i c a l f l u c t u a t i o n s o f th e r a t i o a r e l e s s t h a n
£*005*
A g a in t h e d i s t r i b u t i o n i n a n g l e i s s p h e r i c a l l y
sy<TirafitHQ>
—
- ..............................................................
...
---------
.4 -
Cm
F ig . 7
o p
A
ir
Hang&- number c u r v e a t r e s o n a n c e
a fte r c o rre c tio n
30
90
.1
-
C
F ig , 8
m
of
A
ir
Rang e-number c u r v e s a t 200 Kev
before c o r r e c tio n
30'
90'
150'
L/ l
C m o r A ir
F ig* 9
Range-number c u rv e a t 200 Kev
a fte r c o r r e c tio n
19
Q ppenheim er and b a r b e r
8
have d isc u sse d . r e a c tio n s
a)
a n d (s> a lo n g w i t h t h e r e a c t i o n
11
1
12
, %
3
♦ n x-— 2 * ♦ y
(3)
9
They assum ed a lo n g w i t h o t h e r s t h a t e x p e r i m e n t a l
e v id e n c e in d ic a te d r e a c tio n
a r i s i n g from c a p t u r e o f
an £ p r o t o n and r e a c t i o n (2) from c a p t u r e o f a £ o r cl
By a ssu m in g a s i n g l e r e s o n a n c e l e v e l i n t h e
IS
in te rm e d ia te 2
n u c l e u s i t was s u g g e s t e d t h a t p o s s i b l y
p ro to n #
(2 ) a n d (3 ) f o l l o w t h e same t y p e o f c a p t u r e p r o c e s s
a l t h o u g h O ppenheim er and. C e rb e r
d iffic u lty
8
and Myars
10
b o t h fo u n d
i n d e te r m i.ning a s i n g l e r e s o n a n c e l e v e l i n
a c c o rd a n c e w ith s e l e c t i o n r u l e s and g iv in g th e r e p o r t e d
1
a n g u l a r d i s t r i b u t i o n o f t h e hom ogeneous group# The
M in n e so ta 3
g ro u p upon f i n d i n g an a sy m m e tric d i s t r i ­
b u t i o n f o r p a r t i c l e s o f t h e c o n t i n u o u s gi’oup g r e a t e r t h a n
3 . 0 cm s u g g e s t e d a c l o s e r e l a t i o n b e tw e e n r e a c t i o n s (1 )
and ( 2 ) and f u r t h e r t h a t t h e h o m o g e n e l.y o f t h e l o n g ra n g e
g ro u p m ig h t be o n l y a p p a r e n t r e s u l t i n g f r m a p e c u l i a r i t y
a r i s i n g i n r e a c t i o n (1 ) so t h a t t h e e x i s t e n c e o f r e a c t i o n
(2 ) i s n o t n e c e s s a r y #
Sj#Qppenrheiffler and R # B e rb e r, Phys# Rev# 53# 63-J (1 9 3 8 )
J.H*f.?i l l i a m s . ? U H . r e l l s #J « T # T a te #iii«L #H ill, Phys# Rev#
in
£1* 434 (133 7)
7?R#D#Myers* P h y s . R e v .#
361 (13 38)
E . L . H i l l # R .O .H axby, Phys# **ev# 55# 147 (1939)
Th© p r e s e n t w ork by d e t e r m i n i n g t h e e x i s t e n c e o f
a r e s o n a n c e i n th© c o n t i n u o u s g ro u p o f r a n g e g r e a t e r t h a n
8*1 cia and sh o w in g a l s o t h e s i m i l a r i t y i n t h e a n g u l a r
d i s t r i b u t i o n s o f b o th groups o f p a r t i c l e s g iv e s f u r t h e r
e v i d e n c e f o r s u p p o s in g r e a c t i o n s (1) arid (8 )
re la te d *
t o be
T h a t t h e y b o t h come from c a p t u r e o f an s, p r o t o n
i s i n d i c a t e d by che s p h e r i c a l sym m etry o f t h e i r a n g u l a r
d istrib u tio n s*
H axby, A l l e n and T i l l i a m s
&
i n r e p o r t i n g asym­
m e t r i c a n g u l a r d i s t r i b u t i o n s fo u n d 50 p e r c e n t more y i e l d
a t <***150 d e g r e e s th a n a t a - 9 0 d e g r e e s *
T h is was f o r a
t h i c k t a r g e t $ bom b ard in g e n e r g y o f 190 Kev and in c lu d e d *
p a r t i c l e s o f rang© g r e a t e r t h a n 3*0 cm.
F ig* ? and 9
snow t h a t a n y d i f f e r e n c e b e tw e e n t h e y i e l d a t a*150 d e g r e e s
and o*d0 d e g r e e s may n o t e x c e e d 10 p e r c e n t .
512519
APPENDIX I
DETERMINATION OF THI2KBESS OF IONIZATION KUiABER
A l p h a ~ p a r t i e l e s m ust go a f i n i t e d i s t a n c e
p a s t t h e g r i d s o f t h e i o n i z a t i o n c h a m b e r, F i g . 2 , J ,
b e f o r e t h e y p ro d u c e p u l s e s *
The d i s t a n c e th e y m ust e n t e r
d e p e n d s upon i o n i z a t i o n cham ber d e s i g n , p o t e n t i a l b e tw e e n
e l e c t r o d e s o f i o n i z a t i o n c h a m b e r, a m p l i f i e r g a i n s , e tc *
T h is d i s t a n c e was d e te r m in e d f o r t h e p r e s e n t
cham ber u s i n g a l p h a - p a r t i c l e s from p olon ium *
A *05 i n c h
a p e r t u r e was m ounted i n f r o n t o f t h e i o n i z a t i o n c h a m b e r*
By v a r y i n g t h e d i s t a n c e b e tw ee n p o lo n iu m s o u r c e and
a p e r t u r e t h e c u r v e i n F i g , 10 v a c o b t a i n e d *
The num ber
o f p a r t i c l e s p a ssin g th ro u g h th e a p e r tu r e v a r ie s i n v e r s e ly
w i t h t h e s q u a r e o f t h e d i s t a n c e b e tw e e n a p e r t u r e and so u rc e *
The p o i n t s i n t h e c u r v e h a v e b e e n c o r r e c t e d a c c o r d i n g l y *
The a p p a r e n t mean r a n g e o f t h e a l p h a - p a r t i d e s
m e a su re d fro m t h e s o u r c e t o t h e f r o n t o f t h e i o n i z a t i o n
cham ber i s 2*66 cm*
The mean ra n g e o f p o lo n iu m a l p h a -
p a r t i c l e s i s w e l l known t o be 3*80 era*
T h u s , we d e d u c e
t h a t p a r t i c l e s m ust e n t e r *14 cm i n t o t h e I o n i z a t i o n
hamber to p r o d u c e j j u l s e s ,
P
olonium
A l p h a -P ar n c t e s
3.85
*4
s*
Cm
P rom F
3.8
of
A ir
ront
o f
I
4*.o
o n iz a t io n
C h a m 8 E»
F ig * 10
A p p a r e n t :aean r a n g e o f p o lo n iu m
a lp h a -p a r t i d e s
APFESDIX I I
RAMGE 3ORMS3TI0M
r© may d e d u c e a c o r r e c t i o n f o r t h e o b s e r v e d
rang© o f an a l p h a p a r t i c l e w i t h t h e u se o f t h e f o l l o w i n g
Q u a n titie s*
v * v e l o c i t y o f a l p h a i n c e n t e r o f m ass s y s te m
vc » v e l o c i t y o f c e n t e r o f m ass s y s te m rifch r e s p e c t
t o l a b o r a t o r y s y s te m
v 90* o b s e r v e d v e l o c i t y o f a l p h a
va » o b s e r v e d v e l o c i t y o f a l p h a
]&a « mass o f a l p h a p a r t i c l e
Up * m ass o f p i'o t o n
li
* m ass o f i n t e r m e d i a t e n u c l e u s ( b o r o n + p r o t o n )
S qq » e n e r g y o f a l p h a i n l a b o r a t o r y s y s te m
Ea
m e n e r g y o f a l p h a i n l a b o r a t o r y s y s te m
Ep * e n e r g y o f i n c i d e n t p r o t o n
B
eam
From t h e f i g u r e -
i
v
® \N v V
v
y
V2 * v | + VgQ
(1 )
Vs « V2 + v ~ - sv a vc c o s a
(?)
e q u a t e (1 ) and (2)
2
2
V0O “
8va v c c o s «
( 3)
b u t from c o n s e r v a t i o n o f
momentum
Mve « HpVp
i
*
so
V® = S ilpE p/U ®
'."here Kp= ,ip V p /2 ( 4 )
s u b s t i t u t e ( 4 ) i n t o (2 ) and s i m p l i f y
e 90 * Eo ~
-cos a
I n t h e p r e s e n t w ork we h a v e
« 4
HL **
P
M
80
Eao * \
m
- f v i
12
•cos a /3
F i g . 11 shows t h e c o r r e c t i o n s f o r v a r i o u s v a l u e s
o f a n g l e a*
The c u r v e s may be u s e d w i t h n e g l i g i b l e e r r o r
b e tw e e n 1 6 0 -2 0 0 Kev.
R am ge C o rre c tio n s
fo r
E p s 1 6 0 - 2 0 0 Kcv.
AT
F i g . 11
A n 6UE
Range c o r r e c t i o n s
OC
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