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Coherent K∗ (890) production off deuterium
Volume 28 B, n u m b e r 5
COHERENT
PHYSICS
K*(890)
LETTERS
PRODUCTION
23 D e c e m b e r 1968
OFF
DEUTERIUM
t
R. L . E I S N E R :~, A. C. A M M A N N , D . D . C A R M O N Y , A. F. G A R F I N K E L , L. J. G U T A Y , R. V. L A K S H M I , D. H. M I L L E R , G . W . T A U T F E S T $$ a n d W. L . Y E N $$$ Department of Physics, Purdue University, Lafayette, Indiana 47907, USA Received 15 November 1968
We have studied 76 events of the reaction K-d --" dI~°~ - at 4.5 GeV/c. The r e a c t i o n is dominated by the p r o duction of K*(890) and is analyzed in t e r m s of omega exchange. The density m a t r i x e l e m e n t s are obtained.
T h e f o l l o w i n g a n a l y s i s i s b a s e d on a s t u d y of 76 e v e n t s of t h e r e a c t i o n K - d -* dK°Tr -
(I)
a t a n i n c i d e n t m o m e n t u m of 4.5 G e V / c . T h e s e e v e n t s c o m e f r o m a 4 0 0 000 p i c t u r e e x p o s u r e taken in the 30" deuterium filled bubble chamber at Argonne National Laboratory. The pion contamination in the beam was negligible and the film was scanned twice for all Vee events [i]. Since we have required that the recoiling deuteron be v i s i b l e , t h e s t u d y of r e a c t i o n (1) i s l i m i t e d to events where the deuteron has a laboratory mom e n t u m of a t l e a s t 150 M e V / c . F o r e a c h e v e n t we have obtained a satisfactory two-vertex sevenc o n s t r a i n t k i n e m a t i c a l f i t a n d a l l of t h e V e e s h a v e been unambiguously identified as ~o mesons. We h a v e f o u n d a t o t a l s a m p l e of 76 e v e n t s w h i c h f i t r e a c t i o n (1) w i t h a ×2 p r o b a b i l i t y of a t l e a s t o n e p e r c e n t ~ . Of t h e s e e v e n t s o n l y t h r e e a r e u n a m b i g u o u s , t h a t i s b o t h t h e r a n g e a n d c u r v a t u r e of t h e d e u t e r o n w e r e m e a s u r e d . T h e r e m a i n i n g 73 e v e n t s h a v e a s a t i s f a c t o r y f i t to t h e r e a c t i o n
K - d --*pn~°zr - .
(2)
In fig. la w e show a scatter plot of the neutron m o m e n t u m (Pn) versus the proton m o m e n t u m (Pp) for the events which fit reaction (I) w h e n
--
f
!it //
o
! •I
"
i/l/I/ (a)
".."
... ~,/". . . "lb" / " ~11.
-.
/
,
•
I
I
I
.2
.3
.4
Prolon Momenlurn (~N,~)
(&)
|
40-
30-
"S
!
20-
io-
1.87
356
/
•2 -
o
~" Supported in p a r t by the U.S. Atomic Energy Commission. :~ Now at Brookhaven National Laboratory. ~[$ Deceased. $~[:~ Now at Purdue University Indianapolis Campus. ?'~ We have also examined the events that have an acceptable X2 for r e a c t i o n (1) with an u n s e e n deuteron. F u r t h e r a n a l y s i s of these approximately 100 events indicates a contamination of roughly 50% and hence these events have not been used in the subsequent analysis.
/ /
~[u__ 1.90
I.(J5
M pn (GeV)
Fig. l a . Scatter plot of the n e u t r o n m o m e n t u m v e r s u s the proton m o m e n t u m f o r the events of r e a c t i o n (1) when i n t e r p r e t e d as r e a c t i o n (2). The solid line is the predicted c u r v e ( P n / P p = 0.64). The dotted lines a r e P n / P p = 0.2 and 1.2. lb. The proton n e u t r o n effective m a s s for events which fit reaction (2) with the r a t i o of the n e u t r o n m o m e n t u m to the proton m o m e n t u m in the range 0.2 to 1.2. The shaded events also fit r e a c t i o n (1).
Volume 28B, number 5
PHYSICS
LETTERS
t h e y a r e i n t e r p r e t e d a s r e a c t i o n (2). I d e a l l y if an unbroken deuteron is fitted as a proton neutron e v e n t the r a t i o Pn/Pv s h o u l d b e 0.64 by r a n g e e n e r g y c o n s i d e r a t i o n ' s (2). T h e e v e n t s h a v e 0.2 <
IU1
I .8
(3)
T h e m a s s of the K*(890) i s found to b e 885 + 5 15 MeV and the width of the d i s t r i b u t i o n is 5 5 , 10 MeV. We do not o b s e r v e t h e d* e f f e c t [3] w h i c h c a n not be p r o d u c e d in a o n e p i o n e x c h a n g e d i a g r a m in r e a c t i o n (1). T h e f o u r - m o m e n t u m t r a n s f e r d i s t r i b u t i o n (A2) b e t w e e n the i n c i d e n t K - and t h e K*(890) i s shown in fig. 2b. T h e s e ~d a t a a r e p e r i p h e r a l in the s e n s e t h a t if we d i v i d e the e x p e r i m e n t a l f o u r - m o m e n t u m transfer distribution by the deuteron form factor s q u a r e d [4] the r e s u l t a n t i s of the f o r m e x p - 6 4 2. If we a s s u m e that K*(890) p r o d u c t i o n can be r e p r e s e n t e d by a one p a r t i c l e e x c h a n g e d i a g r a m , t h e d e u t e r o n l i m i t s the i s o t o p i c s p i n of the e x c h a n g e d p a r t i c l e to z e r o . S i n c e the e x c h a n g e of pseudoscalar mesons is apparently unimportant at o u r e n e r g y [5], t h i s c h a n n e l i s o l a t e s the v e c t o r e x c h a n g e c o n t r i b u t i o n to K* p r o d u c t i o n . We a s s u m e that the ¢ m e s o n i s w e a k l y c o u p l e d to the d e u t e r o n [5,6] and h e n c e f o r t h c o n s i d e r only w e x c h a n g e [7] # . T h e d e c a y a n g u l a r d i s t r i b u t i o n of the K*(890) s y s t e m in t e r m s of i t s s p i n s p a c e d e n s i t y m a t r i x elements is ~f We have also examined a plot of Pn/Pp versus cos ~ where ~ is the fitted angle between the neutron and proton in the lab system. The 76 events which we have chosen form a cluster near cos ~ = 1 and satisfy 0.2 < Pn/Pp < 1.2. See footnote on next page.
23 December 1968
•
'1
!
,
{a}
T t.O
I
t
t
f
1.2 MKw
i
1.4 (C.~V)
,
0
,
,04
,08
.12
.16
.20
Fig. 2a. The ~o~.- effective m a s s in the reaction K-d ~ dl~Olr-. The curve is a simple Breit-Wigner fitted to the 53 events above background. (E* = 885 ± ± 5 MeV and r = 55+!5-,vM e V ) . _ 2b. The four momez~[um tran~,=r distribution between the incident K - a n d the K*(890) defined as 850 MeV < MKTI < 950 MeV. The curve is exp(-6A2) times the square of the deuteron form factor. 3
W(0, ~) = ~
[P00 c ° s 2 0 + P l l s i n 2 0 +
(4)
-Pl,-1
sin2 0 c o s 2 ~ - J - 2 R e P l 0 s i n 2 0 c o s ~]
w h e r e 0 and ~ a r e the p o l a r and a z i m u t h a l a n g l e s of the K ° in the K* r e s t f r a m e . O m e g a e x c h a n g e r e q u i r e s that P00 and Re P l 0 b e z e r o and t h u s we would e x p e c t a sin 20 d e c a y a n g u l a r d i s t r i b u t i o n . In fig. 3a and 3b w e g i v e the c o s 8 and ~ p r o j e c -
35'7
Volume 28B, number 5
PHYSICS
Io
P00 + P l l + P - 1 , - I
[
/
i Of I0"
23 December 1968
\\
-0.8
'
I
-0.4
I
l
!
o cos
r
I
0.4
= 1 ,
(6)
d e t e r m i n e s P l l to b e 0.44 ± 0.05. T h e a b o v e i s in good a g r e e m e n t w i t h v e c t o r e x c h a n g e . We n o t e that in c h a r g e d K*(890) p r o d u c t i o n off n u c l e o n s , the P00 d e n s i t y m a t r i x e l e m e n t s h o w s a r a p i d c h a n g e f r o m a b o u t 0,4 to 0.0 in o u r m o m e n t u m t r a n s f e r r e g i o n [8]. D o n a h u e h a s i n t e r p r e t e d t h i s a s i n d i c a t i v e of the p r e s e n c e of both and ¢o e x c h a n g e [9]. O u r r e s u l t s h o w s that the ¢o e x c h a n g e c o n t r i b u t i o n to K*(890) p r o d u c t i o n i s i m p o r t a n t e v e n at low m o m e n t u m t r a n s f e r s . In a f o r t h c o m i n g p u b l i c a t i o n we w i l l t e s t D o n a h u e ' s p r e d i c t i o n that the s i g n of the i n t e r f e r e n c e b e t w e e n 7r and ¢o e x c h a n g e in the r e a c t i o n K - n -* K * - n i s o p p o s i t e to that in K - p --" K * - p in t h i s momentum transfer region.
(a}
,.>,
LETTERS
0.8
0
We would l i k e to thank D r . D. J. G e o r g e f o r v a l u a b l e d i s c u s s i o n s . We a l s o thank the a c c e l e r a t o r and b u b b l e c h a m b e r s t a f f s at A N L and o u r p r o g r a m m e r s and m e a s u r e r s at P u r d u e .
(b)
#We note that an expression for coherent K* production would involve 27 helicity amplitudes. In the Born approximation the helicity amplitudes are of the form r ~ , ~ ~Ev + a c a v / m 2 ~ K
/ O1
-18(
I
I
I
r
I
-90
where V~ is the K,-,~K* vertex function used by Jackson [5] and F~ '~t is the DwD vertex function and where ~.,~.' and g are the helicity of the incident deuteron, the outgoing deuteron and the K* respectively. The D~oD vertex is parameterized as
\ I
I
0
I
1
I
90
180
(degrees)
- ¢(A2) E,5
Fig. 3. The K*(890) decay angular distributions a) for the Jackson angle (cos 0) and b) for the Trieman-Yang angle (~p). The curves represent the best fits to the density matrix elements.
t i o n of the K*(890) d e c a y d i s t r i b u t i o n . T h e c u r v e s s h o w n w e r e o b t a i n e d by f i t t i n g the d e n s i t y m a t r i x e l e m e n t s by the m e t h o d of m o m e n t s . T h e d e n s i t y m a t r i x e l e m e n t s so o b t a i n e d a r e P00
= 0.12 ± 0.1
Pl,-1
=0.38 ±0.1
and
(5) Re Pl0
= 0.04
± 0.04
.
S i n c e p 11 = P- 1, - 1 the t r a c e c o n d i t i o n
358
Y ' ~ " = [¢x(A2) ~ ) ' 6 p -~- .y(A2) do ~'~3"d'v 6~] (d+d')E +
jv
where ot,fl, and ~ denote DcoD coupling constants, were the four vectors do, d'O denote the momenta of the incident and ou,tgbing ~leuteron respectively, and where 6~ and 8'~t denote polarization four vectors of the incident and outgoing deuteron with helicity k and k' respectively. References 1. R. L, Eisner, P h . D . Thesis, Purdue University, 1968 (unpublished). 2. M.A.Abolins, P h . D . Thesis, University of California at San Diego, 1965 (unpublished). 3. M.A. Abolins, D.D. Carmony, R. L. Lander and Ng.-h.Xuong, Phys. Rev. Letters 15 (1965) 125. 4. M. Gourdin and A. Martin, Nuovo Cimento 11 (1959) 67O; I. Butterworth, J. L. Brown, G. Goldhaber, S. Goldhaber, A.A. Hirata, J . A . Kadyk and G. H. Trilling, Phys. Rev. Letters 15 (1965) 500; D. Denegri, A. Callahan, L. Ettlinger, D. Gillespie, G. Goodman, G. Luste, R. Mercer, E. Moses, A. Pevsner and It. Zdanis, Phys. Rev. Letters 20 (1968) 1194.
Volume28B, number 5
PHYSICS
5. J. D. Jackson and H. Pilkuhn, Nuovo Cimento 33 (1964) 9O6; J. D. Jackson, J. T. Donohue, K. Gottfried, R. K e y s e r and B. E. Y. Svensson, Phys. Rev. 139 (1965) B428. 6. H. Sugawara and Frank Von Hippel, Phys. Rev. 145 (1966) 1331.
LETTERS
23 D e c e m b e r 1968
7. D.J. George and L . J . Gutay (Purdue Internal Note). 8. F. Schweingruber, M. Derrick, T. Fields, D. Griffiths, L.G. Hyman, R . J . Jabbur, J. Loken, R. A m m a r , R. E. P. Davis, W. Kropac and J. Mort, Phys. Rev. 166 (1968) 1317. 9. J. T. Donohue, Phys. Rev. 163 (1967) 1549.
359
COHERENT
PHYSICS
K*(890)
LETTERS
PRODUCTION
23 D e c e m b e r 1968
OFF
DEUTERIUM
t
R. L . E I S N E R :~, A. C. A M M A N N , D . D . C A R M O N Y , A. F. G A R F I N K E L , L. J. G U T A Y , R. V. L A K S H M I , D. H. M I L L E R , G . W . T A U T F E S T $$ a n d W. L . Y E N $$$ Department of Physics, Purdue University, Lafayette, Indiana 47907, USA Received 15 November 1968
We have studied 76 events of the reaction K-d --" dI~°~ - at 4.5 GeV/c. The r e a c t i o n is dominated by the p r o duction of K*(890) and is analyzed in t e r m s of omega exchange. The density m a t r i x e l e m e n t s are obtained.
T h e f o l l o w i n g a n a l y s i s i s b a s e d on a s t u d y of 76 e v e n t s of t h e r e a c t i o n K - d -* dK°Tr -
(I)
a t a n i n c i d e n t m o m e n t u m of 4.5 G e V / c . T h e s e e v e n t s c o m e f r o m a 4 0 0 000 p i c t u r e e x p o s u r e taken in the 30" deuterium filled bubble chamber at Argonne National Laboratory. The pion contamination in the beam was negligible and the film was scanned twice for all Vee events [i]. Since we have required that the recoiling deuteron be v i s i b l e , t h e s t u d y of r e a c t i o n (1) i s l i m i t e d to events where the deuteron has a laboratory mom e n t u m of a t l e a s t 150 M e V / c . F o r e a c h e v e n t we have obtained a satisfactory two-vertex sevenc o n s t r a i n t k i n e m a t i c a l f i t a n d a l l of t h e V e e s h a v e been unambiguously identified as ~o mesons. We h a v e f o u n d a t o t a l s a m p l e of 76 e v e n t s w h i c h f i t r e a c t i o n (1) w i t h a ×2 p r o b a b i l i t y of a t l e a s t o n e p e r c e n t ~ . Of t h e s e e v e n t s o n l y t h r e e a r e u n a m b i g u o u s , t h a t i s b o t h t h e r a n g e a n d c u r v a t u r e of t h e d e u t e r o n w e r e m e a s u r e d . T h e r e m a i n i n g 73 e v e n t s h a v e a s a t i s f a c t o r y f i t to t h e r e a c t i o n
K - d --*pn~°zr - .
(2)
In fig. la w e show a scatter plot of the neutron m o m e n t u m (Pn) versus the proton m o m e n t u m (Pp) for the events which fit reaction (I) w h e n
--
f
!it //
o
! •I
"
i/l/I/ (a)
".."
... ~,/". . . "lb" / " ~11.
-.
/
,
•
I
I
I
.2
.3
.4
Prolon Momenlurn (~N,~)
(&)
|
40-
30-
"S
!
20-
io-
1.87
356
/
•2 -
o
~" Supported in p a r t by the U.S. Atomic Energy Commission. :~ Now at Brookhaven National Laboratory. ~[$ Deceased. $~[:~ Now at Purdue University Indianapolis Campus. ?'~ We have also examined the events that have an acceptable X2 for r e a c t i o n (1) with an u n s e e n deuteron. F u r t h e r a n a l y s i s of these approximately 100 events indicates a contamination of roughly 50% and hence these events have not been used in the subsequent analysis.
/ /
~[u__ 1.90
I.(J5
M pn (GeV)
Fig. l a . Scatter plot of the n e u t r o n m o m e n t u m v e r s u s the proton m o m e n t u m f o r the events of r e a c t i o n (1) when i n t e r p r e t e d as r e a c t i o n (2). The solid line is the predicted c u r v e ( P n / P p = 0.64). The dotted lines a r e P n / P p = 0.2 and 1.2. lb. The proton n e u t r o n effective m a s s for events which fit reaction (2) with the r a t i o of the n e u t r o n m o m e n t u m to the proton m o m e n t u m in the range 0.2 to 1.2. The shaded events also fit r e a c t i o n (1).
Volume 28B, number 5
PHYSICS
LETTERS
t h e y a r e i n t e r p r e t e d a s r e a c t i o n (2). I d e a l l y if an unbroken deuteron is fitted as a proton neutron e v e n t the r a t i o Pn/Pv s h o u l d b e 0.64 by r a n g e e n e r g y c o n s i d e r a t i o n ' s (2). T h e e v e n t s h a v e 0.2 <
IU1
I .8
(3)
T h e m a s s of the K*(890) i s found to b e 885 + 5 15 MeV and the width of the d i s t r i b u t i o n is 5 5 , 10 MeV. We do not o b s e r v e t h e d* e f f e c t [3] w h i c h c a n not be p r o d u c e d in a o n e p i o n e x c h a n g e d i a g r a m in r e a c t i o n (1). T h e f o u r - m o m e n t u m t r a n s f e r d i s t r i b u t i o n (A2) b e t w e e n the i n c i d e n t K - and t h e K*(890) i s shown in fig. 2b. T h e s e ~d a t a a r e p e r i p h e r a l in the s e n s e t h a t if we d i v i d e the e x p e r i m e n t a l f o u r - m o m e n t u m transfer distribution by the deuteron form factor s q u a r e d [4] the r e s u l t a n t i s of the f o r m e x p - 6 4 2. If we a s s u m e that K*(890) p r o d u c t i o n can be r e p r e s e n t e d by a one p a r t i c l e e x c h a n g e d i a g r a m , t h e d e u t e r o n l i m i t s the i s o t o p i c s p i n of the e x c h a n g e d p a r t i c l e to z e r o . S i n c e the e x c h a n g e of pseudoscalar mesons is apparently unimportant at o u r e n e r g y [5], t h i s c h a n n e l i s o l a t e s the v e c t o r e x c h a n g e c o n t r i b u t i o n to K* p r o d u c t i o n . We a s s u m e that the ¢ m e s o n i s w e a k l y c o u p l e d to the d e u t e r o n [5,6] and h e n c e f o r t h c o n s i d e r only w e x c h a n g e [7] # . T h e d e c a y a n g u l a r d i s t r i b u t i o n of the K*(890) s y s t e m in t e r m s of i t s s p i n s p a c e d e n s i t y m a t r i x elements is ~f We have also examined a plot of Pn/Pp versus cos ~ where ~ is the fitted angle between the neutron and proton in the lab system. The 76 events which we have chosen form a cluster near cos ~ = 1 and satisfy 0.2 < Pn/Pp < 1.2. See footnote on next page.
23 December 1968
•
'1
!
,
{a}
T t.O
I
t
t
f
1.2 MKw
i
1.4 (C.~V)
,
0
,
,04
,08
.12
.16
.20
Fig. 2a. The ~o~.- effective m a s s in the reaction K-d ~ dl~Olr-. The curve is a simple Breit-Wigner fitted to the 53 events above background. (E* = 885 ± ± 5 MeV and r = 55+!5-,vM e V ) . _ 2b. The four momez~[um tran~,=r distribution between the incident K - a n d the K*(890) defined as 850 MeV < MKTI < 950 MeV. The curve is exp(-6A2) times the square of the deuteron form factor. 3
W(0, ~) = ~
[P00 c ° s 2 0 + P l l s i n 2 0 +
(4)
-Pl,-1
sin2 0 c o s 2 ~ - J - 2 R e P l 0 s i n 2 0 c o s ~]
w h e r e 0 and ~ a r e the p o l a r and a z i m u t h a l a n g l e s of the K ° in the K* r e s t f r a m e . O m e g a e x c h a n g e r e q u i r e s that P00 and Re P l 0 b e z e r o and t h u s we would e x p e c t a sin 20 d e c a y a n g u l a r d i s t r i b u t i o n . In fig. 3a and 3b w e g i v e the c o s 8 and ~ p r o j e c -
35'7
Volume 28B, number 5
PHYSICS
Io
P00 + P l l + P - 1 , - I
[
/
i Of I0"
23 December 1968
\\
-0.8
'
I
-0.4
I
l
!
o cos
r
I
0.4
= 1 ,
(6)
d e t e r m i n e s P l l to b e 0.44 ± 0.05. T h e a b o v e i s in good a g r e e m e n t w i t h v e c t o r e x c h a n g e . We n o t e that in c h a r g e d K*(890) p r o d u c t i o n off n u c l e o n s , the P00 d e n s i t y m a t r i x e l e m e n t s h o w s a r a p i d c h a n g e f r o m a b o u t 0,4 to 0.0 in o u r m o m e n t u m t r a n s f e r r e g i o n [8]. D o n a h u e h a s i n t e r p r e t e d t h i s a s i n d i c a t i v e of the p r e s e n c e of both and ¢o e x c h a n g e [9]. O u r r e s u l t s h o w s that the ¢o e x c h a n g e c o n t r i b u t i o n to K*(890) p r o d u c t i o n i s i m p o r t a n t e v e n at low m o m e n t u m t r a n s f e r s . In a f o r t h c o m i n g p u b l i c a t i o n we w i l l t e s t D o n a h u e ' s p r e d i c t i o n that the s i g n of the i n t e r f e r e n c e b e t w e e n 7r and ¢o e x c h a n g e in the r e a c t i o n K - n -* K * - n i s o p p o s i t e to that in K - p --" K * - p in t h i s momentum transfer region.
(a}
,.>,
LETTERS
0.8
0
We would l i k e to thank D r . D. J. G e o r g e f o r v a l u a b l e d i s c u s s i o n s . We a l s o thank the a c c e l e r a t o r and b u b b l e c h a m b e r s t a f f s at A N L and o u r p r o g r a m m e r s and m e a s u r e r s at P u r d u e .
(b)
#We note that an expression for coherent K* production would involve 27 helicity amplitudes. In the Born approximation the helicity amplitudes are of the form r ~ , ~ ~Ev + a c a v / m 2 ~ K
/ O1
-18(
I
I
I
r
I
-90
where V~ is the K,-,~K* vertex function used by Jackson [5] and F~ '~t is the DwD vertex function and where ~.,~.' and g are the helicity of the incident deuteron, the outgoing deuteron and the K* respectively. The D~oD vertex is parameterized as
\ I
I
0
I
1
I
90
180
(degrees)
- ¢(A2) E,5
Fig. 3. The K*(890) decay angular distributions a) for the Jackson angle (cos 0) and b) for the Trieman-Yang angle (~p). The curves represent the best fits to the density matrix elements.
t i o n of the K*(890) d e c a y d i s t r i b u t i o n . T h e c u r v e s s h o w n w e r e o b t a i n e d by f i t t i n g the d e n s i t y m a t r i x e l e m e n t s by the m e t h o d of m o m e n t s . T h e d e n s i t y m a t r i x e l e m e n t s so o b t a i n e d a r e P00
= 0.12 ± 0.1
Pl,-1
=0.38 ±0.1
and
(5) Re Pl0
= 0.04
± 0.04
.
S i n c e p 11 = P- 1, - 1 the t r a c e c o n d i t i o n
358
Y ' ~ " = [¢x(A2) ~ ) ' 6 p -~- .y(A2) do ~'~3"d'v 6~] (d+d')E +
jv
where ot,fl, and ~ denote DcoD coupling constants, were the four vectors do, d'O denote the momenta of the incident and ou,tgbing ~leuteron respectively, and where 6~ and 8'~t denote polarization four vectors of the incident and outgoing deuteron with helicity k and k' respectively. References 1. R. L, Eisner, P h . D . Thesis, Purdue University, 1968 (unpublished). 2. M.A.Abolins, P h . D . Thesis, University of California at San Diego, 1965 (unpublished). 3. M.A. Abolins, D.D. Carmony, R. L. Lander and Ng.-h.Xuong, Phys. Rev. Letters 15 (1965) 125. 4. M. Gourdin and A. Martin, Nuovo Cimento 11 (1959) 67O; I. Butterworth, J. L. Brown, G. Goldhaber, S. Goldhaber, A.A. Hirata, J . A . Kadyk and G. H. Trilling, Phys. Rev. Letters 15 (1965) 500; D. Denegri, A. Callahan, L. Ettlinger, D. Gillespie, G. Goodman, G. Luste, R. Mercer, E. Moses, A. Pevsner and It. Zdanis, Phys. Rev. Letters 20 (1968) 1194.
Volume28B, number 5
PHYSICS
5. J. D. Jackson and H. Pilkuhn, Nuovo Cimento 33 (1964) 9O6; J. D. Jackson, J. T. Donohue, K. Gottfried, R. K e y s e r and B. E. Y. Svensson, Phys. Rev. 139 (1965) B428. 6. H. Sugawara and Frank Von Hippel, Phys. Rev. 145 (1966) 1331.
LETTERS
23 D e c e m b e r 1968
7. D.J. George and L . J . Gutay (Purdue Internal Note). 8. F. Schweingruber, M. Derrick, T. Fields, D. Griffiths, L.G. Hyman, R . J . Jabbur, J. Loken, R. A m m a r , R. E. P. Davis, W. Kropac and J. Mort, Phys. Rev. 166 (1968) 1317. 9. J. T. Donohue, Phys. Rev. 163 (1967) 1549.
359