c

Volume 24B, n u m b e r 11

PHYSICS

LETTERS

C h a d w i c k f o r c o n s t r u c t i o n of a p p a r a t u s a n d E . G r e e n e f o r p r o g r a m m i n g of t h e P D P - 8 c o m p u t e r .

r e a s o n a n d t h a t q u o t e d a b o v e we s e t a s a n e s t i m a t e of o u r s e n s i t i v i t y to s y s t e m a t i c e r r o r t h e v a l u e of 0.05 n s e c . T h e r e f o r e we q u o t e a n o v e r a l l r e s u l t of 26.04 + 0.05 n s e c . W e h a v e s e l e c t e d a s u b s e t of t h e d a t a of r e f . 1 w h i c h s h o w a m i n i m u m of t h e r i p p l e s m e n t i o n e d therein. We have reanalyzed these data and their associated calibration and find that the mean lifetime is affected by an amount greater than the error as the lower time limit is increass e d . T h i s m a y b e a t t r i b u t e d t o p o o r l i n e a r i t y of the calibration curve and possible undiscovered electronic circuit effects associated with a single detector for both stopped ~'s and decay p's.

1. K. F. Kinsey, F. Lobkowicz and M. E. Nordberg J r . , Phys. Rev. 144 (1966). 2. M. Eckhouse, R. J. H a r r i s J r . , W. B. Shuler, R.T. Siegel and R . E . W e l s h , Phys. L e t t e r s 19 (1966) 348. 3. M. Bardon, U. Dove, D.Dorfan, M . K r i e g e r , V. L e d e r m a n and E . S c h w a r z , Phys. Rev. L e t t e r s 16 (1966) 775. 4. A. F. Dunaitsev, U. M. Kutyin, Yu. D. Prokoshkin. E. A. Rasuvaev and Yu. N. Simonov, Phys. L e t t e r s 23 (1966) 283. 5. F. Lobkowicz, A. C. Melissinos, Y. Nagashima, S. Tewksbury, H. Von B r i e s e n J r . and J. D. Fox, Phys. Rev. L e t t e r s 17 {1966) 548. 6. D.S. Ayres, D.O. Caldwell, A . J . G r e e n b e r g , R. W, Kenney, R . J . Kurz and B. F. Stearns, UCRL 17193, and Phys. L e t t e r s 24B {1967) 483.

W e w i s h to a c k n o w l e d g e t h e a i d a n d c o o p e r a t i o n of t h e 130" C y c l o t r o n s t a f f a n d e s p e c i a l l y R.

K-p

ELASTIC

29 May 1967

SCATTERING

M. DICKINSON, S. M I Y A S H I T A ,

AT

2.24

GeV/c

L. M A R S H A L L L I B B Y

University of Colorado, Boulder, Colorado*

and P. K E A R N E Y ** Colorado State Universily , F o r t Collins, Colorado. USA

Received 14 April 1967

The differential elastic s c a t t e r i n g c r o s s section for 2.24 G e V / c K-p collisions has been m e a s u r e d in film f r o m the Brookhaven 20" bubble c h a m b e r . The total elastic c r o s s section is found to be 6.2 ± 0.7 rob. The exponential dependence on s q u a r e of the momentum t in (GeV/c)2 is fitted by ( d ( r / d ~ e l a s t i c - (12.4 ± ± 1.0 m b / s r ) e x p ( 7 . 8 1 ±0.25)t. A fit to a black disc model r e q u i r e s a radius of 0.95 • 0.05fm.

E l a s t i c s c a t t e r i n g h a s b e e n m e a s u r e d in K - p c o l l i s i o n s a t 2.24 G e V / c i n c i d e n t b e a m m o m e n t u m u s i n g p h o t o g r a p h s o b t a i n e d w i t h t h e 20" h y drogen bubble chamber and the separated Kbeam from the alternating gradient synchrotron at Brookhaven National Laboratory. The incident m o m e n t u m of t h e K - b e a m ( c o n s t r u c t i o n d e s c r i b e d in d e t a i l e l s e w h e r e [1]) w a s d e f i n e d t o 20 M e V . T h e r e l a t i v e a m o u n t s of K - , ~ - a n d ~ h a s t h e r a t i o s 80%, 5%, 15% w i t h a n e r r o r of d e t e r m i n a t i o n of 3%. A b o u t 15 000 p i c t u r e s w e r e s c a n n e d f o r i n t e r a c t i o n s h a v i n g two c h a r g e d s e c o n d a r y t r a c k s a n d no visible downstream "vee" products. These 596

were measured and analysed using the TREDGRIND kinematic and topological fitting programs. The elastic scatter hypothesis was tested together with several three body final state hypot h e s i s ( K - p n ° , K - n n +, K ° p n - , A ° n+Tr-, Z ° ~ + ~ - ) . No e v e n t s w e r e f o u n d t o b e a m b i g u o u s b e t w e e n t h e e l a s t i c f i t a n d a t h r e e b o d y fit. A n a l y s i s of t h o s e i n t e r a c t i o n s w h i c h w e r e f i t t e d to t h e t h r e e body states containing K ° and K- particles has a l r e a d y b e e n p u b l i s h e d [2]. * Supported by the USAEC, c o n t r a c t n u m b e r AT-(11-1)-1537. ** Supported by the National Science Foundation Sum~ m e r Fellowship P r o g r a m .

Volume 24B, number 11

PHYSICS

LETTERS

29 May 1967 Table 1 Total elastic K-p c r o s s section.

PK-lab (GeV/c)

o.li

O

D 1.0

08

0.6

I 0.4

02

~ 0 -0.2

-0.4

-0.6

COS 0 CM

Fig. 1. Differential elastic s c a t t e r i n g c r o s s section for K-p interactions at 2.24 GeV/c incident K- laboratory momentum. F r o m t h e f i l m , 2319 two p r o n g e d e v e n t s w e r e m e a s u r e d a n d 558 w e r e f o u n d to fit e l a s t i c K - p s c a t t e r s , w i t h ×2 .< 11.7 ( c o n f i d e n c e l e v e l = 0.02). T h e s h a p e of t h e ×2 d i s t r i b u t i o n w a s t y p i c a l of t h a t for 4-constraint fits. In c o m p u t i n g t h e t o t a l e l a s t i c c r o s s s e c t i o n , c o r r e c t i o n s f o r l o s s of e v e n t s a t v e r y s m a l l s c a t t e r i n g a n g l e s w a s n e c e s s a r y . T h e f l u x of K - m e s o n s w a s d e t e r m i n e d by c o u n t i n g b e a m t r a c k s in s e l e c t e d f r a m e s a n d c o r r e c t i n g f o r 20% b e a m c o n t a m i n a t i o n . In o n e m e t h o d of a n a l s y i s t h e f o r w a r d l o s s w a s c o m p u t e d by s i m p l e e x t r a p o l a t i o n of an e x p o n e n t i a l fit of t h e d a t a to z e r o m o m e n t u m transfer. The scanning efficiency for elastic e v e n t s w i t h m o m e n t u m t r a n s f e r to t h e p r o t o n g r e a t e r t h a n 0.1 ( G e V / c ) 2 w a s 93%, a n d w a s c o r rected for. This analysis yields a total elastic c r o s s s e c t i o n of (6.2 ± 0 . 7 ) m b . T h i s v a l u e i s compared with scattering cross sections determ i n e d at o t h e r e n e r g i e s in t a b l e 1. F o r d a t a on t o t a l K - p c r o s s s e c t i o n s , s e e r e f . 9. Alternatively the zero degree scattering cross s e c t i o n can be e v a l u a t e d f r o m the total c r o s s s e c t i o n m e a s u r e d by c o u n t e r e x p e r i m e n t s , u s i n g the optical t h e o r e m 1

(k/4~) ~tot = [(d~/d~)oo, scattering ]e,

7(mb)

Reference

0.300 0.400 0.820 1.040 1.150 1.260

44.5±6.4 38.9±4.7 18.7±0.7 23.3± 1.0 17.3±1.1 15.2±0.7

4 4 5 5 5 5

2.0 2.24 3.0 3.46 7.2 9.0

7.18±0.30 6.2 ! 0 . 7 4.95±0.22 4.94±0.39 4.23±0.85 3.95±0.78

3 p r e s e n t data 6 7 8 8

which is a good a p p r o x i m a t i o n at t h e s e e n e r g i e s [3]. T h e r e l a t i v e d i f f e r e n t i a l c r o s s s e c t i o n d e t e r m i n e d by o u r d a t a i s t h e n f i t t e d to t h e c o m p u t e d v a l u e of (dcr/d~2)0o s u b j e c t to the c o n s t r a i n t t h a t t h e t o t a l a r e a u n d e r the c u r v e (the t o t a l e l a s t i c c r o s s section) a g r e e s with the i n t e r p o l a t e d e l a s t i c s c a t t e r i n g c r o s s s e c t i o n o b t a i n e d f r o m fig. 1. No d i s a g r e e m e n t w a s f o u n d b e t w e e n t h e s e two m e t h o d s of a n a l y s i s , w i t h i n s t a t i s t i c a l e r r o r of t h e measurements. The d i f f e r e n t i a l e l a s t i c c r o s s s e c t i o n is shown in fig. 1. A l e a s t s q u a r e s fit to the d a t a h a s b e e n m a d e f o r m o m e n t u m t r a n s f e r t b e t w e e n 0.1 ( G e V / c ) 2 a n d 0.5 ( G e V / c ) 2 a s s u m i n g an e x p o n e n tial t dependence

d~/dt = (~o exp(-yt ) ~/ = (7.81 + 0.25) ( G e V / c ) - 2 cro = (48.12 ± 3.88) m b

(GeV/c) -2 =

= (12.4 ± 1.0) m b / s t e r . T h e s m o o t h c u r v e in f i g . 1 i s a fit of t h e d i f f e r e n t i a l c r o s s s e c t i o n to t h e f o r m da/d~2 = ~(kR2)2 L r c~ = 0.23

J1 (2kRsin½0)] 2 2kRsin½0 J

R = (0.95 ± 0 . 0 5 ) f m .

The computed total elastic cross section for this e x p r e s s i o n i s ( r e l a s t i c = c~nR 2 = 6.5 m b . We thank Dr. N i c h o l a s S a m i o s and his c o l l e a gues at Brookhaven National Laboratory for lendi n g u s t h e f i l m . We t h a n k o u r s c a n n e r s a n d m e a s u r e r s a n d o u r a s s i s t a n t s in p r o g r a m m i n g * . * Supported by the NSF at the University of Colorado. 597

Volume 24B, number 11

PHYSICS

LETTERS

References

6. M.N. Focacci, S. Focardi, G. Giacomelli, L. M o n a r i P. S e r r a and M. P. Zerbetto, Phys. L e t t e r s 19 (1965) 441. 7. J. Gordon, Phys. L e t t e r s 21 (1966) 117. 8. K . J . Foley, S . J . Lindenbaum, W.A. Love, S. Ozaki, J. J. Russell and L. C. L. Yuan, Phys. Rev. L e t t e r s 11 (1963) 503. 9. R. L. Cool, G. Giacomelli, T. F. Kycia, B.A. Leontic, K.K. Li, A. Lundby and J. Leiger, Phys. Rev. L e t t e r s 16 (1966) 1228.

1. G.W. London, R.R. Rau, N. P. Samios, S. S. Yamanoto, M. Goldberg, S. Lichtman, M. P r i m e and J. Leitner, Phys. Rev. 143 (1966) 1034. 2. M. Dickinson, S. Miyashita, D. Huwe, F. Ayer and L. Marshall, Phys. L e t t e r s 23 (1966) 505. 3. R. Crittenden, H . J . Martin, W. Kernan, L. Leipuner, A. C. Li, F. Ayer, L. Marshall and M. L. Stevenson, Phys. Rev. L e t t e r s 12 (1964) 429. 4. P. Nordin J r . , Phys. Rev. 123 (1961)2168. 5. L.Sodiekson, I.Mannelli. D. F r i s h and M.Wahlig. Phys. Rev. 133 (1964) B757

p-d

ELASTIC

29 May 1967

SCATTERING AT ENERGY REGION

1

LARGE 3.5

ANGLES GeV

IN

THE

Y. D. B A J U K O V , N. G. B I R G U E R , G. K. B I S H E V A , V. S. BORISOV, V. B. F E D O R O V , L. L. GOLDIN, L. N. K O N D R A T J E V , M. M. K O R O T K O V , G . A . L E K S I N , V. D. SCHOVANSKY, Z. S. S I D O R E N K O , L. I. S O K O L O V , G. K. T U M A N O V and L. S. V O R O B J E V

Institute for Theorelical and Experimental Physics, Academy of Sciences, Moscow Received 25 April 1967

Differential c r o s s - s e c t i o n s of p-d elastic s c a t t e r i n g at large angles (0c.m. >~ 150o) have been m e a s u r e d in the energy interval 1-3.5 GeV. The r e s u l t s a r e compared with pole model predictions.

In r e c e n t y e a r s c o n s i d e r a b l e a t t e n t i o n h a s b e e n p a i d to t h e b a c k w a r d s c a t t e r i n g p r o c e s s e s w h i c h a r e i n f l u e n c e d by the b a r y o n e x c h a n g e d i a gram. We have measured elastic p-d scattering differential cross-sections, which are very in-

s u f f i c i e n t l y s t u d i e d at h i g h e n e r g i e s . A t t h e v e r y beginning attention w a s paid to the angle r a n g e c o s 0* < - 0 . 8 5 , w h e r e o n e c a n e x p e c t a c o n s i d e r a b l e c o n t r i b u t i o n f r o m t h e n e u t r o n p o l e . It i s w o r t h noticing that all the i s o b a r exchange dia-

Fig. 1. The experimental set-up a r r a n g e m e n t .

598