- Email: [email protected]
c
~
Nuclear Physics B29 (1971) 413-430. North-Holland Publishing Company
ELASTIC SCATTERING OF NEGATIVE KAONS ON POLARIZED PROTONS BETWEEN 865 AND 1330 MeV/c M. G. A L B R O W , S. A N D E R S S O N - A L M E H E D *, B. B O ~ N J A K O V I C **, F. C. E R N E **, Y. K I M U R A $, J. P. L A G N A U X :~:~, J. C. SENS ** and F. UDO C E R N , Geneva, Switzerland
Received 16 March 1971
Abstract: Polarization and differential c r o s s - s e c t i o n data for elastic scattering of negative kaons on p o l a r i z e d protons between 865 and 1330 MeV/c a r e presented. Comparisons are made with predictions given by published energy dependent p h a s e - s h i f t analyses. The Legendre expansion coefficients c h a r a c t e r i z i n g the polarization distributions show r e m a r k a b l e s t r u c t u r e s resulting from excitation of A - and ~ - r e s o n a n c e s . An analysis of the elastic and charge-exchange data in this region of momenta supports the assignments of J P = 9 + for the A(1870) r e sonance. The occurrence of z e r o c r o s s i n g s in the polarization data is discussed.
1. I N T R O D U C T I O N A c o n s i d e r a b l e a m o u n t of e x p e r i m e n t a l d a t a on e l a s t i c KN s c a t t e r i n g h a s b e e n a c c u m u l a t e d o v e r t h e p a s t few y e a r s ; n e v e r t h e l e s s , the p a r t i a l w a v e a m p l i t u d e s h a v e t h u s f a r not b e e n d e t e r m i n e d a c c u r a t e l y o t h e r than f o r m o m e n t a b e l o w 500 M e V / c . The p r e s e n c e of m a n y i n e l a s t i c r e s o n a n c e s in t h i s c h a n n e l m a k e s a m o d e l i n d e p e n d e n t p a r t i a l w a v e a n a l y s i s v e r y d i f f i c u l t . To d i s e n t a n g l e s u c h a c o m p l i c a t e d s t r u c t u r e of t h e a m p l i t u d e s , t h e r e f o r e , s y s t e m a t i c d a t a on p o l a r i z a t i o n s a r e i n d i s p e n s a b l e . M e a s u r e m e n t s of t h e p o l a r t . z a t i o n in e l a s t i c s c a t t e r i n g of n e g a t i v e k a o n s on p r o t o n s h a v e b e e n m a d e by W a n g [1], b y C o x e t al. [2], by D a u m e t al. [3] and by A n d e r s s o n et al. [4]. In t h i s c o n t r i b u t i o n w e p r e s e n t p o l a r i z a t i o n d i s t r i b u t i o n s and d i f f e r e n t i a l c r o s s s e c t i o n s f o r t h e e l a s t i c s c a t t e r i n g of n e g a t i v e k a o n s on p o l a r i z e d p r o t o n s a t 865, 935, 1010, 1035, 1055, 1177, 1250 a n d 1330 M e V / c . T h e r e s u l t s a r e c o m p a r e d w i t h the p r e d i c t i o n s of e n e r g y d e p e n d e n t p h a s e - s h i f t a n a l y s e s by C o n f o r t o e t al. [5] and by B r i c m a n e t al. [6]. T h e d a t a , t o g e t h e r * Visitor from the Institute of P h y s i c s , University of Lund, Sweden. ** Visitor from the Foundation for Fundamental R e s e a r c h of Matter, (FOM), Utrecht, The Netherlands. On leave of absence from the University of Tokyo, Tokyo, Japan. :~:~ Visitor from the Institut I n t e r u n i v e r s i t a i r e des Sciences Nucl~aires, B r u s s e l s , Belgium.
414
M . G . A l b r o w et a l . , l i - e l a s t i c s c a t t e r i n g
with those of ref. [4] and c h a r g e exchange data in the s a m e region of m o menta, have been analysed in t e r m s of a background plus r e s o n a n c e model.
2. MEASUREMENTS AND ANALYSIS The e x p e r i m e n t has been p e r f o r m e d in a 23 m long u n s e p a r a t e d beam at the CERN PS. The incoming b e a m s w e r e identified with a ~ e r e n k o v counter and by t i m e of flight over an 11 m flight path. The m o m e n t u m bite was ± 2 ~ Two-body events w e r e selected by r e q u i r i n g coincidences between s c a t t e r e d kaons and recoil protons in counter hodoscopes placed in the horizontal plane around a v e r t i c a l l y polarized target. In the range of m o m e n t a and angles of the p r e s e n t e x p e r i m e n t the s c a t t e r e d kaons can c l e a r l y be d i s t i n guished f r o m the r e c o i l protons by angle m e a s u r e m e n t s alone. A butanol p o l a r i z e d t a r g e t [7] cooled with liquid 3He (~ 0.5°K, polarization ~ 65%) was used throughout the p r e s e n t e x p e r i m e n t except for the data at 1250 M e V / c where the t a r g e t was cooled with liquid 4He (~ l°K, p o l a r i z a tion ~ 35%). The t a r g e t polarization deduced f r o m NMR signals was r e corded between e v e r y PS burst. The absolute calibration of the polarization was obtained by m e a s u r i n g the natural NMR signal at r e g u l a r intervals. The t a r g e t polarization was r e v e r s e d e v e r y ~ 10 h. In the a n a l y s i s , background events, mostly due to bound protons in the t a r g e t were subtracted out after extrapolating into the elastic peak the a z i muthal distribution of n o n - c o p l a n a r events m e a s u r e d simultaneously. The c.m. angles and effective solid angles w e r e obtained f r o m s t r a i g h t f o r w a r d kinematic calculations taking into account energy l o s s , absorption and m u l tiple s c a t t e r i n g in the t a r g e t , and deflection of the p a r t i c l e s by the magnetic field. At angles c o r r e s p o n d i n g to cos Oc.m. > 0.8, the m o m e n t u m of the r e coil protons b e c o m e s so small (~ 250 MeV/c) that the effective solid angle cannot be calculated accurately. T h e r e f o r e , at these angles the differential c r o s s - s e c t i o n data a r e omitted f r o m the final r e s u l t s and only the p o l a r i z a tion data a r e p r e s e n t e d since these do not depend on the solid angle. The alignment of the counter hodoscopes was checked by r e q u i r i n g a g r e e m e n t of the differential c r o s s - s e c t i o n data in which the kaon s c a t t e r s to the left with those for s c a t t e r i n g to the right. The relative n o r m a l i z a t i o n of the n u m b e r of events was checked to be c o r r e c t by r e q u i r i n g consistency between the polarization data with kaon left and kaon right. In the final r e s u l t s these two sets of data w e r e grouped in c o s O c . m , bins v a r y i n g between 0.02 and 0.08 and replaced by their weighted a v e r a g e s . The details of the apparatus and the data-handling p r o c e d u r e s of the p r e s e n t e x p e r i m e n t have been d e s c r i b e d in ref. [3] and in ref. [8]. The r e s u l t s a r e p r e s e n t e d in tables 1-8 and in figs. 1 and 2. The sign of the polarization is based on the Basel convention. The polarization e r r o r s a r e statistical only. The t a r g e t polarization d e t e r m i n e d f r o m NMR m e a s u r e m e n t s also has a relative uncertainty of about ±5~; this s y s t e m a t i c e r r o r has not been included in the tables and figures. The s y s t e m a t i c e r r o r a r i s i n g f r o m u n c e r t a i n t i e s in the alignment of the c o u n t e r s , the counter inefficiencies, and the effective solid angle is e s t i m a t e d to be 5% and has been included in the differential c r o s s - s e c t i o n data.
M. G . A l b r o w et al., K - elastic s c a t t e r i n g
415
Table 1 Elastic K p scattering. P
dd(~ ~ (mb/sr)
d(~
P~
(mb/sr)
cos 0c.m.
- t (GeV 2)
0.787 0.732 0.686 0.638 0.591 0,544 0.496
0.09 0.12 0.14 0.16 0.18 0.20 0.22
0.20+0.12 0.51 + 0.09 0.44 + 0.09 0.49 + 0.09 0.61 + 0.09 0.70+0.11 0.76 + 0.12
3.10 + 0.31 2.86 + 0.28 2.28 + 0.16 2.06 + 0.15 1.72+0.13 1.37 + 0.12
1.58+0.38 1.26+0.34 1.12-0.19 1.254-0.18 1.20+0.17 1.04+0.15
0,459 0.420 0.369 0.318 0.267 0.226 0.177
0.24 0.26 0.28 0.30 0.32 0.34 0.36
0.66 0.75 0.80 0.81 0.84 0.75 0.79
+ 0.19 + 0.12 + 0.13 + 0.14 + 0.15 + 0.24 + 0.12
1.17 + 0.14 1.20 + 0.10 1.144- 0.10 1.00 + 0.10 0.89 + 0.09 0.77 + 0.11 0.78 + 0.06
0.77+0.18 0.90-0.14 0.91~-0.13 0.81"0.13 0.75+0.12 0.58+0.14 0.62+0.09
0.139 0.077 0.018 -0.053 -0.133 -0.220 -0.304
0.38 0.41 0.43 0.46 0.50 0.54 0.57
0.60 0.61 0.66 0.55 0.27 0.38 0.18
+ 0.25 + 0.16 + 0.19 + 0.14 + 0.21 + 0.16 + 0.27
0.64 0.59 0.59 0.55 0.40 0.36 0.30
+ 0.10 + 0.06 + 0.08 + 0.05 + 0.06 + 0.04 + 0.06
0.39+0.14 0.36+0.08 0.39+0.10 0.30+0.07 0.11+0.07 0.144-0.06 0.05+0.08
-0.367 -0.442 -0.519 -0.593 -0.653 -0.726 -0.803
0.60 0.63 0.67 0.70 0.73 0.76 0.79
-0.11 + 0.28 -0.61 + 0.30 -0.62 + 0.21 -0.59 + 0.23 -0.33 + 0.23 -0.61 + 0.17 - 0 . 7 4 + 0.24
0.25 0.30 0.45 0.69 0.64 1.02 1.02
+ 0.05 + 0.06 + 0.07 + 0.10 + 0.11 + 0.13 + 0.15
-0.03+0.07 -0.18+0.08 -0.28 :e 0.08 -0.41+0.13 -0.21+0.14 -0.63+0.15 -0.75+0.19
I n c i d e n t m o m e n t u m = 865 + 17 M e V / c . Total c . m . e n e r g y = 1730 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
No a b s o l u t e n o r m a l i z a t i o n o f 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 s w a s o b t a i n e d i n t h e p r e s e n t e x p e r i m e n t , d u e to t h e c o m p l e x t a r g e t a s s e m b l y . The method c o m m o n l y a d o p t e d i n s u c h a c a s e i s to n o r m a l i z e t h e d a t a to t h e t o t a l c r o s s sections through the optical theorem by using the differential cross section a t 0° o b t a i n e d f r o m L e g e n d r e e x p a n s i o n o f t h e d a t a a n d t h e r a t i o s o f t h e r e a l to i m a g i n a r y p a r t o f t h e f o r w a r d s c a t t e r i n g a m p l i t u d e s g i v e n b y t h e d i s p e r s i o n r e l a t i o n c a l c u l a t i o n . It w a s f o u n d t h a t t h i s p r o c e d u r e c o u l d n o t b e a p p l i e d to t h e p r e s e n t c a s e , b e c a u s e t h e l a c k o f d a t a a t t h e v e r y f o r w a r d a n g l e s ( c o s O c . m . ~ 0.8) d i d n o t a l l o w a u n i q u e d e t e r m i n a t i o n of the d i f f e r e n o tial cross section at 0 . Therefore the present differential cross-section d a t a w e r e n o r m a l i z e d to t h e p u b l i s h e d d i f f e r e n t i a l c r o s s - s e c t i o n data obt a i n e d b y b u b b l e c h a m b e r s [5, 1 0 - 1 3 ] . A f t e r a n a l y s i s o f t h e d a t a in t e r m s o f
M. G . A l b r o w et a l . , K - e l a s t i c s c a t t e r i n g
416
Table 2 Elastic K-p scattering. c o s 8c.m.
- t ( G e V 2)
ddO" ~ (mb/sr)
P
P d(Y ( m b / s r )
0.830 0.760 0.723 0.680 0.621 0.574 0.524
0.08 0.12 0.14 0.16 0.19 0.21 0.24
-0.12 0.13 0.20 0.28 0.46 0.39 0.41
± 0.14 ± 0.06 ± 0.08 ± 0.05 ± 0.07 ± 0.08 ± 0.08
3.12 2.62 1.90 1.69 1.60
-~0.24 ± 0.11 ± 0.11 ± 0.10 ± 0.10
0.62 0.73 0.88 0.65 0.66
± 0.26 ± 0.13 ± 0.13 ± 0.12 ± 0.12
0.480 0.437 0.359 0.291 0.239 0.197 0.126
0.26 0.28 0.32 0.35 0.38 0.40 0.43
0.61 0.59 0.90 0.86 0.82 0.89 0.83
± 0.13 ± 0.08 ± 0.09 ± 0.19 ± 0.08 ± 0.20 ± 0.11
1.38 ± 0.13 1.09 ± 0.06 0.90 ± 0.06 0 . 8 4 ± 0.10 0.79 ± 0.05 0.79 ± 0.09 0.63 ± 0.05
0.84 0.64 0.81 0.72 0.64 0.70 0.53
± 0.15 ± 0.08 ± 0.08 ± 0.12 ± 0.06 ± 0.12 ± 0.06
0.062
0.47
0.70 ± 0.14
0.61 ± 0.06
0.42 ± 0.08
-0.024 -0.107 -0.165 -0.218
0.51 0.55 0.58 0.60
0.86 ± O.i i 0.85 ± 0.22 0.54 ± 0.18 0.31 ± 0.19
0.51 ± 0.04 0.41 ± 0.06 0.36 ± 0.05 0.47 ± 0.06
0.44 0.35 0.19 0.15
-0.282 -0.349
0.64 0.67
0.25 ± 0.15 0.50 ± 0.19
0.35 ± 0.04 0.40 ± 0.05
0.09 ± 0.05 0.20 ± 0.07
-0.423 -0.501 -0.558 -0.622 -0.678 -0.750 -0.823
0.71 0.74 0.77 0.80 0.83 0.87 0.90
0.12 -0.35 -0.26 -0.58 -0.49 -0.87 -1.00
± 0.13 ± 0.14 ± 0.18 ± 0.12 ± 0.13 ± 0.12 ± 0.18
0.42 0.49 0.65 0.69 0.91 1.04 1.22
± 0.04 ± 0.06 ± 0.08 ± 0.08 ± 0.10 ± 0.11 ± 0.13
0.05 -0.17 -0.17 -0.40 -0.45 -0.90 -1.22
± 0.05 ± 0.08 ± 0.06 ± 0.08
± 0.05 ± 0.07 ± 0.12 ± 0.09 ± 0.12 ± 0.13 ± 0.17
I n c i d e n t m o m e n t u m = 935 ~-19 M e V / c . T o t a l c . m . e n e r g y = 1763 MeV. T h e e r r o r s in t h e p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. T h e e r r o r s in the 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 a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y .
Legendre expansion coefficients (see below), the normalization was slightly a d j u s t e d s o t h a t 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 s f i t to t h e s m o o t h c u r v e drawn through the points given by the bubble chamber experiments. The real error introduced by the normalization process cannot be estimated acc u r a t e l y , b u t i s e x p e c t e d n o t to e x c e e d 10%. T h i s e r r o r i s n o t i n c l u d e d i n the final results presented here.
3.
FEATURES
OF THE DATA
The present differential cross-section data agree fairly well with those o f H o l l e y e t a l . [ 9 ] , C o n f o r t o e t a l . [ 5 , 1 0 ] , T r o w e r e t a l . [ 1 1 ] , L y n c h [12]
417
M. G.Albrow et al., K - e l a s t i c scattering Table 3 Elastic K-p scattering. c o s 0c . m .
- t (GeV 2)
P
~ (mb/sr) dd ~
dO P ~ (mb/sr)
0.819 0.770 0.718 0.661 0.600 0.565 0.516
0.10 0.13 0.16 0.19 0.22 0.24 0.27
-0.22 -0.17 0.04 -0.06 0.12 0.43 0.46
4- 0.06 ± 0.06 ± 0.05 ± 0.06 ± 0.06 ± 0.11 ± 0.09
2.63 2.10 1.55 1.40 1.06
± 0.12 ± 0.12 ± 0.08 ± 0.12 ± 0.08
0.472 0.428 0.377 0.337 0.284 0.232 0.167
0.29 0.32 0.35 0.37 0.40 0.43 0.46
0.71 0.65 0.73 0.86 0.85 0.72 0.96
± 0.17 ± 0.09 ± 0.19 ± 0.12 ± 0.14 ± 0.15 ± 0.13
0.86 0.75 0.67 0.68 0.60 0.50 0.56
± 0.10 ~: 0.05 ± 0.08 ± 0.06 ± 0.06 ± 0.05 ± 0.05
0.61 ± 0.12 0.48 ± 0.06 0.49 ± 0.10 0.58 ± 0.08 0.51 ± 0.07 0.36 ± 0.07 0.54± 0.06
0.104 0.054 -0.009 -0.089 -0.171 -0.223 -0.278
0.50 0.53 0.56 0.60 0.65 0.68 0.71
0.71 0.85 0.56 0.78 0.69 0.53 0.79
± 0.13 ± 0.16 ± 0.11 ± 0.11 ± 0.14 ± 0.16 ± 0.16
0.57 0.51 0.63 0.50 0.49 0.53 0.47
± 0.06 ± 0.05 ± 0.05 ± 0.04 ± 0.05 ± 0.06 ± 0.05
0.40 ± 0.07 0.44 ± 0.07 0.35 ± 0.06 0.39 ± 0.05 0.34± 0.06 0.28 ± 0.08 0.37 ± 0.06
-0.344 -0.410 -0.477 -0.553 -0.653 -0.749 -0.821
0.75 0.78 0.82 0.86 0.92 0.97 1.01
0.42 0.39 0.01 -0.26 -0.48 -0.68 -0.89
± 0.13 ± 0.14 ± 0.10 ± 0.10 ± 0.08 ± 0.12 ± 0.17
0.46 0.54 0.68 0.82 1.03 1.17 1.38
± 0.05 ± 0.06 ± 0.06 :e 0.07 ± 0.07 ± 0.11 ± 0.15
0.19 ± 0.06 0.21± 0.07 0.01 ± 0.07 -0.21 ± 0.08 -0.50 ± 0.08 -0.79 ± 0.13 -1.23 ± 0.18
0.11 -0.12 0.18 0.59 0.48
± 0.12 ± 0.13 ± 0.09 ± 0.14 ± 0.09
I n c i d e n t m o m e n t u m = 1010 ± 20 M e V / c . Total c . m . e n e r g y = 1798 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
a n d L i t c h f i e l d e t a l . [13]. T h e m o s t s t r i k i n g f e a t u r e s a r e t h e r a p i d c h a n g e of the forward slope and of the backward cross sections as a function of the i n c i d e n t m o m e n t u m . B o t h s h o w a m a x i m u m at a r o u n d 1.05 G e V / c , n e a r t h e strongly excited A(1820) resonance. T h e p o l a r i z a t i o n d a t a a t 935 a n d 1010 M e V / c s h o w t h e s a m e f e a t u r e s a s s e e n e a r l i e r i n t h e d a t a a t 982 M e V / c i n r e f . [4]: a v e r y l a r g e p o s i t i v e p o l a r i z a t i o n in the c e n t r a l p a r t of the a n g u l a r r a n g e and a s l i g h t l y n e g a t i v e p o l a r i z a t i o n a t s m a l l a n g l e s . A t t h e h i g h e r m o m e n t a , 1 0 3 5 , 1 0 5 5 , 1 1 7 7 , 1250 a n d 1330 M e V / c t h e p a t t e r n i s r a p i d l y c h a n g i n g t o w a r d s t h a t c h a r a c t e r i s t i c f o r t h e e n t i r e r a n g e o f m o m e n t a b e t w e e n 1082 a n d 2 3 3 0 M e V / c : p o s i t i v e p o l a r i z a t i o n in t h e r e g i o n of the d i f f r a c t i v e p e a k of t h e a n g u l a r d i s t r i b u t i o n , n e g a t i v e p o l a r i z a t i o n in t h e c e n t r a l p a r t and in t h e b a c k w a r d r e g i o n a p o l a r i z a -
418
M. G . A l b r o w et a l . , K - e l a s t i c s c a t t e r i n g Table 4 Elastic K p scattering. cos 0c.m.
d~d~ff( m b / s r )
i P ~d(Y ( m b / s r )
- t (GeV 2)
P
0.820 0.776 0.761 0.726 0.681 0.635 0.587
0.10 0.13 0.14 0.16 0.18 0.21 0.24
0.06 ± 0.08 0.08±0.12 -0.06 ± 0.09 -0.09 ± 0.07 0.06 ± 0.08 0.20 ± 0.09 0.27 ± 0.11
0.523 0.460 0.409 0.357 0.304 0.251 0.187
0.28 0.31 0.34 0.37 0.40 0.43 0.47
0.20 0.52 0.29 0.37 0.80 0.46 0.37
0.122 0.056 -0.026 -0.099 -0.157
0.51 0.54 0.59 0.63 0.67
0.18 0.37 0.33 0.26 0.07
-0.231 -0.322
0.71 0.76
0.35 ± 0.12 0.36 ± 0.12
0.61 ± 0.05 0.59 ± 0.05
0.21 ± 0.07 0.21 ± 0.07
-0.416 -0.485 -0.545
0.82 0.86 0.89
0.10 ± 0.11 -0.00 ± O.16 -0.07 ± 0.12
0.70 ± 0.06 0.71 ± 0.08 0.88 ± 0.08
0.07 ± 0.08 -0.00 ± 0.11 -0.07 ± 0.10
-0.614
0.93
-0.31 ± 0.15
0.76 ± 0.08
- 0 . 2 4 ± 0.11
-0.674 -0.742 -0.819
0.97 1.00 1.05
-0.62 ± 0.14 -0.53 ± 0.12 -0.48 ± 0.16
1.06 ± 0 . i i 1.33 ± 0.12 1.56 ± 0.18
-0.65 ± 0.14 -0.70 ± 0.15 -0.75 ± 0.22
3.12 2.88 2.18 1.54 1.08
± 0.25 ± 0.17 ± 0.14 ± 0.12 ± 0.10
-0.18 -0.27 0.12 0.31 0.30
± 0.27 ± 0.19 ± 0.17 ± 0.14 ± 0.12
± 0.10 ± 0.17 ± 0.18 ± 0.16 ± 0.23 ± 0.20 ± 0.14
0.70 0.45 0.37 0.43 0.37 0.40 0.44
± 0.05 ± 0.06 ± 0.05 ± 0.05 ± 0.06 ± 0.06 ± 0.05
0.14 0.23 0.11 0.16 0.30 0.19 0.16
± 0.07 ± 0.08 ± 0.07 ± 0.07 ± 0.08 ± 0.08 ± 0.06
± 0.18 ± 0.14 ± 0.12 ± 0.16 ± 0.13
0.43 0.49 0.52 0.60 0.56
± 0.06 ± 0.05 ± 0.04 ± 0.07 ± 0.06
0.08 0.18 0.17 0.16 0.04
± 0.08 ± 0.06 ± 0.06 ± 0.09 ± 0.08
I n c i d e n t m o m e n t u m = 1035 ± 21 M e V / c . T o t a l c . m . e n e r g y = 1810 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. T h e e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y . tion which is positive again at least at the lower momenta of this range. The results are compared with the predictions calculated from the energy d e p e n d e n t p h a s e - s h i f t a n a l y s e s b y C o n f o r t o e t a l . [5] a n d B r i c m a n e t a l . [ 6 ] , shown in figs. 1 and 2 as solid respectively dashed lines. It is seen that the results of these analyses are in fairly good agreement with the present data. At 865 MeV/c the region of large positive polarization has shifted towards smaller angles (cos Oc.m. ~ 0.4) and remains positive also in the forward d i r e c t i o n . In t h e a n g u l a r d i s t r i b u t i o n s a t t h e p r e s e n t m o m e n t a , w e c a n n o t identify the dip structures a s c l e a r l y a s a b o v e 1 . 4 G e V / c ( r e f . [3]). H o w ever, the regularity of the zero crossings in the polarization distributions, w h i c h w a s m e n t i o n e d i n r e f . [3], s e e m s to p e r s i s t to i n c i d e n t m o m e n t a a s low as 0.86 GeV/c (ref. [4]). Between 0.86 and 1.25 GeV/c a new zero crossing at constant u ~ 0.15 GeV 2 is observed. At 1.08 GeV/c two other
M.G.Albrow et al., K- elastic scattering
419
Table 5 Elastic K-p scattering. cos 0c.m.
- t ( G e V 2)
d(~ ~ (rob/st)
P
p dff ~-~ ( m b / s r )
0.831 0.790 0.747 0.702 0.657 0.609 0.560
0.10 0.12 0.15 0.18 0.20 0.23 0.26
0.08 -0.04 0.06 0.15 0.17 0.29 0.22
~- 0 . 0 6 + 0.07 + 0.06 + 0.07 + 0.07 ± 0.08 + 0.10
3.42 2.61 2.38 1.91 1.31 0.91
+ 0.27 + 0.22 + 0.13 + 0.12 ± 0.09 ± 0.07
-0.14 0.16 0.35 0.32 0.38 0.20
± 0.30 + 0.26 + 0.15 + 0.14 + 0.11 + 0.09
0.498 0.432 0.380 0.328 0.262 0.197 0.119
0.30 0.34 0.37 0.40 0.44 0.48 0.52
0.42 0.42 0.64 0.50 0.70 0.48 0.54
+ 0.10 + 0.16 + 0.18 + 0.19 + 0.15 ± 0.15 + 0.10
0.61 0.40 0.36 0.35 0.38 0.46 0.50
+ 0.04 + 0.05 + 0.04 ± 0.05 ± 0.04 ± 0.05 + 0.04
0.26 0.17 0.23 0.17 0.27 0.22 0.27
+ 0.06 + 0.06 ± 0.06 + 0.06 + 0.05 + 0.06 ± 0.05
0.031 -0.030 -0.078 -0.135 -0.212 -0.285 -0.346
0.57 0.61 0.64 0.67 0.72 0.76 0.80
0.53 0.38 0.46 0.34 0.48 0.32 0.35
± 0.12 + 0.15 ± 0.14 + 0.11 + 0.11 + 0.12 ± 0.13
0.55 0.59 0.58 0.63 0.62 0.61 0.67
± 0.04 + 0.05 ± 0.06 + 0.05 + 0.04 ± 0.05 + 0.06
0.29 0.23 0.26 0.21 0.30 0.20 0.23
+ 0.06 + 0.08 + 0.08 + 0.07 ± 0.06 + 0.07 + 0.08
-0.408 -0.492 -0.562 -0.626 -0.681 -0.750 -0.822
0.83 0.88 0.92 0.96 0.99 1.04 1.08
0.37 0.22 0.04 -0.22 -0.27 -0,69 -0.82
± 0.12 + 0.10 + 0.12 + 0.10 + 0.13 + 0.12 + 0.17
0.67 0.82 0.85 1.06 1.13 1.30 1.45
± 0.05 + 0.05 + 0.08 + 0.08 + 0.11 + 0.11 + 0.15
0.25 0.18 0.04 -0.24 -0.30 -0.89 -1.19
+ 0.08 + 0.08 + 0.10 ± 0.11 ±~).14 + 0.14 + 0.20
I n c i d e n t m o m e n t u m = 1 0 5 5 + 21 M e V / c . T o t a l c . m . e n e r g y = 1819 M e V . T h e e r r o r s in t h e p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l o n l y . T h e e r r c . r s in 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 d a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y . zero crossings appear, o n e o f w h i c h i s c o n s t a n t i n t , a t t ~ - 0 . 6 G e V 2, t h e o t h e r c o n s t a n t i n u, a t u ~ - 0 . 3 8 G e V 2. T h e l a t t e r t w o h a v e p r e v i o u s l y been observed in the data between 1.4 and 2.4 GeV/c of ref. [3]. Such regularities in u have been discussed recently by Odorico [17] in terms of the Veneziano model. In order to examine the data more closely, we have parametrized the angular and the polarization distributions using Legendre polynomials,
da _X2 ~ A I Pl (cos(9 c m ) , d~ l " " P~dCr = ~2 ~ Bl p~ l
( c o s O c. m . ) '
M. G.Albrow et al., If- elastic scattering
420
Table 6 Elastic K p scattering. P
dO' ~-(mb/sr)
dO" P ~-(mb/sr)
cos 0c.m.
- t ( G e V 2)
0,857 0,813 0,773 0,728 0.686 0.629 0,574
0.10 0.13 0.16 0.19 0.22 0.26 0.30
0.511 0.458 0.405 0.351 0.297 0.230 0.163
0.34 0.38 0.41 0.45 0.49 0.53 0.58
0.59 0.49 0.31 0.28 0.13 0.25 -0.15
+ 0.08 + 0.09 + 0.09 + 0.10 + 0.11 + 0.09 + 0.12
1.07 0.91 0.71 0.57 0.52 0.46 0.48
+ 0.07 + 0.06 -~0.05 + 0.04 + 0.04 + 0.03 + 0.04
0.63 0.45 0.22 0.16 0.07 0.11 -0.07
± 0.08 + 0.08 + 0.06 + 0.06 + 0.06 + 0.04 + 0.05
0.111 0.046 -0.016 -0.089 -0.159 -0.213 -0.297
0.62 0.66 0.70 0.76 0.80 0.84 0.90
-0.37 -0.31 -0.39 -0.38 -0.21 -0.09 0.12
+ 0.13 + 0.11 + 0.13 :e 0.10 ± 0.14 + 0.12 + 0.11
0.43 0.39 0.45 0.40 0.43 0.37 0.34
+ 0.04 + 0.03 + 0.04 + 0.03 + 0.04 + 0.03 + 0.03
-0.16 -0.12 -0.18 -0.15 -0.09 -0.03 0.04
+ 0.05 + 0.04 ± 0.06 + 0,04 ± 0,06 ± 0.04 + 0.04
-0.367 -0.439 -0.519
0.95 1.00 1.05
0.24 + 0.19 0.28 + 0.11 0.24 ± 0.16
0.37 ± 0.05 0.37 + 0.03 0.40 + 0.05
0.09 • 0.07 0.10 + 0.04 0.10 ~: 0.06
-0.585 -0.650 -0.705
1.10 1.14 1.18
0.01 ± 0.11 0.16 + 0.13 0.21 ± 0.15
0.57 + 0.05 0.52 + 0.06 0.58 + 0.07
0.01 :e 0.06 0.08 + 0.07 0.12 ~:0.08
-0.769
1.23
-0.18 ± 0.13
0.73 + 0.09
-0.13 + 0.09
-0.837
1.27
-0.38 ± 0.17
0.64+ 0.10
-0.25 + 0.11
0.234-0.06 0.31-4- 0.05 0.33 + 0.05 0.26 + 0.07 0.34 + 0.04 0.36 + 0.08 0.47 :~ 0.06
3.54± 0.17 3.21 + 0.15 2.94 + 0.21 2.34 + 0.08 2.03 + 0.15 1.36 + 0.06
1.10 ± 0.17 1.07 + 0.15 0.75 + 0.21 0.79 + 0.08 0.74 ~-0.17 0.64+ 0.07
I n c i d e n t m o m e n t u m = 1177 ~-23 M e V / c . Total c . m . e n e r g y = 1876 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the d i f f e r e n t i a l c r o s s - s e c t i o n data include a 5% s y s t e m a t i c u n c e r t a i n t y . w h e r e Pl a n d P ~ a r e L e g e n d r e a n d f i r s t a s s o c i a t e d L e g e n d r e p o l y n o m i a l s r e s p e c t i v e l y , a n d ~ i s t h e c . m . w a v e l e n g t h d i v i d e d b y 2~. In f i t t i n g 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 s , s e v e r a l p o i n t s f r o m t h e b u b b l e c h a m b e r e x p e r i m e n t s w e r e a d d e d to t h e p r e s e n t d a t a in t h e v e r y f o r w a r d and b a c k w a r d r e g i o n s w h i c h could not be r e a c h e d in the p r e s e n t e x p e r i m e n t . T h e A - c o e f f i c i e n t s a r e f o u n d to b e v e r y s e n s i t i v e to t h e s e p o i n t s . T h e r e f o r e , the procedure is justified only by the consistency of the results obtained by the a n a l y s i s of the b u b b l e c h a m b e r d a t a a l o n e . By u s i n g the d i f f e r e n t i a l c r o s s s e c t i o n a t 0° o b t a i n e d f r o m t h e s e L e g e n d r e e x p a n s i o n c o e f f i c i e n t s a n d t h e r a t i o s o f t h e r e a l to i m a g i n a r y p a r t o f t h e f o r w a r d s c a t t e r i n g a m p l i t u d e s g i v e n i n r e f . [5], i t w a s c o n f i r m e d t h a t t h e p r e s e n t d a t a l e a d to t o t a l c r o s s
M. G.Albrow et al., K - elastic scattering
421
Table 7 Elastic K p scattering. c o s 0c.m.
ddo" ~ (mb/sr)
do"
P ~-~ ( m b / s r )
- t ( G e V 2)
P
0.858 0.808 0.767 0.723 0.676 0.627 0.576
0.11 0.14 0.18 0.21 0.24 0.28 0.32
0.17 ± 0.06 0.24 ± 0.06 0.30 ± 0.07 0.21 ± 0.07 0.36 ± 0.07 0.31 ± 0.08 0.34± 0.09
3.41 2.89 2.41 2.10 1.75 1.25
± 0.15 ± 0.13 ± 0.11 ± 0.10 ± 0.08 ± 0.06
0.81±0.22 0.86 ~-0.20 0.51±0.17 0.75-~ 0.16 0.54~- 0.14 0.42 ~-0.12
0.524 0.489 0.452 0.410 0.355 0.282 0.215
0.36 0.39 0.41 0.44 0.49 0.54 0.59
0.35 ± 0.10 0.27 ± 0.15 0.20 ± 0.19 0.34 ± 0.14 0.16 ± 0.13 - 0 . 1 4 ± 0.17 -0.17 ± 0.16
1.09 0.87 0.64 0.51 0.48 0.45 0.36
± 0.06 ± 0.07 ± 0.06 ± 0.04 ± 0.03 ± 0.03 ± 0.03
0.38 ~-0.11 0.23±0.13 0.13±0.13 0.18-~ 0.07 0.07 -~0.06 -0.06 -~0.07 -0.06 ~-0.06
0.148 0.096 0.044 -0.019 -0.103 -0.185 -0.254
0.64 0.68 0.72 0.77 0.83 0.89 0.95
-0.37 ± 0.21 -0.55 ± 0.19 -0.45 ± 0.21 -0.39 ± 0.18 -0.59 ± 0.15 - 0 . 6 4 ± 0.24 -0.45 ± 0.17
0.33 0.39 0.36 0.37 0.38 0.35 0.31
± 0.03 ± 0.03 ± 0.03 ± 0.03 ± 0.03 ± 0.04 ± 0.02
-0.12 ~-0.07 -0.21±0.07 -0.16±0.07 -0.14±0.06 -0.22±0.06 -0.22±0.08 -0.14±0.05
-0.349 -0.425 -0.483 -0.538 -0.594 -0.657 -0.709
1.02 1.07 1.12 1.16 1.20 1.25 1.29
-0.13 0.15 0.15 0.27 0.61 0.38 0.36
0.30 0.25 0.29 0.28 0.25 0.31 0.39
± 0.03 ± 0.03 ± 0.03 ± 0.04 ± 0.03 ± 0.04 ± 0.05
-0.04 ± 0.05 0.04±0.08 0.04±0.07 0.08±0.08 0.15±0.08 0.12 ± 0.08 0.14±0.11
-0.775 -0.842
1.34 1.39
0.50 ± 0.06 0.39 ± 0.06
0.04±0.12 0.04±0.14
± 0.18 ± 0.29 ± 0.22 ± 0.30 ± 0.38 ± 0.26 ± 0.26
0.09 ± 0.23 0.10 ± 0.36
I n c i d e n t m o m e n t u m = 1250 ~-25 M e V / c . Total c . m . e n e r g y = 1909 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
s e c t i o n s c o n s i s t e n t w i t h t h o s e m e a s u r e d b y B u g g e t al. [14] a n d b y C o o l e t a l . [15]. In f i t t i n g t h e p o l a r i z a t i o n d i s t r i b u t i o n s , the differential cross sections calculated with these A-coefficients were used for the forward points at which only polarization data were obtained. The results of the Aa n d B - c o e f f i c i e n t s a r e s h o w n i n t a b l e 9 a n d f i g s . 3 a n d 4. F i g s . 3 a n d 4 a l s o i n c l u d e t h e r e s u l t s f o r t h e e a r l i e r d a t a [3, 4]. F o r t h e s a k e o f c o n s i s t e n c y t h e d a t a o f r e f . [4] h a v e b e e n r e n o r m a l i z e d f o l l o w i n g t h e s a m e p r o c e d u r e a s f o r the data of the present experiment, hence there are slight differences with r e s p e c t to t h e A ' s a n d B ' s o f r e f . [4]. T h e m i n i m u m o r d e r o f t h e f i t w a s d e termined by checking the stability in the A- and B-coefficient as a function
M. G.Albrow et al., K - elastic scattering
422
Table 8 Elastic K p scattering. dd(~ ~ (mb/sr)
dff P ~-~(mb/sr)
c o s Oc.m.
-t (GeV 2)
0.879 0.840 0.798 0.763 0.713
0.10 0.13 0.17 0.19 0.24
0.17 0.17 0.20 0.38 0.27
0.665 0.615
0.28 0.32
0.26 ± 0.06 0.37 ± 0.07
1.31 ± 0.08 1.12 ± 0.07
0.563 0.510 0.456 0.418
0.36 0.40 0.45 0.48
0.40 ± 0.08 0.44 ± 0.09 0.55 ± 0.11 0.30 ± 0.16
0.86 ± 0.06 0.70 ± 0.05 0.55 ± 0.04 0.40 ± 0.05
0.353 0.281 0.216
0.53 0.59 0.64
0.31 ± 0.12 0.37 ± 0.12 0.01 ± 0.25
0.38 ± 0.03 0.28 ± 0.03 0.21 ± 0.04
0.155 0.075 0.023
0.69 0.76 0.80
-0.15 ± 0.12 -0.30 ± 0.16 -0.59 ± 0.19
0.21 ± 0.02 0 . 2 4 ± 0.03 0.24 ± 0.03
-0.041 -0.123 -0.194 -0.248
0.86 0.92 0.98 1.03
-0.47 ± 0.15 -0.75 ± 0.15 -0.64 ± 0.22 -0.41 ± 0.18
0.25 ±0.03 0.23 ± 0.02 0.23 ± 0.03 0.20 ± 0.03
-0.300 -0.351 -0.426 -0.477 -0.531 -0.594 -0.657
1.07 1.11 1.17 1.21 1.26 1.31 1.36
-0.50 ± 0.24 -0.34 ~:0.19 0.04 ± 0.16 -0.21 ~-0.21 -0.29 ± 0.16 0.20 ± 0.16 0.16 ± 0.14
0.23 ± 0.04 0.23 ± 0.03 0.21 ± 0.03 0.24 ± 0.04 0.29 ± 0.04 0.28 ± 0.04 0.36 ± 0.04
-0.08±0.04 0.01±0.03 -0.05 ± 0.05 -0.08±0.05 0.05 ± 0.05 0.06±0.05
-0.712 -0.775 -0.840
1.41 1.46 1.51
0.06 ± 0.17 0.08 ± 0.12 -0.28 • 0.15
0.32 ± 0.05 0.53 ± 0.05 0.53 ± 0.07
0.02±0.06 0.04 =~0.06 -0.15±0.08
P ± 0.06 ± 0.05 ± 0.04 ± 0.08 ± 0.06
2.81 2.31 2.11 1.55
± 0.14 ± 0.08 ~: 0.16 ± 0.09
0.47 • 0.14 0.46 • 0.08 0.80±0.17 0.42 ± 0.09 0.34±0.08 0.41~0.08 0.34±0.07 0.31±0.06 0.30±0.05 0.12 :e 0.06 0.12±0.04 0.10±0.03 0.00~0.05 -0.03 ± 0.03 -0.07 :e 0.04 -0.14±0.04 -0.12±0.03 -0.17±0.03 -0.15±0.04 -0.08±0.03 -0.12±0.05
I n c i d e n t m o m e n t u m = 1330 ± 27 M e V / c . T o t a l c . m . e n e r g y = 1946 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y . of the order of fit, and also the gradient of the improvement of the fit given by the F-ratio. In t h e p r e s e n t e n e r g y r e g i o n 5 t h o r d e r f i t s w e r e f o u n d to b e a d e q u a t e e x c e p t f o r t h e p o i n t s a t 1211 a n d 1 2 5 0 M e V / c , w h e r e 6 t h o r d e r f i t s were required. In f i g s . 3 a n d 4 t h e r e s u l t s f o r t h e 6 t h o r d e r f i t s a r e a l s o s h o w n w i t h d a s h e d e r r o r b a r s f o r 1 1 7 7 , 1282 a n d 1 3 3 0 M e V / c . All A-coefficients except A 1 and A 6 show a strong peak at around 1.05 GeV/c reflecting the strong excitation of the A(1820) resonance. The coefficient A 1 shows a broad maximum at around 1.15 GeV/c, where the A(1870) resonance is predicted by an energy dependent phase-shift analysis [5]. A m i n i m u m i s o b s e r v e d i n a l l A - c o e f f i c i e n t s a t a r o u n d 1 . 2 5 to 1.30 GeV/c.
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2.5
(GeVlc)
Fig. 5. Plot of the coefficient B 2 of the Legendre expansion of the polarization (P dcr/dfl) data of the p r e s e n t experiment and of refs. [3, 4]. The line has been drawn to guide the eye. T h e m o s t p r o m i n e n t f e a t u r e of the B - c o e f f i c i e n t s b e l o w 1.2 G e V / c i s t h e i r s t r o n g v a r i a t i o n w i t h e n e r g y . T h i s b e h a v i o u r can b e a c c o u n t e d f o r q u a l i t a t i v e l y by the i n t e r f e r e n c e of the t h r e e , r a t h e r s t r o n g l y e x c i t e d r e s o n a n c e s p r e s e n t b e t w e e n 0.9 and 1.2 G e V / c (~(1770), A(1820), A(1870)) a m o n g t h e m s e l v e s and w i t h a c o n s t a n t o r s l o w l y v a r y i n g , m o s t l y i m a g i n a r y b a c k g r o u n d of low (l = 0, 1 , 2 ) o r b i t a l a n g u l a r m o m e n t u m . T h i s i s i l l u s t r a t e d in fig. 5 w h i c h g i v e s the B 2 c o e f f i c i e n t a s a f u n c t i o n of m o m e n t u m . In the r e g i o n of the ~ ( 1 7 7 0 , ~ - ) the d o w n g o i n g t r e n d a r i s e s f r o m the i n t e r f e r e n c e of D 5 w i t h an i m a g i n a r y S 1 b a c k g r o u n d w a v e ; n e a r t h e A(1820, ~-+) the u p g o i n g p a r t of t h e c u r v e i s g e n e r a t e d by the i n t e r f e r e n c e of the F 5 w i t h a P l and a P3 b a c k g r o u n d w a v e . In the v i c i n i t y of t h e A(1870), w h i c h h a s b e e n c o n s i d e r e d to h a v e J P = ½+ ( r e f . [16]) but in the m o r e r e c e n t l i t e r a t u r e [5, 6] i s q u o t e d a s J P = 3+ the d o w n w a r d p a r t o r i g i n a t e s m o s t l y f r o m the i n t e r f e r e n c e of t h i s r e s o n a n c e (with e i t h e r J P a s s i g n m e n t ) w i t h the A(1820, ~-+) -p 7+ r e s o n a n c e , and a l s o w i t h a P - w a v e b a c k g r o u n d (P3 f o r d = ~ , ~'1 f o r J P = 23-+). N e a r 1.5 G e V / c , w h e r e the ~ ( 2 0 3 0 , ~T+) i. s l o c a t e d a n o t h e r d o w n w a r d p a r t i s o b s e r v e d w h i c h can b e a c c o u n t e d f o r by the i n t e r f e r e n c e m o s t ly w i t h a D 3 b a c k g r o u n d w a v e , w i t h s m a l l e r c o n t r i b u t i o n s f r o m P3 and F 5 w a v e s . T h e A(2100, ~ - ) i s a g a i n l o c a t e d on an u p w a r d s l o p e w h i c h a r i s e s in the i n t e r f e r e n c e of t h i s r e s o n a n c e w i t h a D 3 b a c k g r o u n d w a v e . A t 1.35 G e V / c a n o t h e r s l o p e i s s e e n in fig. 5 and by d e d u c t i o n one m i g h t s u r m i s e t h a t an a s y e t unknown r e s o n a n c e would b e p r e s e n t at t h a t m o m e n t u m . It m u s t b e s t r e s s e d t h a t a t t h i s m o m e n t u m two e x p e r i m e n t s d o n e w i t h d i f f e r e n t p o l a r i z e d t a r g e t s and d i f f e r e n t d e t e c t i o n e q u i p m e n t j o i n t o g e t h e r ; on the o t h e r hand a v e r y l a r g e ( ~ 40%) e r r o r in the t a r g e t p o l a r i z a t i o n e i t h e r in the e x p e r i m e n t of r e f . [3] o r in the e x p e r i m e n t of r e f . [4] a n d in t h e p r e -
M.G.Albrow et al., II- elastic scattering
429
s e n t d a t a i s r e q u i r e d to e l i m i n a t e t h i s s l o p e a l t o g e t h e r . W e c o n c l u d e t h a t m o r e p o l a r i z a t i o n d a t a w i l l b e n e e d e d a r o u n d 1.35 G e V / c in o r d e r to e s t a b l i s h w h e t h e r t h e s t r u c t u r e in the B - c o e f f i c i e n t s at t h e s e m o m e n t a i s i n d i c a tive for new resonances.
4. S P I N AND P A R I T Y A S S I G N M E N T O F THE A(1870) A s m e n t i o n e d a b o v e , t h e A(1870) h a s b e e n c o n s i d e r e d to b e a J P = ~-+ r e s o n a n c e [16], a l t h o u g h m o r e r e c e n t l y e v i d e n c e h a s b e e n p r e s e n t e d in f a v o u r of J : P = ~+ ( r e f s . [5, 6]). I n s p e c t i o n of the B 1 and B 3 c o e f f i c i e n t s of fig. 4, i . e . s t r o n g s t r u c t u r e in B 1 , b u t n o t in B 3 a t ~ 1.2 G e V / c a l s o f a v o u r s t h e l a t t e r a s s i g n m e n t ; B 1 c o n t a i n s an S 1 - P 3 i n t e r f e r e n c e t e r m , B 3 c o n t a i n s an S 1 - F 7 i n t e r f e r e n c e t e r m ; the s t r o n g s t r u c t u r e in B~, c o m b i n e d w i t h the r a t h e r f l a t b e h a v i o u r of B 3 , i s t h u s i n d i c a t i v e f o r a j r = ~+ w a v e i n t e r f e r i n g with a largely imaginary S1 background amplitude. In o r d e r to c h e c k t h i s r e s u l t m o r e c l o s e l y , w e h a v e f i t t e d the d a t a b e t w e e n 0.98 and 1.34 G e V / c to the b a c k g r o u n d p l u s r e s o n a n c e m o d e l w h i c h w a s a p p l i e d e a r l i e r [6] t o t h e d a t a of r e f . [4]. O t h e r d a t a u s e d in t h e f i t t i n g s a r e t h e s a m e a s t h o s e q u o t e d in r e f . [ 6 ] . W e h a v e c o n f i n e d t h e a n a l y s i s to the two p o s s i b i l i t i e s J P = ~+ o r ~÷ f o r A(1870). F o r the b a c k g r o u n d , t a k e n to v a r y l i n e a r l y w i t h m o m e n t u m , o n l y S1, P 1 , P3 and D 3 w a v e s h a v e b e e n c o n s i d e r e d . O n l y the r e s o n a n c e s A(1830), Z(1765), A(1820), Z(1910) a n d A(1870) h a v e b e e n u s e d in the fit. V a r y i n g the b a c k g r o u n d , w h i l e k e e p i n g t h e r e s o n a n c e s f i x e d , and v i c e v e r s a , l e a d s to s t a b l e f i t s w i t h low ×2 f o r J P ( 1 8 7 0 ) = ~+, b u t r e q u i r e s c o n s i d e r a b l e r e a d j u s t m e n t s a m o n g the v a r i o u2 s r e s o n a n c e p a r a m e t e r s if J P ( 1 8 7 0 ) i s tpa k e n 3+to b e ~7+. T h e b e s t f i t h a s X = 560 f o r 418 d e g r e e s of f r e e d o m f o r J = ~ , and ×2 = 958 f o r 443 d e g r e e s of f r e e d o m f o r J P = -~+. It h a s b e e n c h e c k e d t h a t the r e s u l t d o e s n o t d e p e n d on the c h o i c e of s t a r t i n g v a l u e s in t h e fit. The A - and B - c o e f f i c i e n t s c a l c u l a t e d f o r the two s o l u t i o n s a r e s h o w n in f i g s . 3 and 4. It i s s e e n t h a t a t 1.2 G e V / c B 1 and B 3 i n d e e d b e h a v e a s a n t i c i p a t e d , i . e . v a r y i n g B1 a n d f l a t B 3 f o r J P = ~ , v i c e v e r s a f o r J P = ~~+. It can t h e r e f o r e b e c o n c l u d e d t h a t t h e p r e s e n t p o l a r i z a t i o n d a t a , t o g e t h e r w i t h t h o s e of r e f . [4] s u p p o r t the c o n c l u s i o n t h a t t h e s p i n and p a r i t y of the A(1870) r e s o n a n c e i s ~÷. T h e a u t h o r s w o u l d l i k e to t h a n k t h e P o l a r i z e d T a r g e t G r o u p f o r t h e i r c o n t r i b u t i o n s to t h i s e x p e r i m e n t . W e a r e i n d e b t e d to M. A r b e t f o r t e c h n i c a l a s s i s t a n c e in the c o u r s e of t h e e x p e r i m e n t . T h i s w o r k w a s s u p p o r t e d in p a r t by t h e S t i c h t i n g v o o r F u n d a m e n t e e l O n d e r z o e k d e r M a t e r i e ( F O M ) , w h i c h i s s u p p o r t e d b y the N e d e r l a n d s e O r g a n i s a t i e v o o r Z u i v e r W e t e n s c h a p p e l i j k O n d e r z o e k (ZWO).
RE FERENCES [I] C. L. Wang, University of California, Lawrence Radiation Laboratory report No. 11881, unpublished.
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[2] C. R. Cox, P . J . Duke, K.S. Heard, R. E. Hill, W.R. Holley, D. P. Jones, F. C. Shoemaker, J. J. T h r e s h e r and J. B. Warren, Phys. Rev. 184 (1969) 1443. [3] C. Daum, F. C. Ern6, J. P. Lagnaux, J. C. Sens, M. Steuer and F. Udo, Nucl. Phys. B6 (1968) 273. [4] S. Andersson/Almehed, C. Daum, F. C. Ern6, J . P . Lagnaux, J. C. Sens and F. Udo, Nucl. Phys. B21 (1970) 515. [5] B. Conforto, D.M. Harmsen, T. Lasinski, R. Levi-Setti, M. Raymund, E. Burkhardt, H. Filthuth, S. Klein, H. Oberlack and H. Schleich, preprint No. EFI 70-43. [6] C. Bricman, M. F e r r o - L u z z i and J. P. Lagnaux, Phys. Letters 33B (1970) 511. [7] R. Roubeau, J. Ezratty, H. Glattli, J. Vermeulen and M. Borghini, Nucl. Instr. 82 (1970) 323. [8] M. G. Albrow, S. Andersson/Almehed, B. Bo§njakovic, C. Daum, F. C. Ern6, J. P. Lagnaux, J. C. Sens and F. Udo, Nucl. Phys. B25 (1971) 9. [9] W. R. Holley, E . F . Beall, D. Keefe, L. T. Kerth, J. J. T h r e s h e r , C. L. Wang and W.A.Wenzel, Phys. Rev. 154 (1967) 1273. [10] B. Conforto, D. M. Harmsen, T. Lasinski, R. Levi-Setti, M. Raymund, E. Burkhardt, H. Filthuth, E. Kluge, H. Oberlack and R. R. Ross, Nucl. Phys. B8 (1968) 265. [11] W. P. Tr o wer , J. R. Ficenec, R.I. Hulsizer, J. Lathsop, J. N. Snyder and W. P. Swanson, Phys. Rev. 170 (1968) 1207. [12] G. Lynch, private communication. [13] P. Litchfield et al., Coll~ge de F r a n c e - R u t h e r f o r d - S a c l a y - S t r a s b o u r g Collaboration, to be published. [14] D. V. Bugg, R.S. Gilmore, K. M. Knight, D. C. Salter, G.H. Stafford, E . J . N . Wilson, J . D . Davies, J. D. Dowell, P . N . Hattersley, R. G. Homer, A.W. O'Dell, A.A. C a r t e r , R . J . Tapper and K . F . Riley, Phys. Rev. 168 (1968) 1466. [15] R. L. Cool, G. Giacomelli, T . F . Kycia, B.A. Leontic, K.K. Li, A. Lundby, J. T e i g e r and C.Wilkin, Brookhaven National Laboratory report No. 14047. [16] P a r t i c l e Data Group, Phys. L e t te r s 33B (1970) 1. [17] R. Odorico, Phys. Letters 34B (1971) 65; preprint TH-1303-CERN.
Nuclear Physics B29 (1971) 413-430. North-Holland Publishing Company
ELASTIC SCATTERING OF NEGATIVE KAONS ON POLARIZED PROTONS BETWEEN 865 AND 1330 MeV/c M. G. A L B R O W , S. A N D E R S S O N - A L M E H E D *, B. B O ~ N J A K O V I C **, F. C. E R N E **, Y. K I M U R A $, J. P. L A G N A U X :~:~, J. C. SENS ** and F. UDO C E R N , Geneva, Switzerland
Received 16 March 1971
Abstract: Polarization and differential c r o s s - s e c t i o n data for elastic scattering of negative kaons on p o l a r i z e d protons between 865 and 1330 MeV/c a r e presented. Comparisons are made with predictions given by published energy dependent p h a s e - s h i f t analyses. The Legendre expansion coefficients c h a r a c t e r i z i n g the polarization distributions show r e m a r k a b l e s t r u c t u r e s resulting from excitation of A - and ~ - r e s o n a n c e s . An analysis of the elastic and charge-exchange data in this region of momenta supports the assignments of J P = 9 + for the A(1870) r e sonance. The occurrence of z e r o c r o s s i n g s in the polarization data is discussed.
1. I N T R O D U C T I O N A c o n s i d e r a b l e a m o u n t of e x p e r i m e n t a l d a t a on e l a s t i c KN s c a t t e r i n g h a s b e e n a c c u m u l a t e d o v e r t h e p a s t few y e a r s ; n e v e r t h e l e s s , the p a r t i a l w a v e a m p l i t u d e s h a v e t h u s f a r not b e e n d e t e r m i n e d a c c u r a t e l y o t h e r than f o r m o m e n t a b e l o w 500 M e V / c . The p r e s e n c e of m a n y i n e l a s t i c r e s o n a n c e s in t h i s c h a n n e l m a k e s a m o d e l i n d e p e n d e n t p a r t i a l w a v e a n a l y s i s v e r y d i f f i c u l t . To d i s e n t a n g l e s u c h a c o m p l i c a t e d s t r u c t u r e of t h e a m p l i t u d e s , t h e r e f o r e , s y s t e m a t i c d a t a on p o l a r i z a t i o n s a r e i n d i s p e n s a b l e . M e a s u r e m e n t s of t h e p o l a r t . z a t i o n in e l a s t i c s c a t t e r i n g of n e g a t i v e k a o n s on p r o t o n s h a v e b e e n m a d e by W a n g [1], b y C o x e t al. [2], by D a u m e t al. [3] and by A n d e r s s o n et al. [4]. In t h i s c o n t r i b u t i o n w e p r e s e n t p o l a r i z a t i o n d i s t r i b u t i o n s and d i f f e r e n t i a l c r o s s s e c t i o n s f o r t h e e l a s t i c s c a t t e r i n g of n e g a t i v e k a o n s on p o l a r i z e d p r o t o n s a t 865, 935, 1010, 1035, 1055, 1177, 1250 a n d 1330 M e V / c . T h e r e s u l t s a r e c o m p a r e d w i t h the p r e d i c t i o n s of e n e r g y d e p e n d e n t p h a s e - s h i f t a n a l y s e s by C o n f o r t o e t al. [5] and by B r i c m a n e t al. [6]. T h e d a t a , t o g e t h e r * Visitor from the Institute of P h y s i c s , University of Lund, Sweden. ** Visitor from the Foundation for Fundamental R e s e a r c h of Matter, (FOM), Utrecht, The Netherlands. On leave of absence from the University of Tokyo, Tokyo, Japan. :~:~ Visitor from the Institut I n t e r u n i v e r s i t a i r e des Sciences Nucl~aires, B r u s s e l s , Belgium.
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with those of ref. [4] and c h a r g e exchange data in the s a m e region of m o menta, have been analysed in t e r m s of a background plus r e s o n a n c e model.
2. MEASUREMENTS AND ANALYSIS The e x p e r i m e n t has been p e r f o r m e d in a 23 m long u n s e p a r a t e d beam at the CERN PS. The incoming b e a m s w e r e identified with a ~ e r e n k o v counter and by t i m e of flight over an 11 m flight path. The m o m e n t u m bite was ± 2 ~ Two-body events w e r e selected by r e q u i r i n g coincidences between s c a t t e r e d kaons and recoil protons in counter hodoscopes placed in the horizontal plane around a v e r t i c a l l y polarized target. In the range of m o m e n t a and angles of the p r e s e n t e x p e r i m e n t the s c a t t e r e d kaons can c l e a r l y be d i s t i n guished f r o m the r e c o i l protons by angle m e a s u r e m e n t s alone. A butanol p o l a r i z e d t a r g e t [7] cooled with liquid 3He (~ 0.5°K, polarization ~ 65%) was used throughout the p r e s e n t e x p e r i m e n t except for the data at 1250 M e V / c where the t a r g e t was cooled with liquid 4He (~ l°K, p o l a r i z a tion ~ 35%). The t a r g e t polarization deduced f r o m NMR signals was r e corded between e v e r y PS burst. The absolute calibration of the polarization was obtained by m e a s u r i n g the natural NMR signal at r e g u l a r intervals. The t a r g e t polarization was r e v e r s e d e v e r y ~ 10 h. In the a n a l y s i s , background events, mostly due to bound protons in the t a r g e t were subtracted out after extrapolating into the elastic peak the a z i muthal distribution of n o n - c o p l a n a r events m e a s u r e d simultaneously. The c.m. angles and effective solid angles w e r e obtained f r o m s t r a i g h t f o r w a r d kinematic calculations taking into account energy l o s s , absorption and m u l tiple s c a t t e r i n g in the t a r g e t , and deflection of the p a r t i c l e s by the magnetic field. At angles c o r r e s p o n d i n g to cos Oc.m. > 0.8, the m o m e n t u m of the r e coil protons b e c o m e s so small (~ 250 MeV/c) that the effective solid angle cannot be calculated accurately. T h e r e f o r e , at these angles the differential c r o s s - s e c t i o n data a r e omitted f r o m the final r e s u l t s and only the p o l a r i z a tion data a r e p r e s e n t e d since these do not depend on the solid angle. The alignment of the counter hodoscopes was checked by r e q u i r i n g a g r e e m e n t of the differential c r o s s - s e c t i o n data in which the kaon s c a t t e r s to the left with those for s c a t t e r i n g to the right. The relative n o r m a l i z a t i o n of the n u m b e r of events was checked to be c o r r e c t by r e q u i r i n g consistency between the polarization data with kaon left and kaon right. In the final r e s u l t s these two sets of data w e r e grouped in c o s O c . m , bins v a r y i n g between 0.02 and 0.08 and replaced by their weighted a v e r a g e s . The details of the apparatus and the data-handling p r o c e d u r e s of the p r e s e n t e x p e r i m e n t have been d e s c r i b e d in ref. [3] and in ref. [8]. The r e s u l t s a r e p r e s e n t e d in tables 1-8 and in figs. 1 and 2. The sign of the polarization is based on the Basel convention. The polarization e r r o r s a r e statistical only. The t a r g e t polarization d e t e r m i n e d f r o m NMR m e a s u r e m e n t s also has a relative uncertainty of about ±5~; this s y s t e m a t i c e r r o r has not been included in the tables and figures. The s y s t e m a t i c e r r o r a r i s i n g f r o m u n c e r t a i n t i e s in the alignment of the c o u n t e r s , the counter inefficiencies, and the effective solid angle is e s t i m a t e d to be 5% and has been included in the differential c r o s s - s e c t i o n data.
M. G . A l b r o w et al., K - elastic s c a t t e r i n g
415
Table 1 Elastic K p scattering. P
dd(~ ~ (mb/sr)
d(~
P~
(mb/sr)
cos 0c.m.
- t (GeV 2)
0.787 0.732 0.686 0.638 0.591 0,544 0.496
0.09 0.12 0.14 0.16 0.18 0.20 0.22
0.20+0.12 0.51 + 0.09 0.44 + 0.09 0.49 + 0.09 0.61 + 0.09 0.70+0.11 0.76 + 0.12
3.10 + 0.31 2.86 + 0.28 2.28 + 0.16 2.06 + 0.15 1.72+0.13 1.37 + 0.12
1.58+0.38 1.26+0.34 1.12-0.19 1.254-0.18 1.20+0.17 1.04+0.15
0,459 0.420 0.369 0.318 0.267 0.226 0.177
0.24 0.26 0.28 0.30 0.32 0.34 0.36
0.66 0.75 0.80 0.81 0.84 0.75 0.79
+ 0.19 + 0.12 + 0.13 + 0.14 + 0.15 + 0.24 + 0.12
1.17 + 0.14 1.20 + 0.10 1.144- 0.10 1.00 + 0.10 0.89 + 0.09 0.77 + 0.11 0.78 + 0.06
0.77+0.18 0.90-0.14 0.91~-0.13 0.81"0.13 0.75+0.12 0.58+0.14 0.62+0.09
0.139 0.077 0.018 -0.053 -0.133 -0.220 -0.304
0.38 0.41 0.43 0.46 0.50 0.54 0.57
0.60 0.61 0.66 0.55 0.27 0.38 0.18
+ 0.25 + 0.16 + 0.19 + 0.14 + 0.21 + 0.16 + 0.27
0.64 0.59 0.59 0.55 0.40 0.36 0.30
+ 0.10 + 0.06 + 0.08 + 0.05 + 0.06 + 0.04 + 0.06
0.39+0.14 0.36+0.08 0.39+0.10 0.30+0.07 0.11+0.07 0.144-0.06 0.05+0.08
-0.367 -0.442 -0.519 -0.593 -0.653 -0.726 -0.803
0.60 0.63 0.67 0.70 0.73 0.76 0.79
-0.11 + 0.28 -0.61 + 0.30 -0.62 + 0.21 -0.59 + 0.23 -0.33 + 0.23 -0.61 + 0.17 - 0 . 7 4 + 0.24
0.25 0.30 0.45 0.69 0.64 1.02 1.02
+ 0.05 + 0.06 + 0.07 + 0.10 + 0.11 + 0.13 + 0.15
-0.03+0.07 -0.18+0.08 -0.28 :e 0.08 -0.41+0.13 -0.21+0.14 -0.63+0.15 -0.75+0.19
I n c i d e n t m o m e n t u m = 865 + 17 M e V / c . Total c . m . e n e r g y = 1730 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
No a b s o l u t e n o r m a l i z a t i o n o f 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 s w a s o b t a i n e d i n t h e p r e s e n t e x p e r i m e n t , d u e to t h e c o m p l e x t a r g e t a s s e m b l y . The method c o m m o n l y a d o p t e d i n s u c h a c a s e i s to n o r m a l i z e t h e d a t a to t h e t o t a l c r o s s sections through the optical theorem by using the differential cross section a t 0° o b t a i n e d f r o m L e g e n d r e e x p a n s i o n o f t h e d a t a a n d t h e r a t i o s o f t h e r e a l to i m a g i n a r y p a r t o f t h e f o r w a r d s c a t t e r i n g a m p l i t u d e s g i v e n b y t h e d i s p e r s i o n r e l a t i o n c a l c u l a t i o n . It w a s f o u n d t h a t t h i s p r o c e d u r e c o u l d n o t b e a p p l i e d to t h e p r e s e n t c a s e , b e c a u s e t h e l a c k o f d a t a a t t h e v e r y f o r w a r d a n g l e s ( c o s O c . m . ~ 0.8) d i d n o t a l l o w a u n i q u e d e t e r m i n a t i o n of the d i f f e r e n o tial cross section at 0 . Therefore the present differential cross-section d a t a w e r e n o r m a l i z e d to t h e p u b l i s h e d d i f f e r e n t i a l c r o s s - s e c t i o n data obt a i n e d b y b u b b l e c h a m b e r s [5, 1 0 - 1 3 ] . A f t e r a n a l y s i s o f t h e d a t a in t e r m s o f
M. G . A l b r o w et a l . , K - e l a s t i c s c a t t e r i n g
416
Table 2 Elastic K-p scattering. c o s 8c.m.
- t ( G e V 2)
ddO" ~ (mb/sr)
P
P d(Y ( m b / s r )
0.830 0.760 0.723 0.680 0.621 0.574 0.524
0.08 0.12 0.14 0.16 0.19 0.21 0.24
-0.12 0.13 0.20 0.28 0.46 0.39 0.41
± 0.14 ± 0.06 ± 0.08 ± 0.05 ± 0.07 ± 0.08 ± 0.08
3.12 2.62 1.90 1.69 1.60
-~0.24 ± 0.11 ± 0.11 ± 0.10 ± 0.10
0.62 0.73 0.88 0.65 0.66
± 0.26 ± 0.13 ± 0.13 ± 0.12 ± 0.12
0.480 0.437 0.359 0.291 0.239 0.197 0.126
0.26 0.28 0.32 0.35 0.38 0.40 0.43
0.61 0.59 0.90 0.86 0.82 0.89 0.83
± 0.13 ± 0.08 ± 0.09 ± 0.19 ± 0.08 ± 0.20 ± 0.11
1.38 ± 0.13 1.09 ± 0.06 0.90 ± 0.06 0 . 8 4 ± 0.10 0.79 ± 0.05 0.79 ± 0.09 0.63 ± 0.05
0.84 0.64 0.81 0.72 0.64 0.70 0.53
± 0.15 ± 0.08 ± 0.08 ± 0.12 ± 0.06 ± 0.12 ± 0.06
0.062
0.47
0.70 ± 0.14
0.61 ± 0.06
0.42 ± 0.08
-0.024 -0.107 -0.165 -0.218
0.51 0.55 0.58 0.60
0.86 ± O.i i 0.85 ± 0.22 0.54 ± 0.18 0.31 ± 0.19
0.51 ± 0.04 0.41 ± 0.06 0.36 ± 0.05 0.47 ± 0.06
0.44 0.35 0.19 0.15
-0.282 -0.349
0.64 0.67
0.25 ± 0.15 0.50 ± 0.19
0.35 ± 0.04 0.40 ± 0.05
0.09 ± 0.05 0.20 ± 0.07
-0.423 -0.501 -0.558 -0.622 -0.678 -0.750 -0.823
0.71 0.74 0.77 0.80 0.83 0.87 0.90
0.12 -0.35 -0.26 -0.58 -0.49 -0.87 -1.00
± 0.13 ± 0.14 ± 0.18 ± 0.12 ± 0.13 ± 0.12 ± 0.18
0.42 0.49 0.65 0.69 0.91 1.04 1.22
± 0.04 ± 0.06 ± 0.08 ± 0.08 ± 0.10 ± 0.11 ± 0.13
0.05 -0.17 -0.17 -0.40 -0.45 -0.90 -1.22
± 0.05 ± 0.08 ± 0.06 ± 0.08
± 0.05 ± 0.07 ± 0.12 ± 0.09 ± 0.12 ± 0.13 ± 0.17
I n c i d e n t m o m e n t u m = 935 ~-19 M e V / c . T o t a l c . m . e n e r g y = 1763 MeV. T h e e r r o r s in t h e p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. T h e e r r o r s in the 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 a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y .
Legendre expansion coefficients (see below), the normalization was slightly a d j u s t e d s o t h a t 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 s f i t to t h e s m o o t h c u r v e drawn through the points given by the bubble chamber experiments. The real error introduced by the normalization process cannot be estimated acc u r a t e l y , b u t i s e x p e c t e d n o t to e x c e e d 10%. T h i s e r r o r i s n o t i n c l u d e d i n the final results presented here.
3.
FEATURES
OF THE DATA
The present differential cross-section data agree fairly well with those o f H o l l e y e t a l . [ 9 ] , C o n f o r t o e t a l . [ 5 , 1 0 ] , T r o w e r e t a l . [ 1 1 ] , L y n c h [12]
417
M. G.Albrow et al., K - e l a s t i c scattering Table 3 Elastic K-p scattering. c o s 0c . m .
- t (GeV 2)
P
~ (mb/sr) dd ~
dO P ~ (mb/sr)
0.819 0.770 0.718 0.661 0.600 0.565 0.516
0.10 0.13 0.16 0.19 0.22 0.24 0.27
-0.22 -0.17 0.04 -0.06 0.12 0.43 0.46
4- 0.06 ± 0.06 ± 0.05 ± 0.06 ± 0.06 ± 0.11 ± 0.09
2.63 2.10 1.55 1.40 1.06
± 0.12 ± 0.12 ± 0.08 ± 0.12 ± 0.08
0.472 0.428 0.377 0.337 0.284 0.232 0.167
0.29 0.32 0.35 0.37 0.40 0.43 0.46
0.71 0.65 0.73 0.86 0.85 0.72 0.96
± 0.17 ± 0.09 ± 0.19 ± 0.12 ± 0.14 ± 0.15 ± 0.13
0.86 0.75 0.67 0.68 0.60 0.50 0.56
± 0.10 ~: 0.05 ± 0.08 ± 0.06 ± 0.06 ± 0.05 ± 0.05
0.61 ± 0.12 0.48 ± 0.06 0.49 ± 0.10 0.58 ± 0.08 0.51 ± 0.07 0.36 ± 0.07 0.54± 0.06
0.104 0.054 -0.009 -0.089 -0.171 -0.223 -0.278
0.50 0.53 0.56 0.60 0.65 0.68 0.71
0.71 0.85 0.56 0.78 0.69 0.53 0.79
± 0.13 ± 0.16 ± 0.11 ± 0.11 ± 0.14 ± 0.16 ± 0.16
0.57 0.51 0.63 0.50 0.49 0.53 0.47
± 0.06 ± 0.05 ± 0.05 ± 0.04 ± 0.05 ± 0.06 ± 0.05
0.40 ± 0.07 0.44 ± 0.07 0.35 ± 0.06 0.39 ± 0.05 0.34± 0.06 0.28 ± 0.08 0.37 ± 0.06
-0.344 -0.410 -0.477 -0.553 -0.653 -0.749 -0.821
0.75 0.78 0.82 0.86 0.92 0.97 1.01
0.42 0.39 0.01 -0.26 -0.48 -0.68 -0.89
± 0.13 ± 0.14 ± 0.10 ± 0.10 ± 0.08 ± 0.12 ± 0.17
0.46 0.54 0.68 0.82 1.03 1.17 1.38
± 0.05 ± 0.06 ± 0.06 :e 0.07 ± 0.07 ± 0.11 ± 0.15
0.19 ± 0.06 0.21± 0.07 0.01 ± 0.07 -0.21 ± 0.08 -0.50 ± 0.08 -0.79 ± 0.13 -1.23 ± 0.18
0.11 -0.12 0.18 0.59 0.48
± 0.12 ± 0.13 ± 0.09 ± 0.14 ± 0.09
I n c i d e n t m o m e n t u m = 1010 ± 20 M e V / c . Total c . m . e n e r g y = 1798 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
a n d L i t c h f i e l d e t a l . [13]. T h e m o s t s t r i k i n g f e a t u r e s a r e t h e r a p i d c h a n g e of the forward slope and of the backward cross sections as a function of the i n c i d e n t m o m e n t u m . B o t h s h o w a m a x i m u m at a r o u n d 1.05 G e V / c , n e a r t h e strongly excited A(1820) resonance. T h e p o l a r i z a t i o n d a t a a t 935 a n d 1010 M e V / c s h o w t h e s a m e f e a t u r e s a s s e e n e a r l i e r i n t h e d a t a a t 982 M e V / c i n r e f . [4]: a v e r y l a r g e p o s i t i v e p o l a r i z a t i o n in the c e n t r a l p a r t of the a n g u l a r r a n g e and a s l i g h t l y n e g a t i v e p o l a r i z a t i o n a t s m a l l a n g l e s . A t t h e h i g h e r m o m e n t a , 1 0 3 5 , 1 0 5 5 , 1 1 7 7 , 1250 a n d 1330 M e V / c t h e p a t t e r n i s r a p i d l y c h a n g i n g t o w a r d s t h a t c h a r a c t e r i s t i c f o r t h e e n t i r e r a n g e o f m o m e n t a b e t w e e n 1082 a n d 2 3 3 0 M e V / c : p o s i t i v e p o l a r i z a t i o n in t h e r e g i o n of the d i f f r a c t i v e p e a k of t h e a n g u l a r d i s t r i b u t i o n , n e g a t i v e p o l a r i z a t i o n in t h e c e n t r a l p a r t and in t h e b a c k w a r d r e g i o n a p o l a r i z a -
418
M. G . A l b r o w et a l . , K - e l a s t i c s c a t t e r i n g Table 4 Elastic K p scattering. cos 0c.m.
d~d~ff( m b / s r )
i P ~d(Y ( m b / s r )
- t (GeV 2)
P
0.820 0.776 0.761 0.726 0.681 0.635 0.587
0.10 0.13 0.14 0.16 0.18 0.21 0.24
0.06 ± 0.08 0.08±0.12 -0.06 ± 0.09 -0.09 ± 0.07 0.06 ± 0.08 0.20 ± 0.09 0.27 ± 0.11
0.523 0.460 0.409 0.357 0.304 0.251 0.187
0.28 0.31 0.34 0.37 0.40 0.43 0.47
0.20 0.52 0.29 0.37 0.80 0.46 0.37
0.122 0.056 -0.026 -0.099 -0.157
0.51 0.54 0.59 0.63 0.67
0.18 0.37 0.33 0.26 0.07
-0.231 -0.322
0.71 0.76
0.35 ± 0.12 0.36 ± 0.12
0.61 ± 0.05 0.59 ± 0.05
0.21 ± 0.07 0.21 ± 0.07
-0.416 -0.485 -0.545
0.82 0.86 0.89
0.10 ± 0.11 -0.00 ± O.16 -0.07 ± 0.12
0.70 ± 0.06 0.71 ± 0.08 0.88 ± 0.08
0.07 ± 0.08 -0.00 ± 0.11 -0.07 ± 0.10
-0.614
0.93
-0.31 ± 0.15
0.76 ± 0.08
- 0 . 2 4 ± 0.11
-0.674 -0.742 -0.819
0.97 1.00 1.05
-0.62 ± 0.14 -0.53 ± 0.12 -0.48 ± 0.16
1.06 ± 0 . i i 1.33 ± 0.12 1.56 ± 0.18
-0.65 ± 0.14 -0.70 ± 0.15 -0.75 ± 0.22
3.12 2.88 2.18 1.54 1.08
± 0.25 ± 0.17 ± 0.14 ± 0.12 ± 0.10
-0.18 -0.27 0.12 0.31 0.30
± 0.27 ± 0.19 ± 0.17 ± 0.14 ± 0.12
± 0.10 ± 0.17 ± 0.18 ± 0.16 ± 0.23 ± 0.20 ± 0.14
0.70 0.45 0.37 0.43 0.37 0.40 0.44
± 0.05 ± 0.06 ± 0.05 ± 0.05 ± 0.06 ± 0.06 ± 0.05
0.14 0.23 0.11 0.16 0.30 0.19 0.16
± 0.07 ± 0.08 ± 0.07 ± 0.07 ± 0.08 ± 0.08 ± 0.06
± 0.18 ± 0.14 ± 0.12 ± 0.16 ± 0.13
0.43 0.49 0.52 0.60 0.56
± 0.06 ± 0.05 ± 0.04 ± 0.07 ± 0.06
0.08 0.18 0.17 0.16 0.04
± 0.08 ± 0.06 ± 0.06 ± 0.09 ± 0.08
I n c i d e n t m o m e n t u m = 1035 ± 21 M e V / c . T o t a l c . m . e n e r g y = 1810 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. T h e e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y . tion which is positive again at least at the lower momenta of this range. The results are compared with the predictions calculated from the energy d e p e n d e n t p h a s e - s h i f t a n a l y s e s b y C o n f o r t o e t a l . [5] a n d B r i c m a n e t a l . [ 6 ] , shown in figs. 1 and 2 as solid respectively dashed lines. It is seen that the results of these analyses are in fairly good agreement with the present data. At 865 MeV/c the region of large positive polarization has shifted towards smaller angles (cos Oc.m. ~ 0.4) and remains positive also in the forward d i r e c t i o n . In t h e a n g u l a r d i s t r i b u t i o n s a t t h e p r e s e n t m o m e n t a , w e c a n n o t identify the dip structures a s c l e a r l y a s a b o v e 1 . 4 G e V / c ( r e f . [3]). H o w ever, the regularity of the zero crossings in the polarization distributions, w h i c h w a s m e n t i o n e d i n r e f . [3], s e e m s to p e r s i s t to i n c i d e n t m o m e n t a a s low as 0.86 GeV/c (ref. [4]). Between 0.86 and 1.25 GeV/c a new zero crossing at constant u ~ 0.15 GeV 2 is observed. At 1.08 GeV/c two other
M.G.Albrow et al., K- elastic scattering
419
Table 5 Elastic K-p scattering. cos 0c.m.
- t ( G e V 2)
d(~ ~ (rob/st)
P
p dff ~-~ ( m b / s r )
0.831 0.790 0.747 0.702 0.657 0.609 0.560
0.10 0.12 0.15 0.18 0.20 0.23 0.26
0.08 -0.04 0.06 0.15 0.17 0.29 0.22
~- 0 . 0 6 + 0.07 + 0.06 + 0.07 + 0.07 ± 0.08 + 0.10
3.42 2.61 2.38 1.91 1.31 0.91
+ 0.27 + 0.22 + 0.13 + 0.12 ± 0.09 ± 0.07
-0.14 0.16 0.35 0.32 0.38 0.20
± 0.30 + 0.26 + 0.15 + 0.14 + 0.11 + 0.09
0.498 0.432 0.380 0.328 0.262 0.197 0.119
0.30 0.34 0.37 0.40 0.44 0.48 0.52
0.42 0.42 0.64 0.50 0.70 0.48 0.54
+ 0.10 + 0.16 + 0.18 + 0.19 + 0.15 ± 0.15 + 0.10
0.61 0.40 0.36 0.35 0.38 0.46 0.50
+ 0.04 + 0.05 + 0.04 ± 0.05 ± 0.04 ± 0.05 + 0.04
0.26 0.17 0.23 0.17 0.27 0.22 0.27
+ 0.06 + 0.06 ± 0.06 + 0.06 + 0.05 + 0.06 ± 0.05
0.031 -0.030 -0.078 -0.135 -0.212 -0.285 -0.346
0.57 0.61 0.64 0.67 0.72 0.76 0.80
0.53 0.38 0.46 0.34 0.48 0.32 0.35
± 0.12 + 0.15 ± 0.14 + 0.11 + 0.11 + 0.12 ± 0.13
0.55 0.59 0.58 0.63 0.62 0.61 0.67
± 0.04 + 0.05 ± 0.06 + 0.05 + 0.04 ± 0.05 + 0.06
0.29 0.23 0.26 0.21 0.30 0.20 0.23
+ 0.06 + 0.08 + 0.08 + 0.07 ± 0.06 + 0.07 + 0.08
-0.408 -0.492 -0.562 -0.626 -0.681 -0.750 -0.822
0.83 0.88 0.92 0.96 0.99 1.04 1.08
0.37 0.22 0.04 -0.22 -0.27 -0,69 -0.82
± 0.12 + 0.10 + 0.12 + 0.10 + 0.13 + 0.12 + 0.17
0.67 0.82 0.85 1.06 1.13 1.30 1.45
± 0.05 + 0.05 + 0.08 + 0.08 + 0.11 + 0.11 + 0.15
0.25 0.18 0.04 -0.24 -0.30 -0.89 -1.19
+ 0.08 + 0.08 + 0.10 ± 0.11 ±~).14 + 0.14 + 0.20
I n c i d e n t m o m e n t u m = 1 0 5 5 + 21 M e V / c . T o t a l c . m . e n e r g y = 1819 M e V . T h e e r r o r s in t h e p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l o n l y . T h e e r r c . r s in 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 d a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y . zero crossings appear, o n e o f w h i c h i s c o n s t a n t i n t , a t t ~ - 0 . 6 G e V 2, t h e o t h e r c o n s t a n t i n u, a t u ~ - 0 . 3 8 G e V 2. T h e l a t t e r t w o h a v e p r e v i o u s l y been observed in the data between 1.4 and 2.4 GeV/c of ref. [3]. Such regularities in u have been discussed recently by Odorico [17] in terms of the Veneziano model. In order to examine the data more closely, we have parametrized the angular and the polarization distributions using Legendre polynomials,
da _X2 ~ A I Pl (cos(9 c m ) , d~ l " " P~dCr = ~2 ~ Bl p~ l
( c o s O c. m . ) '
M. G.Albrow et al., If- elastic scattering
420
Table 6 Elastic K p scattering. P
dO' ~-(mb/sr)
dO" P ~-(mb/sr)
cos 0c.m.
- t ( G e V 2)
0,857 0,813 0,773 0,728 0.686 0.629 0,574
0.10 0.13 0.16 0.19 0.22 0.26 0.30
0.511 0.458 0.405 0.351 0.297 0.230 0.163
0.34 0.38 0.41 0.45 0.49 0.53 0.58
0.59 0.49 0.31 0.28 0.13 0.25 -0.15
+ 0.08 + 0.09 + 0.09 + 0.10 + 0.11 + 0.09 + 0.12
1.07 0.91 0.71 0.57 0.52 0.46 0.48
+ 0.07 + 0.06 -~0.05 + 0.04 + 0.04 + 0.03 + 0.04
0.63 0.45 0.22 0.16 0.07 0.11 -0.07
± 0.08 + 0.08 + 0.06 + 0.06 + 0.06 + 0.04 + 0.05
0.111 0.046 -0.016 -0.089 -0.159 -0.213 -0.297
0.62 0.66 0.70 0.76 0.80 0.84 0.90
-0.37 -0.31 -0.39 -0.38 -0.21 -0.09 0.12
+ 0.13 + 0.11 + 0.13 :e 0.10 ± 0.14 + 0.12 + 0.11
0.43 0.39 0.45 0.40 0.43 0.37 0.34
+ 0.04 + 0.03 + 0.04 + 0.03 + 0.04 + 0.03 + 0.03
-0.16 -0.12 -0.18 -0.15 -0.09 -0.03 0.04
+ 0.05 + 0.04 ± 0.06 + 0,04 ± 0,06 ± 0.04 + 0.04
-0.367 -0.439 -0.519
0.95 1.00 1.05
0.24 + 0.19 0.28 + 0.11 0.24 ± 0.16
0.37 ± 0.05 0.37 + 0.03 0.40 + 0.05
0.09 • 0.07 0.10 + 0.04 0.10 ~: 0.06
-0.585 -0.650 -0.705
1.10 1.14 1.18
0.01 ± 0.11 0.16 + 0.13 0.21 ± 0.15
0.57 + 0.05 0.52 + 0.06 0.58 + 0.07
0.01 :e 0.06 0.08 + 0.07 0.12 ~:0.08
-0.769
1.23
-0.18 ± 0.13
0.73 + 0.09
-0.13 + 0.09
-0.837
1.27
-0.38 ± 0.17
0.64+ 0.10
-0.25 + 0.11
0.234-0.06 0.31-4- 0.05 0.33 + 0.05 0.26 + 0.07 0.34 + 0.04 0.36 + 0.08 0.47 :~ 0.06
3.54± 0.17 3.21 + 0.15 2.94 + 0.21 2.34 + 0.08 2.03 + 0.15 1.36 + 0.06
1.10 ± 0.17 1.07 + 0.15 0.75 + 0.21 0.79 + 0.08 0.74 ~-0.17 0.64+ 0.07
I n c i d e n t m o m e n t u m = 1177 ~-23 M e V / c . Total c . m . e n e r g y = 1876 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the d i f f e r e n t i a l c r o s s - s e c t i o n data include a 5% s y s t e m a t i c u n c e r t a i n t y . w h e r e Pl a n d P ~ a r e L e g e n d r e a n d f i r s t a s s o c i a t e d L e g e n d r e p o l y n o m i a l s r e s p e c t i v e l y , a n d ~ i s t h e c . m . w a v e l e n g t h d i v i d e d b y 2~. In f i t t i n g 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 s , s e v e r a l p o i n t s f r o m t h e b u b b l e c h a m b e r e x p e r i m e n t s w e r e a d d e d to t h e p r e s e n t d a t a in t h e v e r y f o r w a r d and b a c k w a r d r e g i o n s w h i c h could not be r e a c h e d in the p r e s e n t e x p e r i m e n t . T h e A - c o e f f i c i e n t s a r e f o u n d to b e v e r y s e n s i t i v e to t h e s e p o i n t s . T h e r e f o r e , the procedure is justified only by the consistency of the results obtained by the a n a l y s i s of the b u b b l e c h a m b e r d a t a a l o n e . By u s i n g the d i f f e r e n t i a l c r o s s s e c t i o n a t 0° o b t a i n e d f r o m t h e s e L e g e n d r e e x p a n s i o n c o e f f i c i e n t s a n d t h e r a t i o s o f t h e r e a l to i m a g i n a r y p a r t o f t h e f o r w a r d s c a t t e r i n g a m p l i t u d e s g i v e n i n r e f . [5], i t w a s c o n f i r m e d t h a t t h e p r e s e n t d a t a l e a d to t o t a l c r o s s
M. G.Albrow et al., K - elastic scattering
421
Table 7 Elastic K p scattering. c o s 0c.m.
ddo" ~ (mb/sr)
do"
P ~-~ ( m b / s r )
- t ( G e V 2)
P
0.858 0.808 0.767 0.723 0.676 0.627 0.576
0.11 0.14 0.18 0.21 0.24 0.28 0.32
0.17 ± 0.06 0.24 ± 0.06 0.30 ± 0.07 0.21 ± 0.07 0.36 ± 0.07 0.31 ± 0.08 0.34± 0.09
3.41 2.89 2.41 2.10 1.75 1.25
± 0.15 ± 0.13 ± 0.11 ± 0.10 ± 0.08 ± 0.06
0.81±0.22 0.86 ~-0.20 0.51±0.17 0.75-~ 0.16 0.54~- 0.14 0.42 ~-0.12
0.524 0.489 0.452 0.410 0.355 0.282 0.215
0.36 0.39 0.41 0.44 0.49 0.54 0.59
0.35 ± 0.10 0.27 ± 0.15 0.20 ± 0.19 0.34 ± 0.14 0.16 ± 0.13 - 0 . 1 4 ± 0.17 -0.17 ± 0.16
1.09 0.87 0.64 0.51 0.48 0.45 0.36
± 0.06 ± 0.07 ± 0.06 ± 0.04 ± 0.03 ± 0.03 ± 0.03
0.38 ~-0.11 0.23±0.13 0.13±0.13 0.18-~ 0.07 0.07 -~0.06 -0.06 -~0.07 -0.06 ~-0.06
0.148 0.096 0.044 -0.019 -0.103 -0.185 -0.254
0.64 0.68 0.72 0.77 0.83 0.89 0.95
-0.37 ± 0.21 -0.55 ± 0.19 -0.45 ± 0.21 -0.39 ± 0.18 -0.59 ± 0.15 - 0 . 6 4 ± 0.24 -0.45 ± 0.17
0.33 0.39 0.36 0.37 0.38 0.35 0.31
± 0.03 ± 0.03 ± 0.03 ± 0.03 ± 0.03 ± 0.04 ± 0.02
-0.12 ~-0.07 -0.21±0.07 -0.16±0.07 -0.14±0.06 -0.22±0.06 -0.22±0.08 -0.14±0.05
-0.349 -0.425 -0.483 -0.538 -0.594 -0.657 -0.709
1.02 1.07 1.12 1.16 1.20 1.25 1.29
-0.13 0.15 0.15 0.27 0.61 0.38 0.36
0.30 0.25 0.29 0.28 0.25 0.31 0.39
± 0.03 ± 0.03 ± 0.03 ± 0.04 ± 0.03 ± 0.04 ± 0.05
-0.04 ± 0.05 0.04±0.08 0.04±0.07 0.08±0.08 0.15±0.08 0.12 ± 0.08 0.14±0.11
-0.775 -0.842
1.34 1.39
0.50 ± 0.06 0.39 ± 0.06
0.04±0.12 0.04±0.14
± 0.18 ± 0.29 ± 0.22 ± 0.30 ± 0.38 ± 0.26 ± 0.26
0.09 ± 0.23 0.10 ± 0.36
I n c i d e n t m o m e n t u m = 1250 ~-25 M e V / c . Total c . m . e n e r g y = 1909 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a include a 5% s y s t e m a t i c u n c e r t a i n t y .
s e c t i o n s c o n s i s t e n t w i t h t h o s e m e a s u r e d b y B u g g e t al. [14] a n d b y C o o l e t a l . [15]. In f i t t i n g t h e p o l a r i z a t i o n d i s t r i b u t i o n s , the differential cross sections calculated with these A-coefficients were used for the forward points at which only polarization data were obtained. The results of the Aa n d B - c o e f f i c i e n t s a r e s h o w n i n t a b l e 9 a n d f i g s . 3 a n d 4. F i g s . 3 a n d 4 a l s o i n c l u d e t h e r e s u l t s f o r t h e e a r l i e r d a t a [3, 4]. F o r t h e s a k e o f c o n s i s t e n c y t h e d a t a o f r e f . [4] h a v e b e e n r e n o r m a l i z e d f o l l o w i n g t h e s a m e p r o c e d u r e a s f o r the data of the present experiment, hence there are slight differences with r e s p e c t to t h e A ' s a n d B ' s o f r e f . [4]. T h e m i n i m u m o r d e r o f t h e f i t w a s d e termined by checking the stability in the A- and B-coefficient as a function
M. G.Albrow et al., K - elastic scattering
422
Table 8 Elastic K p scattering. dd(~ ~ (mb/sr)
dff P ~-~(mb/sr)
c o s Oc.m.
-t (GeV 2)
0.879 0.840 0.798 0.763 0.713
0.10 0.13 0.17 0.19 0.24
0.17 0.17 0.20 0.38 0.27
0.665 0.615
0.28 0.32
0.26 ± 0.06 0.37 ± 0.07
1.31 ± 0.08 1.12 ± 0.07
0.563 0.510 0.456 0.418
0.36 0.40 0.45 0.48
0.40 ± 0.08 0.44 ± 0.09 0.55 ± 0.11 0.30 ± 0.16
0.86 ± 0.06 0.70 ± 0.05 0.55 ± 0.04 0.40 ± 0.05
0.353 0.281 0.216
0.53 0.59 0.64
0.31 ± 0.12 0.37 ± 0.12 0.01 ± 0.25
0.38 ± 0.03 0.28 ± 0.03 0.21 ± 0.04
0.155 0.075 0.023
0.69 0.76 0.80
-0.15 ± 0.12 -0.30 ± 0.16 -0.59 ± 0.19
0.21 ± 0.02 0 . 2 4 ± 0.03 0.24 ± 0.03
-0.041 -0.123 -0.194 -0.248
0.86 0.92 0.98 1.03
-0.47 ± 0.15 -0.75 ± 0.15 -0.64 ± 0.22 -0.41 ± 0.18
0.25 ±0.03 0.23 ± 0.02 0.23 ± 0.03 0.20 ± 0.03
-0.300 -0.351 -0.426 -0.477 -0.531 -0.594 -0.657
1.07 1.11 1.17 1.21 1.26 1.31 1.36
-0.50 ± 0.24 -0.34 ~:0.19 0.04 ± 0.16 -0.21 ~-0.21 -0.29 ± 0.16 0.20 ± 0.16 0.16 ± 0.14
0.23 ± 0.04 0.23 ± 0.03 0.21 ± 0.03 0.24 ± 0.04 0.29 ± 0.04 0.28 ± 0.04 0.36 ± 0.04
-0.08±0.04 0.01±0.03 -0.05 ± 0.05 -0.08±0.05 0.05 ± 0.05 0.06±0.05
-0.712 -0.775 -0.840
1.41 1.46 1.51
0.06 ± 0.17 0.08 ± 0.12 -0.28 • 0.15
0.32 ± 0.05 0.53 ± 0.05 0.53 ± 0.07
0.02±0.06 0.04 =~0.06 -0.15±0.08
P ± 0.06 ± 0.05 ± 0.04 ± 0.08 ± 0.06
2.81 2.31 2.11 1.55
± 0.14 ± 0.08 ~: 0.16 ± 0.09
0.47 • 0.14 0.46 • 0.08 0.80±0.17 0.42 ± 0.09 0.34±0.08 0.41~0.08 0.34±0.07 0.31±0.06 0.30±0.05 0.12 :e 0.06 0.12±0.04 0.10±0.03 0.00~0.05 -0.03 ± 0.03 -0.07 :e 0.04 -0.14±0.04 -0.12±0.03 -0.17±0.03 -0.15±0.04 -0.08±0.03 -0.12±0.05
I n c i d e n t m o m e n t u m = 1330 ± 27 M e V / c . T o t a l c . m . e n e r g y = 1946 MeV. The e r r o r s in the p o l a r i z a t i o n d a t a a r e s t a t i s t i c a l only. The e r r o r s in the 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 a t a i n c l u d e a 5% s y s t e m a t i c u n c e r t a i n t y . of the order of fit, and also the gradient of the improvement of the fit given by the F-ratio. In t h e p r e s e n t e n e r g y r e g i o n 5 t h o r d e r f i t s w e r e f o u n d to b e a d e q u a t e e x c e p t f o r t h e p o i n t s a t 1211 a n d 1 2 5 0 M e V / c , w h e r e 6 t h o r d e r f i t s were required. In f i g s . 3 a n d 4 t h e r e s u l t s f o r t h e 6 t h o r d e r f i t s a r e a l s o s h o w n w i t h d a s h e d e r r o r b a r s f o r 1 1 7 7 , 1282 a n d 1 3 3 0 M e V / c . All A-coefficients except A 1 and A 6 show a strong peak at around 1.05 GeV/c reflecting the strong excitation of the A(1820) resonance. The coefficient A 1 shows a broad maximum at around 1.15 GeV/c, where the A(1870) resonance is predicted by an energy dependent phase-shift analysis [5]. A m i n i m u m i s o b s e r v e d i n a l l A - c o e f f i c i e n t s a t a r o u n d 1 . 2 5 to 1.30 GeV/c.
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Fig. 5. Plot of the coefficient B 2 of the Legendre expansion of the polarization (P dcr/dfl) data of the p r e s e n t experiment and of refs. [3, 4]. The line has been drawn to guide the eye. T h e m o s t p r o m i n e n t f e a t u r e of the B - c o e f f i c i e n t s b e l o w 1.2 G e V / c i s t h e i r s t r o n g v a r i a t i o n w i t h e n e r g y . T h i s b e h a v i o u r can b e a c c o u n t e d f o r q u a l i t a t i v e l y by the i n t e r f e r e n c e of the t h r e e , r a t h e r s t r o n g l y e x c i t e d r e s o n a n c e s p r e s e n t b e t w e e n 0.9 and 1.2 G e V / c (~(1770), A(1820), A(1870)) a m o n g t h e m s e l v e s and w i t h a c o n s t a n t o r s l o w l y v a r y i n g , m o s t l y i m a g i n a r y b a c k g r o u n d of low (l = 0, 1 , 2 ) o r b i t a l a n g u l a r m o m e n t u m . T h i s i s i l l u s t r a t e d in fig. 5 w h i c h g i v e s the B 2 c o e f f i c i e n t a s a f u n c t i o n of m o m e n t u m . In the r e g i o n of the ~ ( 1 7 7 0 , ~ - ) the d o w n g o i n g t r e n d a r i s e s f r o m the i n t e r f e r e n c e of D 5 w i t h an i m a g i n a r y S 1 b a c k g r o u n d w a v e ; n e a r t h e A(1820, ~-+) the u p g o i n g p a r t of t h e c u r v e i s g e n e r a t e d by the i n t e r f e r e n c e of the F 5 w i t h a P l and a P3 b a c k g r o u n d w a v e . In the v i c i n i t y of t h e A(1870), w h i c h h a s b e e n c o n s i d e r e d to h a v e J P = ½+ ( r e f . [16]) but in the m o r e r e c e n t l i t e r a t u r e [5, 6] i s q u o t e d a s J P = 3+ the d o w n w a r d p a r t o r i g i n a t e s m o s t l y f r o m the i n t e r f e r e n c e of t h i s r e s o n a n c e (with e i t h e r J P a s s i g n m e n t ) w i t h the A(1820, ~-+) -p 7+ r e s o n a n c e , and a l s o w i t h a P - w a v e b a c k g r o u n d (P3 f o r d = ~ , ~'1 f o r J P = 23-+). N e a r 1.5 G e V / c , w h e r e the ~ ( 2 0 3 0 , ~T+) i. s l o c a t e d a n o t h e r d o w n w a r d p a r t i s o b s e r v e d w h i c h can b e a c c o u n t e d f o r by the i n t e r f e r e n c e m o s t ly w i t h a D 3 b a c k g r o u n d w a v e , w i t h s m a l l e r c o n t r i b u t i o n s f r o m P3 and F 5 w a v e s . T h e A(2100, ~ - ) i s a g a i n l o c a t e d on an u p w a r d s l o p e w h i c h a r i s e s in the i n t e r f e r e n c e of t h i s r e s o n a n c e w i t h a D 3 b a c k g r o u n d w a v e . A t 1.35 G e V / c a n o t h e r s l o p e i s s e e n in fig. 5 and by d e d u c t i o n one m i g h t s u r m i s e t h a t an a s y e t unknown r e s o n a n c e would b e p r e s e n t at t h a t m o m e n t u m . It m u s t b e s t r e s s e d t h a t a t t h i s m o m e n t u m two e x p e r i m e n t s d o n e w i t h d i f f e r e n t p o l a r i z e d t a r g e t s and d i f f e r e n t d e t e c t i o n e q u i p m e n t j o i n t o g e t h e r ; on the o t h e r hand a v e r y l a r g e ( ~ 40%) e r r o r in the t a r g e t p o l a r i z a t i o n e i t h e r in the e x p e r i m e n t of r e f . [3] o r in the e x p e r i m e n t of r e f . [4] a n d in t h e p r e -
M.G.Albrow et al., II- elastic scattering
429
s e n t d a t a i s r e q u i r e d to e l i m i n a t e t h i s s l o p e a l t o g e t h e r . W e c o n c l u d e t h a t m o r e p o l a r i z a t i o n d a t a w i l l b e n e e d e d a r o u n d 1.35 G e V / c in o r d e r to e s t a b l i s h w h e t h e r t h e s t r u c t u r e in the B - c o e f f i c i e n t s at t h e s e m o m e n t a i s i n d i c a tive for new resonances.
4. S P I N AND P A R I T Y A S S I G N M E N T O F THE A(1870) A s m e n t i o n e d a b o v e , t h e A(1870) h a s b e e n c o n s i d e r e d to b e a J P = ~-+ r e s o n a n c e [16], a l t h o u g h m o r e r e c e n t l y e v i d e n c e h a s b e e n p r e s e n t e d in f a v o u r of J : P = ~+ ( r e f s . [5, 6]). I n s p e c t i o n of the B 1 and B 3 c o e f f i c i e n t s of fig. 4, i . e . s t r o n g s t r u c t u r e in B 1 , b u t n o t in B 3 a t ~ 1.2 G e V / c a l s o f a v o u r s t h e l a t t e r a s s i g n m e n t ; B 1 c o n t a i n s an S 1 - P 3 i n t e r f e r e n c e t e r m , B 3 c o n t a i n s an S 1 - F 7 i n t e r f e r e n c e t e r m ; the s t r o n g s t r u c t u r e in B~, c o m b i n e d w i t h the r a t h e r f l a t b e h a v i o u r of B 3 , i s t h u s i n d i c a t i v e f o r a j r = ~+ w a v e i n t e r f e r i n g with a largely imaginary S1 background amplitude. In o r d e r to c h e c k t h i s r e s u l t m o r e c l o s e l y , w e h a v e f i t t e d the d a t a b e t w e e n 0.98 and 1.34 G e V / c to the b a c k g r o u n d p l u s r e s o n a n c e m o d e l w h i c h w a s a p p l i e d e a r l i e r [6] t o t h e d a t a of r e f . [4]. O t h e r d a t a u s e d in t h e f i t t i n g s a r e t h e s a m e a s t h o s e q u o t e d in r e f . [ 6 ] . W e h a v e c o n f i n e d t h e a n a l y s i s to the two p o s s i b i l i t i e s J P = ~+ o r ~÷ f o r A(1870). F o r the b a c k g r o u n d , t a k e n to v a r y l i n e a r l y w i t h m o m e n t u m , o n l y S1, P 1 , P3 and D 3 w a v e s h a v e b e e n c o n s i d e r e d . O n l y the r e s o n a n c e s A(1830), Z(1765), A(1820), Z(1910) a n d A(1870) h a v e b e e n u s e d in the fit. V a r y i n g the b a c k g r o u n d , w h i l e k e e p i n g t h e r e s o n a n c e s f i x e d , and v i c e v e r s a , l e a d s to s t a b l e f i t s w i t h low ×2 f o r J P ( 1 8 7 0 ) = ~+, b u t r e q u i r e s c o n s i d e r a b l e r e a d j u s t m e n t s a m o n g the v a r i o u2 s r e s o n a n c e p a r a m e t e r s if J P ( 1 8 7 0 ) i s tpa k e n 3+to b e ~7+. T h e b e s t f i t h a s X = 560 f o r 418 d e g r e e s of f r e e d o m f o r J = ~ , and ×2 = 958 f o r 443 d e g r e e s of f r e e d o m f o r J P = -~+. It h a s b e e n c h e c k e d t h a t the r e s u l t d o e s n o t d e p e n d on the c h o i c e of s t a r t i n g v a l u e s in t h e fit. The A - and B - c o e f f i c i e n t s c a l c u l a t e d f o r the two s o l u t i o n s a r e s h o w n in f i g s . 3 and 4. It i s s e e n t h a t a t 1.2 G e V / c B 1 and B 3 i n d e e d b e h a v e a s a n t i c i p a t e d , i . e . v a r y i n g B1 a n d f l a t B 3 f o r J P = ~ , v i c e v e r s a f o r J P = ~~+. It can t h e r e f o r e b e c o n c l u d e d t h a t t h e p r e s e n t p o l a r i z a t i o n d a t a , t o g e t h e r w i t h t h o s e of r e f . [4] s u p p o r t the c o n c l u s i o n t h a t t h e s p i n and p a r i t y of the A(1870) r e s o n a n c e i s ~÷. T h e a u t h o r s w o u l d l i k e to t h a n k t h e P o l a r i z e d T a r g e t G r o u p f o r t h e i r c o n t r i b u t i o n s to t h i s e x p e r i m e n t . W e a r e i n d e b t e d to M. A r b e t f o r t e c h n i c a l a s s i s t a n c e in the c o u r s e of t h e e x p e r i m e n t . T h i s w o r k w a s s u p p o r t e d in p a r t by t h e S t i c h t i n g v o o r F u n d a m e n t e e l O n d e r z o e k d e r M a t e r i e ( F O M ) , w h i c h i s s u p p o r t e d b y the N e d e r l a n d s e O r g a n i s a t i e v o o r Z u i v e r W e t e n s c h a p p e l i j k O n d e r z o e k (ZWO).
RE FERENCES [I] C. L. Wang, University of California, Lawrence Radiation Laboratory report No. 11881, unpublished.
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M. G . A l b r o w et al., K - elastic s c a t t e r i n g
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