- Email: [email protected]
The slope parameter of the differential cross-section of elastic p-p scattering in energy range 12–70 GeV
Volume 30B, number 4
PHYSICS
LETTERS
13 October 1969
THE SLOPE PARAMETER OF THE DIFFERENTIAL CROSS-SECTION OF ELASTIC p-p SCATTERING IN ENERGY RANGE 12-70 GeV G. G. B E Z N O G I K H , A. BUYAK, K . I . I O V C H E V , L . F . K I R I L L O V A , P . K . MARKOV, B. A. M O R O Z O V , V . A . NIKITIN, P . V . NOMOKONOV, M. G. S H A F R A N O V A , V. A. SVIRIDOV, T R U O N G BIEN, V . I . ZAYACHKI, N . K . ZHIDKOV, L . S . Z O L I N Joint Institute f o r Nuclear R e s e a r c h Dubna, USSR S. B. N U R U S H E V and V. L. SOLOVIANOV Institute of High Energy P h y s i c s , SerDukhov, USSR Received 25 August 1969
The measurements of the differential cross section of elastic p-p scattering in relative units were p e r formed in the energy range of 12-70 GeV. The values of the slope parameter were obtained from this data. It was shown that the slope parameter of the differential p-p scattering is monotonously increasing when the proton energy r i s e s in the range 12-70 GeV. We have obtained the slope Pomeranehuk's pole t r a j e c tory from this data: ap' = 0.40 i 0.09. A v e r y thin (~ 3 ~) (CH2) n f i l m t a r g e t with m u l t i p l e t r a v e r s a l s of the i n t e r n a l b e a m of the S e r p u k h o v a c c e l e r a t o r w a s u s e d in t h i s e x p e r i ment. E i g h t s e m i c o n d u c t o r d e t e c t o r s r e g i s t e r e d the a n g l e and the e n e r g y of r e c o i l p r o t o n s . T h r e e s c i n t i l l a t i o n c o u n t e r t e l e s c o p e s r e g i s t e r e d the s e c o n d a r y p a r t i c l e s e m e r g e d f r o m the t a r g e t . An o n - l i n e s y s t e m was u s e d in t h i s e x p e r i m e n t . T h e m e a s u r e m e n t s w e r e p e r f o r m e d f o r the t i m e i n t e r v a l of 2 s e c in e a c h p u l s e of the a c c e l e r a t o r when the m a g n e t i c f i e l d was r i s i n g . T h i s m a k e s it p o s s i b l e f o r us to obtain s o m e i n f o r m a t i o n about 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 of the e l a s t i c p - p s c a t t e r i n g in the e n e r g y r a n g e of ~45 GeV in e a c h p u l s e . T h e m e a s u r e m e n t s w e r e p e r f o r m e d in the "t" i n t e r v a l : 0.008 < [ t t < 0.12 (GeV/c) 2. In fig. 1 one can s e e an e x a m p l e of the m e a s u r 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 which was o b t a i n e d at 58.1 GeV. We h a v e c a r r i e d out 94 s i m i l a r m e a s u r e m e n t s in the e n e r g y r e g i o n of 12-70 GeV. As it f o l l o w s f r o m B e t h e [1], the d i f f e r e n t i a l e l a s t i c p - p c r o s s s e c t i o n can be d e s c r i b e d by the f o l l o w i n g f o r m u l a (for a s m a l l v a l u e of t): dtd~=c I A2 + A2+r A 2 c - 2 A c
(Ar +2nAIln
where AI
d•
exp (~ b I ) pt
274
0~)1
t
0.8
0.~
0.~
Q.~
i
0.0t
!
I
i
I
0,05
i
I
t
I
11
i
i
O. 0 t (GeV/c)
F i g . 1. T h e 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 b i t r a r y units at 58.1 GeV. b I = 11.07 • 0.18
I 2
in a r -
(GeV/c)-2
is the i m a g i n a r y p a r t of t h e e l a s t i c p - p s c a t t e r ing a m p l i t u d e ; b I t h e s l o p e p a r a m e t e r ; A r = ~ A I the r e a l p a r t of the e l a s t i c p - p s c a t t e r i n g a m p l i tude; A c = 2n F(O)/kO 2 the C o u l o m b a m p l i t u d e ; F(O) = exp (½bit) the n u c l e a r f o r m f a c t o r of the n u c l e o n ; n = 1 / 1 3 7 f i ; (p= 1 . 0 6 / k R ; R the n u c l e o n
V o l u m e 30B, n u m b e r 4
PHYSICS
LETTERS
13 O c t o b e r 1969
Table 1 T h e r e s u l t s of the m e a s u r e m e n t s of the e l a s t i c p - p s c a t t e r i n g s l o p e p a r a e e r b in the r e g i o n :
O.O08
£
I
g z 8
syst. error
2
~,
~ 8
, 0 . . . . . . . . ~'0
3'0
' ~b
'~'0
F i g . 2. T h e r e s u l t s of the m e a s u r e m e n t s of the s l o p e p a r a m e t e r . Q : t h i s e x p e r i m e n t ; O : r e f . 2; ~ : r e f . 4; A: r e f . 3. r a d i u s , t = - 2 p 2 ( 1 - c o s 0); 0, P , k t h e s c a t t e r i n g a n g l e , t h e m o m e n t u m a n d t h e w a v e n u m b e r in t h e c . m . s , a n d ~ t h e s p e e d of t h e i n c i d e n t p r o t o n i n t h e l a b s y s t e m . W e u s e d C = ~ = 1. F i g . 2 g i v e s 20 a v e r a g e d v a l u e s o f t h e s l o p e parameters as a function of the lab. energy of p r o t o n s ( s e e a l s o t a b l e 1). F i g . 2 a l s o s h o w s t h e results of other experiments [2-4]. As is seen, the slope parameter is monotonously increasing when the proton energy rises in the 12-70 GeV range. This means in the framework of t h e o p t i c a l model that the interaction radius R = 24-~ is growing from 1.23 to 1.34 fm. We obtained the slope of Pomeranchuk's pole from this data using the Ter-Martirosian's parametrisation f o r p o l e s a n d r e s i d u e s [5]. W e represented b I a s a f u n c t i o n of In
(S/So)
b I = b 0 + 2b I i n
(S/So)
(S o = 1 G e V 2) a n d f o u n d t h e p a r a m e t e r s from our experimental data: b I = 0.47 ± 0.09 X b 0 = 6.8
± 0.3
It f o l l o w s f r o m = 0.40 • 0.09.
2
b0 and b 1
= 2 4 . 8 (20 e x p e r i m e n t a l points). T
the value b I that ap =
E l a b kin
S
bI *
R
(GeV)
(GeV) 2
(GeV/c) -2
(fro)
12.1 14.8 17.9 20.9 23.8 26.7 29.7 32.6 35.5 38.6 40.7 44.2 48.0 51.2 53.4 56.1 59.3 62.6 65.2 69.0
26.2 31.3 37.1 42.7 48.2 53.6 59.3 64.7 70.1 75.9 79.9 86.5 93.6 99.6 103.7 108.8 114.8 121.0 125.9 133.0
9.81 9.98 10.46 10.58 10.59 10.77 10.68 10.66 10.77 10.89 10.87 10.95 11.19 11.31 11.24 11.16 11.40 11.76 11.52 11.38
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ~ ±
0.35 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.11 0.10 0.14 0.10 0.11 0.11 0.12 0.10 0.09 0.12 0.12 0.11
1.236 1.247 1.276 1.284 1.284 1.295 1.290 1.288 1.295 1.302 1.301 1.306 1.320 1.327 1.323 1.319 1.333 1.353 1.339 1.331
± 0.022 ± 0.008 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.006 ± 0.008 ± 0.006 ± 0.006 ± 0.006 ± 0.007 =L 0.006 ± 0.005 ± 0.007 ± 0.007 ± 0.006
* Abi(syst ) = ±0.3
One can compare our results with the predict i o n s r e s u l t i n g f r o m t h e b a s i c p r i n c i p l e s of t h e m o d e r n t h e o r y . M a n y a u t h o r s , f o r e x a m p l e [6], h a v e f o u n d t h a t t h e i n c r e a s i n g of t h e d i f f e r e n t i a l cross section slope parameter should not exceed ln2S. The results of our experiment with prediction.
are
consistent
References 1. B e t h e , Ann. of P h y s . 3 (1958) 190. 2. L. F. K i r i l l o v a et al. Y a d e r n . F i z . (USSR) 1 (1965) 533. 3. K . J . F o l e y , S . J . L i n d e n b a u m , W . A . Love, S. O s a k i , J . J . R u s s e l l and L . C . L . Y u a n , P h y s . Rev. L e t t e r s 11 (1963) 425. 4. G. B e l l e t t i n i , G. C o c c o n i , A . N . D i d d e n s , E. L i l l e t h u n , J . P a h l , J . P . Scanlon, J. W a l t e r s , A . M . W e t h e r e l l and P. Z a n e l l a , P h y s . L e t t e r s 14 (1965) 164. 5. T e r - M a r t i r o s i a n , P r e p r i n t I T E R N (Moskow) N417 (1967). 6. J . D . B e s s i s , Nuovo C i m e n t o 4 5 (1966) 974.
275
PHYSICS
LETTERS
13 October 1969
THE SLOPE PARAMETER OF THE DIFFERENTIAL CROSS-SECTION OF ELASTIC p-p SCATTERING IN ENERGY RANGE 12-70 GeV G. G. B E Z N O G I K H , A. BUYAK, K . I . I O V C H E V , L . F . K I R I L L O V A , P . K . MARKOV, B. A. M O R O Z O V , V . A . NIKITIN, P . V . NOMOKONOV, M. G. S H A F R A N O V A , V. A. SVIRIDOV, T R U O N G BIEN, V . I . ZAYACHKI, N . K . ZHIDKOV, L . S . Z O L I N Joint Institute f o r Nuclear R e s e a r c h Dubna, USSR S. B. N U R U S H E V and V. L. SOLOVIANOV Institute of High Energy P h y s i c s , SerDukhov, USSR Received 25 August 1969
The measurements of the differential cross section of elastic p-p scattering in relative units were p e r formed in the energy range of 12-70 GeV. The values of the slope parameter were obtained from this data. It was shown that the slope parameter of the differential p-p scattering is monotonously increasing when the proton energy r i s e s in the range 12-70 GeV. We have obtained the slope Pomeranehuk's pole t r a j e c tory from this data: ap' = 0.40 i 0.09. A v e r y thin (~ 3 ~) (CH2) n f i l m t a r g e t with m u l t i p l e t r a v e r s a l s of the i n t e r n a l b e a m of the S e r p u k h o v a c c e l e r a t o r w a s u s e d in t h i s e x p e r i ment. E i g h t s e m i c o n d u c t o r d e t e c t o r s r e g i s t e r e d the a n g l e and the e n e r g y of r e c o i l p r o t o n s . T h r e e s c i n t i l l a t i o n c o u n t e r t e l e s c o p e s r e g i s t e r e d the s e c o n d a r y p a r t i c l e s e m e r g e d f r o m the t a r g e t . An o n - l i n e s y s t e m was u s e d in t h i s e x p e r i m e n t . T h e m e a s u r e m e n t s w e r e p e r f o r m e d f o r the t i m e i n t e r v a l of 2 s e c in e a c h p u l s e of the a c c e l e r a t o r when the m a g n e t i c f i e l d was r i s i n g . T h i s m a k e s it p o s s i b l e f o r us to obtain s o m e i n f o r m a t i o n about 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 of the e l a s t i c p - p s c a t t e r i n g in the e n e r g y r a n g e of ~45 GeV in e a c h p u l s e . T h e m e a s u r e m e n t s w e r e p e r f o r m e d in the "t" i n t e r v a l : 0.008 < [ t t < 0.12 (GeV/c) 2. In fig. 1 one can s e e an e x a m p l e of the m e a s u r 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 which was o b t a i n e d at 58.1 GeV. We h a v e c a r r i e d out 94 s i m i l a r m e a s u r e m e n t s in the e n e r g y r e g i o n of 12-70 GeV. As it f o l l o w s f r o m B e t h e [1], the d i f f e r e n t i a l e l a s t i c p - p c r o s s s e c t i o n can be d e s c r i b e d by the f o l l o w i n g f o r m u l a (for a s m a l l v a l u e of t): dtd~=c I A2 + A2+r A 2 c - 2 A c
(Ar +2nAIln
where AI
d•
exp (~ b I ) pt
274
0~)1
t
0.8
0.~
0.~
Q.~
i
0.0t
!
I
i
I
0,05
i
I
t
I
11
i
i
O. 0 t (GeV/c)
F i g . 1. T h e 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 b i t r a r y units at 58.1 GeV. b I = 11.07 • 0.18
I 2
in a r -
(GeV/c)-2
is the i m a g i n a r y p a r t of t h e e l a s t i c p - p s c a t t e r ing a m p l i t u d e ; b I t h e s l o p e p a r a m e t e r ; A r = ~ A I the r e a l p a r t of the e l a s t i c p - p s c a t t e r i n g a m p l i tude; A c = 2n F(O)/kO 2 the C o u l o m b a m p l i t u d e ; F(O) = exp (½bit) the n u c l e a r f o r m f a c t o r of the n u c l e o n ; n = 1 / 1 3 7 f i ; (p= 1 . 0 6 / k R ; R the n u c l e o n
V o l u m e 30B, n u m b e r 4
PHYSICS
LETTERS
13 O c t o b e r 1969
Table 1 T h e r e s u l t s of the m e a s u r e m e n t s of the e l a s t i c p - p s c a t t e r i n g s l o p e p a r a e e r b in the r e g i o n :
O.O08
£
I
g z 8
syst. error
2
~,
~ 8
, 0 . . . . . . . . ~'0
3'0
' ~b
'~'0
F i g . 2. T h e r e s u l t s of the m e a s u r e m e n t s of the s l o p e p a r a m e t e r . Q : t h i s e x p e r i m e n t ; O : r e f . 2; ~ : r e f . 4; A: r e f . 3. r a d i u s , t = - 2 p 2 ( 1 - c o s 0); 0, P , k t h e s c a t t e r i n g a n g l e , t h e m o m e n t u m a n d t h e w a v e n u m b e r in t h e c . m . s , a n d ~ t h e s p e e d of t h e i n c i d e n t p r o t o n i n t h e l a b s y s t e m . W e u s e d C = ~ = 1. F i g . 2 g i v e s 20 a v e r a g e d v a l u e s o f t h e s l o p e parameters as a function of the lab. energy of p r o t o n s ( s e e a l s o t a b l e 1). F i g . 2 a l s o s h o w s t h e results of other experiments [2-4]. As is seen, the slope parameter is monotonously increasing when the proton energy rises in the 12-70 GeV range. This means in the framework of t h e o p t i c a l model that the interaction radius R = 24-~ is growing from 1.23 to 1.34 fm. We obtained the slope of Pomeranchuk's pole from this data using the Ter-Martirosian's parametrisation f o r p o l e s a n d r e s i d u e s [5]. W e represented b I a s a f u n c t i o n of In
(S/So)
b I = b 0 + 2b I i n
(S/So)
(S o = 1 G e V 2) a n d f o u n d t h e p a r a m e t e r s from our experimental data: b I = 0.47 ± 0.09 X b 0 = 6.8
± 0.3
It f o l l o w s f r o m = 0.40 • 0.09.
2
b0 and b 1
= 2 4 . 8 (20 e x p e r i m e n t a l points). T
the value b I that ap =
E l a b kin
S
bI *
R
(GeV)
(GeV) 2
(GeV/c) -2
(fro)
12.1 14.8 17.9 20.9 23.8 26.7 29.7 32.6 35.5 38.6 40.7 44.2 48.0 51.2 53.4 56.1 59.3 62.6 65.2 69.0
26.2 31.3 37.1 42.7 48.2 53.6 59.3 64.7 70.1 75.9 79.9 86.5 93.6 99.6 103.7 108.8 114.8 121.0 125.9 133.0
9.81 9.98 10.46 10.58 10.59 10.77 10.68 10.66 10.77 10.89 10.87 10.95 11.19 11.31 11.24 11.16 11.40 11.76 11.52 11.38
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ~ ±
0.35 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.11 0.10 0.14 0.10 0.11 0.11 0.12 0.10 0.09 0.12 0.12 0.11
1.236 1.247 1.276 1.284 1.284 1.295 1.290 1.288 1.295 1.302 1.301 1.306 1.320 1.327 1.323 1.319 1.333 1.353 1.339 1.331
± 0.022 ± 0.008 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.007 ± 0.006 ± 0.008 ± 0.006 ± 0.006 ± 0.006 ± 0.007 =L 0.006 ± 0.005 ± 0.007 ± 0.007 ± 0.006
* Abi(syst ) = ±0.3
One can compare our results with the predict i o n s r e s u l t i n g f r o m t h e b a s i c p r i n c i p l e s of t h e m o d e r n t h e o r y . M a n y a u t h o r s , f o r e x a m p l e [6], h a v e f o u n d t h a t t h e i n c r e a s i n g of t h e d i f f e r e n t i a l cross section slope parameter should not exceed ln2S. The results of our experiment with prediction.
are
consistent
References 1. B e t h e , Ann. of P h y s . 3 (1958) 190. 2. L. F. K i r i l l o v a et al. Y a d e r n . F i z . (USSR) 1 (1965) 533. 3. K . J . F o l e y , S . J . L i n d e n b a u m , W . A . Love, S. O s a k i , J . J . R u s s e l l and L . C . L . Y u a n , P h y s . Rev. L e t t e r s 11 (1963) 425. 4. G. B e l l e t t i n i , G. C o c c o n i , A . N . D i d d e n s , E. L i l l e t h u n , J . P a h l , J . P . Scanlon, J. W a l t e r s , A . M . W e t h e r e l l and P. Z a n e l l a , P h y s . L e t t e r s 14 (1965) 164. 5. T e r - M a r t i r o s i a n , P r e p r i n t I T E R N (Moskow) N417 (1967). 6. J . D . B e s s i s , Nuovo C i m e n t o 4 5 (1966) 974.
275