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Polarization in p-p elastic scattering Keeler, Richard Kirk 1978

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POLARIZATION IN P-P ELASTIC SCATTERING by RICHARD KIRK KEELER B . S c , M c G i l l U n i v e r s i t y , 1976 THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (PHYSICS) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA MARCH 197 8 © R i c h a r d K i r k K e e l e r , 197 8 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f PHYSICS The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 Date A p r i l 24 , 1978 ABSTRACT The absolute n o r m a l i z a t i o n of the p o l a r i z a t i o n i n proton-proton e l a s t i c s c a t t e r i n g at 24° l a b has been determined by a double s c a t t e r i n g experiment to an accuracy of ±2% over the energy range 250-520 MeV. The f i r s t energy dependant double s c a t t e r i n g experiment has been performed a t the Triumf v a r i a b l e energy c y c l o t r o n . Data were taken at f i v e primary beam e n e r g i e s , 500, 467, 425, 367, and 307 MeV, and f o r the f i r s t time hydrogen was used both as p o l a r i z e r and a n a l y s e r . i i i CONTENTS I. Introduction and Formalism 1 II . Apparatus 12 I I I . Execution of Double Scattering Experiment 25 IV. Data Analysis 34 V. Conclusions • 49 VI. Bibliography 51 i v TABLES 1-1. Tensors Making Up the S c a t t e r i n g M a t r i x . .4 1-2. Behavior of Rotation I n v a r i a n t s under Space R e f l e c t i o n , Time R e v e r s a l , and The P a u l i E x c l u s i o n P r i n c i p l e 5 1- 3. Table of Previous Measurements 10 2- 1. P r o p e r t i e s of the Secondary Targets Used i n the Double S c a t t e r i n g Experiment .17 2-2. Energy l o s s i n Primary Beam, Energy l o s s i n Secondary Beam 21 2-3. The Factor X/LRAD i s Tabulated f o r each Element i n the Secondary Beamline; w i t h and without Helium Gas Bags 22 2- 4. Coulomb S c a t t e r i n g RMS Angular Divergence of Secondary Beam 24 3- 1. Solenoid Currents C a l c u l a t e d to Precess Protons to ±90° 28 4- 1. Table of Times of F l i g h t f o r E l a s t i c and I n e l a s t i c Protons, and f o r Pions 36 4-2. Asymmetries f o r CP^ Target, Carbon Target, and L i q u i d Hydrogen Target Empty, Averaged f o r each Energy 3 8 4-3. Rates f o r Carbon and L i q u i d Hydrogen Target Empty Data Normalized to Rates f o r CH2 Data 3 8 4-4. Generalized Carbon Background.. 41 4-5. F i n a l Asymmetries 41 4-6. Table of Background Asymmetries and Rates; Smoothed and Unsmoothed 44 4-7. F i n a l Asymmetries w i t h Smoothed Parameters 42 4-8. Ratios of P(24 0 )/P (24.79 0 ) 45 4-9. Added World Data 45 V 4- 10. Values of P(24°) Lab Between 200 and 500' MeV....47 5- 1. Comparison of Experimental R e s u l t s t o Previous Phase S h i f t P r e d i c t i o n 49 v i FIGURES 1-1. Kinematic Diagram f o r Proton-Proton S c a t t e r i n g . . . . 3 2-1. A Schematic Diagram of the Experimental C o n f i g u r a t i o n , . .13 2- 2. Four F o l d Coincidence P o l a r i m e t e r 19 3- 1. D i s t r i b u t i o n of Protons on the Second Target, C a l c u l a t e d by the Monte C a r l o Program REVMOC 27 3-2. Optimum quadrapole c u r r e n t ( a r b i t r a r y u n i t s ) versus momentum (MeV/c) 29 3-3. S e n s i t i v i t y of p o l a r i m e t e r t o beam s t e e r i n g 31 3- 4. E l e c t r o n i c L o g i c Diagram 32 4- 1. Times of F l i g h t (ns) 35 4-2. L i n e a r F i t s to Carbon and Empty Target Asymmetries and Rates Versus Beam Energy 43 4-3. P o l a r i z a t i o n at 24° Lab versus Energy 48 v i i ACKNOWLEDGEMENT I thank my c o l l e a g u e s f o r t h e i r h elp i n completing t h i s experiment - D. Axen, J . Beveridge, C. Amsler, A. Clough, C. Oram, G. Waters, D. S t r a t f o r d , D.V. Bugg, R. Dubois, J . Edgington, L. Felawka, D. Gibson, G. Ludgate, J.R. Richardson, L.P. Robertson, R. Gibson and N. Stewart. I would l i k e t o thank Jack Beveridge and Tony Clough f o r t h e i r long hours of help i n s e t t i n g up t h i s experiment, and Graham Waters f o r h i s e x c e l l e n t t e c h n i c a l a s s i s t a n c e . I would a l s o l i k e t o thank Claude Amsler f o r h i s a i d i n i n t e r p r e t i n g the r e s u l t s , and C h r i s Oram f o r h i s guidance i n completing t h i s t h e s i s . My s p e c i a l thanks to P r o f e s s o r Dave Axen, my s u p e r v i s o r , f o r h i s l e a d e r s h i p and encouragement throughout the experiment and the w r i t i n g of t h i s t h e s i s . 1 INTRODUCTION AND FORMALISM T h e e l a s t i c s c a t t e r i n g o f n u c l e o n s h a s b e e n t h e s u b j e c t o f n u m e r o u s p a p e r s a n d e x p e r i m e n t s . I n 1 9 5 4 W o l f e n s t e i n " ' " p r o p o s e d a s e r i e s o f m e a s u r e m e n t s o n t h e s p i n d e p e n d e n c e o f t h e n u c l e o n - n u c l e o n i n t e r a c t i o n . T h e s e e x p e r i m e n t s i n v o l v e d p r e p a r i n g b e a m s o f n u c l e o n s i n c e r t a i n s p i n s t a t e s a n d s c a t t e r i n g t h e m f r o m u n p o l a r i z e d t a r g e t s . T h i s t h e s i s i s c o n c e r n e d w i t h t h e p o l a r i z a t i o n p a r a m e t e r , d e n o t e d P ( E , 9 ) . E x c e l l e n t r e v i e w s o f t h e d e r i v a t i o n o f t h i s 2 3 p a r a m e t e r e x i s t . ' A s y n o p s i s o f W o l f e n s t e i n ' s o r i g i n a l c a l c u l a t i o n s i s g i v e n h e r e . F o r a d e s c r i p t i o n o f e l a s t i c p r o t o n - p r o t o n s c a t t e r i n g i n t h e c e n t r e o f m a s s f r a m e t h e i n c i d e n t p r o t o n ' s momentum i s l a b e l l e d k a n d t h e s c a t t e r e d p r o t o n ' s momentum .k'. The c o n s e r v a t i o n o f momentum may t h e n b e w r i t t e n a s |k| = | k " | = k . The s c a t t e r i n g i s k i n e m a t i c a l l y d e t e r m i n e d b y t w o p a r a m e t e r s , w h i c h may b e c h o s e n a s k a n d 6 t h e c e n t r e -1 c m . o f m a s s s c a t t e r i n g a n g l e . The w a v e f u n c t i o n o f t h e s c a t t e r e d p a r t i c l e i n t h e a s y m p t o t i c l i m i t , a s r b e c o m e s m u c h l a r g e r t h a n t h e r a n g e o f t h e i n t e r a c t i o n ( - 1 . 5 f m ) , i s g i v e n b y , < # \ ^ i k • r . i k r . . . i M r l X - j ^ e X i + e x f ( D r w h e r e x^ i s t n e i n i t i a l s t a t e s p i n o r a n d X f i s t n e f i n a l s t a t e s p i n o r . B v e x p r e s s i n g t h e a m p l i t u d e f ( k , 8 ) f o r e a c h cm p a r t i c l e s p i n s t a t e i n a c o n v e n i e n t m a t r i x n o t a t i o n M ( k , 8 ) , r r ' cm ' t h e r e l a t i o n s h i p b e t w e e n t h e i n c i d e n t a n d s c a t t e r e d s p i n f u n c t i o n c a n be w r i t t e n a s , X F = M X i (2) where x F i s the f i n a l s t a t e s p i n o r . Determining the s p i n dependence i s now mathematically equivalent to f i n d i n g the matrix of s c a t t e r i n g amplitudes M(k,0 ). The most convenient way to formulate t h i s problem i s to use the d e n s i t y matrix r e p r e s e n t a t i o n . In t h i s r e p r e s e n t a t i o n the beam of i n c i d e n t protons i s c h a r a c t e r i z e d i n s p i n space as. a weighted average of pure s t a t e d e n s i t y m a t r i c e s , i" p. = EOJ Y. Y . , Zbi (3) 1 a A i a A i a / a a a where co^  i s the p r o b a b i l i t y of the system being i n the pure s t a t e x • The s c a t t e r e d p a r t i c l e ensemble i s then described by the f i n a l s t a t e d e n s i t y matrix p f = Mp.M + (4) Three orthonormal b a s i s vectors may be constructed from the kinematic q u a n t i t i e s as:<P = (k + k^) / (|k +^k^|), £ = ~ }l) / ( l k / - - k | ) , and-N = (~k x-k") / ( | k x k / | ) , ( f i g u r e 1-1). The matrix of s c a t t e r i n g amplitudes depends on the spins and momenta of the i n c i d e n t and s c a t t e r e d protons. The most general s c a t t e r i n g amplitude i s a l i n e a r combination of a l l the p o s s i b l e products of the tensors formed from the s p i n vectors of each proton, o}^ and o}^ , and the tensors formed from the co-ordinate vectors<PyK, and N (Table 1-1). Since angular momentum i s conserved the system, and hence the s c a t t e r i n g amplitudes, must be r o t a t i o n a l l y i n v a r i a n t . Hence acceptable products of the s p i n and kinematic tensors are s c a l a r s or pseudoscalars. S i m i l i a r l y v a rious combinations are e l i m i n a t e d by the conservation of p a r i t y , time r e v e r s a l i n v a r i a n c e , and the P a u l i e x c l u s i o n p r i n c i p l e (Table 1-2). An F I G U R E 1-1 KINEMATIC DIAGRAM FOR PROTON PROTON SCATTERING. 4 TABLE 1-1 Tensors making up the S c a t t e r i n g Amplitude Rank Tensors of the Spin V e c t o r s 0 .a ( 1 > V 2 ) Kinematic Tensors 1 K«P N • K £ ( 2 ) • £ ( 1 ) - £ ( 2 ) a ( 1 ) x V 2 ) •K P a . ( 1 ) o f 2 ) + a a ) a . ( 2 ) i 3 3 1 K. K . i 3 P.P. i 3 N.N . K.P . + K.P. 1 3 3 i K.N. + K.N. 1 3 3 i P.N. + P.N. I D D 1 5 TABLE 1-2 Behavior of Rotation I n v a r i a n t s Under Space R e f l e c t i o n , Time Rev e r s a l , and The P a u l i E x c l u s i o n P r i n c i p l e Y i s Invariance N i s no Invariance Rotation Space Time E x c l u s i o n I n v a r i a n t R e f l e c t i o n Reversal P r i n c i p l e 1 y Y Y £ U ) - £ ( 2 ) Y y Y p_ U )+ a ( 2 ) ..K N N Y •N Y Y Y •P N Y Y £ ( 2 ) *K N N N •N Y Y N •P N Y N a ( 1 ) x a ( 2 ) - K N Y N *N Y N N •P N N N a . ( 1 ) a f 2 ) + olUo™ K i K j Y Y Y N±N=. Y Y Y P.P. Y Y Y I D K.P.+K.P. Y N Y i 3 J i K.N.+K.N. N N Y i 3 3 i P.N.+P.N. N Y Y l 3 3 l 4 e x p r e s s i o n f o r t h e m a t r i x o f s c a t t e r i n g a m p l i t u d e s i s , M = a (k , 9 ) + i c ( k , 6 ) (a ( 1 ) «N +- a ( 2 ) «N) ' cm ' cm — — — — + m ( k , 9 c m ) (a ( 1 ) - N a ( 2 )-N) + g ( k , 9 ) ( a ( 1 ) « P c ( 2 ) - P + a ( 1 ) « K a ( 2 ) - K ) cm — — — _ _ _ _ _ + h ( k , 9 ) - ( a ( 1 ) - P - a ( 2 ) - P - a ( 1 ) - K - a ( 2 ) v K ) (5) cm — — — — — — — — T h e t w o e x p e r i m e n t s o f c o n c e r n i n t h i s t h e s i s a r e : 1) The m e a s u r e m e n t 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 , - d a = 1(6 ,4)) = T r (Mp . M + ) / T r (p . ) (6) dH 1 1 f o r a p o l a r i z e d beam o n a n u n p o l a r i z e d t a r g e t . S i n c e t h e r e i s o n l y o n e r e l e v a n t s p i n v e c t o r , t h e d e n s i t y m a t r i x c a n b e e x p a n e d i n P a u l i m a t r i c e s g i v i n g p. = 1 ( 1 + < £ ( l ) > a ( l ) ) (7) 1 2 ( i ) F o r a n i n c i d e n t beam h a v i n g a p o l a r i z a t i o n <a > = P ^ u , t h e r e s u l t o f t h e m e a s u r e m e n t c a n b e e x p r e s s e d i n t h e f o r m , 1(0,<j)) = I (1 + P P ) (8) o l a w h e r e I i s 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 f o r a n u n p o l a r i z e d b e a m , a n d P t h e a n a l y z i n g p o w e r , a 2) The s e c o n d e x p e r i m e n t i s t o d e t e r m i n e t h e f i n a l s t a t e p o l a r i z a t i o n a f t e r a n u n p o l a r i z e d beam i s s c a t t e r e d f r o m a n u n p o l a r i z e d t a r g e t . The e x p e c t a t i o n v a l u e o f t h e f i n a l s p i n s t a t e i s g i v e n b y , IQ<o{f)> = T r (a ( F \MM1")_ ( 9 ) w h e r e < a ^ > i s k n o w n a s t h e p o l a r i z i n g p o w e r . F r o m t h e p r o p e r t i e s o f t h e M m a t r i x , W o l f e n s t e i n s h o w s t h e f o l l o w i n g t w o r e s u l t s . F i r s t , t h e p o l a r i z a t i o n i n d u c e d when a n u n p o l a r i z e d beam s c a t t e r s f r o m a n u n p o l a r i z e d t a r g e t i s 7 perpendicular to the s c a t t e r i n g plane. This i s a consequence of the conservation of p a r i t y . The second theorem s t a t e s t h a t the p o l a r i z i n g power i s equal to the an a l y z i n g power. This can be proved using time r e v e r s a l i n v a r i a n c e and i m p l i e s t h a t , P = < a ( f ) > = P(E,9) (10) cl where P(E,0 ) i s defined as the p o l a r i z a t i o n parameter, cm ^ e This r e l a t i o n i s the fundamental p r i n c i p l e upon which double s c a t t e r i n g experiments are based. In a double s c a t t e r i n g experiment an unp o l a r i z e d beam i s d i r e c t e d a t an u n p o l a r i z e d t a r g e t . The r e s u l t i n g , p o l a r i z e d , s c a t t e r e d beam i s then s c a t t e r e d from a second t a r g e t . The d i f f e r e n t i a l cross s e c t i o n f o r the second s c a t t e r i s given by, I 2 = I 0 2 ( 1 + PfE-^O )P(E_,e2)cos<|>2) (11) where the s u b s c r i p t s are included to note the d i f f e r e n c e i n energy and s c a t t e r i n g angle f o r the two s c a t t e r s , and <f> i s measured from the K a x i s . The l e f t - r i g h t asymmetry i n the number of p a r t i c l e s s c a t t e r e d from the second t a r g e t i s I 2 ( 6 , ( j ) = 0) - I2(e,<f> = TT) e =' • (12) i 2 (er<p = o) + i2(e,<j> = TT) This asymmetry i s a l s o given by e = P ( E 1 , 9 1 ) P ( E 2 , 9 2 ) (13) T y p i c a l l y the s c a t t e r i n g angles 0^, 0 2 are chosen to be equal and i d e a l l y i f the energies E^ and E 2 are equal then equation (12) reduces to the p a r t i c u l a r l y simple 8 e x p r e s s i o n e = P 2 (14) Previous measurements of P have i n v o l v e d two d i f f e r e n t techniques; double s c a t t e r i n g and p o l a r i z e d t a r g e t s . Double s c a t t e r i n g measurements have p r e v i o u s l y been used t o normalize the p o l a r i z a t i o n parameter f o r experiments where p o l a r i z e d beams were produced by s c a t t e r i n g a t smal l angles from carbon and b e r y l l i u m . 5 ' 6 ' 7 ' 8 ' 9 ' 1 0 Protons s c a t t e r e d e l a s t i c a l l y at sma l l angles have onl y s m a l l energy l o s s e s , and reasonable p o l a r -i z a t i o n s (-30% f o r carbon-proton s c a t t e r i n g a t 6° and 400 MeV i n c i d e n t k i n e t i c energy). In t h i s angular range both 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 and the p o l a r i z a t i o n vary r a p i d l y as a f u n c t i o n of angle and as a r e s u l t the measurements are extremely s e n s i t i v e t o i n a c c u r a c i e s i n the measurement of the s c a t t e r i n g angle. A l l of the p o l a r i z a t i o n measurements have used some technique to e l i m i n a t e i n s t r u m e n t a l asymmetries. One method has been to f l i p the s p i n of the proton a f t e r i t s i n i t i a l s c a t t e r . T h i s e l i m i n a t e s f a l s e asymmetries t o f i r s t o r d e r . Spin f l i p p i n g was accomplished by p r e c e s s i o n of the s p i n i n 5 6 7 a s o l e n o i d , ' or by changing the d i r e c t i o n of the f i r s t s c a t t e r ( i e , changing from l e f t t o r i g h t s c a t t e r i n g at the same a n g l e ) . Other groups decided not to r i s k a l t e r i n g the beam d i r e c t i o n 9 11 and i n s t e a d e l e c t e d t o f l i p the p o l a r i m e t e r ' used t o measure the f i n a l asymmetry, thus r e v e r s i n g l e f t and r i g h t d e t e c t o r s . However i t i s d i f f i c u l t t o b u i l d and a l i g n a de v i c e t h a t r o t a t e s p r e c i s e l y about the a x i s of the s c a t t e r e d beam. 9 P o l a r i z e d t a r g e t s are f r e e of these 12 13 14 d i f f i c u l t i e s . ' ' S c a t t e r i n g an u n p o l a r i z e d beam from a p o l a r i z e d t a r g e t and measuring the r e s u l t i n g asymmetry, gi v e n by e = P(E,9)P(Target) (15) i s the same as performing the second s c a t t e r i n double s c a t t e r i n g . The p o l a r i z a t i o n of the t a r g e t i s measured independently by n u c l e a r magnetic resonance (N.M.R.) techniques and s p i n f l i p p i n g can be accomplished by a s l i g h t s h i f t i n the frequency of the R.F. f i e l d a p p l i e d t o the t a r g e t . The N.M.R. technique f o r measuring the p o l a r i z a t i o n i s accurate t o ±4%. Due to nonuniformity of the p o l a r i z a t i o n over the volume of the t a r g e t and the v a r i a t i o n w i t h time of the p o l a r i z a t i o n , the o v e r a l l accuracy i s reduced t o 6%. T y p i c a l l y the e r r o r s on pr e v i o u s double s c a t t e r i n g experiments have a l s o been 6% (see Table 1-3 f o r a l i s t of p r e v i o u s p o l a r i z a t i o n measurements ). The measurement d e s c r i b e d i n t h i s t h e s i s was designed t o e v a l u a t e P a t 24° t o b e t t e r than 2%, The double s c a t t e r i n g technique u s i n g f r e e proton-proton e l a s t i c s c a t t e r i n g was chosen. F i v e measurements were made between 200 and 500 MeV. A superconducting s o l e n o i d was used f o r s p i n f l i p p i n g . . In pp e l a s t i c s c a t t e r i n g at 24° there i s a l a r g e energy change a f t e r the f i r s t s c a t t e r (eg. 100 MeV i s l o s t i n the case of a primary beam energy of 500 MeV). Thus the simple formula^ , e - P 2, i s no longer v a l i d . The complete formula , e = P (E)P (f (E)) i s necessary. I f n measurements 10 TABLE 1-3 TABLE OF PREVIOUS MEASUREMENTS Energy Angle C M . Experimental T o t a l Ref MeV deg Value of Ppp E r r o r + 276 49.9 0.295 0.027 15 307 + 11 50.1 ± 2.7 0.362 0.016 7 328 ± 6 52.2 ± 1 0.349 0.038 14 334 . 5 ± 5.8 51.68 ± 1.83 0.27 0.05 13 415 ± 7.8 51.5 ± 1. 0.382 0.037 5 418 ± 6.6 52.41 ± 1.81 0.34 0.03 13 312 ± 11 56 ± 6 0.26 0 .05 11 315 ± 6.4 53.4 ± 2.95 0.303 0.025 15 394 ± 12 48.0 ± 3.6 0.419 0 . 017 7 429 ± 7 45 ± 1.7 0.40 0.06 16 439 ± 6 44.8 ± 11.5 0 ,335 0.030 8 498 ± 11 48.7 ± 3.1 0.452 0.020 7 500 ± 8 . 3 53.13 ± 1.79 0.46 0.03 13 500 ± 4.2 52.4 ± 2.6 0.435 0.04 12 520 ± 20 58 ± 10 0.403 0.038 17 are made, there are 2n unknown p o l a r i z a t i o n s . Using the Triumf v a r i a b l e energy c y c l o t r o n i t i s p o s s i b l e t o measure the p o l a r i z a t i o n a t a s e r i e s of d i f f e r e n t e n e r g i e s , each primary energy s e t equal to the secondary beam energy, f ( E ) , from the pr e v i o u s measurement. T h i s reduces the number of unknowns to n + 1 f o r n_ measurements. Now the unknown p o l a r i z a t i o n s can be i n t e r p o l a t e d t o w i t h i n the accuracy of the measured e ( i e . /2 POp-a^). As a g e n e r a l i z a t i o n of t h i s procedure a n o n ^ l i n e a r f i t was used t o f i t the p o l a r i z a t i o n . The r e s u l t i n g e r r o r on the measurement depends on the s t a t i s t i c a l e r r o r i n the s e t of e's, the number of p o i n t s , and the smoothness of the a c t u a l p h y s i c a l v a r i a t i o n P (E). T h i s method proved h i g h l y 2 h s u c c e s s f u l . The d e t a i l s of the measurement of P (E) are g i v e n 2 k i n the next c h a p t e r s . The apparatus i s o u t l i n e d and i t s arrangement and use i s d i s c u s s e d . The data c o l l e c t i o n procedure i s d e s c r i b e d and the a n a l y s i s of the data i s c a r r i e d out. The measured val u e s of P (E) are t a b u l a t e d and compared wi t h a 2 h p r e v i o u s phase s h i f t p r e d i c t i o n . CHAPTER II  Apparatus The important f e a t u r e s of the experimental apparatus are reviewed i n t h i s chapter. They are g i v e n i n an upstream to downstream or d e r . A schematic view of the experiment i s gi v e n i n f i g u r e 2-1. Primary Beam Monitor In the primary beamline there was a p o l a r i m e t e r o r i g i n a l l y designed f o r use i n the Basque p o l a r i z e d beam experiments. I t has a l r e a d y been d e s c r i b e d e x c e l l e n t l y i n 19 2 0 p r e v i o u s theses. ' For t h i s measurement i t was used as a monitor of primary beam i n t e n s i t y . The d e v i c e c o n s i s t e d of a CE'2 t a r g e t 5 0 ym t h i c k suspended i n the beam p i p e . S c a t t e r e d protons were observed i n four t e l e s c o p e s composed of two s c i n t i l l a t o r s each. The two "forward" t e l e s c o p e s were mounted a t ±26 degrees t o the beam a x i s and the two r e c o i l arms were at the conjugate angle of 60 degrees. Coincidences between the forward arms and the complementary r e c o i l arms were s c a l e d . L i q u i d Hydrogen Target The l i q u i d hydrogen t a r g e t c o n s i s t e d of a 20 cm long by 5 cm diameter f l a s k . The t a r g e t w a l l s are 250 ym and the end windows are 50 ym of s t a i n l e s s s t e e l . The assembly was separated from the beamline vacuum by 120 ym s t a i n l e s s s t e e l windows. The hydrogen t a r g e t was l i q u i f i e d and r e f r i g e r a t e d by a P h i l l i p s A-20 cr y o g e n e r a t o r . The maximum power of the FIGURE 2-1 A SCHEMATIC DIAGRAM O F THE EXPERIMENTAL CONFIGURATION SCINTILLATORS B 1 B V « ^ V E R T I C A L POLARIMETER COLLIMATOR LIQUID H Y D R O G E T A R G E T PRIMARY B E A M MONITOR BENDING MAGNET STEERING M AGNET QUADRAPOLE D O U B L E T AND CH2 / C T A R G E T S t i r l i n g engine l i m i t e d the primary beam r a t e to between 250-300 nA, because at higher c u r r e n t s the energy l o s t by protons t r a v e r s i n g the t a r g e t was s u f f i c i e n t t o b o i l the hydrogen. T h i s was c o n t i n u a l l y monitored d u r i n g the experiment by o b s e r v i n g the temperature and p r e s s u r e of the f l a s k , r e s e v o i r , and other r e l e v a n t components. The t a r g e t can be emptied i n one hour and f i l l e d i n roughly twelve. Design d e t a i l s and o p e r a t i n g c h a r a c t e r i s t i c s of t h i s t a r g e t are d e s c r i b e d i n r e f e r e n c e (21). Bending Magnet (4AB2) T h i s d i p o l e magnet, p o s i t i o n e d d i r e c t l y a f t e r the l i q u i d hydrogen t a r g e t , was used to sweep u n s c a t t e r e d protons through 35°. The d e f l e c t i o n angle f o r charged p a r t i c l e s i n a d i p o l e magnet can be c a l c u l a t e d u s i n g the e x p r e s s i o n , 9 = e J B«dl (.1) where e i s the charge, and p i s the momentum of the i n c i d e n t p a r t i c l e . I t has been c a l c u l a t e d from a magnetic f i e l d survey t h a t protons s c a t t e r e d by 2 4 degrees from the hydrogen t a r g e t were d e f l e c t e d by the f r i n g e f i e l d of t h i s m a g n e t 0.82 ± 0.16 degrees to the r i g h t . C o l l i m a t o r F o l l o w i n g the l i q u i d hydrogen t a r g e t was a l a r g e c o l l i m a t o r , 3 0 cm t h i c k and roughly 3.5 m lo n g , designed f o r use i n neutron experiments. I t was c o n s t r u c t e d from two load b e a r i n g s t e e l p l a t e s , 50 mm t h i c k , f i l l e d w i t h l e a d . The t o t a l weight i s 25 tons. There are 11 e q u a l l y spaced p o r t s 15 from -3° to 27°. Each p o r t i s d i v i d e d i n t o two equal s e c t i o n s . The upstream end i s 10 cm i n diameter and the downstream end i s 12.5 cm i n diameter. The nominally 24° p o r t , a c t u a l l y 23.97°, was used i n t h i s experiment t o d e f i n e the d i r e c t i o n of the secondary beam. T h i s p o r t was 3.54 m long and was l i n e d with a 130 ym p l a s t i c i n s e r t i n f l a t e d with helium gas to reduce m u l t i p l e s c a t t e r i n g . Unused p o r t s were f i l l e d w ith s t e e l p l u g s . Superconducting S o l e n o i d The s o l e n o i d was designed at the Rutherford High Energy lab. and i s 1 m long with a 14 cm warm bore. I t i s capable of producing a uniform 6 t e s l a magnetic f i e l d over the e n t i r e bore when operated with the maximum r a t e d c u r r e n t , 212A. The angle of p r e c e s s i o n of the proton s p i n i n a magnetic f i e l d can be c a l c u l a t e d u s i n g the e x p r e s s i o n , a = ey_ \ B'dl (2) P J where e i s the proton charge, y i s the magnetic moment of the pr o t o n , and p i s i t s momentum. The l i n e i n t e g r a l of the magnetic f i e l d through the s o l e n o i d was c a l c u l a t e d t o be 0.028187 T-m-A , where the l i m i t s of i n t e g r a t i o n were from -294 cm t o +294 cm along the beam a x i s . T h i s was e x p e r i m e n t a l l y confirmed t o 0.7% by a magnetic survey. Quadrupole Magnets A quadrupole doublet was borrowed from the U n i v e r s i t y 22 of A l b e r t a . T h i s r i s of standard d e s i g n , having 10 cm ap e r t u r e s , and 0.5T maximum magnetic f i e l d a t the pole t i p s . 16 S t e e r i n g Magnets This i s a standard Triumf beamline element. I t has a 100 mm pole gap and can be run at a maximum current of ±7A. The l i n e i n t e g r a l of the magnetic f i e l d was measured as 0.0272 T-m at 5A. S c i n t i l l a t o r s and Second Target Two s c i n t i l l a t o r s were used to def i n e the secondary beam and to make time of f l i g h t determinations. The f i r s t s c i n t i l l a t o r , l a b e l l e d B l , was 10 cm diameter by 0.3 cm, and was mounted on a perspex l i g h t guide. The second s c i n t i l l a t o r , B2, measured 2 cm ( h o r i z o n t a l l y ) by 1 cm ( v e r t i c a l l y ) and was 1.5 mm t h i c k . I t was glued t o the i n s i d e of an aluminum f o i l cone or " a i r l i g h t guide." This e l i m i n a t e d the d i f f i c u l t y of having a lar g e mass of perspex (containing hydrogen) adjacent to the second t a r g e t . The s c i n t i l l a t o r , B2, and a block of CE^ or carbon juxtaposed, formed a u n i t t h a t was the second t a r g e t . The l a r g e s t C I ^ t a r g e t measured 2 cm ( h o r i z o n t a l l y ) by 1 cm ( v e r t i c a l l y ) and was 2.5 cm t h i c k . A s i m i l i a r piece of C H ^ was made w i t h 0.5 cm height f o r use at secondary beam energies between 200 and 3 00 MeV. This allowed the r e c o i l protons to escape from the t a r g e t w i t h s u f f i c i e n t energy to be detected. Two carbon t a r g e t s were a l s o constructed. They were designed to have roughly the equi v a l e n t amount of carbon as the corresponding CE^ t a r g e t s and have roughly the same s i z e . This was accomplished by using 2.5 cm by 2 cm carbon sheets 25 ym t h i c k ; and gl u e i n g t h e i r edges to four small carbon s l a t s which held them, e q u a l l y spaced, i n a stack. Table 2-1 gives the s i z e s , 17 TABLE 2-1 PROPERTIES OF THE SECONDARY  TARGETS USED IN THE DOUBLE SCATTERING EXPERIMENT M a t e r i a l Type CH2 Dimensions LxWxD CM 2.5 x 2.0 x 1.0 Mass grams 4 . 825 CH2 CARBON CARBON 2.5 x 2.0 x 0.5 2.5 x 2.0 x 1.0 2.5 x 2.0 x 0.4 2.4125 4.2672 2.0648 m a t e r i a l s and masses of each t a r g e t . A l l of the t a r g e t s were supported by r e s t i n g them on a 2 cm by 2.5 cm by 25 ym sheet of carbon attached t o the end of a l e n g t h of t h i n w a l l s t a i n l e s s s t e e l t u b i n g . P o l a r i m e t e r A p o l a r i m e t e r was designed to measure l e f t - r i g h t asymmetry of e l a s t i c proton s c a t t e r i n g i n a plane p e r p e n d i c u l a r to the i n c i d e n t p o l a r i z a t i o n . Because the f i r s t s c a t t e r i n g plane i s h o r i z o n t a l , the p o l a r i z a t i o n i s i n the v e r t i c a l p l ane. However the s o l e n o i d precesses the proton s p i n s ±90° i n t o the h o r i z o n t a l . Thus the polarimeter was mounted i n the v e r t i c a l p l a n e . The p o l a r i m e t e r was b a s i c a l l y f o u r s c i n t i l l a t o r t e l e s c o p e s . See f i g u r e 2-2. There were two "forward" t e l e s c o p e s of two s c i n t i l l a t o r s each, a l i g n e d a t ±24°. Complementary to the forward arms were two r e c o i l t e l e s c o p e s a t ±62°. The nomenclature f o r the s c i n t i l l a t o r s i s shown i n f i g u r e 2-3 a l s o . T h i s arrangement de t e c t e d only e l a s t i c proton-proton events with a s c a t t e r i n g angle i n the l a b of approximately 24°. Any e l a s t i c event i n the forward arms, UF(DF), must be accompanied by an o b s e r v a t i o n of an event i n the r e s p e c t i v e r e c o i l arm UR(DR). The angle between the r e c o i l and forward arms was chosen as the e l a s t i c s c a t t e r i n g opening angle f o r protons between 200 and 400 MeV (84'5° ^ 89°) . The p o l a r i m e t e r was designed so t h a t the s o l i d angle acceptance was determined wholly by the forward arms, and was about 16 msr. F I G U R E 2 - 2 F O U R F O L D C O I N C I D E N C E P O L A R I M E T E R 1 s t L E T T E R 2 n d LETTER N U M B E R U U P D DOWN F FORWARD R R E C O I L 1 FRONT 2 R E A R 20 The s c i n t i l l a t o r s i n the forward arms were each 4 cm by 8 cm and 0.3 cm t h i c k . They were lo c a t e d at r a d i a l distances of 25 cm and 45 cm from the t a r g e t centre. Thus the angles of acceptance were ±2.58° about 24° and ±5.08° i n the h o r i z o n t a l plane. The r e c o i l s c i n t i l l a t o r s had the f o l l o w i n g dimensions. R l was 8 cm by 10 cm and 1.5 mm t h i c k , while R2 was 14 cm by 16 cm and 1.5 mm t h i c k . They were lo c a t e d at r a d i a l d istances of 15 cm and 35 cm r e s p e c t i v e l y . Helium Bags The divergence of proton beams i s increased by coulomb s c a t t e r i n g . The mean square s c a t t e r i n g angle was 23 estimated using the expression, < 6 2 > = Z 2 (21.2 MevV -X (3) ^ pv } LRAD Where; Z i s the charge of the i n c i d e n t p a r t i c l e , p i s i t s momentum, v i s i t s v e l o c i t y , and LRAD i s the r a d i a t i o n length of the m a t e r i a l i n the beam. Therefore the s u b s t i t u t i o n of helium gas f o r a i r t h e o r e t i c a l l y r e s u l t s i n a re d u c t i o n of O-.-r, by a f a c t o r of/L~ = 1.53. Helim nags were used from RMS 1 J He ^ V L A i r the upstream end of the c o l l i m a t o r to the second t a r g e t . They were i n two s e c t i o n s , the downstream end having a l a r g e r r a d i u s . The upstream s e c t i o n had 125 ym CH_ end windows and the downstream s e c t i o n had 100 ym mylar end windows. In t a b l e 2-2 the various beam elements are l i s t e d 24 and the energy l o s s by the beam i s given f o r each element 25 and each primary beam energy. In t a b l e 2-3 the f a c t o r X/LRAD i s l i s t e d f o r each element of the secondary beam wit h and 2 1 T A B L E 2 - 2 E n e r g y l o s s i n p r i m a r y beam E n e r g y o f M a c h i n e MeV 500 467 4 2 5 367 3 07 E n e r g y a t C e n t r e o f L H „ T a r g e t » * _ T T *^ MeV 496 463 422 362 302 E n e r g y a f t e r 2 4 . 7 9 ° S c a t t e r MeV 3 9 1 366 334 288 242 E n e r g y l o s s i n s e c o n d a r y beam I n i t i a l A m o u n t o f E n e r g y L o s t i n E n e r g y L H „ A i r He M y l a r CH C H 2 Mev E n e r g y a t MeV T a r g e t MeV MeV MeV MeV Mev C e n t r e o f T a r g e t MeV 3 9 1 2 . 7 0 . 4 9 9 . 6 1 7 . 0 4 3 3 1 . 3 5 3 . 6 2 382 366 2 . 7 7 . 5 1 8 . 6 3 8 . 0 4 8 1 1 . 4 0 3 . 7 5 357 334 2 . 8 3 . 5 3 9 . 6 7 0 . 0 5 0 3 1 . 5 7 4 . 2 1 324 288 2 . 9 9 . 590 . 7 2 7 . 0 5 1 4 1 . 6 1 4 . 3 0 278 242 3 . 5 8 . 6 5 2 . 805 . 0 5 7 6 1 . 8 0 4 . 8 2 230 22 TABLE 2-3 The f a c t o r \ X i s tabulated f o r each ERAD element i n the secondary beamline; w i t h and without Helium Gas Bags. A i r Case Helium Gas Bags included Case M a t e r i a l X LRAD M a t e r i a l X LRAD L i q u i d Hydrogen 7.02 x 10 L i q u i d Hydrogen 7.02 x 10 -3 S t a i n l e s s s t e e l 3.49 x 10 -4 S t a i n l e s s s t e e l 3.49 x 10 -4 A i r Mylar 4.22 x 10 -2 3.54 x 10 A i r Helium 9.95 x 10 -3 1.17 x 10 CH ( s c i n t i l l a t o r ) 1.11 x 10 -2 Mylar CH, 3.54 x 10 5.29 x 10 -4 CH ( s c i n t i l l a t o r ) 1.11 x 10 -2 without helium bags. Taking Q^jyjq - {£<©?>} 2, then one sees i t h a t the use of helium bags decreases the coulomb m u l t i p l e s c a t t e r i n g by 1.44. The v a l u e s of 6_„_ c a l c u l a t e d w i t h the RMS helium bags i n c l u d e d are t a b u l a t e d f o r each primary beam energy i n t a b l e 2-4. The gas f o r the helium bags was s u p p l i e d by the exhaust from the superconducting s o l e n o i d . T h i s amounted to roughly 30,000 1 per day. Since the volume of the gas bags was roughly 610 1, the gas was changed every 3 0 minutes. 24 TABLE 2-4 Coulomb s c a t t e r i n g RMS angular divergence of secondary beam Energy of 8RMS t o t a l Primary Beam f o r Secondary beam MeV m i l l i - r a d i a n s 500 5.5 467 5.9 425 6.4 367 7.4 307 8 . 8 25 CHAPTER I I I Exec u t i o n of Double S c a t t e r i n g Experiment The d i s c u s s i o n of t h i s experiment i s d i v i d e d i n t o two s u b t o p i c s ; the beam dynamics and the procedure f o r t a k i n g data. The f i n a l beamline c o n f i g u r a t i o n maximized the i n c i d e n t proton f l u x onto the second t a r g e t w h ile m i n i m i z i n g the e f f e c t s of f l i p p i n g the p o l a r i z a t i o n of the secondary beam. The i n c i d e n t primary beam had a cr o s s s e c t i o n of l e s s than 1 sq. cm at the l i q u i d hydrogen target? thus the i l l u m i n a t e d t a r g e t , viewed a t a 24° angle, appeared t o be 1 cm ( v e r t i c a l ) by 8.2 cm ( h o r i z o n t a l ) . T h i s shape i s pres e r v e d by c o n v e n t i o n a l beamline f o c u s s i n g systems. P l a c i n g the p o l a r i m e t e r i n the h o r i z o n t a l plane, where the beam i s widest, would cause a high random rate? moreover to f l i p the s p i n the s o l e n o i d would have to be used w i t h no c u r r e n t , or wit h enough c u r r e n t t o precess the s p i n 180°. L o c a t i n g the p o l a r i m e t e r i n the v e r t i c a l plane removes the s c i n t i l l a t o r s from the h o r i z o n t a l l y spread beam, and the s o l e n o i d i s used i n the symmetric mode of p r e c e s s i n g the s p i n ±90°. Two computer codes were used t o analyze v a r i o u s beamline c o n f i g u r a t i o n s b e f o r e the apparatus was i n s t a l l e d . ,It was l e a r n t t h a t to g a i n maximum acceptance and r a t e the quadrupole d o u b l e t should be p l a c e d as near t o the c o l l i m a t o r as p o s s i b l e . To minimize beam image r o t a t i o n the s o l e n o i d should be upstream from the q u a d r i p o l e s . A sample d i s t r i b u t i o n 2 6 generated by the Monte C a r l o program REVMOC i s gi v e n i n f i g u r e 3-1. T h i s output shows the c a l c u l a t e d d i s t r i b u t i o n of protons over the secondary t a r g e t . The f i n a l beamline c o n f i g u r a t i o n was used as in p u t t o REVMOC and 2 5,0 00 i n i t i a l protons were s t a r t e d from the p o s i t i o n of the l i q u i d hydrogen t a r g e t with'a" uniform h o r i z o n t a l d i s t r i b u t i o n of ±5 cm and ±15 mr and a uniform v e r t i c a l d i s t r i b u t i o n of ±0.5 cm and ±7.5 mr. The output shows t h a t the proton d i s t r i b u t i o n i s peaked a t the t a r g e t c e n t r e . The beamline was i n s t a l l e d and c a r e f u l l y a l i g n e d . The p o l a r i m e t e r and beam s c i n t i l l a t o r s were plateaued at 42 5 MeV primary beam energy. For each of the f i v e primary beam en e r g i e s (500,467,425,367,307 MeV) the s o l e n o i d c u r r e n t was c a l c u l a t e d to correspond t o the energy of the beam at the c e n t r e of the magnet. The c u r r e n t s are t a b u l a t e d i n t a b l e 3-1. The quadrupoles were optimized by maximizing the r a t i o of the r a t e s , Bl«B2/Bl (where B1,B2 are the counts i n the beam d e f i n i n g s c i n t i l l a t o r s ) f o r both p o l a r i t i e s of the s o l e n o i d . As expected the quadrupole f i e l d s s c a l e d l i n e a r l y w i t h momentum. T h i s i s i l l u s t r a t e d i n f i g u r e 3-2. At 500 MeV primary beam energy the beam p r o f i l e a t the second t a r g e t was determined t o be 3 cm ( h o r i z o n t a l ) by 2.4 cm ( v e r t i c a l ) FWHM when the upstream quadrupole was h o r i z o n t a l l y d e f o c u s s i n g . The r e v e r s e c o n f i g u r a t i o n gave a beam spot 6 cm ( h o r i z o n t a l ) by 1.6 cm ( v e r t i c a l ) FWHM and was r e j e c t e d . The s e n s i t i v i t y of the p o l a r i m e t e r to v e r t i c a l S ! S T " ! B U T I O N DF P A R T I C L E S F I N A L L Y A C C E P T E D sSPACE » o : D I S T R I B U T I O N OF P A R T I C L E S AS A F U N C T I O N OF Y AT 06 ( E L F M F N T » 11J I X AT 0 6 (ELEMENT « I I ) (ALONG H O R I Z O N T A L A X I S ) (ALONG V E R T I C A L A X I S ) - -0,9000 •0,7000 -0,5000 •0,3000 •0,1000 0,1000 0,3000 0,5000' 0,7000 0,9000 SUM OF ROWS -1,30 0.0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 - 1 , '1 0 O'.O 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 »1,U0 0,0 0,0 <l,000 11,000 11,000 17,000 17,000 9,000 0,0 0,0 75,000 -0,oO 0.0 0,0 15,000 23,000 33,000 27,000 30,000 lb,000 0,0 0,0 113,000 -0,20 0.0 0,0 11,000 30,000 31,000 31,000 27,000 15,000 0,0 0,0 1S1,000 0,20 O'.O • 0,0 12,000 33,000 21,000 31.000' 23,000 12,000 0,0 0,0 113,000 0,o0 0.0 0,0 13,000 26,000 29,000 37,000 17,000 12,000 0,0 0,0 131,000 1,00 0.0 0,0 11,000 13,000 17,000 13,000 10,000 6,000 0,0 0,0 70,000 1,10 0.0 • 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 I,SO O'.O 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,0 SUMS OF COLUMNS! 121,000 69,000 0,0 0,0 06,000 139,000 151,000 162,000 0,0 0,0 FIGURE 3-1 D i s t r i b u t i o n o f p r o t o n s on the second t a r g e t , c a 1 c u l a t e d by the Monte C a r l o p rogram REVMOC. 28 TABLE 3-1 S o l e n o i d c u r r e n t s c a l c u l a t e d t o precess protons ±90° i Primary Beam S o l e n o i d Current Energy MeV Amps 500 62.0 467 59.9 425 57.2 367 52.3 307 47.1 29 FIGURE 3 - 2 Optimum quadrapole current (arbitrary units) versus momentum ( MeV / c ) 9501 9004 8501 % 800 7504 7004 6504 upstream quad i downstream quad f i i ' I f—i r — i 1 1 1 1 1 j 1 1 1 1 1 1 1 1 1 1 r-50 100 150 200 250 Arbitrary Units (Current) 30 s t e e r i n g of the beam was checked at 425 MeV. Figure 3-3 i s a graph showing the r e l a t i o n s h i p between the current i n the s t e e r i n g magnet and the asymmetry e measured i n the pol a r i m e t e r . The r e s u l t i s t h a t e changes by only 0.27% ± 0.8% per mm. V e r t i c a l s t e e r i n g by the s o l e n o i d was measured by a d j u s t i n g the current i n the s t e e r i n g magnet to maximize the i n c i d e n t f l u x on the second t a r g e t . The d i f f e r e n c e between the optimum currents f o r opposite s o l e n o i d p o l a r i t i e s gave a d i r e c t measure of the beam s t e e r i n g . I t was l e s s than 0.33 m i l l i r a d or 1.1 mm at the second t a r g e t . 27 Image r o t a t i o n by the so l e n o i d was c a l c u l a t e d to be ±17° depending on the so l e n o i d p o l a r i t y . The percentage change i n f l u x on the second t a r g e t was measured f o r d i f f e r e n t s o l e n o i d p o l a r i t i e s and was found to be approximately 8%. An event t r i g g e r , produced using standard Nim l o g i c u n i t s , was defined by (U + D)»B1«B2 = (U + D)«B. A diagram of the l o g i c i s given i n f i g u r e 3-4. The event t r i g g e r was sca l e d along w i t h the s i n g l e s r a t e s f o r U,D, and B the coincidences i n the arms of the primary beam monitor (denoted L and R). Beam bursts of 5 ns d u r a t i o n a r r i v e d every 4 4 ns, the p e r i o d of the r a d i o frequency, RF, of the Triumf c y c l o t r o n . This feature was e x p l o i t e d by d e l a y i n g one input of each coincidence by 44 ns and then s c a l i n g them (see f i g u r e 3-4). The r a t e of "delayed" coincidences d i r e c t l y measured the 31 FIGURE 3 - 3 Sensitivity of polarimeter to beam steeri ng -3.0 -2.0 - 1 . 0 0. 1 .0 2.0 Current in Steering Magnet ( Amps) UF 1 UF 2 E UR1 |UR2 [DFjJ DF 2 DR1 DR2 SCALER UR L D = ? S C A L E R B F A N O U T F P -o S C A L E R DR D SCALER a 2 ^B1B2y D E L A Y — O S C A L E R 26 ns U D S C A L E R U-B S C A L E R -{54 n; S T O P T D C L A T C H S C A L E R T R I G G E R !1>D. S C A L E R B RF' S T A R T T D C O S C A L E R 55 ns S T O P T D C D-B 2 7 n s I f 1 L A T C H ) • S C A L E R D S C A L E R JO—" T O F A N O U T S VjO ho FIGURE 3 - 4 ELECTRONIC LOGIC DIAGRAM random r a t e i n the undelayed c o i n c i d e n c e s . Timesof f l i g h t i n the secondary beamline were measured w i t h an L.R.S. (2228) time to d i g i t a l c o n v e r t e r ; s t a r t e d by RF«(U + D)«B and three channels stopped by U,D, and B. These three timesof f l i g h t - were histogrammed and w r i t t e n on computer tape, along w i t h the s c a l e r s , a t the end of every run. The data were recorded at a r a t e of about 3 3 events per second w i t h the CH 2 t a r g e t , 6 events per second w i t h the carbon t a r g e t , and- 1 an event per second w i t h the l i q u i d 2 hydrogen t a r g e t empty. Runs were roughly t h i r t y to s i x t y minutes long and the s o l e n o i d c u r r e n t was r e v e r s e d f o r a l t e r n a t e runs. At each energy approximately 400,000 events were taken with a CH 2 t a r g e t , 70,000 events with a carbon t a r g e t and 2000 events w i t h the LH 2 t a r g e t empty and CH 2 i n the second t a r g e t . CHAPTER IV Data A n a l y s i s The data a n a l y s i s was performed o f f l i n e . An IBM 370/16 8 was used to read the data tapes and p r i n t the s c a l e r i n f o r m a t i o n and time of f l i g h t (T.O.F.) histograms f o r each •run. The RF to Up and RF to Down time of f l i g h t spectra were searched f o r t h e i r peak channels. A cut was made ±24 channels from the maximum and then the peak was i n t e g r a t e d to y i e l d the t o t a l counts. The asymmetry and i t s u n c e r t a i n t y was then c a l c u l a t e d as e = B*U-- B'D B»U + • B«D (1) A £ R =(B-U + B-D)~h(l - e^)* A t y p i c a l time of f l i g h t spectrum i s shown i n f i g u r e 4-1. The cut width was chosen to in c l u d e the e n t i r e peak f o r every spectrum. The a c t u a l width of the peaks v a r i e d from 6.5 to 20 channels FWHM. There were 0.2 ns per channel, thus the f u l l width of the cut was 9.2 ns. This corresponds to an o v e r a l l momentum b i t e of about 200 MeV/c. Timesof f l i g h t c a l c u l a t e d f o r each energy are tabulated i n t a b l e 4-1. The time of f l i g h t d i f f e r e n c e f o r i n e l a s t i c protons, + pp->-pnTT versus e l a s t i c protons, and f o r pions from the r e a c t i o n pp->TT d are a l s o t a b u l a t e d i n t a b l e 4-1. I n e l a s t i c events are c l e a r l y separated from the e l a s t i c events. The s e n s i t i v i t y of the data to the time of f l i g h t cut 35 UJ < o if) >• cc < tr cr < CD 5 Z to •I— z ZD o o ENERGY DIFFERENC 0 50 ) 100 2 0 2 E OF FLIGHT ( n s ) 4 FIGURE 4 - 1 36 T A B L E 4 - 1 T a b l e o f t i m e o f f l i g h t s f o r e l a s t i c a n d i n e l a s t i c p r o t o n s , a n d f o r p i o n s . P r i m a r y T . O . F . f o r D i f f e r e n c e D i f f e r e n c e Beam e l a s t i c p r o t o n s i n T . O . F . f o r i n T . O . F . E n e r g y i n e l a s t i c p r o t o n s f o r p i o n s MeV T n s AT n s AT n s 500 5 9 . 7 5 1 1 . 4 7 - 1 2 . 7 5 467 6 0 . 8 6 H . 8 - 1 2 . 8 5 425 6 2 . 6 7 1 7 . 9 0 - 1 2 . 9 0 367 6 5 . 6 8 3 1 . 5 6 - 1 0 . 8 9 307 6 9 . 6 9 N o n e P o s s i b l e + 1 0 . 1 2 37 was c h e c k e d . The a s y m m e t r i e s c a l c u l a t e d w i t h c u t s o f ±30 c h a n n e l s and ±18 c h a n n e l s w e r e a l l w i t h i n t h e s t a t i s t i c a l e r r o r o f t h e a s y m m e t r y c a l c u l a t e d w i t h a ±24 c h a n n e l c u t . No s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e was o b s e r v e d when t h e pe a k c h a n n e l was c h a n g e d by ±2. B r o a d t i m e o f f l i g h t s p e c t r a w e r e c h e c k e d f o r R . F . s h i f t s . T h i s was done by c o l l e c t i n g some d a t a r u n s i n an e v e n t by e v e n t mode. A f t e r d i v i d i n g t h e s e r u n s i n t o s u b s e c t i o n s w i t h r e s p e c t t o t i m e , one f o u n d no d i f f e r e n c e s i n w i d t h s o r p e a k c h a n n e l , i n d i c a t i n g t h a t t h e r e w e r e no s u d d e n jumps i n t h e R . F . t i m i n g . The raw a s y m m e t r i e s f r o m s e q u e n t i a l r u n s w i t h o p p o s i t e s o l e n o i d e x c i t a t i o n s w e r e p a i r e d and t h e t r u e a s y m m e t r y , e , was c a l c u l a t e d f r o m c+Ae = K e J - e~) ± 1 1 R R 2 % (2) w h e r e i s g i v e n b y e q u a t i o n (1) and t h e ^ r e f e r t o t h e R s o l e n o i d p o l a r i t y . A d j a c e n t r u n s h a v i n g t h e same s o l e n o i d p o l a r i t y w e r e c o m b i n e d i n t o one r u n by t a k i n g t h e w e i g h t e d mean. T n + + 2 / 1 1 + - 2 £ R = ^ ^ R V ' ^ ' / ^ ^ ( 3 ) Ae* = {E ( A e * ) T 2 } " % (4) i = l The f i n a l a s y m m e t r y was t a k e n as t h e w e i g h t e d mean o f t h e p a i r e d a s y m m e t r i e s . The p r e v i o u s p r o c e d u r e was r e p e a t e d f o r " t a r g e t f u l l " d a t a , " c a r b o n " d a t a , and " l i q u i d h y d r o g e n t a r g e t empty" d a t a a t a l l e n e r g i e s . The f i n a l r e s u l t s a r e t a b u l a t e d i n t a b l e 4-2. 38 TABLE 4-2 Asymmetries f o r CH 2 t a r g e t , carbon t a r g e t , and l i q u i d hydrogen t a r g e t empty, averaged f o r each energy.  Primary beam Energy MeV CH 2 t a r g e t £CH„ Carbon t a r g e t e L i q u i d hydrogen t a r g e t empty GMT 500 0.1337 + 0.0014 0.0781 + 0.0027 .1222 + .0183 467 .1238 + .0018 .0821 + .0039 .1091 + .0063 425 .1252 + .0014 .0734 + .0034 .0827 + .0204 367 .1115 + .0018 .0733 + .0037 .1592 + .0369 307 .0966 + .0019 .0713 + .0042 .1040 + .0237 TABLE 4-3 Rates f o r Carbon and L i q u i d Hydrogen t a r g e t empty data normalized t o r a t e s f o r CH 2 data. Primary Carbon L i q u i d hydrogen beam r a t e t a r g e t empty Energy r r MeV ° 500 0.247 ± 0.004 0.039 ± 0.001 467 0.239 ± 0.010 0.046 ± 0.008 425 0.215 ± 0.013 0.020 ± 0.004 367 0.261 ± 0.005 0.022 ± 0.001 307 0.225 + 0.003 U n r e l i a b l e The background asymmetry from carbon and the hydrogen t a r g e t f l a s k was subtracted from the CH,, data to y i e l d the asymmetry due to fre e e l a s t i c proton-proton s c a t t e r i n g . This i n v o l v e d c a l c u l a t i n g the r e l a t i v e c o n t r i b u t i o n of carbon and t a r g e t empty events to e l a s t i c proton events. The r a t i o s UB + DB, UB + DB, and B were used. The f i r s t two L + R B L + R r a t i o s s p e c i f y the r a t e at which the beam scatters- from the second t a r g e t i n t o the polarim e t e r f o r a p a r t i c u l a r " i n c i d e n t f l u x . " Thus any of these normalize the r e l a t i v e r a t e s f o r d i f f e r e n t secondary t a r g e t s , ( i . e . , carbon and CH 2). The f i r s t versus empty. The coincidences BU, BD, B, and L + R were scaled as monitors f o r every run. Each r a t i o was cor r e c t e d f o r randoms and averaged over a l l the runs f o r a p a r t i c u l a r s o l e n o i d p o l a r i t y , t a r g e t , and energy. The e r r o r was assigned as the maximum observed f l u c t u a t i o n from the mean, t h i s being l a r g e r than the standard d e v i a t i o n . The r a t e from carbon normalized to CH 2 was taken as or (1) (±) ( 2 ) ( ± ) UB + DB~ / UB + DB" L + R ' 7 L R UB + DB~ r / UB + DB~ B 7 B -CH, CH, (5) (6) which ever had the sm a l l e s t u n c e r t a i n t y . The normalized r a t e f o r t a r g e t empty i s given by + "MT = B L + R MT B CH, (7) L + R The e r r o r on each normalized r a t e i s the e r r o r on the monitor r a t i o s added i n quadrature. The r a t e s were then averaged over 40 the s o l e n o i d p o l a r i t i e s . The r e s u l t i n g r a t e s are l i s t e d i n t a b l e 4-3. The number of carbon n u c l e i i n the carbon t a r g e t must be normalized to the number of carbon n u c l e i i n the CH 2 t a r g e t . Define the r a t i o mass of C i n CH 2 t a r g e t = k (8) mass of C i n C t a r g e t One gets k = 0.970 f o r primary beam en e r g i e s of 500, 467, and 425 MeV ( i . e . , f o r 1x2x2.5 cm 3 t a r g e t s ) and k = 0,939 f o r 367, 3 and 307 MeV ( i e . 0.5x2x2.5 cm t a r g e t s ) . U s u a l l y the carbon r a t e would be normalized t o the same number of s c a t t e r i n g c e n t r e s by m u l t i p l y i n g by k. Care was taken to i n c l u d e the e f f e c t of the B2 s c i n t i l l a t o r . I t i s p r i m a r i l y composed of CH, and as noted i n Chapter I I , i t i s an i n t e g r a l p a r t of the second t a r g e t . I t c o n t r i b u t e s a< smal l background at a l l e n e r g i e s with a r a t e of 0.077 r e l a t i v e to the CH.,, denoted r B 2 • T h i s was determined from a measurement of the asymmetry at 42 5 MeV with n e i t h e r carbon nor CH 2 i n the second t a r g e t . Thus the r a t e of s c a t t e r i n g from the hydrogen i n CH 2 i s g i v e n by r = r„„ - r_,„ (1 - k) + kr p CH„ B2 c Z (9) = r C H 2 " R c where one d e f i n e s a g e n e r a l i z e d carbon background r a t e , R , which i n c l u d e s the e f f e c t of B2. The valu e s of R are: c TABLE 4-4  G e n e r a l i z e d Carbon Background Primary Beam Energy R MeV c 500 0.242 ± 0.004 467 0.234 ± 0.010 425 0.211 ± 0.019 367 0.250 ± 0.005 307 0.216 ± 0.003 The f i n a l c o r r e c t e d asymmetry f o r each energy was then c a l c u l a t e d from £ = e C H 2 " R c £ c " rMT £MT ( 1 Q )  1 " R c " rMT where the e r r o r i s g i v e n by { A £ C H 2 + R C A £ C + rMT A EMT + ( £ + £ C ) 2 A R C + (11) + ( £ + G M T ) 2 A r M T } ) / { 1 " R c - rMT } The f i n a l asymmetries are: TABLE 4-5 F i n a l Asymmetries Primary Beam Energy e ± Ae MeV 500 0.1530 ± 0.0024 467 0.1383 ± 0.0030 425 0.1405 ± 0.0026 367 0.1232 ± 0.0030 307 rMT r e^-^ 3 i^ >^- e At 3 07 MeV primary beam energy, the hydrogen t a r g e t d a t a were u n r e l i a b l e . The parameters e , e„ m, R , and r., m c MT c MT were l i n e a r l y f i t t e d and the values at 307 MeV extrapolated. The f i t s are plotted i n figure 4-2. A table summarizing the o r i g i n a l parameters and the smoothed parameters i s given i n table 4-6. The f i n a l asymmetries were recalculated using the "smoothed" parameters. They are given i n table.'. 4-6, and are l i s t e d here. TABLE 4-7 F i n a l Asymmetries with Smoothed Parameters P.B.E. f i n a l asymmetry MeV e 500 0.1527 ± 0.0024 467 0.1390 ± 0.0030 425 0.1409 ± 0.0026 367 0.1228 ± 0.0030 307 0.1309 ± 0.0028 These smoothed asymmetries agree with the o r i g i n a l c a l c u l a t i o n to within quoted errors and are used i n the remainder of the analysis. One can now deduce the p o l a r i z a t i o n parameter from the f i n a l asymmetries by using equation (1-13), given e x p l i c i t l y as, £ i = p ( E i » 2 4 . 7 9 ° ) P ( K ( E i ) ,24°) (1-13) where K(E^) i s the energy of the secondary beam, derived from two body kinematic c a l c u l a t i o n s . (A table of the energy c a l c u l a t i o n i s given i n table 2-3). The equation (1-13) can be rewritten as, e iP(E i,24°) = P(E i,24°)P(K(E i) ,24°) (12) P(E i , 2 4.79°) 43 FIGURE 4-2 LINEAR FITS TO CARBON AND EMPTY TARGET ASYMMETRIES AND RATES VERSUS " BEAM ENERGY >-LU f?.05 00 < 1 300 A 0 T m T C !eV T i. 1 .15 i d < .5 0 3 I T R c r r n t r 400 «1eV 500 TABLE 4-6 Table of background asymmetries and r a t e s ; smoothed and unsmoothed UNSMOOTHED PARAMETERS Primary Beam Energy MeV £CH 2 £ c £MT R c r'f MT F i n a l e 500 .1337±. 0014 ,0781±.0027 .12221 .0183 .242 + .004 .039±.001 .15301 .0024 467 .1238+. 0018 .0821+.0039 .1091± .0063 .234± .010 .046±.008 .1383± .0030 425 .1252±. 0014 .0734+.0034 .0827± .0204 .211± .019 .020±.004 .1405± .0026 367 .1115±. 0018 .0733+. 0037 .15921 .0369 .250± .005 .022±.001 .12321 .0030 307 .0966±. 0019 .0713±.0042 ,1040± .0237 .216± .003 U n r e l i a b l e SMOOTHED PARAMETERS P.B.E. MeV £ c £MT ^MT F i n a l 500 .0796±. 0027 .11181. 0183 .2361.004 .0421 .001 .15271 . 0024 467 .0781±. 0039 .11321. 0063 .2341.010 .0361 .008 .13901 .0030 425 .07631. 0034 .11491. 0204 .2311.019 .0291 .004 .14091 .0026 367 .07351. 0037 .11741. 0369 .2271.005 .0191 .001 .12281 .0030 307 .07081. 0042 .11991. 0237 .2241.003 .0091 .001 .10391 .0028 T h i s form has the advantage of having o n l y one independant v a r i a b l e , , on the r i g h t hand s i d e of the equ a t i o n . The r a t i o of the p o l a r i z a t i o n parameter a t 24° versus 24.79° i s 2 8 known from phase s h i f t a n a l y s i s t o 0.3%. The f o l l o w i n g t a b l e g i v e s the energie s and p o l a r i z a t i o n r a t i o s used i n equation (12). TABLE 4-8 Ratios of P(24°)/P(24 .79°) PBE MeV E. M£V K (E ) MeV 1 P(E. ,24°)/P(E. ,24.79°) 500 496 391 0.9546 467 463 366 0.9567 425 422 334 0.9588 367 362 288 0.9630 307 302 242 0.9668 In a d d i t i o n t o the p o i n t s measured i n t h i s experiment the v a l u e s of P(24°) a t 9 8 1 0 , 140.7 2 9, 601 7 and 702 ? MeV, were added from world data to f i x the p o l a r i z a t i o n parameter o u t s i d e the energy range measured here. TABLE 4-9  Added World Data Energy P(24°) MeV 98 0.110 ± 0.010 140.7 0.200 ± 0.010 601 0.465 ± 0.021 702 0.511 ± 0.027 The p o l a r i z a t i o n parameter was w r i t t e n as a f o u r t h order power s e r i e s . 4 P(E,24°) = E a (E-400) n (13) n=o The asymmetry i s th e r e f o r e given by, e.P(E.,24°) = I I The energies were s h i f t e d 400 MeV so as to reduce the covariance of the f i t t i n g parameters, a^. Equation(14) was used to n o n l i n e a r l y f i t the data by min i m i z a t i o n of the chi-square. A n o n s t a t i s t i c a l e r r o r equal to the s t a t i s t i c a l e r r o r was added i n quadrature to the e r r o r of each asymmetry to account f o r small i n s t a b i l i t i e s i n the time of f l i g h t s pectra and the ra t e monitors. The chi-square of the f i t was 1.01, corresponding to a 40% confidence l e v e l . to a l l the measured energies due to the u n c e r t a i n t y i n the f i r s t s c a t t e r i n g angle. This was added i n quadrature to the e r r o r on the c a l c u l a t e d p o l a r i z a t i o n s . parameter at 24° over the range of k i n e t i c energies from 200 t o 520 MeV i n 20 MeV steps i s given i n t a b l e 4-10. A graph showing the e n t i r e f i t t i n g range i n c l u d i n g the world data i s given i n f i g u r e 4-3. The data from the experiment i s p l o t t e d as e 2 at the average energy (E^ + K(E^))/2. This i s i n analogy t o previous s i n g l e energy double s c a t t e r i n g 2 experiments where e = P . There i s another systematic e r r o r of ±0.004 common A t a b l e of the f i n a l values f o r the p o l a r i z a t i o n 47 TABLE 4-10 V a l u e s o f P(24°) l a b b e t w e e n 200 and 500 MeV E n e r g y MeV P ( 2 4 0 ) 200 0.278 ± 0.009 220 0.298 ± 0.008 240 _ 0.315 ± 0.007 260 0.329 ± 0.006 280 0.341 + 0.005 300 0.351 + 0.005 320 0.360 ± 0.006 340 0.367 + 0.005 360 0.374 ± 0.005 380 0.380 ± 0.005 400 0.386 + 0.005 420 0.392 ± 0.006 440 0.398 ± 0.006 460 0.404 ± 0.006 480 0.410 ± 0.006 500 0.417 ± 0.008 520 0.425 ± 0.010 0.6-0.5 -z. o < 0.4 cr < o a. 0.3 0.2 0.1 ® Added World Data V Phase Shift Error Envelope 100 200 300 400 500 600 700 MeV POLARIZATION AT 24° LAB VERSUS ENERGY FIGURE 4 - 3 CHAPTER V  CONCLUSIONS The p o l a r i z a t i o n parameter was measured wi t h an absolute n o r m a l i z a t i o n of b e t t e r than 2% i n the energy region between 250 MeV and 500 MeV. The most p r e c i s e values have an e r r o r of about 1.5% i n the neighbourhood of 42 5 MeV. The r e s u l t s presented i n t h i s t h e s i s agree w e l l w i t h phase s h i f t p r e d i c t i o n s , based on the world data set of p-p measurements. However we have s u b s t a n t i a l l y reduced, from 6% to 2%, the n o r m a l i z a t i o n u n c e r t a i n t y . This i s c l e a r l y demonstrated i n the f o l l o w i n g t a b l e . TABLE 5-1 Comparison of Experimental Results to Previous Phase S h i f t P r e d i c t i o n . Energy P(24°) P(24°) Mev Experiment Phase S h i f t ( P r e v i o u s ) 200 .278 ± .009 0.280 ± .017 250 .323 ± .007 0.314 + .019 300 .351 ± .005 0.340 ± .020 350 .371 ± .005 0.361 ± .022 400 .386 ± .005 0.380 ± .023 450 .401 ± .006 0.398 ± .024 500 .417 ± .008 0.414 ± .049 The envelope of e r r o r from the phase s h i f t a n a l y s i s i s p l o t t e d on f i g u r e 4-3. I t i s f e l t t h a t a new phase s h i f t c a l c u l a t i o n w i l l show s u b s t a n t i a l l y reduced e r r o r s as a r e s u l t of the small e r r o r on the data presented i n t h i s t h e s i s . One should a l s o see some small changes i n the phase s h i f t p r e d i c t i o n f o r P(24°) as the experimentally determined p o l a r i z a t i o n s d i f f e r i n a number of cases (see t a b l e 5-1) from the p r e v i o u s l y c a l c u l a t e d p o l a r i z a t i o n by more than the e r r o r on the experimental r e s u l t . 50 The r e s u l t s of t h i s study f i x the a b s o l u t e n o r m a l i z a t i o n of t o ±2%, and hence normalize a l l v a l u e s of P (9), 0° <0<9O°, over the energy range of 200 to 500 MeV, s i n c e the angular dependence of P i s w e l l determined by phase s h i f t a n a l y s e s . 51 BIBLIOGRAPHY 1. L. W o l f e n s t e i n , Phys. Rev. 96.(1954) 1654 2. L. W o l f e n s t e i n , Ann. Rev, Nuc. S c i . 6.(1956) 43 3. M.H. MacGregor, Ann. Rev. Nuc. S c i . 10(1960) 291 4. M. Moravcsik, "The Two Nucleon I n t e r a c t i o n " , Oxford Press (1963) 5. A. Beretvas, Phys. Rev. 171 (1968) 1392 6. P. Limon e t a l , Phys. Rev. 169 (1968) 1026 7. D. Cheng e t a l , Phys. Rev. 163 (1967) 1470 8. H.G. deCarvalho e t a l , Phys. Rev. 9± (1954) 1796 9. J.H. T i n l o t e t a l , Phys. Rev. 124 (1961) 890 10. A.E. T a y l o r e t a l , N U c . Phys. 16. (1960) 320 11. J . M a r s h a l l e t a l , Phys. Rev. 95_ (1954) 1020 12. G. C o z z i k a e t a l , Phys. Rev. 164 (1967) 1672 13. M. Albrow e t a l , N uc. Phys. B23 (1970) 445 14. F. Betz e t a l , Phys. Rev. 148 (1966) 1289 15. O. Chamberlain e t a l , Phys. Rev. 105 (1957) 28 8 16. R. Roth e t a l , Phys. Rev. 140 (1965) B1533 17. P. Hansen Surko, T h e s i s , UCRL-19451, Jan. 15, 1970 18. J . B y s t r i c k y , " E l a s t i c Nucleon-Nucleon S c a t t e r i n g Data 270 - 3000 MeV", CEA-N-1547(E) 19. G. Ludgate, T h e s i s , R u t h e r f o r d High Energy Lab P u b l i c a t i o n , HEP/T/62, Oct. 1976. 20. C. Oram, T h e s i s , R u t h e r f o r d High Energy Lab P u b l i c a t i o n , HEP/T/65, May 1977. 21. T. Hodges, Triumf I n t e r n a l Report, TRI-I-73-2 (1973) 22. G.M. S t i n s o n , Triumf I n t e r n a l Report, TRI-NA-76-1 (1976) 23. E. Segre, " N u c l e i and P a r t i c l e s " , W.A. Benjamin Inc. (1965) 52 24. "Studies i n P e n e t r a t i o n of Charge P a r t i c l e s i n Matter," N a t i o n a l Academy of S c i e n c e s , NRC P u b l i c a t i o n 1133, (1964) 25. "Reviews of P a r t i c l e P r o p e r t i e s , " Rev. Mod. Phys. 48(2) (1976) S50 26. P. K i t c h i n g , Triumf I n t e r n a l Report, TRI-71-2 (1971) 27. A. Banford, "Transport of Charged P a r t i c l e Beams," E & F.N. Spon L t d . (1966)" 28. D.V. Bugg, P r i v a t e Communication 29. G. Cox e t a l , Nuc. Phys. B4 (1967) 353 

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