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UBC Theses and Dissertations

Polarization transfer in deuterium at intermediate energies Felawka, Larry Thomas 1978

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POLARIZATION TRANSFER IN DEUTERIUM AT INTERMEDIATE ENERGIES LARRY THOMAS FELA8KA B.Sc. , U n i v e r s i t y of Manitoba, 196 8 M. Sc., U n i v e r s i t y o f B r i t i s h Columbia, 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES Department of Ph y s i c s 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 June, 1978 Larry Thomas Felawka , 1978 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 requirements for an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree 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 reference and s tudy . I f u r t h e r agree 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 of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department or 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 tha t c o p y i n g or pub l i ca t ion of 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 thout my w r i t t e n p e r m i s s i o n . Depa rtment The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 i i ABSTRACT A s e t of experiments to determine the optimum p o l a r i z a t i o n t r a n s f e r parameter f o r the p r o d u c t i o n of p o l a r i z e d neutron beams using the r e a c t i o n D(p,"n) 2p and t o determine the optimum neutron production angle are d e s c r i b e d . Measurements of the v a r i a t i o n of neutron p o l a r i z a t i o n w i t h energy at a neutron production angle of 9° i n the l a b . and of the a n a l y z i n g power f o r neutrons of a p o l a r i m e t e r c o n t a i n i n g a 6 cm. t h i c k carbon t a r g e t are a l s o d e s c r i b e d . The p o l a r i z a t i o n t r a n s f e r parameter R was found t o be about 5 times as l a r g e as the parameter D f o r neutrons emerging at 9° i n the l a b . at 210 and 343 MeV i n c i d e n t proton e n e r g i e s , and of the same order as D a t 516 MeV. The neutron t p o l a r i z a t i o n peaked at about 10° a t 210 and 343 MeV and was r e l a t i v e l y i n s e n s i t i v e to angle at 516 MeV. For neutrons emerging at 9°, • R was observed to decrease from -.94±, 12 a t 237 t HeV to -.49±.07 at 516 MeV. Table of Contents CHAPTER I. INTRODUCTION ................... 1 CHAPTER I I . SCATTERING FORMALISM 13 1. D e n s i t y Matrix Formalism and S c a t t e r i n g Matrix ..... 13 2. P a r t i a l Save Decomposition of S c a t t e r i n g Matrix .... 28 CHAPTER I I I . APPARATUS AND TECHNIQUES 35 CHAPTER IV. EXPERIMENTS, RESULTS AND DISCUSSION .......... 53 1. Experiment #1: A Measurement o f Neutron Beam P o l a r i z a t i o n vs. Angle . 5 3 a. Data A n a l y s i s ................................... 58 b. R e s u l t s 62 c. The P o l a r i z a t i o n T r a n s f e r Parameters Rfc and D t . . 7 0 2. Experiment #2: Measurement of Analyz i n g Power of Carbon (Neutrons) ........... ................ ........ 75 a. Data A n a l y s i s ................... ................ 79 3. Experiment #3: A Measurement of Neutron P o l a r i z a t i o n vs. Energy 85 a. Data A n a l y s i s ................................... 88 b. R e s u l t s ......................................... 89 CHAPTER V. SUMMARY AND CONCLUSIONS 94 BIBLIOGRAPHY 98 APPENDIX A. A Monoenergetic P o l a r i s e d Neutron Beam from 200 to 500 MeV 100 APPENDIX B. D, R, R» and P i n pp E l a s t i c S c a t t e r i n g from 209 to 515 MeV 105 i v L i s t o f Tables Table I. 2S Hyperfine S t a t e s of Hydrogen i n a Magnetic Table I I . Analyzing Power of Proton Beam P o l a r i z a t i o n M on x t oir «• • • • • • » * • * *' •«». • •••.-'•«/• *> • •'•"•'••''•'•'**.•• v.* • • » * .^3 Table I I I . Magnetic F i e l d Survey of Dipo l e #1 (UCLA) .... 48 Table IV. Magnetic F i e l d Survey o f Dipole #2 (PLA) ...... 49 Table V. Summary of Angles and E n e r g i e s a t Which Data were Taken (Experiment #1) ................................. 54 Table VI. Asymmetries f o r R Measurement (210 MeV) ...... 64 Table VII. Asymmetries f o r R Measurement (343 MeV) ..... 65 Table VIII. Asymmetries f o r R t Measurement (516 MeV) .... 66 Table IX. Asymmetries f o r D t Measurement (343 MeV) ...... 67 Table X. Asymmetries f o r D t Measurement (516 MeV) ....... 68 Table XI. ; R t Parameter ................................ 73 Tabl e XII. D Parameter . . 7 4 Table XIII. Summary of C a l c u l a t i o n o f Low-energy C u t o f f i n Carbon P o l a r i m e t e r 83 Table XIV. Analyzing Power o f Carbon P o l a r i m e t e r f o r Neutrons .............................................. 84 Table XV. R t (Experiment #3) ........................... 92 V L i s t o f F i g u r e s Figure 1. Types of P o l a r i z a t i o n Experiments ............ 6 Fi g u r e 2. Experimental Layout f o r BASQUE n-p Experiment (Not to Scale) ........................................ 9 Figu r e 3. or t h o g o n a l U n i t V e c t o r s K, P and N i n CM. Frame (Wolfenstein) ......................... ................ 21 Figu r e 4. R e l a t i o n s h i p Between P o l a r i z a t i o n V e c t o r s and S c a t t e r i n g Asymmetry .............. 25 F i g u r e 5. Orthogonal Unit Vectors i n Lab. Frame (Hoshizaki) ........................................... 26 Fi g u r e 6., Schematic of P o l a r i z e d Ion Source (POLISIS) . 3 6 Fi g u r e 7. E n e r g y - l e v e l Diagram o f 2S L and 2PX S t a t e s of Hydrogen i n a Magnetic F i e l d .......................... 37 F i g u r e 8. E n e r g y - l e v e l Diagram I l l u s t r a t i n g Sona Z e r o - c r o s s i n g Method o f O b t a i n i n g 100% P o l a r i z a t i o n ... 40 Fi g u r e 9. Apparatus f o r Experiment #1: Neutron P o l a r i z a t i o n vs. A ngle ........................ ,......,. 42 Fig u r e 10. Carbon P o l a r i m e t e r L o g i c .................... 51 F i g u r e 11. Data T r i g g e r L o g i c .......................... 52 Fig u r e 12. H o r i z o n t a l Slope of Scat t e r e d Proton Beam vs. H o r i z o n t a l I n t e r c e p t ............................... 56 Fi g u r e 13. V e r t i c a l Slope of S c a t t e r e d Proton Beam vs. H o r i z o n t a l I n t e r c e p t .............................. 57 F i g u r e 14. T i m e - o f - f l i g h t Spectrum o f Neutrons Emitted from Deuterium at 6° (210 MeV) ........................ 63 Fig u r e 15. Asymmetry r a t i o vs. Angle (R -type) .......... 71 v i F i g u r e 16. asymmetry r a t i o vs. Angle (D t-type) .......... 72 F i g u r e 17. R t Parameter ............................... 76 Fig u r e 18. D t Parameter ............................... 77 F i g u r e 19. Apparatus f o r Experiment #2: Analyzing Power of Carbon f o r Neutrons 78 F i g u r e 20. T i m e - o f - f l i g h t Spectra of Neutrons Emitted from Carbon at 21° (516 MeV) ............................... 81 F i g u r e 21. Apparatus f o r Experiment #3: Neutron P o l a r i z a t i o n vs. Energy a t 9° ......................... 86 F i g u r e 22. R e l a t i o n s h i p Between P o l a r i z a t i o n V e c t o r s ...87 F i g u r e 23. Measurement of F vs. P r e c e s s i o n Angle ,. 91 F i g u r e 24. Values of R Obtained from Experiment #3 .... 93 v i i ACKNOWLEDGEHENT I t i s with great p l e a s u r e that I t a k e t h i s o p p o r t u n i t y t o express my h e a r t f e l t thanks t o my Research S u p e r v i s o r , Dr. David ft, Axen, f o r h i s s t e a d f a s t support and encouragement. I would a l s o l i k e t o express my thanks to the TBIBH?-staff> to the other members of the BASQUE Group and i n p a r t i c u l a r t o Dr. Claude Amsler f o r t h e i r v a l u a b l e a s s i s t a n c e . I should a l s o l i k e t o express my a p p r e c i a t i o n t o the Nat i o n a l Research C o u n c i l of Canada f o r f i n a n c i a l support. 1 CHAPTER I INTRODUCTION The measurements of p o l a r i z a t i o n t r a n s f e r i n deuterium which are d e s c r i b e d i n t h i s t h e s i s form an i n t e g r a l part o f a study of the N-N i n t e r a c t i o n undertaken by the BASQUE group a t TRIUMF. I t i s w e l l known that the N-N f o r c e i s both energy-dependent and spin-dependent; i t s study r e q u i r e s the use of p o l a r i z e d beams and/or t a r g e t s over a wide range of e n e r g i e s . P r e v i o u s s t u d i e s have been made at a few e n e r g i e s u s i n g beams produced by fixed-energy c y c l o t r o n s . I t was rec o g n i z e d e a r l y i n the development of TRIUMF th a t the c o n t i n u o u s l y - v a r i a b l e f e a t u r e of the c y c l o t r o n made a comprehensive study of the N-N i n t e r a c t i o n p o s s i b l e i n the energy r e g i o n 200-500 MeV. A p o l a r i z e d i o n source was developed at the o u t s e t s p e c i f i c a l l y f o r t h i s s e r i e s of measurements. Beam i n t e n s i t i e s o f 1-10 nanoamperes are s u f f i c i e n t f o r proton-proton s c a t t e r i n g experiments. Extremely good energy r e s o l u t i o n i s not re q u i r e d i n t h i s energy r e g i o n because the dominant i n e l a s t i c process i s pi o n production o c c u r r i n g above a t h r e s h h o l d of 290 MeV., T h i s r e a c t i o n removes a minimum o f 140 MeV from the p-p system and can e a s i l y be separated from e l a s t i c events by us i n g t i m e - o f - f l i g h t techniques. These f a c t o r s have allowed the proton-proton system t o be determined t o an accuracy of a few percent during the 1950's and e a r l y 1960*s. The neutron-proton system can be s t u d i e d e i t h e r by 2 s c a t t e r i n g protons from neutrons bound i n deuterium n u c l e i or by s c a t t e r i n g neutrons from hydrogen. The l a t t e r method r e l i e s on the production of neutrons by charge exchange r e a c t i o n s i n n u c l e i . The r e s u l t i n g neutron f l u x i s low, 10 3/sec./na. o f proton beam being t y p i c a l (Reay, 1966). The development of a 100 na. p o l a r i z e d proton beam (80% p o l a r i z a t i o n ) a t TRIOMF made the production of an i n t e n s e p o l a r i z e d neutron beam p o s s i b l e by t r a n s f e r r i n g p o l a r i z a t i o n to neutrons i n charge exchange r e a c t i o n s . The energy of the neutrons produced by charge exchange i n deuterium i s expected t o be peaked at the h i g h e s t energy allowed k i n e m a t i c a l l y because o f the strong f i n a l - s t a t e i n t e r a c t i o n between the r e s i d u a l proton p a i r . Bowen e t a l . have measured the energy spectrum o f neutrons at 0° produced by charge exchange i n v a r i o u s n u c l e i u s i n g an u n p o l a r i z e d beam of 143 HeV protons (Bowen, 1962). With deuterium as a t a r g e t they observed a peak i n the neutron spectrum at the high-energy end with a f u l l width a t h a l f maximum (FWHM) of 20 HeV. Larsen, i n d e s c r i b i n g an experiment to measure the pion-nucleon c o u p l i n g constant u s i n g a neutron beam, r e p o r t e d that the energy spectrum of neutrons produced by 740 MeV protons on deuterium was Gaussian with a FWHM of 8 MeV (Larsen, 1960). The p r o d u c t i o n of a v a r i a b l e - e n e r g y monoenergetic u n p o l a r i z e d neutron beam i n the range 50-150 MeV f o r use i n the n-p experiments was d e s c r i b e d by fleasday (Measday, 1966)., Clough et a l . have i n v e s t i g a t e d the energy s p e c t r a of neutrons from deuterium a t angles of 0°-40° f o r i n c i d e n t proton e n e r g i e s of 30 and 50 MeV (Clough, 1968). Comparisons between t h e i r measurements and t h e o r e t i c a l 3 c a l c u l a t i o n s made by P h i l l i p s ( P h i l l i p s , 1964) i n d i c a t e d good agreement a t s m a l l e r angles, A b r i e f survey of common methods used to produce p o l a r i z e d f a s t neutron beams i s given by S a l t e r (Walter, 1971). An e a r l y method was based on the g e n e r a l o b s e r v a t i o n t h a t p a r t i c l e s produced i n a nuclear r e a c t i o n u s i n g an u n p o l a r i z e d beam are p o l a r i z e d at angles away from 0° (Wouters, 1951; Roberts, 1954; Bradner, 1955; S t a f f o r d , 1957; Bowen, 1962), The r e s u l t i n g p o l a r i z a t i o n , however, was u s u a l l y l e s s than 20% and l i m i t e d the u s e f u l n e s s of the method. Another method was to use the s p i n - o r b i t i n t e r a c t i o n a r i s i n g from the motion o f the magnetic moment o f the neutron i n the strong Coulomb f i e l d of a heavy nucleus to produce a p o l a r i z e d beam {Schwinger, 1948). Schwinger estimated t h a t c l o s e t o 100$ p o l a r i z a t i o n c o u l d be obtained with a l e a d t a r g e t and 1 MeV neutrons. T h i s method has the u s e f u l f e a t u r e that the magnitude of the p o l a r i z a t i o n i s i n s e n s i t i v e t o v a r i a t i o n s i n the o p t i c a l - m o d e l parameters used i n the c a l c u l a t i o n , a l l o w i n g a c c u r a t e e s t i m a t e s of the p o l a r i z a t i o n t o be made. T h i s circumstance would then o b v i a t e the requirement o f a separate c a l i b r a t i o n of the p o l a r i r a e t e r . In a d d i t i o n , the p o l a r i z a t i o n v a r i e s l i t t l e with energy, p e r m i t t i n g the use of t h i c k t a r g e t s . There e x i s t severe experimental d i f f i c u l t i e s , however, due to the requirement t h a t the neutrons be taken at angles s m a l l e r than 2°, p l a c i n g s t r i n g e n t l i m i t a t i o n s on neutron beam divergence. A t h i r d method (and the one d e s c r i b e d i n t h i s t h e s i s ) i s t o bombard n u c l e i with p o l a r i z e d protons and to take advantage of the l a r g e t r a n s f e r of p o l a r i z a t i o n to the neutrons. 4 C a l c u l a t i o n s of p o l a r i z a t i o n t r a n s f e r i n deuterium i n the energy range 30-150 MeV u s i n g the impulse approximation p r e d i c t e d l a r g e values (up to 50%) and s t r o n g l y suggested t h a t t h i s r e a c t i o n would be s u i t a b l e f o r the pro d u c t i o n o f p o l a r i z e d beams ( P h i l l i p s , 1959; Dass and Queen, 1968). I n a d d i t i o n , Dass and Queen pointed out t h a t the r e s u l t s are very s e n s i t i v e t o the set of nucleon-nucleon phase s h i f t s used i n the c a l c u l a t i o n and suggested t h a t measurements of p o l a r i z a t i o n t r a n s f e r i n deuterium would be a t e s t of ambiguous s e t s of phase s h i f t s p r e v i o u s l y e x t r a c t e d from n-p e l a s t i c s c a t t e r i n g d ata. P o l a r i z a t i o n t r a n s f e r measurements have been made by Beay et a l . , who measured .R f o r D(p%n")2p at neutron l a b . angles from 0-20° using 203 MeV p o l a r i z e d protons (Reay, 1966). The values of B v a r i e d from -.269±.094 at 0 ° , peaking a t 10° with a value ~.992±.094, and decr e a s i n g t o -.607±.117 at 20°. Robertson e t a l . measured p o l a r i z a t i o n t r a n s f e r at 0° f o r s e v e r a l t a r g e t s ( i n c l u d i n g deuterium) at 30 and 50 MeV (Robertson, 1969). No p r i o r measurements of p o l a r i z a t i o n t r a n s f e r f o r e n e r g i e s exceeding 200 MeV have been made. P r e d i c t i o n s of p o l a r i z a t i o n t r a n s f e r i n deuterium (Folkmann and Measday, 196 8) i n d i c a t e d that the t r a n s f e r parameter R i s l a r g e and r e l a t i v e l y i n s e n s i t i v e t o v a r i a t i o n s i n energy and angle. These p r e d i c t i o n s were based on the MAW IX Livermore phase s h i f t s (HacGregor, 1968), which i n c o r p o r a t e d a l l the p-p data, the n-p cr o s s s e c t i o n data and the n-p p o l a r i z a t i o n data that were a v a i l a b l e . Some attempt was made to i n c l u d e the e f f e c t of . . . . 5 charge exchange; the r e s u l t s were found to be i n s e n s i t i v e to the amount of the charge exchange i n t r o d u c e d . A s p i n one-half p a r t i c l e can have i t s p o l a r i z a t i o n v e c t o r p o i n t i n g along any d i r e c t i o n i n space; hence fo u r r e a l q u a n t i t i e s are r e q u i r e d t o s p e c i f y the d i r e c t i o n and degree of p o l a r i z a t i o n . A system c o n s i s t i n g of a s p i n o n e - h a l f i n c i d e n t p a r t i c l e and s p i n o n e - h a l f t a r g e t p a r t i c l e i s thus d e s c r i b e d by 16 r e a l q u a n t i t i e s ; t r a n s i t i o n s between i n i t i a l and f i n a l s t a t e s of the system are d e s c r i b e d by 256 r e a l q u a n t i t i e s . The s i t u a t i o n s i m p l i f i e s c o n s i d e r a b l y i f i n v a r i a n c e of the i n t e r a c t i o n i s assumed under time r e v e r s a l ; c o o r d i n a t e r e v e r s a l ( p a r i t y ) and i n t e r c h a n g e of the neutron and proton ( i s o t o p i c s p i n ) ; the number of non-zero independent r e a l q u a n t i t i e s i s reduced to 9 (5 complex s c a t t e r i n g amplitudes). Experimental d e t e r m i n a t i o n of these amplitudes can be done by measuring 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 s p i n c o r r e l a t i o n s , , The s p i n - c o r r e l a t i o n parameters a r e r e f e r r e d to e i t h e r as H o l f e n s t e i n parameters or t r i p l e - s c a t t e r i n g parameters (see F i g . 1). In i s o s p i n n o t a t i o n the p-p i n t e r a c t i o n i s d e s c r i b e d as a pure 1=1 s t a t e whereas the n-p i n t e r a c t i o n i s a l i n e a r combination o f 1=1 and 1=0 s t a t e s . The i m p l i c a t i o n o f the i s o s p i n formalism i s t h a t the 1=0 component of the nucleon-nucleon f o r c e can be s t u d i e d e x p e r i m e n t a l l y by doing p o l a r i z a t i o n e x p e r i m e n t s u s i n g a neutron t a r g e t such as deuterium or a neutron beam (but not both). In order to take advantage of the unique f a c i l i t y e x i s t i n q at TBIUMF a 6 P D R A ft A' P o l a r i z a t i o n S p i n C o n f i g u r a t i o n P a r a m e t e r Figure 1. Types of Polarization Experiments 7 c o l l a b o r a t i o n of experimental groups from Bedford C o l l e g e , AERE Harwell, Surrey U n i v e r s i t y , J2ueen Mary C o l l e g e , U n i v e r s i t y of B r i t i s h Columbia and U n i v e r s i t y of V i c t o r i a proposed to measure the 1=0 component o f the N-N i n t e r a c t i o n . The s p e c i f i c p r o p o s a l was t o measure the n-p d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n and the n-p H o l f e n s t e i n parameters P, D, A, R, D t, A t and B t . C o n s u l t a t i o n with S i g n e l l i n d i c a t e d t h a t a measurement of 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 t o an accuracy of ±1% and Wolf e n s t e i n parameters t o an accuracy o f ±.03 would be s u f f i c i e n t t o r e s o l v e the a m b i g u i t i e s i n the e x i s t i n g phase s h i f t s o l u t i o n s . T h i s estimate was subsequently confirmed by Bugg (Bugg, 1975). Since 9 measurements are r e q u i r e d t o determine the n-p system, one a d d i t i o n a l independent measurement i s needed. The 8 measurements l i s t e d above represent the maximum amount of i n f o r m a t i o n which can be obtained from an experimental setup which uses a p o l a r i z e d beam, un p o l a r i z e d t a r g e t and one p o l a r i z a t i o n - s e n s i t i v e d e t e c t o r . A d e c i s i o n as to the n e c e s s i t y of f u r t h e r work with the a d d i t i o n of e i t h e r a p o l a r i z e d t a r g e t or another p o l a r i m e t e r w i l l be made upon completion of t h i s work. I t should be noted, however, t h a t 8 at lower e n e r g i e s , where the i n e l a s t i c component of the i n t e r a c t i o n i s s m a l l , these experiments completely determine the n-vp system. I n v e s t i g a t i o n s of t h e accuracy r e q u i r e d i n these measurements a l s o i n d i c a t e d t h a t u n c e r t a i n t y i n the 1=1 component c o n t r i b u t e d a s i z a b l e e r r o r t o the 1=0 component. For t h i s reason a p r o p o s a l was made to a l s o measure D, B, B* and P f o r the p-p system at 4 e n e r g i e s and f o r centre-of-mass anqles r a n q i n g from 12° to 54°, usinq the same apparatus as was needed f o r the n-p measurements. The apparatus r e q u i r e d f o r the n-p s c a t t e r i n q experiments i s shown i n F i q . 2. The e s s e n t i a l components are the p o l a r i z e d beam, beam p o l a r i z a t i o n monitor, superconductinq s o l e n o i d f o r p r e c e s s i n q the beam p o l a r i z a t i o n v e c t o r i n t o the r e a c t i o n plane, l i g u i d deuterium t a r g e t , d i p o l e magnet to remove charged p a r t i c l e s from the neutron beam, neutron beam c o l l i m a t o r , d i p o l e #1 f o r p r e c e s s i n g neutron s p i n i n the h o r i z o n t a l plane and d i p o l e #2 to precess the neutron s p i n i n the v e r t i c a l plane. The combination of d i p o l e s #1 and #2 allowed r o t a t i o n o f the p o l a r i z a t i o n v e c t o r of the neutron beam t o any d i r e c t i o n . The remaining elements are the hydrogen t a r g e t , neutron counter a r r a y and carbon p o l a r i m e t e r . The neutron counter array c o n s i s t e d of two v e r t i c a l s t a c k s of p l a s t i c s c i n t i l l a t o r b l o c k s placed s i d e by s i d e ; each stack contained 7 15X15X105 cm. b l o c k s and each block was viewed by p h o t o m u l t i p l i e r tubes mounted on both ends. A t h i n p l a s t i c s c i n t i l l a t o r counter NV i n f r o n t of the neutron counter a r r a y was used to veto charged p a r t i c l e s . 9 P O L A R I Z E D P R O T O N S C A R B O N P O L A R i M E T E R F i g u r e 2. n-p Experimental l a y o u t f o r BASQUE Experiment (Not t o Scale) 10 The carbon p c l a r i m e t e r c o n s i s t e d of 6 m u l t i w i r e p r o p o r t i o n a l chambers mounted on both s i d e s of a carbon t a r g e t , and l a r g e p l a s t i c s c i n t i l l a t o r counters S1-4. For the case of protons both i n c i d e n t and s c a t t e r e d proton t r a c k s are d e f i n e d and asymmetry i n s c a t t e r i n g from the carbon t a r g e t can be determined. For the case of neutrons only the t r a c k of the proton r e s u l t i n g from charge exchange i n carbon can be determined by the r e a r chambers; the i n c i d e n t neutron t r a j e c t o r y must be determined by other means. In order to a t t a i n the d e s i r e d accuracy i n the BASQUE experiments the beam p o l a r i z a t i o n monitor had t o be c a l i b r a t e d f o r t r c t o n s and the carbon p o l a r i m e t e r had to be c a l i b r a t e d f o r both protons and neutrons. The BASQUE experiments which have been completed are (the order was d i c t a t e d by f a c t o r s such as experimental area l o g i s t i c s and beam a v a i l a b i l i t y ) : c a l i b r a t i o n of carbon p o l a r i m e t e r f o r protons, measurement of p-p SFolfenstein parameters P, D and B (at l a b . angles 6 ° , 9°, 15° and 24°) and B* (at 15°) i n the energy range 209-515 HeV, measurement of the r e l a t i v e p o l a r i z a t i o n of neutrons produced by charge exchange i n deuterium as a f u n c t i o n of angle f o r i n c i d e n t proton e n e r g i e s 210, 343 and 516 HeV, c a l i b r a t i o n of the carbon p o l a r i m e t e r f o r neutrons produced by charge exchange a t 343 and 516 MeV, measurement of p o l a r i z a t i o n o f neutrons r e s u l t i n g from charge exchange i n deuterium a t 9° as a f u n c t i o n o f energy from 200-500 MeV, D a 2) a 3) a 4) a 5) a 6) a measurement o f n-p H o l f e n s t e i n parameters P, D, A, R, D t, A f c # and R t and 7) 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 produced i n p-p s c a t t e r i n g at 24° by double s c a t t e r i n g . Experiments 3, 4 and 5 are d e s c r i b e d i n t h i s t h e s i s . The p o l a r i z a t i o n t r a n s f e r data f o r e n e r g i e s above 200 MeV were r e q u i r e d i n the BASQUE experimental programme f o r the f o l l o w i n g reasons: 1) the angle g i v i n g the highest p o l a r i z a t i o n had t o be determined to optimize the data t a k i n g and 2) the r e l a t i v e magnitude of R and D had t o be t t determined; a l a r g e value of D would mean a l a r g e s a v i n g i n l i q u i d helium c o s t s because the superconducting s o l e n o i d would not be needed t o precess the i n c i d e n t proton s p i n i n t o the r e a c t i o n plane. ; I t was necessary to perform s e p a r a t e c a l i b r a t i o n experiments f o r protcn and neutrons on carbon; the l a t t e r r e a c t i o n i n v o l v e s charge exchange while the former i n v o l v e s mainly e l a s t i c p rocesses. A b r i e f d i s c u s s i o n of the use of the d e n s i t y matrix formalism i n p o l a r i z a t i o n experiments and the r e l a t i o n o f the experimental q u a n t i t i e s to phase s h i f t s i s qiven i n chapter I I . A d i s c u s s i o n of decomposition of the s c a t t e r i n q matrix i n t o phase s h i f t s i s qiven f o r the sake of completeness, s i n c e the phase s h i f t p a r a m e t r i z a t i o n of the N-N system played a key r o l e i n q u i d i n q the p o l a r i z a t i o n t r a n s f e r measurements. 12 The experimental apparatus ( i n c l u d i n g t h e p o l a r i z e d i o n source) i s d e s c r i b e d i n some d e t a i l i n Chapter I I I . Chapter IV c o n t a i n s a d e s c r i p t i o n o f the experimental methods, data a n a l y s i s and r e s u l t s of the p o l a r i z a t i o n t r a n s f e r measurements. P u b l i c a t i o n s d e s c r i b i n g the TBIUMF p o l a r i z e d neutron beam and measurements of the B o l f e n s t e i n parameters f o r the p-p system are i n c l u d e d as Appendices. The l a t t e r experiment, though not part of the m a t e r i a l o f t h i s t h e s i s , r e p r e s e n t s work which c o n t a i n s c o n t r i b u t i o n s by the author. 13 CHAPTER I I SCATTERING FORMALISM 1. Density Matrix Formalism and S c a t t e r i n g Matrix In s c a t t e r i n g experiments i n v o l v i n g p o l a r i z a t i o n phenomena one u s u a l l y d e a l s with p a r t i c l e s whose s p i n s t a t e s a r e s h a r p l y d e f i n e d . C a l c u l a t i o n s must i n v o l v e some s o r t of averaging procedure and a method used e x t e n s i v e l y i n the past i s t o perform the c a l c u l a t i o n f o r each s p i n s t a t e and then average the r e s u l t s using weights which r e f l e c t the p r o b a b i l i t y t h a t the p a r t i c l e i s i n a p a r t i c u l a r i n i t i a l spin s t a t e . T h i s method, though l e a d i n g to the c o r r e c t r e s u l t s , n e c e s s a r i l y r e q u i r e s that a s p e c i f i c s t a t e r e p r e s e n t a t i o n be s e t up. A l o g i c a l l y more s a t i s f y i n g method (and one g e n e r a l l y e a s i e r from the s t a n d p o i n t of c a l c u l a t i o n ) i s t o employ the d e n s i t y matrix formalism. T h i s method c h a r a c t e r i z e s mixed s t a t e s i n terms of r e a l parameters which u s u a l l y have a d i r e c t r e l a t i o n s h i p to raeasureable p h y s i c a l q u a n t i t i e s and which i n v o l v e s t h e use o f o p e r a t o r s and thus does not appeal t o a p a r t i c u l a r s t a t e r e p r e s e n t a t i o n . For a review of the d e n s i t y matrix formalism see Fano (Fano, 1957). The a p p l i c a t i o n of the d e n s i t y matrix formalism t o nucleon-nucleon s c a t t e r i n q has been summarized i n a review a r t i c l e by H o s h i z a k i 14 (Hoshizaki, 1 968) . I f the p r o b a b i l i t y t h a t the system i s i n a s t a t e \ty > i s p ± , then the mean va l u e o f a measurement of a q u a n t i t y Q can be w r i t t e n as <Q> = I P 1 < Q > i » i where <Q> ± denotes the mean value of Q which would be o b t a i n e d i f the system were known to be c e r t a i n l y i n the s t a t e \..i>±>. The mean value <Q> i s given by <o>. = <ib. I Q U . > , 1 1 1 1 1 where the symbol Q on the r i g h t hand s i d e denotes the o p e r a t o r which corresponds to the observable q u a n t i t y Q. S u b s t i t u t i n g i n t o the expression f o r <Q>, <Q> = I P i <^ 1 lQl^ i > • i The s t a t e s \ ip^> can be expanded i n terms of an orthonormal set of b a s i s v e c t o r s | <J> > to gi v e i j k which upon rearrangement l e a d s t o 15 <Q> = II Q j kpk j , J k where Q j k = < * j l Q l * k > and The q u a n t i t i e s Q , and p are matrix elements of o p e r a t o r s j k k j with r e s p e c t t o the b a s i s v e c t o r s |<j^  >. P i s the " d e n s i t y m a t r i x " corresponding t o the " d e n s i t y operator" p = I I v v ^ i i The above e x p r e s s i o n f o r <Q> can be compactly expressed as <Q> = Tr(pQ) , where " T r " means "the t r a c e o f " . The s t a t i s t i c a l d i s t r i b u t i o n of the r e s u l t s of a measurement Q can be p r e d i c t e d using t h i s simple equation, given the s t a t i s t i c a l d i s t r i b u t i o n of the i n i t i a l s t a t e s . 16 The d e n s i t y operator P can be expanded i n terras o f a s e t of independent Hermitian o p e r a t o r s S v which are " o r t h o g o n a l " i n the sense t h a t T r ( s V ) = N6 uv where N i s a n o r m a l i z a t i o n constant (Fano, 1957).,, The d e n s i t y operator becomes v where a are c o n s t a n t s . I t f o l l o w s t h a t T r ( p S P ) = I a T r ( S V S y ) = Na = <SP> . v y The d e n s i t y o p e r a t o r may thus be w r i t t e n as —1 r V V P = N I <S >S { 1 ) v and may be evaluated by performing measurements of <S V>. In the s c a t t e r i n g of two p a r t i c l e s with s p i n the s t a t e o f the system before and a f t e r s c a t t e r i n g can be rep r e s e n t e d by column v e c t o r s x and f r e s p e c t i v e l y and which are r e l a t e d fey the equation 17 f = M X (2) The matrix H i s the "amplitude matrix" and i s r e l a t e d t o t h e p r o b a b i l i t y of t r a n s i t i o n from a p a r t i c u l a r i n i t i a l s t a t e to a p a r t i c u l a r f i n a l s t a t e . The d e n s i t y matrix r e p r e s e n t i n g t h e system a f t e r s c a t t e r i n g i s given by where f<k> i s the i t h element of the k t h column vector, S u b s t i t u t i n g the e x p r e s s i o n f o r f given by Eg. (2), f i i L L u i - k xm^n i n n ^ u u xm ni k i i A n J k m n J k m n = T J M. M +. (p .) u u xm ni x mn m n or p f = M P ±M + , * 3 ) where P± i s the d e n s i t y matrix r e p r e s e n t i n g the system be f o r e s c a t t e r i n g . I f the i n i t i a l s t a t e v e c t o r s are normalized so t h a t 18 then IrCP,) - I C P ^ - I I P k x f > x f > 4 - 1 • "| x tc The f i n a l s t a t e v e c t o r s are not normalized ( ^ f - f - ^ 1 ) i and T r ( P f ) = I , where I i s the d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n , a q u a n t i t y r e l a t e d t o the p r o b a b i l i t y of s c a t t e r i n g i n t o a given s o l i d a n gle. From Eq. (1) we have P. = if 1 I <sv>.sv l L x v S u b s t i t u t i n g i n t o Eq. (3) , p, = N"1 I <SV>.MSV . < a ) f L x A set of base matrices s u i t a b l e f o r d e s c r i b i n g N-N s c a t t e r i n g i s the set o f 16 t e n s o r products 19 "KD ,(2) a x l v 1<X> x ^<2> +(D ^ ( 2 ) a x a - H i ) -j U ) where CT are P a u l i s p i n m a t rices and 1 are u n i t m a t rices i n P a u l i s p i n space. The l a b e l 1 r e f e r s t o the s p i n space o f t h e i n c i d e n t p a r t i c l e and t h e l a b e l 2 r e f e r s t o the s p i n space of the t a r g e t . F o r t h i s case N=U. The average value o f the observable S y a f t e r s c a t t e r i n g i s given by <Sy>f = Tr(S y p f)/Tr (p f ) . S u b s t i t u t i n g the expre s s i o n f o r p f given by Eg. (4), KS y> f = i I <SV>.Tr(MSVM+Sy) , (5) v where I i s the d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n . The amplitude matrix M depends on p ± and p f , the i n g o i n g and outgoing momenta o f t h e p r o j e c t i l e i n the cent re-of-mass frame, and on the P a u l i s p i n o p e r a t o r s a * l ) and o ^ 2 > . Wolfenstein ( W o l f e n s t e i n , 1952) d e f i n e d t h r e e l i n e a r l y independent u n i t v e c t o r s 20 P = (p ±+P f)/ P ± + P f , N = P ± x P f / P ± x P f K = (vf4±)/\vf4±\ = N x P These v e c t o r s are shown i n F i g . 3. For the n o n - r e l a t i v i s t i c case these v e c t o r s have a convenient meaning in the l a b . frame; P i s i n the d i r e c t i o n of the s c a t t e r e d nucleon, (minus) K i s i n the d i r e c t i o n o f t h e r e c o i l nucleon and S i s i n the d i r e c t i o n p e r p e n d i c u l a r t o the plane of s c a t t e r i n g . Onder the assumption that the amplitude matrix M i s i n v a r i a n t under space r o t a t i o n s , space i n v e r s i o n , r o t a t i o n s i n i s o t o p i c s p i n space and time r e v e r s a l , H takes the gen e r a l form H . . + C ( ^ » , + ^ V ) + « < W M 1 ) 4 2 ) ) , (1) ( 2 ) (DX2) + h ( a p a p - a K a R ) where a, c, m, g and h are complex f u n c t i o n s of angle and energy ( c a l l e d the W o l f e n s t e i n amplitudes) and a** * denotes a ( t ) « N , e t c . For the case of s c a t t e r i n g of an u n p o l a r i z e d beam from an un p o l a r i z e d t a r g e t a l l the <sv> are zero except the u n i t o p erator and the e x p r e s s i o n f o r the u n p o l a r i z 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 becomes 21 F i g u r e 3. Orthogonal U n i t V e c t o r s K, P and N i n CM. Frame (Wolfenstein) 22 I <1> = 1 = \- Tr(MM +) . o f o 4 Assuming an u n p o l a r i z e d beam and t a r g e t , the p o l a r i z a t i o n o f e i t h e r p a r t i c l e a f t e r s c a t t e r i n g i s given by I <a ( ± )> = f Tr(MM +^ ( i )) . (6) o f 4 From charge independence i t f o l l o w s t h a t Tr(MM io^ 1' )) = T r ( M M + a ^ ) , so t h a t the p o l a r i z a t i o n s of the s c a t t e r e d and r e c o i l p a r t i c l e s a re egual. The v e c t o r <o<i)> f i s an a x i a l v e c t o r and the r i g h t hand s i d e of Eq. (6) i s a f u n c t i o n only of p and ~p . .. • The only a x i a l vector which can be formed from p\ and p\- i s p.* p , showing that the d i r e c t i o n o f the p o l a r i z a t i o n v e c t o r i s along N. The p o l a r i z a t i o n of e i t h e r p a r t i c l e a f t e r s c a t t e r i n g i s t h e r e f o r e < c J ( 1 ) > f = PN , where l + (i) I P = 7- Tr (MM a„ ') o 4 N 23 In the case o f s c a t t e r i n g o f a p o l a r i z e d beam from an u n p o l a r i z e d t a r g e t a l l <S v> i are ze r o except < a < » > > i ( a = 1,2,3) and the u n i t operator. The expression f o r the d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n becomes I = — {Tr(MM +) + < a ^ 1 ' ) > i « T r ( M o ^ 1 ' ) M + ) } . The terms on the r i g h t hand s i d e o f the above eguation a re s c a l a r s ; the t r a c e i n the second term must y i e l d an a x i a l v e c t o r , because < a V M ' > i s an a x i a l v e c t o r . By the same argument as used p r e v i o u s l y , t h e r e f o r e , the t r a c e i n the second term i s an a x i a l v e c t o r d i r e c t e d along N; thus I = I (1 + A<a^>.-N) , |7) o 1 * where I A = 7 TrCMa^ V ) . o 4 The parameter A i s c a l l e d t he " a n a l y z i n g power". I t f o l l o w s from time r e v e r s a l i n v a r i a n c e ( H o s h i z a k i , 1968) t h a t TrCMc^ yM ) = Tr(MM a ) , i m p l y i n g that the a n a l y z i n g power A i s equal t o the p o l a r i z a t i o n P. Eq. (7) i s t h e ba s i s f o r measurement of p o l a r i z a t i o n . As an example, i f the z - a x i s i s alonq the d i r e c t i o n of p o l a r i z a t i o n o f 24 the i n c i d e n t p a r t i c l e and i f s c a t t e r i n g occurs i n t h e x-y plane, then the number of p a r t i c l e s s c a t t e r e d l e f t N L and the number s c a t t e r e d r i g h t N R (see F i g . 4) are given by N = k ( l + A«j(lh.) Lt IN X N R = k ( l - A<a< 1 )> ±) , where k i s a constant. The r a t i o N T / L i s thus given by V N R ° (1 + A < a ^ 1 ) > 1 ) / ( 1 -A<a^ 1 )>.) . S o l v i n g f o r A<o^> , A < a U K l = ( N L " V / ( NL + V ~ £ • where e i s the "asymmetry". The p o l a r i z a t i o n o f the i n c i d e n t p a r t i c l e i s determined from a measurement o f t h e asymmetry e , together with a knowledge of the " a n a l y z i n g power" A.. The p o l a r i z a t i o n of the i n c i d e n t p a r t i c l e can a l s o be determined by measuring the asymmetry o f the r e c o i l p a r t i c l e , i n which case e i s r e p l a c e d by - e i n the above r e l a t i o n . H o s h i z a k i has in t r o d u c e d s e t s of orthonormal v e c t o r s i n the la b . frame { i l l u s t r a t e d i n F i g . 5) which are convenient f o r r e l a t i n g the above equation t o experiment: 25 Figure 4. R e l a t i o n s h i p Between P o l a r i z a t i o n Vectors and S c a t t e r i n g Asymmetry 26 F i g u r e 5. Orthogonal U n i t Vectors i n Lab. Frame (Hoshizaki) 27 P i ~ P i ' P i ! ' n = P i x P f / ] P i x P f 1 •» s. = nxp. P f = P j / I P j l , n (as above) , s f • =-nxp P V = P^/|P^| » n (as above) , s = nxp The s u p e r s c r i p t - L - r e f e r s t o the lab. frame and p., p f and p L are the momenta o f t h e i n c i d e n t , s c a t t e r e d and r e c o i l r p a r t i c l e s r e s p e c t i v e l y . These v e c t o r s are r e l a t e d t o the p r e v i o u s l y d e f i n e d centre-of-mass u n i t v e c t o r s N, P and K by p. = -Ksin^e + Pcos-^-0 x 2 2 1 " 1 s. = Kcos-^Q + Psin^6 x 2 2 p = P , s = K , p = - K , s = P and n = N , where e i s the centre-of-mass s c a t t e r i n g angle. The p o l a r i z a t i o n o f t h e r e c o i l p a r t i c l e i n terms o f these v e c t o r s i s K a ( 2 ) > = I {(P+D < a ( 1 ) > . ) n + (A <a ( 1 )>.+R < o ( 1 ) > . ) s f o v t n l' v t p. i t s . i ' r x x - (A'<a ( 1 )>.+R'<a ( 1 )>.)p } , (8) v t p. X t s. x'*x s X X where D , A , R , A* and R* are the p o l a r i z a t i o n t r a n s f e r t t t t t r parameters. T h i s e x p r e s s i o n f o l l o w s d i r e c t l y from Eg.(5); c r o s s terms drop out because s c a l a r and pseudoscalar terms cannot be mixed. The n o n - r e l a t i v i s t i c e x p r e s s i o n s f o r these parameters i n 28 terms'of •the-Wolfenstein amplitudes are (Hos h i z a k i , 1968) I = |a| 2+|m| 2+2|c| 2+2|g| 2+2|h| 2 I P = 2Re{(a+m)c*} o I (1-D ) = Ia-mI 2+4Ih I 2 o t i i i i * 9 * * . 9 I Q R t = - 4 R e ( i c g )cosr^ + 2Re{(a+m)g +(a-m)h } s i n — * 9 * *, 9 l Q A t = 4 R e ( i c g ) s i n 2 " + 2Re{(a+m)g +(a-m)h j c o s y * 9 * 9 I Q R ^ = 2Re{(a+m)g -(a-m)h J-cosy + 4 R e ( i c g J s i n ^ -^ A Q ic 0 I Q A ^ = -2Re{(a+m)g -(a-m)h }s±n^ + 4 R e ( i c g )cos-^ 2. P a r t i a l Wave Decomposition of S c a t t e r i n g Matrix I t i s not convenient to work with the Wolfenstein amplitudes d i r e c t l y , s i n c e they i n v o l v e 5 independent complex f u n c t i o n s of angle and energy. The lack of a s a t i s f a c t o r y t heory of N-N s c a t t e r i n g makes these 5 f u n c t i o n s e s s e n t i a l l y unknown. The problem of d e s c r i b i n g the N-N i n t e r a c t i o n i s eased somewhat by expanding the amplitudes i n terms o f angular momentum wave f u n c t i o n s , the c o e f f i c i e n t s o f which g i v e the s c a t t e r i n g i n f o r m a t i o n i n the form of phase s h i f t s . T h i s procedure o f f e r s t h e s e a d d i t i o n a l advantages: 1. The u n i t a r i t y of the amplitude matrix can be e a s i l y 29 i n t r o d u c e d t o a l l o r d e r s i n the expansion. 2. The high angular, momentum s t a t e s , which have l i t t l e e f f e c t on the s c a t t e r i n g , can be neglected t o g i v e a f i n i t e number o f terms i n the expansion. The r e l a t i o n s h i p between the amplitude matrix M and the s c a t t e r i n g matrix S f o r the case of e l a s t i c s c a t t e r i n g of 2 p a r t i c l e s i s giv e n i n t e x t s d e a l i n g with s c a t t e r i n g theory (see, for example, T a y l o r , 197 2) as <pV|S - l|pV = i(2TTm)~ 16(E p,-E p)M ? , ? ( p ' , p ) , where . g and £• l a b e l the s p i n s t a t e s , p and p* are the centre-of-mass momenta before and a f t e r s c a t t e r i n g , m i s the reduced mass of the 2 - p a r t i c l e system and E p and E p I are the i n i t i a l and f i n a l e n e r g i e s . The d e l t a f u n c t i o n ensures t h a t energy i s conserved i n t h e s c a t t e r i n g . In the development t h a t f o l l o w s , i t w i l l be convenient t o use the ei g e n v a l u e s o f t o t a l s p i n s, ms to l a b e l the s p i n components of the 2 - p a r t i c l e s t a t e ; t h e r e f o r e <p's'm'iRlpsm > = i ( 2 T T m ) - 1 6 ( E ,-E )M , , , r s' ' s p p s m : sm s s where R = S-1. Expanding the l e f t hand s i d e i n terms of o r b i t a l angular momentum e i g e n s t a t e s lElm p>, 30 The t r a n s f o r m a t i o n from t h e momentum r e p r e s e n t a t i o n to the angular momentum r e p r e s e n t a t i o n i s ( T a y l o r , 197 2 ) ->i 1 - M £ * <p E£m > = . 6 (E - E ) Y (p) , 1 £ i — p % /mp m £ where p i s the u n i t v e c t o r i n the d i r e c t i o n o f p and Y £ are s p h e r i c a l harmonics. S u b s t i t u t i n g i n t o the above equation. £ m £ £ <\ x<E , £ ' m ' s ' m ' R E £m„sm >Y„ (p) p ' £ s ' 1 p £ s £ The H-matrix may be expressed i n terms of the e i q e n s t a t e s of the t o t a l anqular momentum J=iT+l5 by u s i n q the t r a n s f o r m a t i o n j |E £m sm > = £ £ C(£m sm |jm)|E £sjm> , p J 6 S , r\ . X / S p 3=0 m=-j where C(lm sm fjm) are t h e Clebsch-Gordan c o e f f i c i e n t s and £ s m=m^+ms. S u b s t i t u t i n q i n t o the e x p r e s s i o n f o r t h e B-matrix, 31 <?W|R|Jsm > --fzzl I H I I I I Y ' ( P ' ) C ( £ ' m ' s ' m ; | j ' m ' ) vpp £ m £ m j m j m x<E ,£'s'j'm'|R|E £sjm>C(£m sm |jm)Y (p) P p S At The o p e r a t o r s S and R commute with J 2 and the Hamiltonian, so t h a t the R-matrix has the form < E , £ ' s ' j ' m ' I R I E £sjm> = 5 ( E , - E ) 6 . . , 6 , , „ p J P P P 33 mm' £'s';£s ' where R ~ | , , i s independent o f m and m* because of r o t a t i o n a l i n v a r i a n c e . S u b s t i t u t i n g i n t o the above e q u a t i o n . <p's'm'|R|psm > = (mp) <5(E ,-E ) I I H H Y ,(p')Y (p) r £ m„ £ m. j m £ £ x C (£ 'm|s'm'g | jm) C ( £ m £ s m s I J m ) R j , g , . £ g The amplitude matrix M i s thus given by M s ' m ; ; S m s = 2 , ( i p ) - 1 I I H H Y r ( p ' ) Y / ( P) £' m' £ m„ i m £ £ J xC (£ 'm^s 'm' | jm)C ( £ m £ s m s | jm)R^ , g , . £s The matrix H has 16 elements corre s p o n d i n g t o the t r a n s i t i o n s between the p o s s i b l e i n i t i a l and f i n a l s p i n s t a t e s . 32 The elements corresponding t o t r a n s i t i o n s between s i n g l e t and t r i p l e t s p i n s t a t e s are zero i f one assumes c o n s e r v a t i o n o f t o t a l angular momentum, p a r i t y and exchange symmetry. ; For example, i f s c a t t e r i n g occurs from a s i n g l e t s t a t e ( t o t a l s p i n s», o r b i t a l angular momentum 1») to a t r i p l e t s t a t e ( t o t a l s p i n s, o r b i t a l angular momentum 1), then the t o t a l angular momentum i s 1* f o r the s i n g l e t s t a t e and i s one of 1-1,1,1+1 f o r the t r i p l e t s t a t e . I f p a r i t y i s t o be conserved, then 1=1*. A c o n t r a d i c t i o n i s e v i d e n t a t t h i s p o i n t i n t h e case o f p-p s c a t t e r i n g , because the exchange symmetry f o r t h e product o f the s p i n s t a t e and s p a t i a l wave f u n c t i o n i s not conserved. A c o n t r a d i c t i o n occurs a l s o f o r n-p s c a t t e r i n g i f one assumes charge independence, because the exchange symmetry f o r the product o f the i s o t o p i c s p i n s t a t e , o r d i n a r y s p i n s t a t e and s p a t i a l wave f u n c t i o n i s again not conserved., For a given t o t a l angular momentum j , t h e r e f o r e , the o n l y non-zero elements of R are those which correspond t o the f o l l o w i n g t r a n s i t i o n s : R_. : 1 '=j < > l = j s p i n 0 R. . ! l ' = j < > l = j s p i n 1 3 > J R. x 1 . : l'=j±l < > l = j ± 1 s p i n 1 R J : l'=j±l < > 1=3+1 s p i n 1 T r a n s i t i o n s such as l»=j+1 < > l=j are forbidden because they v i o l a t e c o n s e r v a t i o n of p a r i t y . The amplitudes f o r the l a s t two t r a n s i t i o n s are egual because of time r e v e r s a l i n v a r i a n c e . The 5 non-zero elements of M are r e l a t e d t o the Wolfenstein amplitudes as f o l l o w s (Stapp, 1955): 3 = i ( 2 M l l + M00 + M 8 8 ) c = i / 2 ( M 1 ( ) - M Q 1) 8 = X i " M l - 1 " M00 } h = | ( c o s e ) ~ 1 ( M 1 1 - M 1_ 1 - M Q 0) m = — (-2M + M - M ) m 4^  1-1 00 ss ; The s u b s c r i p t s r e f e r t o the s p i n components along the q u a n t i z a t i o n a x i s and " s s " i s the s i n g l e t - s i n g l e t t r a n s i t i o n . The 6 amplitudes l i s t e d are r e l a t e d by / 2 ( M 1 0 + M 0 1 ) = tane(M n - - M^) The previous d i s c u s s i o n has shown t h a t the elements of M can be expanded as an i n f i n i t e s e r i e s , each term of which corresponds t o t o t a l angular momentum j (the " p a r t i a l wave expansion").; Under the r e p r e s e n t a t i o n chosen ( i . e . The t o t a l angular momentum re p r e s e n t a t i o n ) the R-matrix decomposes i n t o 2 1X1 matrices R^  and and i n t o a symmetric 2X2 matrix R RJ R U n i t a r i t y o f the S-matrix i m p l i e s t h a t 34 216, R. = e 2 - 1 216. R. . = e J J - 1 Any symmetric, u n i t a r y 2X2 matrix can be w r i t t e n i n the form 16_ e 0 16. + cos2e i s l n 2 e l s i n 2 e cos2e i 6 _ e 0 16 + where 5_ , 6 + and e are t h e "bar phase s h i f t s " d e f i n e d by Stapp (Stapp, 1955)., C a r r y i n g through the m u l t i p l i c a t i o n s , one o b t a i n s 1 ( 6 . . , . + 6. . .) R J = i s i n 2 l . e 216 R.., . = cos2e. e J ±1,3 J j±l,j 3 5 CHAPTER I I I APPARATUS AN 0 TECHNIQUES A beans of p o l a r i z e d H- io n s with an i n t e n s i t y of 3 0 0 na, was produced by the p o l a r i z e d i o n source, i n j e c t e d i n t o t h e TRIUMF c y c l o t r o n and a c c e l e r a t e d t o e n e r g i e s up t o a maximum of 5 2 0 MeV. The o p e r a t i o n o f the p o l a r i z e d i o n source (POLISIS) i s dep i c t e d s c h e m a t i c a l l y i n F i g . 6 . The source e x p l o i t s the Lamb s h i f t i n hydrogen (the s m a l l s h i f t i n energy between the 2 s x and 2p, l e v e l s ) to s e l e c t h y p e r f i n e s t a t e s o f d e f i n i t e n u c l e a r p o l a r i z a t i o n . A beam of 5 0 0 eV protons produced by a Duo-plasmotron i o n source i s n e u t r a l i z e d by e l e c t r o n t r a n s f e r i n cesium vapour. N e u t r a l atoms i n the 2 s s t a t e are metastable, with the dominant decay mode being a t r a n s i t i o n to the ground s t a t e v i a two-photon emission with a mean l i f e t i m e o f 1/7 seconds. The s t a t e s are s e l e c t e d by t h e a p p l i c a t i o n of magnetic and e l e c t r i c f i e l d s i n the s p i n - f i l t e r r e gion. The e n e r g y - l e v e l diagrams f o r the 2s. and 2p, s t a t e s o f hydrogen i n a magnetic f i e l d are shown i n F i g . 7 . , At a magnetic f i e l d of 5 7 5 Gauss t h e 2 s , l e v e l s l a b e l l e d 3 and 4 become degenerate with the 2px l e v e l s . The a p p l i c a t i o n of a sm a l l t r a n s v e r s e e l e c t r i c f i e l d induces e l e c t r i c d i p o l e t r a n s i t i o n s from the 2 P i s t a t e to ground s t a t e , so t h a t s t a t e s 3 and 4 are guenched. As shown i n Tab l e I , i n a r e g i o n of low magnetic f i e l d 36 P o l . I o n H + C e s i u m C h a r g e E x c h a n g e H(2S) S p i n H Q S ) S e l e c t i v e S o u r c e H(1S) F i l t e r H A S ) I o n i z e r F i g u r e 6. Schematic of P o l a r i z e d Ion Source (POLISIS) 37 T 1 r 1 1 r I i i i i i 1 — 0 200 400 600 MAGNETIC FIELD (Gauss) Figure 7, E n e r g y - l e v e l Diagram of 2S^ and 2P^ S t a t e s of Hydrogen i n a Magnetic F i e l d 2 38 T a b l e I. 2S Hyperfine S t a t e s of Hydrogen i n a Magnetic F i e l d 1 — — - r — •• -" • -1 Hyperfine S t a t e J Proton P o l a r i z a t i o n | i T r ~ i (|++>=f+> , |+> , etc.) 1 el p , zero |high *ve \high -ve f f i e l d j f i e l d | f i e l d ) It.. |+ +> 1 1 1 1 1 -1 I |2. A ( l + 6 ) | + - > + A(i-<$)|-+> t 0 | -1 1 1 I 13. 1- -> 1 -1 I - 1 I 1 I -Ad-fi) |+-> + A d + 6 ) | - + > 1 0 1 1 i -1 I 4 , , „_ i.. . ...X ... . ,„. .,i , ,. i .6 = x-//I+x2 ; X = B/.B (B = 63.4 g a u s s ) 39 s t r e n g t h the remaining two s t a t e s , c o n s i s t i n g of s t a t e 1 with 100$ nuclear p o l a r i z a t i o n and s t a t e 2 with z e r o p o l a r i z a t i o n produce a r e s u l t a n t beam of 50$ p o l a r i z a t i o n . P o l a r i z a t i o n can be i n c r e a s e d by a p p l y i n g a procedure suggested by Sona whereby the remaining atoms i n s t a t e s 1 and 2 are passed through a region where the magnetic f i e l d i s re v e r s e d (Sona, 1967). I f the time taken to r e v e r s e the f i e l d i s s h o r t compared to the p r e c e s s i o n time the d i r e c t i o n of pr e c e s s i o n does not change and s t a t e s 1 and 2 become s t a t e s 1* and 2* r e s p e c t i v e l y ( F i g . .8). In the h i g h - f i e l d l i m i t both s t a t e s 1" and 2* have 100$ nuclear p o l a r i z a t i o n , r e s u l t i n g i n a beam of 100$ p o l a r i z a t i o n . The f i n a l s tep i n the process i s t o s e l e c t i v e l y i o n i z e the n e u t r a l 2s atoms by e l e c t r o n t r a n s f e r i n argon i n a r e g i o n o f high magnetic f i e l d . T h i s r e a c t i o n has the d e s i r a b l e f e a t u r e of p r e f e r e n t i a l l y i o n i z i n g the 2s atoms over the ground s t a t e atoms (which are much more p l e n t i f u l ) . The beam of p o l a r i z e d H~ i o n s i s i n j e c t e d i n t o the c e n t r e of the TRIOMF c y c l o t r o n where i t i s a c c e l e r a t e d t o e n e r g i e s approaching 520 MeV. The TRIUMF c y c l o t r o n i s an isochronous s e c t o r - f o c u s s i n g a c c e l e r a t o r ; i . e . the s y n c h r o n i z a t i o n of the R-F a c c e l e r a t i n g v o l t a g e : with the p a r t i c l e p o s i t i o n at the a c c e l e r a t i n g "dee's" i s achieved by shaping the s t a t i c magnetic f i e l d r a t h e r than changing the R-F.. frequency. T h i s s y n c h r o n i z a t i o n i s necessary because o f r e l a t i v i s t i c e f f e c t s . The c y c l o t r o n r a d i u s i s 7.92 m. and the maximum s t a t i c magnetic f i e l d i s 5.2 k i l o g a u s s . The a c c e l e r a t e d beam i s e x t r a c t e d at the outer edqe of the c y c l o t r o n by p l a c i n g a f o i l i n the beam Sona F i g u r e 8. E n e r g y - l e v e l Diagram I l l u s t r a t i n g Z e r o - c r o s s i n g Hethod of O b t a i n i n g 100$ P o l a r i z a t i o n 41 path at a r a d i a l p o s i t i o n c o r r e s p o n d i n g t o the d e s i r e d energy, thereby a l l o w i n g the energy of the beam to be c o n t i n u o u s l y v a r i e d . The e l e c t r o n s are s t r i p p e d from the H~ i o n s and the r e s u l t i n g protons, having o p p o s i t e charge, are d e f l e c t e d away from the c e n t r e of the c y c l o t r o n by the f i e l d of the main c y c l o t r o n magnet and are e x t r a c t e d . The experimental c o n f i g u r a t i o n used i n the measurement o f neutron p o l a r i z a t i o n vs. angle i s shown i n F i g . 9. The beam p o l a r i z a t i o n was monitored by a p o l a r i m e t e r which uses a .05 mm.-thick p o l y e t h y l e n e t a r g e t (CH 2) as p o l a r i z a t i o n a n a l y z e r . Two counter t e l e s c o p e s c o n s i s t i n g o f a p a i r o f 1.5 mm.-thick p l a s t i c s c i n t i l l a t o r s subtending a s o l i d angle o f 12 mster. were set up to detec t protons e l a s t i c a l l y s c a t t e r e d from hydrogen t o the l e f t and to the r i g h t a t 26° i n the l a b . , An a d d i t i o n a l p a i r of counter t e l e s c o p e s was s e t up to d e t e c t the r e c o i l protons from p-p s c a t t e r i n g and thus e l i m i n a t e events i n which protons s c a t t e r e d e l a s t i c a l l y from the carbon i n the t a r g e t . The counting r a t e i n the s c i n t i l l a t o r s n e arest the t a r g e t was 1.5X10 6 s e c - 1 f o r a beam i n t e n s i t y of 10 na. P o l y e t h y l e n e was p r e f e r r e d as a t a r g e t because i t has a high c o n c e n t r a t i o n of hydrogen. The a n a l y z i n g power of the p o l a r i m e t e r was c a l c u l a t e d from p-p phase s h i f t s f o r hydrogen (Axen, 1977) and was c o r r e c t e d f o r the presence of carbon by d i v i d i n g by the carbon c o r r e c t i o n f a c t o r f . The carbon c o r r e c t i o n f a c t o r f was obtained by comparing the s c a t t e r i n g r a t e s using p o l y e t h y l e n e and pure carbon t a r g e t s . The a n a l y z i n g power of hydrogen, the carbon c o r r e c t i o n f a c t o r f and the e f f e c t i v e a n a l y z i n g power f o r polyethylene are l i s t e d i n Table I I . Measurements o f the 42 P o l a r i z e d P r o t o n s F i g u r e 9. Apparatus f o r Experiment #1: Neutron P o l a r i z a t i o n v s . Angle 43 Table I I . Analyzing Power of Proton Beam P o l a r i z a t i o n Monitor t •"- " r | Beam| | Energy | 1 (MeV) | Analyzi n g Pow er (By drogen) | Carbon | C o r r e c t i o n | F a c t o r f 1 - 1 | Analyzing | I Power | I(Po l y t h e n e ) | { 237 | . 290 |1.0 27±.002 I .282 \ I 343 | .327 I1.050±.002 1 .311 | 1 445 J .351 J1.0 56±.00 2 1 .332 | | 516 | 1 - L . .368 |1.056±.004 - i . : I .348 f - i J 44 v a r i a t i o n of the monitor asymmetry with beam i n t e n s i t y and s t u d i e s of the long-term s t a b i l i t y of the monitor i n d i c a t e d t h a t the s c a t t e r i n g asymmetry c o u l d be determined to w i t h i n ±.005 i f the d u r a t i o n of data t a k i n g p e r i o d s ' i s l i m i t e d t o 2 h r s . P e r i o d i c checks f o r d r i f t i n the beam p o s i t i o n were made by observing the asymmetry obtained with u n p o l a r i z e d beam. The proton beam emerged from the c y c l o t r o n with the p o l a r i z a t i o n v e c t o r d i r e c t e d v e r t i c a l l y . An e a r l y phase s h i f t p r e d i c t i o n by Fclkmann and Heasday (Folkmann and Measday, 1968) i n d i c a t e d t h a t R t was the l a r g e s t of the p o l a r i z a t i o n parameters i n f r e e n-p s c a t t e r i n g . A superconducting s o l e n o i d manufactured at Butherford Laboratory (Gallagher-Daggit, 1974) was used to r o t a t e the p o l a r i z a t i o n v e c t o r of the i n c i d e n t proton beam about the beam a x i s i n t o the plane of s c a t t e r i n g and thus take advantage of the l a r g e p o l a r i z a t i o n t r a n s f e r that occurs f o r t h i s s p i n c o n f i g u r a t i o n . The s o l e n o i d i s composed o f 23,000 t u r n s of C361/100 and C241/100 niobium-titanium superconducting m a t e r i a l * wound t o form a c o i l of diameter 14 cm. ( c o l d bore) and length 1 m. The c o i l was kept i n thermal c o n t a c t with a r e s e r v o i r of l i g u i d helium of 60 1. c a p a c i t y . A s h i e l d of l i q u i d n i t r o g e n minimized l e a k s due t o thermal r a d i a t i o n . The magnetic f i e l d and jndl vs. e x c i t a t i o n c u r r e n t were c a l c u l a t e d from the geometry of the s o l e n o i d and the p r e c e s s i o n r a t e of the p o l a r i z a t i o n v e c t o r was c a l c u l a t e d u s i n g t h e r e l a t i v i s t i c 1 IMI L t d . , Birmingham, D.K formulas (Bargmann, 1959) 45 a) b) 2 \ = ( f - 1 ) Y . L where eH UL. = — L Y m Y = ( 1 - v2 ) " The g u a n t i t i e s g, e, m and v are the gyromagnetic r a t i o , charge, mass and v e l o c i t y of the p a r t i c l e and H i s the magnetic f i e l d . The equations are expressed using the Gaussian system of u n i t s with c-1. Formula (a) g i v e s the pr e c e s s i o n r a t e of the t r a n s v e r s e component of p o l a r i z a t i o n i n a s o l e n o i d a l magnetic f i e l d and formula (b) g i v e s the p r e c e s s i o n r a t e of the l o n g i t u d i n a l component i n the presence o f a d i p o l e f i e l d . Computations of the magnetic f i e l d generated by the s o l e n o i d were done at the B u t h e r f o r d Laboratory; the computations show t h a t a magnetic f i e l d of 6 T i s generated with an e x c i t a t i o n c u r r e n t o f 212 amps (G a l l a g h e r - D a q g i t , 1974). The LD 2/LH 2 t a r g e t assembly was designed f o r use i n proton beams having i n t e n s i t i e s of 10 ua at 150 MeV, assuming t h a t a cryogenerator o f adequate c a p a c i t y i s a v a i l a b l e {Hodges,1S73). The t a r g e t v e s s e l was a c y l i n d e r of l e n g t h 20 cm. and diameter 5 cm.; i t was p o s i t i o n e d with the c y l i n d e r a x i s p a r a l l e l t o the beam a x i s . The t a r g e t w a l l s and end windows were made of .25 mm, and .05 mm. t h i c k n e s s e s of AISI s t a i n l e s s s t e e l r e s p e c t i v e l y . Another t a r g e t v e s s e l i d e n t i c a l t o the f i r s t but 46 c o n t a i n i n g no l i g u i d was mounted above the f i r s t v e s s e l and e i t h e r t a r g e t v e s s e l c o u l d be i n s e r t e d i n t o or removed from the beam by a c t i v a t i n g an e l e c t r i c motor connected to the assembly. The purpose of t h e second t a r g e t was to si m u l a t e t a r g e t empty c o n d i t i o n s and thus dispense with the time-consuming t a r g e t emptying procedure. The 4AB2 bending magnet s i t u a t e d immediately downstream of the LB 2 t a r g e t was used t o e l i m i n a t e charged p a r t i c l e s from the neutron beam. P r e c e s s i o n of the neutron s p i n i n the f i e l d of the 4AB2 magnet d i d not occur i n the D t measurements because the neutron p o l a r i z a t i o n v e c t o r was v e r t i c a l . P r e c e s s i o n d i d occur, however, i n t h e measurement of R t as a f u n c t i o n of energy a t 9°. The angle o f p r e c e s s i o n ( t y p i c a l l y about 25°) was c a l c u l a t e d using data from magnetic f i e l d surveys of the 4AB2 magnet. In the experiment t o measure R t as a f u n c t i o n of a n g l e the charged p a r t i c l e contamination i n the neutron beam was found t o be <2%, so t h a t f o r t h i s s e r i e s o f measurements the 4AB2 magnet was turned o f f . An a r r a y of c o l l i m a t o r s arranged a t 3° i n t e r v a l s i n the range -3° to 27° r e l a t i v e to t h e proton beam d i r e c t i o n was used to d e f i n e the neutron beam. A c o l l i m a t o r port was d e f i n e d by two s e c t i o n s o f s t e e l pipe of diameters 10.2 cm. and 12.7 cm. welded together a t the ends and having a t o t a l l e n g t h o f 3.3 m. The array of s t e e l pipes was welded t o a s t e e l frame and the e n t i r e s t r u c t u r e was f i l l e d with l e a d . The unused p o r t s were f i l l e d with removable 30.5 cm.-long s t e e l plugs. D i p o l e s #1 and #2 (obtained from UCLA and the B u t h e r f o r d HI Laboratory) s u p p l i e d v e r t i c a l and h o r i z o n t a l magnetic f i e l d s f o r p r e c e s s i n g the neutron p o l a r i z a t i o n v e c t o r to the d e s i r e d d i r e c t i o n . P r e c e s s i o n angles as a f u n c t i o n of e x c i t a t i o n c u r r e n t were c a l c u l a t e d using the r e s u l t s of magnetic f i e l d mappings summarized i n Tab l e s I I I and IV. The l i q u i d hydrogen t a r g e t was i n s t a l l e d a t the 9° neutron beam l i n e a f t e r the completion o f the neutron p o l a r i z a t i o n measurements i n d i c a t e d that the p o l a r i z a t i o n was a maximum near t h i s angle. The t a r g e t v e s s e l was made of 0.36 mm. Mylar with 20 l a y e r s o f 6 micron a l u m i n i z e d Mylar wrapped around i t t o reduce heat l o s s by r a d i a t i o n . When f i l l e d the t a r g e t presented a t h i c k n e s s o f 50 cm. The t a r g e t was surrounded by a vacuum jac k e t made from 1.14 mm. aluminum. The carbon p o l a r i m e t e r c o n s i s t e d of a 6 cm. t h i c k carbon t a r g e t , 6 multiwire p r o p o r t i o n a l chambers (MWPC*s) of a c t i v e area 0.5 m. X 0.5 m. upstream of the t a r g e t and 6 MWPC's of area 1 m. X 1 m. downstream. , Each MWPC c o n s i s t e d of two planes o f wires with a high v o l t a g e impressed upon them (about 6KV) surrounding a plane o f sense wires spaced 2 mm. apart. These planes of wires were mounted on a frame and enclosed i n a gas chamber with 0.12 mm. Melinex windows ( B o u c l i e r , 1970; Charpak, 1972). The chambers were operated with a mixture o f 56% argon, 46% isobutane, 41 methylal and 0.4% f r e o n . Two adjacent wires were e l e c t r i c a l l y connected t o g i v e an e f f e c t i v e r e s o l u t i o n o f 4 mm. The carbon t a r g e t , 12 MWPC's and p l a s t i c s c i n t i l l a t o r c ounters S1, S2, S3 and S4 were a l l mounted on a s t e e l frame which was i n turn mounted on c a s t o r s which enabled the 48 Table I I I . Magnetic F i e l d Survey of D i p o l e #1 (OCLA) r T 1— - T — -1 E x c i t a t i o n f Potentiometer I B at Centre | / B d l Current j S e t t i n g | of Magnet J (kG-m) (Amperes) I 1 (KG) | •- i j ! r i ' • 500 | 170 } 4.89 J 6.69 1000 1 340 1 9.76 | 13.30 1500 I 510 I 14.24 | 19.11 2000 I 672 I 17.24 | 22.73 2500 I 822 I 19.17 | 24.98 i „, X _ .. _x _._ _ _ x . i 49 Table IV. Magnetic F i e l d Survey o f D i p o l e #2 (PLA) r - T E x c i t a t i o n 1 B at Centre J / B d l Current 1 o f Magnet | (kG-m) (Aiperes) 1 (kG) | L 1 _ r T 50 I 1. 69 | 2.91 100 1 3.18 | 5.49 150 1 4. 67 | 8.04 200 J 6.19 | 10.67 250 1 7.67 j 13,20 300 ! 9.06 | 15.57 350 I 10.37 | 17.79 400 i 11.60 | 19.81 450 1 12.61 | 21. 40 492 ! 13. 35 | 22.55 l — J ~ _ _ —j r 50 po l a r i m e t e r to be e a s i l y moved t o v a r i o u s angles. Data a c q u i s i t i o n was c o n t r o l l e d by a PDP-11/20* computer i n t e r f a c e d v i a CAMAC modules t o the MWPC readout system, NIM l o q i c modules, M i n i a t u r e L o g i c System (MLS) modules (Milborrow) and o n - l i n e d i s p l a y u n i t s . Data accumulated during a run was t r a n s f e r r e d to magnetic tape e i t h e r on an event-by-event b a s i s f o r multi-parameter experiments or a f t e r the t e r m i n a t i o n o f a run i n the form o f histograms. A schematic diagram of the experimental l o g i c used f o r the neutron p o l a r i z a t i o n measurements i s shown i n F i g s . 10 and 11. Data a n a l y s i s of the multi-parameter type of experiments (neutron p o l a r i z a t i o n vs. angle and neutron p o l a r i z a t i o n vs. energy) was done o f f - l i n e on the IBM-370 computer s i t u a t e d at the U n i v e r s i t y o f B r i t i s h Columbia campus u s i n q s u b r o u t i n e s which generated p a r t i c l e t r a c k s from the MWPC data and which accumulated and d i s p l a y e d histograms and s c a t t e r p l o t s . B i a s i n the asymmetry a r i s i n g from the n o n - s p h e r i c a l geometry of the carbon p o l a r i m e t e r was e l i m i n a t e d by ensuring t h a t a l l p o i n t s l y i n g w i t h i n the cone formed by r o t a t i n g the t r a j e c t o r y o f the r e c o i l proton i n t e r c e p t e d t h e carbon t a r g e t . . 1 D i q i t a l Equipment C o r p o r a t i o n , Maynard, Massachusetts, U.S.A. F i g u r e 10. Carbon P o l a r i m e t e r L o g i c CHAPTEE I EXPERIMENTS, RESULTS AND DISCUSSION 1. JxjDeriment JM.: A Measurement c f Neutron Beam P o l a r i z a t i o n y s y .-Angle The experimental c o n f i g u r a t i o n i s s c h e m a t i c a l l y d e p i c t e d i n F i g . 9. The d e t e c t i o n of a neutron i n the carbon p o l a r i m e t e r was i n d i c a t e d by a V1«S 1«S2»S3»S4 c o i n c i d e n c e ; the c o i n c i d e n c e i n t u r n s i g n a l l e d the computer t o i n i t i a t e readout of MHPC and CAMAC data. Upon completion of the readout sequence the data was screened to e l i m i n a t e events i n which the angle of the proton t r a c k i n the r e a r chambers was l e s s than 1° with r e s p e c t to the c e n t r e l i n e of the p o l a r i m e t e r . The screened data was s t o r e d i n a b u f f e r area of the computer memory and was t r a n s f e r r e d to magnetic tape whenever the b u f f e r became f u l l . The 4AB2 magnet was used to sweep away charged p a r t i c l e s d u r i n g runs i n which D t was measured, but was turned o f f during the B t runs to avoid the c o m p l i c a t i o n of p r e c e s s i o n of the h o r i z o n t a l component of the neutron p o l a r i z a t i o n v e c t o r (the neutron p o l a r i z a t i o n v e c t o r had no h o r i z o n t a l component i n the D t r u n s ) . Table V g i v e s a summary of the angles and e n e r g i e s f o r which data was taken. 54 Tab l e V. Summary of Angles and Energies at Which Data were Taken (Experiment #1) 55 Alignment o f the carbon p o l a r i m e t e r was not necessary dur i n g the s e r i e s of moves from angle t o angle, s i n c e i t was p o s s i b l e i n the o f f - l i n e a n a l y s i s o f t h e data t o c o r r e c t f o r misalignment by using proton d a t a . 99% of the protons passed through the carbon t a r g e t without s c a t t e r i n g and thus by using the t r a c k i n f o r m a t i o n from the wire chambers before and a f t e r the carbon t a r g e t an estimate o f the slope of the i n c i d e n t proton beam was obtained. I t was assumed t h a t the i n c i d e n t neutrons had the same average s l o p e as the protons, and the s c a t t e r i n g angles were c a l c u l a t e d a c c o r d i n g l y . A n a l y s i s of the proton data showed a s t r o n g c o r r e l a t i o n between the h o r i z o n t a l s l o p e of the proton t r a c k s and the h o r i z o n t a l i n t e r c e p t o f the t r a c k s with the carbon t a r g e t ( F i g . 12), i n d i c a t i n g d i s p e r s i o n of the beam i n the h o r i z o n t a l plane. No such r e l a t i o n s h i p was evident between the v e r t i c a l slope and h o r i z o n t a l i n t e r c e p t ( F i g . 13). D i s p e r s i o n was a l s o observed i n the v e r t i c a l plane t o a l e s s e r e x t e n t . A s t r a i g h t l i n e was f i t t e d to the s l o p e - i n t e r c e p t data; the r e s u l t s were used t o parametrize the i n c i d e n t neutron slope as a f u n c t i o n of t a r g e t i n t e r c e p t . A n a l y s i s of the proton data a l s o y i e l d e d s m a l l c o r r e c t i o n s f o r r e l a t i v e misalignments of the wire chambers r e l a t i v e t o the main frame of the carbon p o l a r i m e t e r . From the r e c o i l proton t r a c k s seen i n the rear wire chambers and the neutron t r a c k s o b t a i n e d from proton data i t was p o s s i b l e t o c a l c u l a t e the a x i a l and azimuthal s c a t t e r i n g angles e and <j> f o r each event. The azimuthal s c a t t e r i n g angle <i> determined whether the s c a t t e r i n g occurred i n the "up", "down", 56 -.125 O. .125 Horizontal Slope F i g u r e 12. H o r i z o n t a l Slope o f S c a t t e r e d Proton Beam vs. H o r i z o n t a l I n t e r c e p t 57 F i g u r e 13. V e r t i c a l Slope of S c a t t e r e d Proton Beam vs. H o r i z o n t a l I n t e r c e p t 58 " l e f t " or " r i g h t " d i r e c t i o n . A " l e f t " s c a t t e r i n g was taken by convention t o mean the d i r e c t i o n of s c a t t e r i n g when l o o k i n g downstream towards the t a r g e t . In order t o determine the e f f e c t of background r e s u l t i n g from r e a c t i o n s i n the LD^ t a r g e t f l a s k , the t a r g e t f l a s k f i l l e d with l i q u i d deuterium was r e p l a c e d by a empty t a r g e t f l a s k f o r each anqle and enerqy. a. Data A n a l y s i s (i) R measurements: t The i n c i d e n t proton p o l a r i z a t i o n v e c t o r was a l i g n e d i n the d i r e c t i o n of s. ( F i g . 5) . From equations (7) and (8) 1 = 1 , <a^> = P and <a ( 2 )> - R <a ( 1 )>. . ( 9 ) o ' n f s f t s . x The r e l a t i o n between < o ^ > and the up-down asymmetry s f r e XS UD 7 e n n = " A < o ( 2 ) > f ' < 1 0 ) 2 UD nc s f r where A n c i s the a n a l y z i n g power f o r the r e a c t i o n 1 2C(n,p)X. The f a c t o r TT/2 a r i s e s from the averaging of 59 cos from 0 to I T . S u b s t i t u t i n g Eg. (9 ) i n t o Eg. ( 1 0 ) : ^ e T T =R<°[1)>. , (11) 2 A "UD ~ t s. x ' nc x In order t o account f o r the i n s t r u m e n t a l asymmetry i n the carbon p o l a r i m e t e r , was separated i n t o two terms; thus obs _ o eUD ~ £UD EUD ' where e ° ^ s i s the observed asymmetry and e ° D i s the i n s t r u m e n t a l asymmetry. S u b s t i t u t i n g i n t o Eg.(11), TT , Obs O . ( 1 ) 2 A ~ ( £UD " £UD ) " V C T s . \ nc x I f we denote two proton p o l a r i z a t i o n v e c t o r o r i e n t a t i o n s by < o > + and < a > _ , then „ TT , obs o b s N , , R = - ^ — ( e + - e_ )/(<a> + - <a>_) nc o , obs , obs . ,/ , e = (<a> e. + <a> e )/(<a> - <a> ) — + ~r — ~r — The proton beam p o l a r i z a t i o n <a> i s r e l a t e d to the beam p o l a r i m e t e r asymmetry e b by 60 e" = A <a> , PP where A p p i s the a n a l y z i n g power f o r p-p e l a s t i c s c a t t e r i n g . T h e r e f o r e R = - £ ( A /A ) { ( e f S - £ ° b S ) / ( ^ - £ b ) } t 2 pp nc + - + -o , b obs , b obs N ,, h b N e = ( e _ e + + e + e _ ) / ( e + - e_) The r a t i o ( e ° b s - e ° b s ) / ( £ b - e b ) , f o r a g i v e n proton energy and carbon p o l a r i m e t e r r e c o i l angle, i s p r o p o r t i o n a l to H . t I i i ) D measurements: t The i n c i d e n t proton p o l a r i z a t i o n v e c t o r was a l i g n e d i n the d i r e c t i o n of n ( F i g . 5 ) . From Eg. (7) and Eg. (8) and I = I (1 + P<a ( 1 )>.) , o n ±J 1 < 0 n 2 ) > f " I o ( P + V a n 1 ) > i ) < a ( 2 ) > = 0 . s f r The r e l a t i o n between < a^> and the l e f t - r i g h t n f asymmetry e i s 61 •TT » (2) 2 LR nc n f Thus IT _ ir , obs _ o v 2A LR 2A LR LR nc nc = (P + D t < a n 1 ) > i ) / ( 1 + P < a n 1 ' > > i ) ' where e o b s and e ° are the observed and i n s t r u m e n t a l LR LR l e f t - r i g h t asymmetries. Denoting the two proton s p i n o r i e n t a t i o n s by <a> + and <a> as before, Dfc = j~{(eJbS-e°bs)/(<a>+-<a>_}(l+P<a>+)(l+P<a>_) + P 2 nc Since <a>+^-<a>_, p z « D and P * « 1 , the above expre s s i o n s i m p l i f i e s t o TT , obs obs. , , N °t " 2 A — ( £ + " £ - ) / ( < 0 > + " < a > - } nc ° ± (A /A ) { ( e ? b s - e ° b S ) / ( s b - E b ) } / pp nc + - + — ( i i i ) R e s t r i c t i o n s a p p l i e d to data 62 As was shown i n t h e p r e v i o u s s e c t i o n , the primary experimental q u a n t i t i e s are the asymmetries, which were obtained by t a l l y i n g those events having azimuthal s c a t t e r i n q angle $ l y i n q i n the d e s i r e d range. The general purpose histogramming r o u t i n e used i n the a n a l y s i s allowed r e s t r i c t i o n s ("cuts") on the data t o be made e a s i l y . R e s t r i c t i o n s on t h e time between the a p p l i c a t i o n of the R-F f i e l d and the d e t e c t i o n of a r e c o i l proton i n the carbon p o l a r i m e t e r e l i m i n a t e d y*s r e s u l t i n q from decay of T T 0 ' S produced i n the-LD t a r g e t . T h i s r e s t r i c t i o n was not severe, s i n c e t h e t i m e - o f - f l i g h t s p e c t r a were g e n e r a l l y q u i t e narrow ( F i g . 1 4 ) . Charged p a r t i c l e s not vetoed by V1, S1 and S2 were e l i m i n a t e d by demanding t h a t no wires f i r e i n the f r o n t s i x MWPC's. The most important r e s t r i c t i o n was a check to determine whether the cone formed by v a r y i n g $ from 0 t o 2TT f o r a g i v e n s c a t t e r i n g angle e i n t e r s e c t e d a c t i v e r e g i o n s of the p o l a r i m e t e r . T h i s t e s t e l i m i n a t e d b i a s i n the asymmetry due to the non-spherica 1 geometry of the po l a r i m e t e r . b. R e s u l t s The asymmetries f o r 2 opposite i n c i d e n t s p i n o r i e n t a t i o n s ( l a b e l l e d and " - " ) , the asymmetry r a t i o r = ( e o b s _ e o b s ) / ( e b - e b) (which i s a measure o f neutron p o l a r i s a t i o n ) and the i n s t r u m e n t a l asymmetry o f t h e carbon 63 ~f I I I | I I I I | I I I I—| I I I—I | I I I I | l 25K Run No. 655 2IO MeV 6° (Lab.) 2 OK £ 15K 3 O o 10K 5K .J I L_J I L 0 J L_J I L__L 10 15 TIME (ns) J I I I I L 20 25 Figure 14. T i m e - o f - f l i g h t Spectrum of Neutrons Emitted from Deuterium a t 6° (210 HeV) 64 Tabl e VI. asymmetries f o r H Measurement (210 MeV) Neutron A ngle, Bun#(+) , Hun#(-) , b e4 ' B e c o i l Proton angle (degr.) obs £+ obs e_ asymmetry Ha t i o r I n s t r . asymmetry 6° j 7- 12 -4. 3041. 101 0.6741. 12 -.1284.041 -1.8840.79 656 | 13- 18 -3. 2440.91! 0 . 794 0 . 91 .1044 . 03 31 -1.2840.64 655 | 19- 24| -4. 0540. 88| 2.5140. 88 -.1694.032! -0.8640.62 18.85*.14| 25- 301 -5. 9641.80| 2.8341. 80 •-.2274. 0661 -1.6841.27 -19.904. 14 | 0- 180 -3. 8740.50| 1.2640. 51 | — .1324.018 -1.3840.36 9° | 7- 12 -4. 8941.12| 4.0141.40 — .2214.045 -0.6140.89 664 | 13- 18 I-4. 3440.92! 1. 394 1. 14 i - .1424.0361 -1.5940.73 666 | 19- 24| -4. 5640.90} 4.7141.10 .2304.035 -0.1140.71 19.364. 13| 25- 30 -6. 0241.79J 2.4542.24 - .2104.071 -1.9541.42 -20.924.15| 0- 180 -4. 4 8+0. 5 11 3.0840.63 — .1884.02 01 -0. 8540.40 9° | 7- 12 -4. 1141.12| 1.4241. 12 - .1374.039 -1.4540.79 670 | 13- 18 -4. 0040.921 2. 414 0. 93 .1584.0321 -0.9140.65 672 | 19- 24| -4. 0340.901 -2.4240. 88 j -.1594. 031) -0.9240.63 19.514.13| 25- 30| -6. 0141.80| 4.6241.80 .2624.06 3! -0.8941.27 -20.994.12| 0- 180 -3. 8940.511 2.1940.51 j — .1504.018| -0.9640.36 12° | 7- 12 -2. 8541.62] 4.5541.61 — .1824.056 0.7141. 14 676 | 13- 18] -3. 5441.33| 2.974 1. 31 !- .1604.0461 -0.4140.94 673 | 19- 24| -6. 1941.27! 4.3941.29 - .2604.045 -1. 1040.91 19.604.17f 25- 30 -7. 1742.621 3.1142.60 .2534. 091| -2.2241.85 -21.104.17| 0- 180 -4. 3140.74| 3.7540.73 - .1984.0261 -0.4340.52 65 Table V I I . Asymmetries f o r R Measurement (343 MeV) t Neutron Angle, Run# (•) , Run|(-) , R e c o i l Proton Angle (degr.) obs obs Asymmetry Ra t i o r I n s t r . Asymmetry e° m 6° f 5- 13 -1.10±1.111 0. 9841. 10 .0504.0371-•0.0540.78 263 J 14- 16 -1. 17±1.52| 3. 5941. 52 | - .1134.051! 1.2341.08 262 | 17- 19 -1.02±1.43| 5. 1341.44 | -.1474.0491 2.0 941.02 21.134.62J 20- 29 0.29i0.99f 4.4941.00 .1004.0341 2.4140.71 -20.724. 63 J 0- 180 -0.55t0. 59J 3. 25±0.60 j -.0914.020J 1.3740.42 9° | 5- 13 - 1.61H. 10| 3. 1041. 08 | — • | .1154.0381 0.7240.77 255 \ 14- 16 -0.7941. 50 | 1. 0741. 49 | - .0454.052! 0.1341.06 256 | 17- 19| 0.44±1.44| 4. 1941.41 | -.0914.0491 2.3041.01 20.334.60| 20- 29| -3. 4040. 99| 3. 9840. 98 | - .1804.034! 0.264 0.70 -20.71t.61l 0- 180 -1.6640.59| 3. 1940.58 i .1184.020! 0.744 0.42 12° | 5- 13 -3. 8241. 431 0.1941.38 r .0984.049J-•1.8541.00 243 | 14- 16 -4. 15±2.Q4| 6. 2541. 88 1" .2 554.06 8! 0.9641.40 244 | 17- 19| -3. 9541.89! 7. 7641.80 .2874.06 4} 1.8011.31 20.0 44. 671 20- 29| -2.3441.32J 4. 0241.26 | - . 1564. 04 5 J 0.7840.92 -20.774.67J 0- 180 -3. 3740.78J 3. 8040. 75 | - .1764.0271 0.1540.55 . .15* I 5- 13' 0.8841.61J 2. 5641.61 i — .0 504. 06 8! 1.7741. 14 277 | 14- 16 1.3642.13! 0. 33t2. 16 .0314 .091| 0.8141.52 276 | 17- 191 2.2542.02J 4 . 0541.97 | -.0544.O85J 3. 2141.41 17.774.64| 20- 29| 1. 1941. 42! 4 . 9141. 40 .1114.0601 3.1741.00 - 15.61±.64| 0- 180 1. 5240.851 3. 0740.85J- .0464.036! 2.3540.60 18° ! 5- 13 2.9942.331 6. _ „ _ „ _ , , . | _ 1842.38!- .091i.095| 4.4941.67 289 | 14- 16 2.6 542.92J -0. 524 2. 94 .090t.118| 1.1642.08 290 | 17- 19 2. 1142.651 2. 42 42.67 | -.0094.107! 2.2641. 88 16.52±.60J 20- 29| 1. 5941. 86J 2. 86+1.88 | -.0364.0751 2. 1941.32 -18.73+. 611 0- 180 1.97t1. 16| 3. 1241. 17 .0334.047J 2.514 0.83 66 Table V I I I . asymmetries f o r E t Measurement (516 MeV) r • T r — - r T 1 — — J | Neutron \ R e c o i l | | Angle, \ Proton | obs 1 e ' obs 1 e • I n s t r . | ! Run#(+) , | Angle ! + j + 1 Asymmetry 1 asymmetry 1 I Eun#{-) , | (degr. ) 1 {%) 1 Ra t i o r | 0 1 £ ' 1 D • I b . 1 £ I 1 1 1 1 ! I 6° I 7- 121 -1. 37H.25J 0.57t1.311 - .0 391.0361 -0.4910.91J | 638 | 13- 181 -0. 43i1. 10! 2.0611.15| - .0501.0321 0.7110.801 1 639 | 19- 241 -3.8211.141 1.0611.21J - .0 971.03 31 -1.6010.831 I 22.901.15| 25- 301 -0.6112.36J ^ 0.6 912.51| . 0 021. 06 9 J -0.6511.72| 1-27.32±.15f 0- 180| -1. 8510.611 1.15l0.64! — .0601.018! -;0.4810.44 1 1 6° 1 7- 12| -0. 20 + 1.24! -0.3411.21! ,003i.034| -0. 26±0.87| 1 642 | 13- 18| -3. 3211.091 1.4811.08! - .0 951.030J -1.1210.77J | 643 | 19- 24J -3.9011.12! 2.27H. 11| - .1221.0311 -1.0710.791 ! 23. 17±. 151 25- 30| -0.84i2.37j 1.40+2.281 - .0441.0651 0. 1911.66} 1-27.37±.14| 0- 180| -2. 26l0. 601 1.2410. 59! - .0691.0171 -0.66±0. 42J I 9 0 [ 7- 12| -0. 25H.331 -2.6511.231 1 .0481.0361 -1.3510.911 I 621 | 13- 18| -2. 5411. 161 -0.75H. 081 - .0361.032! - 1.7210.801 I 620 | 19- 24| -5,69t1.21| 0.45+1.12! - .1231.03 31 -2.87t0.83! I 22.981. 15| 25- 30J -7,72+2. 461 -2.6712.36| - .1011.068! -5.40H.72! J-27.001.14J 0- 180| -3. 1110.65! -0.46i0.601 - iQ53i,018J -1.8910.45J 1 9° 1 7- 12| 0.66H.24! 1.09±1.221 — .0091.035! 0.8610.871 1 625 1 13- 18J -2.6711. 10 | 0.86+1. 09! - . 0701.03 1J -1.0410.781 1 623 1 19- 24| -3.4411.12} -0.45H. 12J - .0591. 031} -2.0610.79! 1 23.201.14| 25- 30| 1.7312.32! -1.84±2.33| .0711.065! 0.0911.65J 1-27.16i. 141 0- 180| - 1.8010.61! 0.34i0.601 - .0421.017! -0.8110.431 | 12° | 7- 12| -2.9311.24! 0.34H. 24 1 — .063+.034I -1.4110.881 | 601 J 13- 18J -1.99l1.07| 0.6011. 071 - .0501.030| -0.7810.76) I 602 J 19- 24| -2.61*1. 101 2.3111.10! - .0961.0301 -0.32l0.78| I 24.021.12J 25- 30! -6.5312.23| 0.4012. 23! - .1351.06 2! -3. 30H.60 ! 1-27.491.121 0- 180| -2. 32±0. 601 0.5410. 60| - .0561.016| -0.9910.43! 1 1 2 ° I 7- 12| -0.2511.221 -1.2011.21 I .0181.0331 -0.6910. 861 I 603 ! 13- 18J -0.83+1.07J 0. 1911. 051 - .0201 .029| -0.3610.75| I 604 I 19- 24| -1.0511.07| 3.1111.08J - .0811.0301 0.8910.761 J 23.971.121 25^ 30! -2.5712.25J 2.7712.29J - .1041. 0621 -0.0811.61 I 1-27 .521. 12| 0- 1801 -0.7310.591 0. 58i0. 59| - .0251.0161 -0.1210.421 l . _ L .... ,1 L — A — —1 1 67 Table IX. asymmetries f o r D t Measurement (343 MeV) 1 T R e c o i l Proton Angle (degr.) Neutron Angle, Run# (•) , Eun|(-) , . e+ ' b obs + obs e ($) Asymmetry Ratio r I n s t r . Asymmetry o e 6° 1 5- 131 2. 5211,57! 0.75H. 53 .040i.049| 1.6111.10 259 | 14- 16 -1.31l2.09| -0.5512.14 -.0171.0671 -0.9211.50 258 J 17- 19 -2.68l2.09| -0.9011.98 -.0401.0651 -1.77H.44 22 .941.85J 20- 29 -2.07H. 41! 3.08+1.38 .1151.04 41 0.5810.99 -21 .691.92! 0-180| -0.7710.85J 0.97+0.83 — .039l.027| 0.1210.59 .60 J 5- 13 -0. 35t1. 35 -2. 38i1. 38 .0461.044 -1.4710.97 260 | 14- 16 1.33H. 85J -1.5311.87| .0651.060 -0.2511.32 261 I 17- 19| -0.9311.731 1. 1811. 81 - .0481.057! 0.2 4H.27 24 .291.78! 20- 29 - 1..12*1. 22) 3. 57i 1.24 -.1071.040) 1.4710.88 -19.67i.79! 0-180 -0.6410. 72! 0.4410. 74 — .0251.023! -0.0410.52 9° J 5- 13 1. 00+1. 41 1.1111. 49 — .0 031.047 1.0611.03 253 J 14- 16 j 0.2311.98J 1.8112.07) -.0361.0651 1.04± 1.43 251+252 J 17- 19| -0. 24i1.85| 2.0711. 99 - .0531.0621 0.94H.36 22 .341.7 0! 20- 29 -1.3611. 30! 0.77H. 35 -.0491.043| -0.2710.94 -21 .431.771 0-180 0.09±0.77| 0.5810.81 — .0 111.026! 0.3410.56 12° J 5- 13 -1.8111. 32! 0.23H. 17 - .0471.041 -0.7710.88 242 J 14- 16! 0.00+1.771 -0.85H. 66! .020t.056| -0.4 411.21 241 J 17- 19| 0.8 4H.701 -0. 50*1. 55 .0311.0531 0.1511.15 22.0 8+. 62! 20- 29! -2.22l1.21| 1.4311.08J -.0851.038! -0.3510.81 -21 .07±.56! 0-1801 -1.05t0.71J 0.27±0. 64 | -.0 311.0221 -0.38±0.48 68 Table X. Asymmetries f o r D Measurement (516 MeV) Neutron Angle, Bun# (•) , Bun#(-) , b V ' b R e c o i l Proton Angle (degr.) obs (%) obs e 1%) Asymmetry Ratio r I n s t r . Asymmetry o (!) 6<» J 7- 12| -0. 4341.09 1.9341. 23 - .0484.0331 0.8740.84! 647 I 13- 18 -2. 2340.96! -0.3341.08! -.0394.029 -1.1910.731 646 | 19- 24 -2. 8541.001 0 .764 1. 11 - .0734.0301 -0.8740.76 | 27. 12±.13J 25- 30 -2. 3012.05 0.6842.29 -.0604.06 2 -O . 6 6 11.56! -22.23±.15J 0- 180 -2.2040.531 0.6440.60 .0584.016 -0.6440.41 I 9° 1 7- 12 -2. 2841. 10 - I . 2 I 4 I . 11 — .0224.031 -1.7140.781 631 | 13- 18 -1.1040.97! 0.0440.95! -.0234.0271 -0.4940.68! 630 I 19- 24 -1. 17H. 00 J -0.6140. 98 - .0114.0281 -0.8740.70! 26.634.12| 25- 30] -4.4 242.03 4.4342. 05 - .1784.058 0.3341.45! -23.034.1 2 ! 0- 180 -1.3240.541 -0.0740.53 — .0254. 015 -0.6540.38! 9° | 7- 12 1.7341. 11! -0.7441.09 .0494.031 ^ 0.4340.78| 633 1 13- 18 -1.2440.981 -0.5240.96! -.0144.027! -0.8640.69 I 632 | 19- 24| -2. 5841. 00i -0.294 0. 99 - .0464.0281 -1.3840.70! 26.244.12| 25- 30| -3. 8542. 06 -1.4942.03j -.0474.0581 -2.6141.45J -23.694.12| 0- 180 -1.1640.541 -0.274 0.53 — .0184.015 -0.6940.381 12° 1 7- 12 -0. 40 + 1. 10 0.2041.11 - .0124.030 < < j -0.0840.78J 614 | 13- 18 -1. 5640.96! -1.5240.98) -.0014.0271 -1.5440.69J 613 ! 19- 241 -2.7740.98! 0.7740. 99 - .0694.027! -0.884 0.701 27.404.10| 25- 30! -4.7942.05 2. 7942.04! - .1484.056) -0.7541.451 -23.981. 11| 0- 180| -1.6540.541 0.0340.54 -.0334.015] -0.7540.381 69 p c l a r i m e t e r are recorded i n Tables VI-X. The beam monitor b asymmetries £ were not c o r r e c t e d f o r the presence of carbon i n the p o l y e t h y l e n e t a r g e t of the monitor s i n c e o n l y r e l a t i v e p o l a r i z a t i o n was d e s i r e d . , The c e n t r e s of the proton angle bins correspond to the angles a t which the carbon p o l a r i m e t e r was c a l i b r a t e d i n Experiment #2 (describe d i n the next s e c t i o n ) . This b i n n i n g procedure i s not necessary f o r purposes of comparison, but i s u s e f u l f o r combining the r e s u l t s o f t h i s experiment and those of Experiment #2 to e x t r a c t the values of and Dfc, The r e l a t i v e p o l a r i z a t i o n i s best d i s p l a y e d by averaging over the e n t i r e angular range of the carbon p o l a r i m e t e r to take advantage of the high e r s t a t i s t i c a l p r e c i s i o n . The e r r o r s given i n the t a b l e s are s t a t i s t i c a l and were ob t a i n e d by assuming Poisson d i s t r i b u t i o n s f o r the number of proton t r a c k s detected i n the "up", "down", " l e f t " and " r i g h t " s p a t i a l r e g i o n s and by using the formula 2 a 2 + '9f V 1 L9x 2 J to combine e r r o r s . In t h i s e xpression f r e p r e s e n t s a f u n c t i o n of s e v e r a l random v a r i a b l e s x 2 , ••• and a 2 i s the v a r i a n c e of f . The q u a n t i t i e s o*, ••• are the v a r i a n c e s c o r r e s p o n d i n g t o the random v a r i a b l e s X j , x 2 , • • • . The r e s u l t s of the background measurements are not quoted here because the f r a c t i o n of events due to 70 background was <3% i n a l l cases, and the asymmetry of the background was o f the same order as the foreground. The asymmetry r a t i o s f o r the Rfc and Dfc c o n f i g u r a t i o n s are p l o t t e d i n F i g s . 15 and 16 r e s p e c t i v e l y . R f c i s c o n s i d e r a b l y l a r g e r than D t below 516 Me? (a r e s u l t p r e d i c t e d by Folkmann and Measday), i n d i c a t i n g t h a t the R c o n f i g u r a t i o n i s most s u i t a b l e f o r the p r o d u c t i o n o f p o l a r i z e d neutron beams. The p o l a r i z a t i o n i s peaked near 10° f o r the R^-type c o n f i g u r a t i o n a t 343 MeV, a r e s u l t c o n s i s t e n t with previous measurements a t 2 03 MeV (fieay, 1966) and with phase s h i f t p r e d i c t i o n s (Fclkmann, 1S68). No such peaking i s observed at 516 MeV. c. The P o l a r i z a t i o n Transfer. Parameters R and D _ _ t t The r e s u l t s of the measurement of a n a l y z i n g power of carbon f o r neutrons (Experiment #2) were combined with the asymmetry measurements to e x t r a c t the t r a n s f e r parameters R and D a t 343 and 516 MeV (Tables XI and X I I ) . The t t ' b i n n i n g of the proton angles i n the p o l a r i m e t e r r e s u l t e d i n asymmetries which are s m a l l and of the same order as both the s t a t i s t i c a l u n c e r t a i n t i e s i n the asymmetries and the i n s t r u m e n t a l asymmetries o f the p o l a r i m e t e r . To o b t a i n the maximum amount of i n f o r m a t i o n from the data i t was necessary to weight the v a l u e s a c c o r d i n g to t h e i r p r e c i s i o n when combining the r e s u l t s f o r each b i n . I t was a l s o 71 T 1 1 r A 2 IO MeV O 343 M e V • 5 I 6 M e V O, 0 0 0 o' 6° 9" 12° 15° 18' Neutron Angledab.) F i g u r e 15.. BsymHietry r a t i o vs. , ftngle <* - t y p e ) 72 ~i r O 3 4 3 MeV • 5 16 MeV 6° 9°~ Vp 7^  N e u t r o n A n g l e ( l a b . ) 18' F i g u r e 16. Asymmetry r a t i o vs. Angle (D t-type) Table XI. 73 Parameter r — JEnergy, I Neutron I ftngle T ~ Angle of R e c o i l P r o t o n i n P o l a r i m e t e r r — j I Weighted! M A a n I r " I •- • 9° I 1 r 15° ! 1 18° 1 21° J T 24° | 27° •5 rlean ] I 343 I 6° |_ 1 I —• 41 | -±.30 | I 1.05 J-±.47| .85 ±. 28| — t -.49 J ±. 16 1 -- I-.58 1 1 ±.14 | I 343 | 9° 1 —• 93 |-±•311 .42 I -±.48| .53 ±. 28J — ] ^.87 | ±. 17J — I-.78 1 ! ±.15 J | 343 | 12» 1 — • 80 J-±.401 2*35 | ""* ±.63| 1.65 J ±. 37| — ! -. 75 J ±. 22 1 — J-1.04 J I ±.19 ! | 343 | 150 1 — * 41 I ±. 561 .28 J-±. 84! .31 ±. 491 — 1 -.54 J ±. 29 J I-.42 J ! ±.22 | ! 343 | 18° J —. 74 | 1.77} .83 |-±1.08! .05 ±. 61J — 1 -.17 J ±. 36} — I - . 16 | I ±» 28 | | 516 j 6° 1"™ • 11 I" ±. 16 J .69 | ±.21 ! — |-.52 ! ±.111 "" !" . 14 ±.30 1 | ^ !-.42 ! 1 ±.09 J 1 1 | 516 | 9° | I . 12 |-±. 16J .50 J ±.21} — .43 ! ±. 11! ~ i " • P7 ±.30 r - — i I-.28 J 1 ±.08 J | 516 | 12° L. f —. j 14 |-±. 15J „ ., i , „ .33 | ±.19! ....... X — .42 I ±.10J , 1 . — 1 .75 ±.27 t 1 I-.36 1 ! ±. 08 1 L _ _ , _ i 74 Table XII. D t Parameter r ™ -~ T-I Energy,| IReutron r-1 Angle | An g l e of P e c o i l Proton i n P o l a r i m e t e r T — 1 1 Weighted| 9° | 15° | ..., | . 180 r 21° I 1 24° 1 270 N 1 n c d U | I 343 |-1 6° 1 I „ . j .35 |-±. 27 J .26 | ±.41 I , .„, 1 _ .26 ±. 25J ! .53 | ±. 14 | 1 . 28 1 1 ±.11 1 | 343 | I 9° 1 (_ __x_ .02 1 ±.38| 1 .33 | ±.601 . 30 ±. 36| " ! .24 J ±.211 1 .22 J 1 ±. 16 1 | 343 1 | 12° | I — h-I 516 | I 6° | .39 J-±•331 . 18 |-±.521 . 18 ±. 311 " ! .41 J ±. 18 1 > | .25 J I ±. 14 J . 30 \ ±••211 .36 | ±. 281 — i .35 | ±.141 •" ! . 38 ±.39 1 . 34 J 1 ±.11 1 1 1 | 516 |-I 9o | .09 | ±; 14| .18 | ±. 18J — ! . 14 J ±.09J ~ ! .71 ±.26 T —1 | . 13 I I ±.07 J | 516 | I 12° | 1 a, .07 | ±. 19 | — — 1 _ .01 J ±.25J __ . X — J . , .33 J ±. 13 J 1 - ... X . .93 ±.35 I .26 | ! ±. 10 J t 1 75 important to analyze p a i r s of measurements t h a t were taken c l o s e t o g e t h e r i n time because of the v a r i a t i o n i n chamber e f f i c i e n c i e s (and hence of i n s t r u m e n t a l asymmetries) with time. The r e s u l t s are p l o t t e d as a f u n c t i o n o f l a b . angle i n Figures 17 and 18. These r e s u l t s show the same shape as the r e l a t i v e measurements d e s c r i b e d i n the previous s e c t i o n where no b i n n i n g procedure was used, i n d i c a t i n g t h a t no s i g n i f i c a n t s y s t e m a t i c e r r o r s were i n t r o d u c e d by the b i n n i n g procedure or by the carbon c a l i b r a t i o n measurements. A 6% u n c e r t a i n t y i n the n o r m a l i z a t i o n of the proton beam p o l a r i z a t i o n was i n c l u d e d i n the f i n a l e r r o r (the n o r a m i l a z a t i o n was f i x e d to b e t t e r than 1% i n a l a t e r BASQUE experiment). The phase s h i f t p r e d i c t i o n s f o r f r e e n-p s c a t t e r i n g are i n d i c a t e d by s o l i d l i n e s f o r comparison (Bugg, 1975). The p r e d i c t i o n s agree with the 343 MeV data but d i s a g r e e completely with the 516 MeV data. 2» Experiment #2j. Measurement of A n a l y z i n g Power of Carbon JUSiJilcnsl The experimental c o n f i g u r a t i o n i s shown i n F i g . 19. A 1cm.-thick carbon p l a t e was i n s e r t e d i n t o the p o s i t i o n normally occupied by the LD 2/LH t a r g e t assembly and the neutrons produced by the r e a c t i o n l 2 C ( p , n ) X were detected by the 76 F i g u r e 17, B Parameter 77 i 1 1 1 r A : O 3 4 3 M e V B: • 5 I 6 Me V I i i i i : i 0° 3° 6° 9° 12° 15° 18° Neutron Angle (Lab.) F i g u r e 18. Dfc Parameter 78 P o l a r i z e d P r o t o n s ' / N e u t r o n s F i g u r e 19. Apparatus f o r Experiment #2: An a l y z i n g Power of Carbon f o r Neutrons 79 combination of veto counter and 2.54 cm.-thick p l a s t i c s c i n t i l l a t o r neutron d e t e c t o r . The number of neutrons detected f o r proton p o l a r i z a t i o n v e c t o r up was d i f f e r e n t than f o r p o l a r i z a t i o n v e c t o r down, and the r a t i o of the number of neutrons d e t e c t e d i s r e l a t e d to the a n a l y z i n g power. The a n a l y z i n g power so obtained was assumed t o be equal to the -+ ->-a n a l y z i n g power f o r the r e a c t i o n **C(n,p)X which occurs i n the carbon p o l a r i m e t e r because o f charge independence. a. Data A n a l y s i s The d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n i s given by Eg.(7) : I = I (1 + A<a^>.-N) . o 1 The number o f neutrons e j e c t e d at angle 6 when the i n c i d e n t proton s p i n i s up (down) i s given by = kMyU - A(G)<a> u) N D = k M ^ l + A(6)<a> D) , where M y and M D are the number of i n c i d e n t protons d e t e c t e d by the beam p o l a r i z a t i o n monitor f o r proton s p i n up and down, and k i s a constant. 80 D i v i d i n g and s o l v i n g f o r A ( 6) , A(6) = ( N ^ - N u M D ) / ( N A < a > D + N ^ a ^ ) • ( 1 2 ) During the course of data t a k i n g a spectrum of the time between the beginning of a c y c l e of a c c e l e r a t i o n i n the c y c l o t r o n and the d e t e c t i o n o f a neutron i n the 2.54 cm. counter was accumulated. The c o r r e l a t i o n between these two events was i n c r e a s e d by u t i l i z i n g the c y c l o t r o n beam chopper, which ensured that protons were i n j e c t e d i n t o the c y c l o t r o n near the beginning of an R-F c y c l e by b l o c k i n g the proton beam a f t e r a c e r t a i n time had e l a p s e d from the s t a r t of the c y c l e . A time r e s o l u t i o n of 2 ns. was o b t a i n e d u s i n g t h i s technique. The r e s u l t i n g c o i n c i d e n c e time window enabled contamination by •s t o be e l i m i n a t e d and allowed the a n a l y z i n g power t o be measured over a range of neutron e n e r g i e s . T h i s c a p a b i l i t y was necessary to a l l o w c o r r e c t i o n s f o r the l o s s of low-energy protons by a b s o r p t i o n i n the 6 cm. carbon t a r g e t . T y p i c a l neutron t i m e - c f - f l i g h t s p e c t r a f o r two i n c i d e n t proton s p i n o r i e n t a t i o n s are shown i n F i g . 20. The s p e c t r a shown i n t h i s f i g u r e were normalized to the same number of i n c i d e n t protons. The c a l c u l a t e d low-energy c u t o f f f o r the carbon p o l a r i m e t e r i s i n d i c a t e d by a v e r t i c a l arrow. The asymmetry i n the r e g i o n of t h e q u a s i - e l a s t i c peak (corresponding to an a n a l y z i n g power of 81 10K S p i n Up S p i n D o w n i 516 MeV 21° (Lab. i/) l— "Z. => O 5K 0 10 20 30 TIME ( n s ) 4 0 5 0 Figure 20. T i m e - o f - f l i g h t S p e c t r a of Neutrons Emitted from Carbon a t 21° (516 MeV) 82 about -.2) i s g r e a t e r than t h a t of the low-energy continuum. These s p e c t r a were i n t e g r a t e d from a c a l c u l a t e d low-energy c u t o f f to the high energy peak and the t o t a l s were used i n the c a l c u l a t i o n of the a n a l y z i n g power i n Eg.(12). A summary of the c u t o f f c a l c u l a t i o n i s given i n Table X I I I . In t h i s c a l c u l a t i o n i t was assumed t h a t a neutron knocks out a proton from a carbon nucleus s i t u a t e d at the c e n t r e of the 6 cm. carbon b l o c k v i a a q u a s i - e l a s t i c r e a c t i o n . The f i r s t column i n Table XIII (a) g i v e s the r e c o i l ( k n o c k o u t ) proton angle, the second column g i v e s the d i s t a n c e from the p o i n t of i n t e r a c t i o n to the p o i n t of e x i t and the t h i r d column q i v e s the minimum proton e x i t energy. The maximum proton energy was c a l c u l a t e d by assuming s c a t t e r i n g from f r e e nucleons at the c e n t r e of the carbon t a r g e t (Table X I I I ( b ) ) . The r e s u l t i n g a n a l y z i n g powers are l i s t e d i n T a b l e XIV. The e f f e c t o f averaging the a n a l y z i n g power over the peak and continuum i s to decrease the a n a l y z i n g power by a f a c t o r of two. The neutron e n e r g i e s i n Experiment #1 d i d not correspond e x a c t l y to the e n e r g i e s i n t h i s experiment because the neutron angle was v a r i e d from 6° to 18° i n Experiment #1. The v a r i a t i o n i n energy, however, was never more than 40 fleV; the v a r i a t i o n of the a n a l y z i n g power over t h i s range was s m a l l . 83 Table XIII. Summary of C a l c u l a t i o n of Low-energy C u t o f f i n Carbon P o l a r i m e t e r — i , Carbon P o l a r i m e t e r R e c o i l | Carbon angle | t h i c k n e s s | (g/cmz) I — -J : Minimum r e c o i l proton energy a t e x i t (MeV) Minimum v e l o c i t y / c Exp. #2: iPlight path l e n g t h of neutron (m.) go , 150 I 18° ! 21° | 24° | 27o | 1_ 5. 4 5. 5 5. 6 5.7 5.8 6.0 77 78 79 79 80 82 . 382 .384 . 386 . 386 . 388 .392 6.03 6.03 6.05 6.09 6.15 6. 23 1 — — — r T— - —r T — — — — T--•'- - T I Maximum | Maximum ! Maximum JTime d i f f . ! !Energy! Angle !proton energy! proton energy I v e l o c i t y / c |max.-min. ) ! (MeV) ! (°) Jat s c a t t e r i n g ! at e x i t !energy(ns)| ! p o i n t (MeV) j po i n t (HeV) J 343 J 9 ! 333 J 318 I .665 I . ,. j ! 22.4 J 15 I 316 J 298 ! .651 ! 21.5 J 18 J 305 J 287 I .643 ! 20.9 J 24 J 278 J 258 ! .620 I 19.8 J t 516 | 9 I 500 J 492 ! .754 | 26.0 J 15 J 473 | 460 J .741 I 25.2 ! 21 | 434 ! 411 I .718 ! 24.3 J 27 ! 388 | 370 ! .696 I 23. 1 | i- , _ , . . . . J. i — j . j . . . . . j . 1 84 Table XIV. A n a l y z i n g Power of Carbon P o l a r i m e t e r f o r Neutrons r —r— - i — i Beam Energy f Angle \Analyzing Power} (HeV) | (degrees) 1 A 1 I I n c i 1 i i 1 ! j 343 I 9 I - . 0 6 0 ± . 0 O 5 1 I 15 I - . 0 5 3 ± . 0 0 5 J | 18 f - . 0 8 5 ± . 0 0 4 J | 24 | - . 1O1±.0O5 J 516 \ 9 J - . 0 8 6 ± . 0 0 5 | ! 15 I - .058+.005 ] I 21 I - . 1 1 5 ± . 0 0 5 | I 27 J - . 0 8 7 ± . 0 0 5 S _ i . , _x_ _ 1 85 3• Experiment #3; A Measurement of Neutron P o l a r i z a t i o n v§;_ Energy. The experimental arrangement i s shown i n F i g . 21. Since a measurement of Rfc was d e s i r e d , the superconducting s o l e n o i d c u r r e n t was a d j u s t e d so as t o precess the proton p o l a r i z a t i o n v e c t o r i n t o the plane o f s c a t t e r i n g . The UAB2 magnet was used t o c l e a r charged p a r t i c l e s from the beam and another d i p o l e magnet was used t o precess the p o l a r i z a t i o n v e c t o r of the neutrons. An a d d i t i o n a l 50 cm. long l e a d c o l l i m a t o r of 11 cm. diameter was i n s e r t e d between the poles of the p r e c e s s i o n magnet t o provide good neutron beam d e f i n i t i o n . The r e l a t i o n s h i p between the p o l a r i z a t i o n v e c t o r s i s shown i n F i g . 22. A p p l i c a t i o n of a magnetic f i e l d i n the d i r e c t i o n -n caused the neutron p o l a r i z a t i o n v e c t o r t o precess i n the d i r e c t i o n shown. A measurement of R and <5 gave val u e s of R -L t and R". t Two s c i n t i l l a t o r t e l e s c o p e s were mounted at 29° from t h e neutron beam so t h a t s c a t t e r i n g from the L H 2 t a r g e t o c c u r r e d i n a v e r t i c a l plane; each t e l e s c o p e subtended a s o l i d angle of 62 mster. T i m e - o f - f l i g h t between the R-F pulse and the f r o n t counters enabled Y* s and i n e l a s t i c neutrons t o be e l i m i n a t e d . 86 P O L A R I Z E D P R O T O N S f i g u r e 21. Apparatus f o r Neutron P o l a r i z a t i o n vs. Experiment Energy at #3: 9° 87 Figure 22, R e l a t i o n s h i p Between P o l a r i z a t i o n Vectors 88 Data A n a l y s i s Using Eq. (8) , with <o > = <a> and s± i p < C T ^ > = < a ^ > = 0, t h e neutron p o l a r i z a t i o n i s n i p. i <a> = Pn + R <a> s - R'<a> p n t p r t p r I f <a> precesses an angle cp about -n, then <a> = Pn + (R cosd>+R'sin<p)<a> s + (R sin<p-R'costb)<a> p n t r t T p r t Y t Y p * r As i n the pr e v i o u s measurement, the component o f p o l a r i z a t i o n i n the d i r e c t i o n s r i s r e l a t e d to the up-down asymmetry by - ( e ° b s - e°)/A = (R coscp + R' sind>) <a> np t t p = R cos(<p+S)<a> J_ P = R cos((f)+6)£ b/A J_ PP Taking measurements with two s p i n o r i e n t a t i o n s and o e l i m i n a t i n g E as before, obs _ £ o b s ) / ( £ b _ £ b ) = _ R / A ) c o s ( ( j ) + 6 ) _ + - + - i np pp 89 The p r e c e s s i o n angle <|> can be w r i t t e n as the sura of the p r e c e s s i o n angle <t>' due t o the d i p o l e magnet and the p r e c e s s i o n angle n due to the 4AB2 bending magnet; thus _ _ , obs o b s w , b b. F = (e, - e ) / ( e , - e ) = A cos(d>'+6') , + — + — where A = - R A /A J_ np pp and 6' = 6 + n b. B e s u l t s The data have been f i t t e d to the two-parameter f u n c t i o n F = A cosCtjj ' + S ' ) , where A and <$' are the parameters and <t>' i s the independent v a r i a b l e . A background of 10% was measured at 445 MeV with the IH t a r g e t empty and the data at a l l e n e r q i e s were 2 90 c o r r e c t e d a c c o r d i n g l y . The a n a l y z i n g powers A and A np pp were obtained from n-p and p-p e l a s t i c s c a t t e r i n g phase s h i f t s (Axen, 1977). The data and r e s u l t i n g f i t s are shown i n F i g . 23. The r e s u l t s o f the f i t s are given i n Table XV. The parameters B and a* were c a l c u l a t e d from R and <5. The l a t t e r t t j_ parameter was estimated by s u b t r a c t i n g the angle of p r e c e s s i o n n of the neutron i n the f i e l d of the 4AB2 magnet from the angle 6* obtained i n the f i t . The angle n was c a l c u l a t e d u s i n g magnetic f i e l d survey data. The l e a d i n g cause o f e r r o r i n .a and B£ i s u n c e r t a i n t y i n the values of A and A (11% and 6% r e s p e c t i v e l y ) . np pp The values of R are p l o t t e d i n F i g . 24, t o g e t h e r with the r e s u l t s of the neutron p o l a r i z a t i o n vs. angle experiment. The two s e t s of measurements are i n agreement. The s o l i d band i s a phase s h i f t c a l c u l a t i o n using e x i s t i n g world data and p r e l i m i n a r y r e s u l t s of BASQUE measurements of D and P t f o r the n-p system. The width o f the band r e p r e s e n t s a rough estimate o f the o v e r a l l n o r m a l i z a t i o n u n c e r t a i n t y i n the phase s h i f t a n a l y s i s . 91 l i i i— i — i — i— i — i — i— i — i — i— i — i — r 5 1 I—L_J I 1 I I I I I I I I I I 0 ° 3 0 ° 6 0 ° 9 0 ° 1 2 0 ° 1 5 0 ° d>' F i g u r e 23. Heasurement of F vs. P r e c e s s i o n Angle 92 Table XV. R (Experiment #3) r T" f Pro ton| I Energy| t r, neutron I Energy| A 1 « - i i — 6 I (deg.)l T -A ' np 1 A ' PP » R ; j _ ' T " T " n I R , I (deg.M t l — • > R 1 R t ! | 237 | 220 1 .3651 I t .018J ... | — 27.61-±2.2! - » 1 .1241 1 ., . , - | .290| 1 . 94! ±. 12| I I 23. 3 |-.070 | ±4.7l±.084| . . j -.94 1 ±.12! | 34 3 | 325 1 "I1 1 .463) !±.018 J , j „ 23.71-±1.5! , | .2221 1 ,. I .3271 1 .751 ±.09| _ _ ! ^ . i 26.21.033 | ±5.2|±.071| 1 -.75! ±.09| J 445 | 425 | . | I .409} It.008 J 28.5J-±1.01 . . | .2321 1 |, .351 1 1 _ ,., t .68! ±.09| , ••-., | ,,.. . ] 27.91-.0O7J ±5.6j±.067l 1 -.681 ±.09| | 516 | l . X. 495 I 1 1 .3021 !±.Q10I i . 1-__.„ | _ 30.8J-±1.3! L... j .242! 1 — i . -I .368 J 1 1_ . 51 I ±. 06 | X-1 1 29.6 !-. 011 ! ±5.9!±.054} J J . j -.51! ±.06! ., i 93 Figure 24. Values of R Obtained from Experiment #3 94 CH ftPTER V SUMMARY AND CONCLUSIONS The f o l l o w i n g measurements have been performed and are desc r i b e d i n t h i s t h e s i s : - the r e l a t i v e p o l a r i z a t i o n of neutrons produced i n the charge exchange r e a c t i o n D{p%S)2p f o r neutron l a b . angles v a r y i n g i n 3° steps from 6°-12° at 210 and 516 HeV i n c i d e n t proton e n e r g i e s and from 6°-18° at 34 3 HeV; the i n c i d e n t proton s p i n was t r a n s v e r s e t o the beam d i r e c t i o n and l a y i n the plane d e f i n e d by the i n c i d e n t proton and the f i n a l neutron (Retype c o n f i g u r a t i o n ) > - the r e l a t i v e p o l a r i z a t i o n o f neutrons produced i n the charge exchange r e a c t i o n D(p,n)2p f o r neutron l a b . angles 6°, 9° and 12° at 343 and 516 MeV proton e n e r g i e s with the i n c i d e n t proton s p i n i n a d i r e c t i o n p e r p e n d i c u l a r t o the r e a c t i o n plane (D t~type c o n f i g u r a t i o n ) , -»- -> - the a n a l y z i n g power of carbon f o r the r e a c t i o n * 2C(p,n)X f o r neutron l a b . angles v a r y i n g i n 6° st e p s from 9°-27° at 343 and 516 MeV i n c i d e n t proton e n e r g i e s and - the p o l a r i z a t i o n of neutrons produced at 9° i n the l a b . i n the charge exchange r e a c t i o n D(p,n)2p f o r i n c i d e n t proton e n e r g i e s v a r y i n g i n 100 MeV steps from 23 7-516 HeV (Retype c o n f i g u r a t i o n ) . ft maximum i n t h e neutron p o l a r i z a t i o n f o r the R -type 95 c o n f i g u r a t i o n was observed at a neutron lab. angle near 10° f o r 210 and 343 MeV protons, whereas the p o l a r i z a t i o n remained r e l a t i v e l y i n s e n s i t i v e to v a r i a t i o n s i n angle f o r the D t-type measurements at both energies and f o r the H -type measurement a t 516 MeV. The r a t i o o f neutron p o l a r i z a t i o n a t 12° and 343 MeV proton energy f o r R — t y p e and D t-type measurements was about 6:1, i n agreement with p r e v i o u s p r e d i c t i o n s (Folkmann and Measday, 1968; bugg, 1975). The a n a l y z i n g power o f carbon f o r the r e a c t i o n i 2C(t>,n)X was dependent upon the energy of the f i n a l - s t a t e neutron; the value was found t o be s m a l l i n the low-energy r e g i o n and was comparable i n magnitude to t h e a n a l y z i n g power f o r the r e a c t i o n * 2C(p",p)X i n the q u a s i - e l a s t i c peak. When averaged over the energy range which corresponds to the range of proton e n e r g i e s accepted by the carbon p o l a r i m e t e r the a n a l y z i n g power was of the order of -0.1 and was not s e n s i t i v e t o v a r i a t i o n s i n energy and angle. A p p l i c a t i o n of the carbon p o l a r i m e t e r a n a l y z i n g power measurements to the measurements of r e l a t i v e neutron p o l a r i z a t i o n y i e l d s a value of B of -.78±.15 a t 343 MeV and -.28±;08 at 516 MeV f o r neutrons produced a t 9° i n the l a b . Measurements of neutron p o l a r i z a t i o n a t 9° (which were done u s i n g a method independent of the f i r s t measurement) r e s u l t e d i n values of P which drop from a v a l u e o f -,94±.12 a t 237 MeV proton energy t o -,49±.07 a t 516 MeV. Assuming t h a t the p o l a r i z e d i o n source produces a proton beam o f 80% p o l a r i z a t i o n , the neutron beam has a p o l a r i z a t i o n o f 75% at 237 MeV. The 96 value of R* (which was also o b tained from t h i s measurement) was found to be very s m a l l at a l l e n e r g i e s . The r e s u l t s summarized above have an important b e a r i n g on the BASQUE experimental programme., F i r s t l y , the P - t y p e c o n f i g u r a t i o n i s o b v i o u s l y more a t t r a c t i v e because of the l a r g e value o f R . •. T h i s c o n f i g u r a t i o n r e g u i r e s t h e use of a superconducting s o l e n o i d to precess the spi n of the i n c i d e n t protons i n t o t h e s c a t t e r i n g plane, and thus the expense due t o the use of l a r g e amounts of l i q u i d helium (about 100 1. per day) cannot be avoided. The peaking of the p o l a r i z a t i o n at 10° suggests s e t t i n g up the neutron beam l i n e a t t h i s angle (a value of 9° was a c t u a l l y chosen as a compromise between beam i n t e n s i t y and p o l a r i z a t i o n ) . The neutron beam p o l a r i z a t i o n remains high up t o the h i g h e s t TRIO HF e n e r g i e s , so t h a t t h i s method o f producing a p o l a r i z e d neutron beam can be used f o r the e n t i r e s e r i e s of BASQUE n-p experiments without m o d i f i c a t i o n . The measurements of neutron beam p o l a r i z a t i o n d e s c r i b e d i n t h i s work i n d i c a t e t h a t the p o l a r i z a t i o n drops o f f r a p i d l y above 500 MeV; r e c e n t phase s h i f t p r e d i c t i o n s which use p r e l i m i n a r y BASQUE measurements of D and P i n d i c a t e , however, t h a t t h e decrease i s t not as r a p i d as was p r e v i o u s l y b e l i e v e d and t h a t the u s e f u l n e s s of the technique might be extended to h i g h e r e n e r g i e s . The unexpectedly s m a l l v a l u e o f the carbon p o l a r i m e t e r a n a l y z i n g power f o r neutrons suggests t h a t a measurement of W o l f e n s t e i n parameters D, A, and R f o r the n-p system w i l l be d i f f i c u l t f o r s m a l l s c a t t e r i n g angles. A p r o p o s a l to f i l l these gaps i n the BASQUE n-p measurements by using a p o l a r i z e d 97 hydrogen t a r g e t and p o l a r i z e d neutron beam i s being c o n s i d e r e d . 98 BIBLIOGRAPHY D. Axen, L. Felawka, S. J a c c a r d , J . Vavra, G. A. Ludgate, N. M. Stewart, C. Amsler, 6. C. Brown, D, V. Eugg, J. A. Edgington, C. J . Oram, K. Shakarchi and A. S. Clcugh, L e t t e r e a l Nuovo Cimento, V o l . 20, No. 5 (1977), 151. V. Bargmann, L o u i s M i c h e l and V. I. T e l e g d i , P h y s i c a l Beview L e t t e r s 2 (1959), 435. B. B c u c l i e r , Nuclear Instruments and Methods 88 (1970), 149. P. H. Bowen, G. C. Cox, G. B. Huxtable, J . P. Scanlon, J . J . Thresher and A. 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S o u t e r s , P h y s i c a l Review 84 (1951), 1069. APPENDIX A ^ J |> N U C L E A R I N S T R U M E N T S A N D M E T H O D S 144 ( 1977) 401 -405 ; © N O R T H - H O L L A N D P U B L I S H I N G GO. A M O N O E N E R G E T I C POLARISED N E U T R O N B E A M F R O M 200 T O 500 MeV C. AMSLER, R. C. BROWN*, D. V. BUGG, J. A. EDGINGTON, C. ORAM Queen Mary College, London, England D. AX EN, R. DUBOIS, L. FELAWK.A, S. JACCARDf, R. KEELER, J. VAVRA+ University of British Columbia, Vancouver, Canada A. CLOUGH, D. GIBSON University of Surrey, Guildford, England G. A. LUDGATE-, N. M. STEWART Bedford College, London, England L. P. ROBERTSON University of Victoria, Victoria, Canada and J. REGINALD RICHARDSON University oj California, Los Angeles, U.S.A. Received 14 March 1977 A variable energy neutron beam with high polarisation and narrow energy spread has been produced at TRIUMF using the polarised proton beam and a liquid deuterium target. The neutron polarisation has been measured at 237, 343, 445, and 516 MeV incident proton energy by two independent methods. At the lowest energy the neutron polarisation is 73% at 9° laboratory angle. It decreases slowly to 3896 at the highest energy. 1. Introduction describe the properties of the beam, and the exper-It has been shown previously that a neutron i m e n t s Performed to determine them. Firstly we beam with high polarisation can be obtained by n a v u e investigated the optimum scattering angle for scattering a transversely polarised proton beam h l § h Polarisation transfer and the energy depen-from a deuterium target. Reay et al.1) found that d e n c e - T h e angular distribution of /?, was mea-at 203 MeV the proton to neutron polarisation sured at 343 and 516 MeV using a carbon analyser transfer parameter R, reaches 95% for neutrons (experiment 1). In addition a measurement of Z)t scattered forward in the laboratory at an angle of w a s Performed at 516 MeV. Secondly the magni-.15°. Due to the final state interaction between t u d e a n d d i r e c t l 0 n o f t h e n e u t r o n polarisation has the two protons recoiling slowly in the lab, the b e e n determined. The angle between the neutron emerging neutron beam is in addition fairly mon- fli8ht direction and polarisation was measured ochromatic2). Using the Livermore phase shift an- ™th a typical uncertainty of ±1.5 at 237, 343, alysis, Folkmann and Measday3) predicted Rx to be 4 4 5 ' a n d 5 1 6 MeV using a hydrogen target as po-slowly varying between 200 and 500 MeV. Thus lansat.on analyser (experiment 2). far no experimental check had been available - r ,. u i , n C » w 2. Formalism above 203 MeV. ^ . . . . . . A polarised neutron beam has been produced at T h e Polarisation O n ) of neutrons emerging from T R I U M F using the variable energy polarised pro- the deuterium target is given with respect to the ton beam and a liquid deuterium target. Here we orthonormal vectors N, K, and P shown in fig. 1, by [l + ('(0) O p >-JV] <o * Now at Rutherford Lab, Chilton, Oxon, England. t Now at SIN, Villigen, Switzerland. = {P(°) + Di(°) \ffo)'N> Rt(.0) O p > 5 > + Now at Carleton University, Ottawa, Canada. ( 5 Now at University of Victoria, Victoria, Canada. K,(fl) <o-p> • St , 101 402 C . A M S L E R et al'.\ Fig. 1. A scattering event in the lab. LD 2 - liquid deuterium target, (tip) - proton polarisation, <an> - neutron polarisation. Rt and R't are given in units of (o^S. The angle 5 to be mea-sured in experiment 2 is shown. where (a^> is the polarisation of the incident pro-ton beam. For an initially transversely polarised proton beam we have <*„>± = ±Rt{0) 0 P>, ±R[(B) <*„>]; p f Fig. 2. Apparatus. P - polarized proton beam, S - counter po-larimeter, SS - superconducting solenoid, M - clearing magnet, C - coll imator, N - neutron beam, H - horizontal precession magnet, V - vertical precession magnet, T - target position. 50 100 150 200 mm Fig. 3. Horizontal (H) and vertical (V) neutron beam profiles at the target position T. whereas for an initially vertically polarised beam < o ±-( i±i>(0)<s> '°'°r Thus #t(Z)t) a r e measured by the tip-down (left-right) asymmetry in a second scatter of known analysing power whilst P is measured by the rate asymmetry at the first scatter between initial polarisation up and down. 3. T h e n e u t r o n b e a m The experimental layout is shown in fig. 2. The polarisation of the variable energy proton beam is analysed by a four-arm counter polarimeter S, de-tecting protons scattered at 26° lab from hydrogen in a C H 2 foil 0.05 mm thick. The beam polarisa-tion is deduced from the left-right asymmetry, us-ing the analysing power of hydrogen from our la-test phase shift analysis4). A background correc-tion of 696 has been measured separately using a carbon sheet. The polarisation is typically 7896. A 6 T m superconducting solenoid is used to rotate the polarisation from the vertical into the scatter-ing plane. Neutrons from a 20 cm long liquid deuterium target are collimated by a 350 cm long lead colli-mator into channels ranging from 0° to 27° in 3° steps. In the final arrangement the 9° port was chosen. A clearing magnet M deflects the primary 102 M O N O E N E R G E T I C P O L A R I S E D N E U T R O N B E A M 403 5 6 7 F i g . 4. N e u t r o n t i m e - o f - f l i g h t d i s t r i b u t i o n w i t h respect t o t h e c y c l o t r o n r f f o r a c a r b o n target ( C ) a n d f o r t h e d e u t e r i u m tar -get (d). beam towards a shielded dump. The neutron po-larisation is precessed to any required direction by a horizontal and a vertical dipole magnet which also sweep away charged particles. A n additional 50 cm long lead collimator located in the gap of the first magnet is used to provide the final def-inition of the beam at the target position T. The beam profile at T is elliptical and has full widths at half maximum of 92 mm horizontally x 72 mm vertically (fig. 3). For a typical primary proton beam current of 25 nA, the neutron intensity at T is 1.5xl0 5 /s. Fig. 4 compares a typical neutron time of flight spectrum (with respect to the cyclotron RF) from the deuterium target to that obtained from a car-bon target. The width of the spectrum from deu-terium is determined by the cyclotron bunch width of 2 nsec: the neutron energy spread is cal-culated to be 11 MeV fwhm at 516 MeV and 9° 4. Choice of the production angle Folkmann and Measday predicted that the transfer mechanism /?, would give much better neutron polarisation than D t , and that the former peaks at about 9° lab. This small angle is exper-imentally convenient, as the neutron energy is very close to that of the initial proton beam. Tn.e angular distribution of the neutron polarisa-tion has been measured at 343 and 516 MeV (ex-periment 1). The neutron detector and polarisation anaiyser consisted of a 6 cm carbon converter fol-lowed by six riiultiwire proportional chambers 1 m 1 6° 1 10° 1 15° Olab — -.2 \ c> ' I T < 1 T zy M X /• .6 < — -.8 Rt 1 \ F i g . 5. P r o t o n t o n e u t r o n p o l a r i s a t i o n t r a n s f e r / ? , as a f u n c t i o n o f t h e n e u t r o n l ab a n g l e a t 516 M e V (<^) a n d 343 M e V ( ^ ) . A l s o s h o w n are da t a at 203 M e V (*) f r o m ref. 1- T h e f u l l c u r v e s are p r e d i c t i o n s f r o m t h e L i v e r m o r e p h a s e s h i f t a n a l -y s i s 3 ) at 200 M e V ( A ) , 350 M e V (B) a n d 500 M e V ( C , f o r t h e 0 - 7 5 0 M e V s o l u t i o n , C 2 f o r t h e 0 - 4 0 0 M e V s o l u t i o n ) . square each. The azimuthal distribution of protons emerging from the carbon was measured over scattering angles from 0° to 32°. The minimum en-ergy for a scattered proton to be detected was 75 MeV. Two scintillation counters vetoed incom-ing charged particles. Time-of-flight information with respect to the cyclotron rf was used to reject inelastic neutrons and y's. • The analysing power of the reaction nC—pX has been measured in a separate experiment on the charge symmetric reaction pC-^nA'. For this, the liquid deuterium target was replaced by a 1 cm thick carbon target. A scintillation counter 2.5 cm thick, preceeded by a veto counter to eliminate charged particles, was used to detect neutrons. The asymmetry in the scattering rates between initial proton polarisation up and down was mea-TABLE l V a l u e s o f Rt a n d Dl f r o m d e u t e r i u m ( e x p e r i m e n t 1). E r r o r s are s t a t i s t i c a l o n l y . P r o t o n energy 0 l a b P a r amete r ( M e V ) (deg) 6 -0.41 + 0.08 9 . - 0 . 3 4 ± 0 . 1 0 12 Ri - 0 . 3 4 + 0.08 6 Di 0.14 + 0.08 9 i\ 0.10 + 0.07 12 0.13 + 0.07 6 - 0 . 5 5 - 0 . 1 3 9 «, - 0 . 7 7 ± 0 . 1 3 15 Rt - 0 . 4 1 - 0 . 2 1 18 -0.15 + 0.28 103 .404 C. AMSL sured using the polarimeter S as a monitor of the incident flux. Time of flight was again recorded to reject neutrons with an energy less than the threshold of 75 MeV. Results for at 516 and 343 MeV are listed in table 1 and plotted in fig. 5, together with the data of Reay et al.1) and the predictions from the Liv-ermore phases3) at 500, 350, and 200 MeV. At 500 MeV both predictions from the 0-750 MeV phase shift analysis (curve C,) and from the 0-400 MeV phase shift analysis (curve C 2) are shown. At 343 MeV, /?, remains large and peaks at 9°, as predicted. At 516 MeV, Rt has decreased significantly, and there is no clear maximum. Re-sults for O, at 516 MeV (table 1) are low as pre-dicted. Therefore Z), is not suitable for the produc-tion of a highly polarized neutron beam. 5, Polarisation of the 9° neutron beam Neutrons emerge from the deuterium produc-tion target with transverse polarisation Rt(ap) and •longitudinal polarisation R[(a); the latter was pre-dicted to be small, and we confirm this below. The fringe field of magnet M precesses the neu-tron polarisation through about 25°, so that the polarisation of the emerging neutron beam is at an angle 8 to the transverse direction. We have per-formed an experiment to determine 8 accurately, and to check the magnitude of the neutron polar-isation (experiment 2). The horizontal bending magnet was used to pre-cess the horizontal component of the neutron po-larisation by an angle <p ranging from 0° to 150°. A cylindrical liquid hydrogen target, 50 cm long, 11 cm in diameter was used at position T as a po-larisation analyser. Two scintillation counter tele-scopes detected recoil protons from the hydrogen target at 29° lab in the vertical plane. The solid angle subtended by each telescope was 62 msr and the rate 60/s for 25 nA primary proton beam. The up-down asymmetry was measured as a function of the excitation current in the bending magnet for both directions of the initial proton polarisation (and hence both directions of the neutron polar-isation), to minimise and determine instrumental asymmetries. The total number of good events for each magnet setting was 2 x l 0 5 . Time of flight between the rf and a signal from the front coun-ters in the polarimeter was used to eliminate inelastic neutrons. An unpolarized background of 10% from the empty target was measured at 445 MeV. LR et al. - F i \ 2 3 7 MeV 1 1 ' ' 1 ' 1 f \ i -.i 1 L 1 1 M e V > 1 i 1 I s* 1 1 1 t i 1 1 1 1 -.1 -1 -.1 1 1 1 1 1 W.5 MeV \ i ' 1 Si l ^ 1 1 i i i i 1 i > 1 -.1 -1 1 1 1 I i 516 MeV Ts. 1 1 1 > 1 1 1 1 -.t -~ . l | 1 t 1 i i t i i i \ > ' — — -( 1 1 I 1 ' 1 i -.1 -1 -1 1 . 3CP • 1 1 1 60° i 1 I 90° i 1 1 i2d° 1 1 1 -A 150° -1 1 Fig. 6. Normalized asymmetries from hydrogen vs the preces-sion angle <j> in the magnet H. . •• The up-down scattering asymmetry in the L H 2 target is shown in fig. 6 as a function of the pre-cession angle 4> in the bending magnet for 237, 343, 445, and 516 MeV incident proton energy. The asymmetries shown have been normalised to those in the incident beam polarimeter S and av-eraged over both spin directions to eliminate small instrumental asymmetries. A l l errors shown are statistical. The data have been fitted to the two-parameter function F(<f>) = A cos(tf> + c5), where A = (Rf + R[2)> P n p(29° 1ab)/Pp p(26° lab). Here Pnp and Ppp are the analysing powers for re-coil protons at the quoted angles in np and pp elastic scattering. For (j) = \n — 8 the horizontal neutron polarisation is purely longitudinal. Results for A and 8 are shown in table 2. A 1096 background correction has then been applied at all energies. The polarisation transfer parameters Rx 104 M O N O E N E R G E T I C P O L A R I S E D N E U T R O N B E A M 405 TABLE 2 The polarisation <<7n> of the neutron beam for a polarisation of 7896 in the proton beam. The polarisation transfer Rt and R[ have been obtained using the values of Paf and Ppp given here. Proton energy Neutron energy (MeV) (MeV) 237 • 220 343 325 445 425 516 495 A 0.365 ±0.018 0.463 ±0.018 0.409 . ±0.008 0.302 ±0.010 SO 27.6 ±2.2 23.7 ±1.5 28.3 ±1.0 30.8 ±1.3 PnvW° lab) / y 26° la-b) -0.124 0.290 -0.222 0.327 -0.232 0.351 -0.248 0.368 Rt(9° lab) -0.94 ±0.12 -0.75 ±0.10 -0.68 ±0.09 -0.49 ±0.07 R[(9e lab) -0.07 ±0.08 0.03 ±0.07 -0.01 ±0.07 -0.01 ±0.05 0.73 ±0.09 0.59 ±0.08 0.53 ±0.07 0.38 ±0.05 and R[ have been calculated from A and 8 after subtraction of the spin precession in the fringe field of the magnet M , using Pnp(29°) and P p p(26°) K, at 9° lab from experiments 1 ($) and 2 (+). Errors Fig. 7 shown include uncertainties of and 696 respectively in the predictions for />np (29°) and Ppf{26°: predicted by our phase shift analysis. The leading error is due to uncertainties in Pap and PVP estimat-ed to be presently ±1196 and ±696 respectively. The values for'/?! at 237, 343, and 516 MeV are in good agreement with those in experiment 1 at 9°, and with those of ref. 1. A l l results are shown in fig. 7. The last row of table 2 gives the neu-tron polarisation for a typical proton beam polar-isation of 7896. 6. Conclusions The proton to neutron polarisation transfer Rt in deuterium is a slowly varying function of incident energy, and is a suitable mechanism to obtain pol-arised neutron beams up to 500 MeV. The op-timum polarisation transfer is reached for neutrons emerging at about 9° lab with respect to the inci-dent proton beam. Values obtained at the highest energy are however lower than those expected from phase shift predictions. This is not too sur-prising since large uncertainties remain in the present phase shift analysis of the np system- in this energy range. The authors are indebted to T. Hodges and J. Nelson for designing and running the deuterium target, to J. Beveridge for setting up the polarized ion source and to G. Waters for technical assis-tance in running the solenoid and the multiwire proportional chambers. R e f e r e n c e s ') N. W. Reay, E. H. Thorndike, D. Spalding and A. R. Tho-mas, Phys. Rev. 150 (1966) 801. 2) C. W. Bjork, P. J: Riley, B. E. Bonner, J. E. Simmons, K. D. Williamson, M. L. Evans, G. Glass, J. C. Hiebert, M. Jain, R. A. Kenefick, L. C. Northcliffe, C. G. Cassapakis, PI. C. Bryant, B. D. Dieterle, C. P. Leavitt, D. M. Wolfe and D. W. Werren, Phys. Lett. 63B (1976) 31. 3) F. Folkmann and D. F. Measday, CERN MSC report C-17/675 (1968): 4) D. Axen, L. Felawka, S. Jaccard, J. Vavra, G. A. Ludgate, N. M. Stewart, C. Amsler, R. C. Brown, D. V. Bugg, J. A. Edgington, C. J. Oram, K. Shakarchi and A. Clough, to be published. 105 APPENDIX B L E T T E R E A L N U O V O C I M E N T O V O L . 20, N . 5 1 Ottobre 1977 D, R, E' and P in pp Elastic Scattering from 209 to 515 MeV (*). D . A X E N , L . F E L A W K A , S . J A C C A R D (**) and J . V A V R A (***) University of British Columbia - Vancouver, BC, Canada G. A . L T J D G A T E and N . M . S T E W A R T Bedford College - London, UK C . A M S L E R , E . C . B R O W N (* .*) , D . V . B T J G G, J. A . E D G I N G T O N , C. J . O R A M and K. S H A K A R C H I Queen Mary College - London, UK A . S . C L O T J G H University of Surrey • Guildford, UK (rieevuto it 27 Giugno 1977) Phase-shift analyses (*) show that pp elastic-scattering amplitudes are unique up to 600 MeV. However, significant uncertainties remain, particularly at the higher en-ergies. The objectives of this experiment are to determine the amplitudes accurately at small angles, and to make a definitive measurement of gl, the ~°pp coupling constant. The parameters P, D, and B have been measured at laboratory angles of 6°, 9°, 15 3, and 21°, and the parameter R' at 15°, with a typical uncertainty of +0.02, by scattering a polarized proton beam on an unpolarized proton target and analysing the final-state polarization in a. carbon polarimeter. The final-state polarization <0/> is given by (l + P<ai>-n)<[a,> = (P + n<:af>-n)n + <aiy-nxkt(Bnxk, + B'k/) + + <[oi}-ki(Anxk/ +A'k,), where n is a unit vector parallel to fc^x/i/, and kt, k; are the momenta of incident and scattered protons i n the laboratory. Also <o<> is the polarization of the incident beam. (•) Research supported by the Atomic Energy Control Board and the National Research Canada. (**) Nov; at SIN, Villigen, Switzerland. (***)Now at Carleton University, Ottawa, Ontario, Canada. (*,*) Now at Rutherford Laboratory, Chilton, Oxon, U K . ( ' ) K . A. Aia-OT, R. H . H A C K M A X and L. D . R O P H R : Phys. Rev. C, 9, 555 ( 1 9 7 4 ) . 151 106 152 D. AXEN, L. FELAWKA, S. JACCABD, J. VAVRA, G. A. LTJDGATE, ETC. The experimental lay-out i s shown i n fig. 1. The polarized proton beam at T R I U M F , •with an intensity of 2 nA and 7 8 % polarization, was scattered, from a 20 cm liquid-hydrogen target. The beam energy was readily varied by means of the radial position of the f o i l which strips the H~ ions accelerated i n the cyclotron. Energies are known with an accuracy of ± l M e V from the cyclotron field. The beam polarization was monitored continuously by four counter telescopes 2' detecting pp elastic scattering from a 0.75 mm C H 2 f o i l at a laboratory angle of 26°. The background contribution from carbon of (5-^10)% was measured with a carbon f o i l . A superconducting sole-noid SS precessed the polarization of the incident beam into the scattering plane for the B and B' experiments. Fig. 1. - Experimental lay-out for D,R,R' and P measurements. SS, superconducting solenoid; LH,, liquid hydrogen target. MWPC are shown dotted; S, scintillation counters; V, vetoes unscattered protons; O, carbon analyser; T, motion oi beam polarization. Elastically scattered protons were identified i n a telescope of scintillation counters SDA< S O B , and S, defining a solid angle of 0.1 msr. Inelastic protons were rejected by-time of flight. Pions were rejected by both time of flight and momentum analysis in a small magnet deflecting elastic protons by 10 mr. For the B' measurement the small magnet was replaced by a magnet precessing the longitudinal polarization by 90°. The polarization of the scattered protons was analysed by a 6 cm carbon block i n a polarimeter made of 12 multiwire proportional chambers (MWPC). The front six chambers were (50x50) cm 2, and the last six were (100 X 100) cm 2. The coincidence S 0 1. 2 > I V triggered on scatters between 4° and 32°, for which the analysing power, averaged over azimuth and scattering angle, was about 0.35. Roughly one proton in 14 scattered, and typically 60 scatters/s wore recorded. The experiment proceeded i n three stages. F i r s t l y the MWPC polarimeter was calibrated at 10 energies with a statistical accuracy of ± 2 % using protons of known polarization. This beam was derived by scattering unpolarized protons from the liquid-hydrogen target through 24° laboratory (and 15° at 515 MeV). The polarization at this angle is known from previous experiments and phase-shift analysis with an ab-solute uncertainty of ± 6 % . Details of this calibration w i l l bo provided elsewhere. Secondly P, D, B, and B' were measured as outlined above. Thirdly an additional measurement of P was made by reversing the beam polarization, using the polari-meter T and counter telescopes at 9°, 15° and 24° laboratory. Again, values for P at 9°, 15° and 26° were normalized to the value of P at 24°. 107 D > B, B', AND P IN pp ELASTIC SCATTERING FKOJI 209 TO 515 MeV 153 Results for P, D, P, and B' are shown in fig. 2 and 3. A l l errors shown are statistical. In addition, there are normalization uncertainties, common to one energy, of A P A P _ AR' _ A D _ "P" = 2P = 2P/ = 2D ~~ ± This normalization uncertainty has li t t l e effect on the following phase-shift analysis and on the determination of gl- It is our intention to eliminate i t later by a double-scattering experiment. Figure 2 and 3 show the best fits obtained by our phase-shift analysis of these meas-urements together with existing data ( 1 , a). The phase shifts are listed i n table I. Our " 30 60 8' (degrees) 200 300 «)0 C(MeV) B l - 2. - Results for D, B and R' (15° lab) at 515 (a)), 425 (6)), 379 ( c ) ) , 324 (d)) and 209 MeV ( e » . 6* is the scattering angle in the cm. system. The curves aro phase-shift fits. Errors shown are statistical. («) J . BrSTBiOKY, F. L E H A R and Z. J A N O U T : CEA-N-1547(E) (1972). 108 154 D. AXEN, L. FELAWKA, S. JACCARD, J . VAVRA, G. A. LUDGATE, ETC. data reduce the errors significantly at the higher energies, and agree well with the precise existing data at 210 MeV. A t 380 and 515 MeV the minima wore previously poor, but are now deep and well defined. A t 325 MeV S-wave TC-production was as-sumed to be the dominant inelastic process, arid hence the inelasticity was treated as a free parameter i n 3P1. A t the higher energies, where isobar production dominates, the inelasticity was treated as a free parameter i n 1D2. - S* (degrees) Fig. 3. - Results for P. There is a serious discrepancy at 380 MeV between 31^2 and 3JF3 and smooth curves through other energies We believe that additional data, particularly D around 90°, are required at this energy to'eliminate faulty measurements i n the original data set. The shape of D(6) is very sensitive to ei, which is i n turn very sensitive to the 7r-exchange (OPE), but insensitive to the exchange of the heavy bosons a, rt, p, and co (HBE). Our values of H agree with OPE within the errors at al l energies. We have calculated H B E contributions to high partial waves from sets of coupling constants given by several authors (3"s). A l l agree that H B E contributions to e4 are one order of ( J ) R . A . B R Y A N and B. L . S C O T T : Phys. Rev., 135, B 434 (1964). ( 4 ) A . S C O T T I and D . Y . W O N G : Phys. Rev., 138, B 145 (1965). ( ' ) T . I N O , M . M A T S U D A and S . S A W A D A : Proy. Theor. Phys., 33, 489 (1965). (") R . A . A R N D T , R . A . B R Y A N and M . H . M A C G R E G O R : Phys. Lett., 21, 314 (1966). (') G. Kor-p and P. S O D I N G : Phys. Lett., 23, 494 (1966). (•) D. V. BciGO: Nucl. Phys., S B , 29 (196S). T A B L E I. - Phase-shijl solutions. Values in parentheses are taken from OPE + HBE. Errors include the normalization uncertainty and the error in g*. Coulomb amplitudes and phase shifts have been used with a dipole form factor for each proton. The phase shifts s t i l l include the effect of the Coulomb barrier. Inelasticities arc given by t) = cos 20. A l l phases are i n degrees. Phase 210 MeV 325 MeV 380 MeV 425 MeV 515 MeV 3P0 — 2.18±0.51 —13.10±1.63 . —10.93±3.11 — 20.62±1.47 —17.68±3.38 ISO 4.85±0.52 — 9.05±0.G2 —16.08±0.87 — 18.12±0.74 — 22.(57±3.25 3P1 — 22.46±0.22 — 31.35±1.04 — 33.63±0.79 — 35.99±0.57 — 34.07±1.97 3P2 15.96±0.17 1G.70±0.37 17.70±0.08 17.51 ±0.35 21.33 ±0.46 e2 — 2.81±0.12 — 2.80 + 0.25 0.04±0.37 — 1.99±0.3S 2.07±0.73 3P2 1.25±0.20 0.81+0.40 — 2.36±0.67 — 0.84±0.46 — 0.97±0.81 1D2 7.33±0.28 9.10±0.48 12.05±0.31 12.48 ±0.45 15.58±0.70 3P3 — 2.53±0.17 — 2.90±0.59 0.58±0.60 — 2.75±0.36 2.38±0.54 3P4 1.96±0.16 2.85±0.14 2.64±0.50 3.03±0.20 5.00±0.34 e4 (- 1-21) (- 1.58) (- 1.83) (- 1-94) (- 2.31) 3-ET4 — 0.15±0.20 0.55±0.17 — 0.25±0.47 — 0.38±0.22 — 3.13 ±0.54 1G4 1.14 + 0.10 1.12+0.20 2.30±0.19 1.9S±0.25 4.78 ±0.56 3/25 — 0.84±0.17 — 1.67±0.34 — 1.63 ±0.45 — O.S8±0.38 — 1.83±0.46 3J30 — 0.02±0.13 0.55 ±0,12 0.60±0.33 0.22±0.17 — 0.94±0.3S 0(3P1) 3.52±0.17 0(1Z>2) 6.82 ±0.03 10,71±0.41 22.00 ±0.00 9% 14.05±0.91 13.25 ±0.94 13.91 ±0.92 (13.85) (13.So) 3/J4(0PE + H B E ) 0.41 0.65 0.72 0.90 — 1.4C 37I5(0PE + ITBE) — 0.91 - 1.19 — 1.24 — 1.58 —' 1.7S 3/Z6(OPE + HBE) 0.21 0.44 0.55 0.72 0.98 b S! O M w > O O H W 2 3 o 1=1 » o to o 1-3 o o VO 110 156 D . A X E N , L . F E L A W K A , S . J A C C A R D , J . V A V R A , G . A . L T J D G A T E , E T C . magnitude less than experimental errors. We therefore set £4 at O P E plus a mean value for H B E from these authors. Wc set waves above 37J6 to O P E . At the higher energies, and 37J6 seem to f a l l below values from O P E + H B E , so we leave them free at all energies. We are undecided about 37J5^it shows no systematic disagreement with O P E + H B E , and has a large O P E component, so is potentially helpful i n fixing gl. The coupling constant g20 has been determined from the lowest three energies •with and without 37J5 free i n the phase-shift analysis. The mean value is 9l = 13.84 with a statistical error of ± 0.54 and a total error, covering systematic uncertainties, of 4; 0.65. This value is insensitive to the treatment of inelasticity at 32a MeV and 380 MeV, and to the normalization of our P, D, B, and B' data. From TWJV scattering, the 7r-pn coupling constant is /L = 0.0790 ±0.0010 ( 9), from which gt = (2M/rt_)~ fL — 14.30 ± 0.18 if one substitutes M = mean nucleon mass, fi^ = ix--mnss. It is an open question whether / 2 is charge independent^ or g2, or neither. If /2 were charge independent, gl = {231Ju0)2P would be 15.25 ±0.19. The value determined from this experiment is two standard deviations lower, and favours g% being charge independent rather than /2. The measured widths of the A(1230) resonance i n its + + and 0 charge states favours the same conclusion ( 1 0), particularly with the latest Coulomb corrections of Tromborg et al ( u). The J V J V O P E potential depends on (72exp[—j.ir\jjjfl r; we conclude that its volume integral, which enters into nuclear binding energies, depends on <72 and is charge independent. » * * It is a pleasure to acknowledge our gratitude to Dr. J . E . R I C H A R D S O N and the staff of T R I U M F for making us welcome and for their efforts in making this experiment possible. We are greatly indebted to Dr. J. B E V E E I D G E , for getting the polarized beam working so quickly, and to G . W A T E R S for design and maintenance of the equipment. (•) D . V. BUGG , A. A. CARTER and J . E. CARTER: Phys. Lett., 44 B , 278 (1973). ( 1 0) J. B , . CARTER, D. V. BUGG and A. A. CARTER: Nucl. Phys., 58 B , 378 (1973). ( " ) B . TROMBORG, S . WALDENSTROM and I. OVERBO: Nordita-76/30. PUBLICATIONS Felawka, L.T., J.G. Holnar, J.D. Chen and D.G. Boase, "GAMAN - a computer program for the qualitative:and quantitative evaluation of Ge(Li) gamma-ray spectra11, AECL-4217 (1973) Felawka, L.T., "Detection efficiency of plastic scintillators for elastically scattered positive pions", MSc. Thesis, University of British Columbia (1973) Axen, D., G. Duesdieker, L, Felawka, C.H.Q. Ingram, G. Jones, M. Salomon and ¥. Westlund, "A high-resolution scintillation counter vrith particle identification for use with pions", Nucl. Instr. Meth. JJ8 (1974),.p. 435 Poutissou, J.-M., L. Felawka, C.H.Q. Ingram, R. MacDonald, D.F. Measday, M, Salomon and J. Spuller, "A new limit on the decay U?—*rQ?-rl6+lf "» Nucl. Phys. B80 (1974), p. 221 ' Axen, D., G. Duesdieker, L. Felawka, Q. Ingram, R. Johnson, G. Jones, D, Lepatourel, M. Salomon and W. Westlund, "The interaction between positive pions and deuterons at 47.5 MeV", Nucl. Phys. A256 (1976) Axen, D., L. Felawka, S. Jaccard, J. Vavra, G.A. Ludgate, N.M. Stewart, C. Amsler, R.C. Brown, D.V. Bugg, J.A. Edgington, C.J. Oram, K. Shakarchi and A.S. Clough, "D, R, R* and P in pp elastic scattering from 209 to 515 MeV", Lett. Nuov. Cim., Vol. 20, No. 5 (1977), p. 151 Amsler, C,, R.C. Brown, D.V. Bugg, J.A. Edgington, C. Oram, D. Axen, R. Dubois, L. Felawka, S, Jaccard, R. Keeler, J. Vavra, A. Clough, D. Gibson, G.A. Ludgate, N.M. Stewart, L.P. Robertson and J. Reginald Richardson, "A monoenergetic polarised neutron beam from 200 to 500 MeV", Nucl. Instr. Meth. i i i (1977), P. 401 

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