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Measurement of the free neutron-proton elastic differential cross section at 212 and 418 MEV over the… Dubois, Richard 1980

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C.I HEASOBEHENT OP THE FREE NEUTRON-PROTON ELASTIC DIFFERENTIAL CBOSS SECTION AT 12 AND HI 8 HEV OVER THE FOIL ANGOLAS RANGE B.Sc. ..HcGill University (1976) If. Sc. UBC (1978) A THESIS SUBMITTED IN PARTIAL FULFILLHENT THE BEQUIBEMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF GRADUATE STUDIES (DEPARTMENT OF PHYSICS) WE ACCEPT THIS THESIS AS CONFORMING TO THE REQUIRED STANDARDS The University of B r i t i s h Columbia June,1980 © Eichard Dubois, 1980 by Richard Dubois In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb ia , I ag ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s 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 o f 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 o f 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 o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f P n Y s i c s  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 Vancouver, Canada V6T 1W5 Date 27 Aug J98O A B S T B f t C T The f r e e neutron-proton e l a s t i c d i f f e r e n t i a l c r o s s s e c t i o n has been measured at neutron beam e n e r g i e s of 212 and 418 MeV. . The experiment determined the angular d i s t r i b u t i o n over the range 15°-180° (CM) i n two segments, having the same o v e r a l l n o r m a l i z a t i o n . The 15°-90° range was measured by d e t e c t i n g s c a t t e r e d neutrons i n a s c i n t i l l a t o r and HWPC arra y . N o r m a l i z a t i o n was o b t a i n e d by ucving the ar r a y i n t o the d i r e c t neutron beam. Energy s e l e c t i o n was made v i a a time of f l i g h t <TOF) measurement r e l a t i v e to the TEIUHF c y c l o t r o n RF. The neutron d e t e c t o r was c a l i b r a t e d a b s o l u t e l y u sing an a s s o c i a t e d p a r t i c l e technigue, i n which the r e c o i l proton was d e t e c t e d . The r a t i o of c o i n c i d e n t a l l y observed neutron-proton p a i r s to protons alone y i e l d e d the e f f i c i e n c y , which was used to c a l i b r a t e neutron beam monitors. The remainder o f the angular d i s t r i b u t i o n was obtained by d e t e c t i n g the s c a t t e r e d protons i n a magnetic spectrometer., Proton s e l e c t i o n was made using the TOP through the spectrometer and the momentum. Energy s e l e c t i o n was made v i a the BF TOF. N o r m a l i z a t i o n was provided by the same monitors as used i n the measurement of the forward h a l f of the angular d i s t r i b u t i o n . The n o r m a l i z a t i o n of &<T/dJl has been determined t o about 3%, with s t a t i s t i c a l a c c u r a c i e s of i i about 1-3% on the i n d i v i d u a l data p o i n t s . These d a t a have been i n c l u d e d i n a phase s h i f t a n a l y s i s t o g e t h e r w i t h a l l world d a t a , showing an improvement i n the energy dependence 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 near 0 ° CM and i n the phase s h i f t s , n o t a b l y , Together w i t h the p r e v i o u s l y measured B o l f e n s t e i n p a r a m e t e r s , unambiguous phase s h i f t s i n the 1=0 system are o b t a i n e d f o r the f i r s t tirce i n the TEI0MF energy r a n g e , . i i i ACKNOWLEDGEMENTS I would l i k e to express my appreciation to the members of the BASQUE group at TRIUMF for th e i r invaluable help i n performing these measurements. They are Claude Amsler, Ed Auld, Tony Clough, Martin Comyn, John Edgington, Beg Gibson, George Ludgate, Beg Bichardson, l y l e Robertson, and Noel Stewart. In pa r t i c u l a r , I would like to thank David Bugg f o r ca l c u l a t i n g the corrections to the data, and for his ove r a l l guidance of the experimental program. Many possibly tedious hours of my l i f e have been diverted to more useful endeavours through the use of the excellent histogramming package, FIORA, developed at TRIUMF by Arthur Haynes., My thanks go to ray supervisor, Mike Craddock, f o r his guidance and support during the four years of my education at the University of B r i t i s h Columbia and TRIUMF. Much of that graduate and undergraduate education was shared with my fr i e n d and fellow student, Richard Keeler, with whom I have had uncounted hours of stimulating discussion and argument. His grasp of physics has often helped me with d i f f i c u l t problems. I V I would l i k e to express my deep g r a t i t u d e t o David &xen f o r t e a c h i n g me the a r t of experimental p h y s i c s . He has been the backbone of the BASQUE group, combining l e a d e r s h i p , diplomacy and some l a r c e n y to keep i t on course. He i s l a r g e l y r e s p o n s i b l e f o r the progress I have iuade i n t h i s work. , My l o v i n g wife, Deborah, has always given me the g r e a t e s t support and encouragement throughout these four years and e s p e c i a l l y these l a s t months of i n t e n s i v e work in completing the data a n a l y s i s and p r e p a r a t i o n of t h i s t h e s i s . V T H I S T S E S I S I S D E D I C A T E D TO D E B O B A H v i TABLE OF CONTENTS I . INTBODOCTION , 1 1 .1 h i s t o r i c a l review . . . . . . . . . . . . . , . . . . . . . . . . * . . . 1 1 .2 m o t i v a t i o n f o r the experiment . . . . . . . . . . . . . . . . , 4 1.3 d e s c r i p t i o n c f the e x p e r i m e n t a l method . . . . . . . 6 I I . PEINCIPLE OF THE EXPEEIHENT 10 I I I . EXPERIHE NT ft L EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 111.1 f i x e d equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 I I I . 1 .1 the c y c l o t r o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 111 .1 .2 p r o t c n p o l a r i m e t e r . . . . . . . . . . . . . . . . . . . . . . . 22 111.1.3 n e u t r o n p r o d u c t i o n t a r g e t . . . . . . . . . . . . . . . . 25 111.1.4 neutron c o l l i m a t o r . . . . . . . . . . . . . . . . . . . . . . . , 2 8 111.1 .5 n e u t r o n beam i n t e n s i t y moni tor 29 I I I . 1.6 c l e a n u p c o l l i m a t o r and sweep magnet . . . . . . 32 111.1.7 l i g u i d hydrogen t a r g e t . . . . . . . . . . . . . . . . . . . 34 111.1.8 downstream hel ium bag and beam dump . . . . . . 37 111.1.9 hydrogen t a r g e t moni tor . . . . . . . . . . . . . . . . . . 38 111.2 t h e neutron d e t e c t o r . . . . . . . . . . . . . . . . . . . . . . . 41 I I I . 2. 1 the t r i g g e r s c i n t i l l a t o r s 44 111.2.2 the veto c o u n t e r s . . . . . . . . . . . . . . . . . . . . . . . . 46 111.2.3 t h e m u l t i - w i r e p r o p o r t i o n a l chambers . . . . . ,46 I I I . 4 a p p a r a t u s f o r the e f f i c i e n c y measurement . . . 48 I I I .6 t h e p r o t o n d e t e c t o r . . . . . . . . . . . . . . . . . . . . . . . . 52 I ' l l . 7 e l e c t r o n i c s (................................ 57 IV.ANALYSIS AND BESOMS ............................. 64 IV.1 analysis of neutron counter data ............. 64 IV.1.1 event selection ........................... 65 IV. 1.1.1 time of f l i g h t 67 IV. 1. 1. 2 flWPC track f i t t i n g ...................... 73 IV,1.2 the neutron beam .......................... 80 IV. 2 measurement of the absolute e f f i c i e n c y of the neutron detector .............................. 84 IV.2.1 p r i n c i p l e and reguirements of the measuremen t ................................... 84 IV.2.2 data taking ............................... 91 IV. 2.3 corrections to the number of nucleons incident on the detectors ....................;. 94 IV.2.4 analysis with no exit track angle cut ..... 97 IV.2.5 analysis with a 17° exit track angle cut .,101 IV.2.6 error analysis ............................ 108 IV.3 the neutron monitors ........................ 112 IV.3.1 monitor s t a b i l i t y .........................112 IV.3.2 monitor l i n e a r i t y with neutron flux .......115 IV.3.3 random coincidences in the monitors ....... 118 IV.4 analysis of the forward hemisphere data .....119 IV.4.1 elimination of backgrounds ................119 IV.4.2 corrections due to eguipment problems .....121 IV.4.3 empty target subtraction .................. 122 I V . 4 . 4 z e r o degree data . . . . . . . . . . . . . . . . . . . . . . . . . . 123 I V . 4 . 5 time of f l i g h t c u t s on the data . . . . . . . . . . . 125 I V . 4 . 6 c o r r e c t i o n s to the raw data . . . . . . . . . . . . . . . 126 I V . 4 . 6 , 1 i n c i d e n t beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 I V . 4 . 6 . 2 d a t a at non-Zero a n g l e s . . . . 1 2 7 I V . 4 . 7 parameters needed to c a l c u l a t e dtf/dJ}. . . . . . . 129 IV. 4.8 e r r o r e s t i m a t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 1 I V . 4 . 9 a n g u l a r d i s t r i b u t i o n s . . . . . . . . . . . . . . . . . . . . . 134 I V . 4 . 1 0 c r o s s c a l i b r a t i o n of the m o n i t o r s . . . . . . . . 136 I V , 4 . 1 0 . 1 a b s o l u t e monitor e f f i c i e n c i e s . . . . . . . . . . 136 I V . 1 0 . 2 e r r o r e s t i m a t e . . . . . . . . . . . . . . . . . . . . . . . . , . . 1 3 8 I V . 5 a n a l y s i s o f the backward hemisphere data . . . ,;I39 I V . 5 , 1 s e l e c t i o n o f events .141 I V . 5 . 3 t o t a l energy c o u n t e r . . . . . . . . . . . . . . . . . . . . . . 152 I V . 5 . 3 r e d u c t i o n c f the raw data . 155 I V . 5 . 4 empty t a r g e t data . . . . . . . . . . . . . . . . . . . . . . . . . 155 I V . 5 . 6 c o r r e c t i o n s t o the data due t o eguipment a b e r r a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 I V . 5 . 7 c o r r e c t i o n s t o the raw data . . . . . . . . . . . . . . . 158 I V . 5 . 8 parameters needed t o c a l c u l a t e d^/dP-, . . . . . 160 I V . 5 . 9 e r r o r e s t i m a t i o n . . . . . 1 6 2 I V , 5 . 1 0 a n g u l a r d i s t r i b u t i o n s . . . . . . . . . . . . . . . . . . . . 165 I V . 6 i n r e t r o s p e c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 I V . 7 comparison o f e x p e r i m e n t a l t e c h n i q u e s . . . . . . . 1 7 3 V.INTEEPSETftTION OF THE ESTA 175 ix V.I p r i n c i p l e of phase s h i f t analysis ............175 V.2 current status of the phase s h i f t analysis ...179 V. 3 new data in the phase s h i f t analysis ...182 V. 2. 1 data near 212 Mev ...182 V.2.2 data near 418 MeV 187 V.3 energy dependencies 190 7.4 conclusion ...................................195 Eeferences .......................................... 196 APPENDIX A.MWPC TRACK FITTING CRITERIA ....201 APPENDIX B.CORRECTION FOR INCOMPLETE AZ IMUTHAL ACCEPTANCE OF DETECTORS ..204 B.1 p r i n c i p l e of the algorithm 205 B.2 application to the neutron detector .......... 214 APPENDIX C.DENSITIES OF LIQUID AND GASEOUS HYDROGEN IN THE TARGET 2 17 APPENDIX D. INVENTORY OF MATERIALS ..223 X LIST OF FIGURES 1. EXPERIMENTAL CONFIGURATIONS ...................... 8 2. SCATTERED NDCLEON KINETIC ENERGY VERSUS LABORATORY ANGLE ........................ ............... ^ 3. OVERVIEW CF APPARATUS USED IN THE MEASUREMENTS 4..THE TRIUMF FACILITY ......................... 1 9 5. BEAK LINE 4 A . . . . . . 2 3 6. , PROTON POLABIMETER , 2^ 7. THE LIQUID DEUTERIUM TARGET ...................... 2 6 8. NEUTRON EBAH INTENSITY MONITORS . . . . . . . 3 0 9. CLEANUP COLLIMATOR AND SHEEP MAGNET 33 10. ,THE LIQUID HYDROGEN TARGET . . 3 5 11. TARGET MONITOR 39 12. THE NEUTRON DETECTOR . . . . . . . ' t 2 13. SCHEMATIC OF THE PV AND P2 SCINTILLATOR ARRAYS . . . 5 14. MULTI-WIRE PROPQRTIAL CHAMBERS .................. ^9 15. THE RECOIL PROTON TELESCOPE .....50. 16. THE PROTON SPECTROMETER ......................... 53 17. ELECTRONICS FOR THE NEUTRON MONITORS 59' 18. ELECTRONICS FOR THE NEUTRON DETECTOR ............ 6 0 19. ELECTRONICS FOR THE PROTON SPECTROMETER ......... ^ 20. ELECTRONICS FOR THE COMPUTER GATING AND EVENT READOUT ....................... ................... ;6? xi 21. MEASUREMENT OF THE FORWARD HEMISPHERE OF THE DIFFERENTIAL CROSS SECTION . . . . . . . . . . . . . . . . . . . . . . . . 66 22. RESOLUTION OF THE TIME OF FLIGHT MEASUREMENT AS A FUNCTION OF KINETIC ENERGY . . . . . . . . 468 23., TIME DIFFERENCE BETWEEN ELASTICALLY SCATTERED NEUTRONS AND BACKGROUNDS .........................;;Z0 24. TIME OF FLIGHT OF CHARGED PARTICLES THROUGH THE NEUTRON LET ECTOR 72 25. VERTICAL PROFILE OF EVENTS FROM THE CARBON CONVERTER WITH NO EXIT TRACK ANGLE C UT . . . . . . . . . . . : 75 . 26. DETERMINATION OF THE MAXIMUM ALLOWABLE EXIT TRACK ANGLE FROM THE CONVERTER ......................... \-76, 27. VERTICAL PROFILE OF EVENTS AT THE CARBON WITH AN EXIT TRACK ANGLE CUT OF 17° . . . . . . . . . . . . . . . . . . . . . . J78 28. VERTICAL AND HORIZONTAL PROFILES OF THE NEUTRON EE AM .81 29. .CALIBRATION OF THE NEUTRON DETECTOR ,85 30. ENVELOPE OF ACCEPTED NEUTRONS DETERMINED BY THE RECOIL ARM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 7 . 3 1 . , HORIZONTAL AND VERTICAL PROFILES OF NEUTRONS AT THE CARBON IN THE CALIBSATION .................... 90; 32. TOF AND ADC SPECTRA IN THE CALIBRATION MEASUREMENT . . 93 33. EXIT TRACK ANGLE DISTRIBUTION . . . . . . . . . . . . . . . . . . . '38. 34. NEUTRON DETECTOR EFFICIENCIES WITHOUT EXIT TRACK x i i C UTS ............................................ . 1.00 35. RATIO OF EFFICIENCIES WITH AND WITHOUT THE EXIT TRACK ANGLE CUT .1 02 36. NEUTRON DETECTOR EFFICIENCIES WITH EXIT TRACK CUTS 105 37. RATIO OF IN - BEAM TO OUT-0 F-BEAM MONITOR COUNTS AS A FUNCTION OF TIME . . . . . . . . . . . . . . . , . . , . . , , . , 1 1 3 . . ' 38. RELATION BETWEEN THE OUT-OF-BEAM MONITOR AND PROTON POLABIHETER COUNT RATES ................... 1.1.16; 39. TYPICAL P1-RF TOF SPECTRUM FOR THE NEUTRON DETECTOR ........................... . . ............. 120 • 40. NEUTRON BEAM RF TIME OF FLIGHT SPECTRUM 124 41. CONFIGURATION FOR THE BACKWARD HEMISPHERE MEASUREMENT ............................. ... ...... 140. 42. PARTICLE IDENTIFICATION IN THE SPECTROMETER 144 -43. , MOMENTUM DIFFERENCE BETWEEN ELASTIC PROTONS AND MOST ENERGETIC INELASTIC PROTONS ................. 1^ 5:^  44. CORRELATION OF MOMENTUM AND RF TOF .............. 1A7 . 45. PROFILE OF EVENTS FROM THE LIQUID HYDROGEN TARGET ..................................................... 148 ^ 46. INTERSECTION OF TRACKS FROM THE TWO HALVES OF THE SPECTROMETER AT THE MAGNET CENTER ................150* 47. MOMENTUM OF THE FULL ENERGY ELASTIC PROTONS ......151 48. CORRELATION OF PULSE HEIGHT IN S4 WITH THE TOF FROM S1 TO S2 ......................153 49. .PULSE HEIGHT IN S4 FOR FULL ENERGY PROTONS ...... 15V 50. AVERAGE POLAR SCATTERING ANGLE ......., . ,. 51. BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION AT 212 MEV .......................................... 1 68 52. PREVIOUS BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION DATA NEAR 212 MEV . . . . , , . , , 1 6 9 . 53. BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION AT 418 ME V ..... ...................... . , . ..... >.. . ... 1 7 0 V 54. PREVIOUS BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION DATA NEAR 418 MEV . . . . . . . . . . . , . , . , . . , 1 7 1 . 55., ENERGY DEPENDENCE OF THE DIFFERENTIAL CROSS SECTION \<yi: ^  56. ENERGY DIP EN DEN CI OF THE 1=0 PHASE SHIFTS . . , . . . , 1 9 3 ; " 57. ENERGY DEPENDENCE OF THE 1=1 PHASE SHIFTS f^-E1. ALLOWED REGIONS OF THE AZIMUTHAL SCATTERING ANGLE . , . . . . . . . 2 0 6 E2. GEOMETRY OF THE (f> ALGORITHM ................. 208: B3. ROTATION OF THE EXIT TRACK ELLIPSE BY THE INCIDENT AZIMUTHAL ANGLE .................211- h B4. DEFINITION GF THE EIGHT POSSIBLE INTERS ECTIONS OF THE ELLIPSE AND THE DETECTOR BOUNDARIES . . 2 1 3 B5. VERTICAI PROFILE AT THE CARBON WITH P2E FAILED ..2 1 6 . ' • CI. TEMPERATURE OF THE LIQUID AS A FUNCTION OF THE PRESSURE . . . ............. ... . . ... ,-,> ....... . . ..... %\f C2. DENSITY OF THE LIQUID HYDROGEN AS A FUNCTION OF xiv TE8PEBATUBE . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . .21 9 -C3. HYDROGEN GAS PRESSURE AND DENSITY AS FUNCTIONS OF ENTROPY 221 CU. HYDROGEN GAS DENSITY AS A FUNCTION OF TEMPERATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 2 2 2 Dl. MEAN PATB LENGTH OF SCATTERED PROTONS IN HYDROGEN 226 XV I I S T O F T A B L E S 1. W O R L D D A T A F O B T H E N - P D I F F E R E N T I A L C R O S S S E C T I O N 7 2. D I M E N S I O N S O F T H E N E U T R O N B E A M M O N I T O R C O U N T E R S . . . 31 3. D I M E N S I O N S O F T H E H Y D R O G E N T A R G E T M O N I T O R C O U N T E R S *t0 4. D I M E N S I O N S O F T H E N E U T R O N D E T E C T O R S C I N T I L L A T O R S . .•".43 5. D I M E N S I O N S O F T H E R E C O I L A R M C O U N T E R S 51 6. D I M E N S I O N S O F T H E S P E C T R O M E T E R S C I N T I L L A T O R S . . . . . .~55 7. N E U T R O N B E A M P R O P E R T I E S . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 8. R E C O I L A R M A N D N E U T R O N D E T E C T O R C O N F I G U R A T I O N S . . . . 89 9. R U L T I P L E S C A T T E R I N G A N D A T T E N U A T I O N C O R R E C T I O N S . . . 96. 10. N E U T R O N D E T E C T O R E F F I C I E N C I E S W I T H O U T E X I T T R A C K C U T S . . . . . . . . . . . 99 11. N E U T R O N D E T E C T O R E F F I C I E N C I E S W I T H E X I T T R A C K C U T S 106 . 12. E R R O R E S T I M A T E S F O R T H E E F F I C I E N C Y O F T H E N E U T R O N D E T E C T O R 110., 13. C O R R E C T I O N S T O T H E M O N I T O R S F O R I N D U C E D A C T I V I T Y . 1 1 7 14. C O R R E C T I O N S T O T H E F O R W A R D H E M I S P H E R E D A T A . . . . , . , 1 2 0 15. V A R I A T I O N O F Df/QSl F O R V A R I O U S C H O I C E S O F T H E C U T S . . . . ............................... ... ........... ... . 133 16. R E S U L T S F O R T H E D I F F E R E N T I A L C R O S S S E C T I O N A T 212 A N D 418 M E V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 5 17, A B S O L U T E E F F I C I E N C I E S O F T H E N E U T R O N M O N I T O R S . . . .1:37-X 18. CALCULATED CORRECTIONS TO THE DATA ...............159= 19. SENSITIVITY OF THE BACKWARD DIFFERENTIAL CROSS SECTION TO THE RF COTS ...........................163 20. BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION AT 212 ME V ..... .;. ................................... i 66 21. BACKWARD HEMISPHERE DIFFERENTIAL CROSS SECTION AT 418 MEV- ..,.,......,»,.,........,,..,,.........,,. i 67 22. PHASE SHIFTS PREDICTED FROM THE PREVIOUS DATA AT 212 AND 418 MEV .................................. 181 23. PHASE SHIFT FITTED VALUES OF THE NORMALIZATIONS FOR DATA NEAR 212 MEV 185 24. PHASE SHIFTS FROM THE CURRENT ANALYSIS AT 212 MEV 186 25. PHASE SHIFT FITTED NORMALIZATIONS FOR DATA NEAR 418 M EV: .....188 26. PHASE SHIFT RESULTS FROM THE CURRENT ANALYSIS AT 4 18 MEV ................ 191 D1. THICKNESS OF MATEEIALS BETWEEN THE HYDROGEN TARGET AND S PECT ROM ETER .................. . . .......... , . . 22"5 1 INTBODUCTION 1.1 HISTOJBICftL BEVIEW Study of the nucleon-nucleon (N-N) f o r c e has been a c e n t r a l occupation f o r p h y s i c i s t s s i n c e the d i s c o v e r y of the neutron by Chadwick*. Kucleons are the most a c c e s s i b l e t o o l s f o r a study of the s t r o n g i n t e r a c t i o n . Furthermore, as they are c o n s i d e r e d to be the b a s i c c o n s t i t u e n t s of n u c l e i , knowledge of t h e i r i n t e r a c t i o n i s r e l e v a n t t c an understanding of n u c l e a r p r o p e r t i e s . Hith these two g o a l s i n mind, a tremendous amount o f e f f o r t has been i n v e s t e d i n the experimental de t e r m i n a t i o n and t h e o r e t i c a l e x p l a n a t i o n of the nucleon-nucleon i n t e r a c t i o n . The f i r s t decade of r e s e a r c h was devoted to i d e n t i f y i n g the p r o p e r t i e s of the f o r c e : t h a t i t was energy dependent 2; that the core r e g i o n was s t r o n g l y r e p u l s i v e 3 ; t h a t a new symmetry, I s o s p i n 4 , was respected by i t ; and t h a t n o n - c e n t r a l f o r c e s 5 , tensor and s p i n - o r b i t , were present as w e l l . H i t h t h i s i n f o r m a t i o n , the most g e n e r a l form of the i n t e r a c t i o n p o t e n t i a l was 2 c o n s t r u c t e d 6 , a l t h o u g h t h e r e was l i t t l e o r no u n d e r s t a n d i n g o f the p r o c e s s e s which g e n e r a t e d the f o r c e . ft major s u c c e s s was made by Yukawa 7 i n h i s g e n e r a l i z a t i o n of the i d e a s o f e l e c t r o d y n a m i c s , i n which he p o s t u l a t e d the s t r o n g f o r c e to be mediated by the exchange o f v i r t u a l p a r t i c l e s t h a t , by n e c e s s i t y , had f i n i t e mass to a c c o u n t f o r the s h o r t range o f the f o r c e . With t h e d i s c o v e r y o f the p i o n , by P o w e l l 8 i n 1947, and f u r t h e r e x p e r i m e n t a l e v i d e n c e , i t was shown 9 t h a t h i s view w e l l d e s c r i b e d t h e l o n g range { g r e a t e r t h a n a few p i o n Compton wavelengths) p r o p e r t i e s o f t h e f o r c e . ,> In l i g h t o f t h i s s u c c e s s , much e f f o r t was poured i n t o the meson t h e o r e t i c a p p r o a c h 1 0 which hoped t o show t h a t the s h o r t and medium range components of the s t r o n g i n t e r a c t i o n were due t o t h e exchange of o t h e r , h e a v i e r mesons. Two s h o r t - c o m i n g s were a p p a r e n t i n t h i s a p p r o a c h : the s t r o n g f o r c e d i d n o t l e n d i t s e l f t o p e r t u r b a t i o n t h e o r y ; a n d , i n o r d e r to f i t t h e e x p e r i m e n t a l d a t a , a medium mass meson, the <f~, was r e q u i r e d 1 1 . The <f meson has never been found e x p e r i m e n t a l l y . , a t t h i s t i m e , p h e n o m e n o l o g i c a l a p p r o a c h e s 1 2 were t a k e n t o d e s c r i b e t h e i n t e r a c t i o n . C o m b i n i n g knowledge of the form o f the p o t e n t i a l w i t h e x p e r i m e n t a l measurement of 3 a limited number of NH observables, analyses sere undertaken that parametrized the amplitudes i n terms of phase s h i f t s . The high angular momentum (and so, long range) phases were calculated from the one pion exchange (OPE) potential and the remainder were determined from the data. These values of the phase s h i f t s were then available for use in nuclear theory calculations. An outgrowth of the meson exchange ideas has been combined with the technigue of dispersion r e l a t i o n s 1 3 - 1 5 to provide the currently accepted mode of calculation. Through applications of the pr i n c i p l e s of a n a l y t i c i t y , u n i t a r i t y , and crossing, the dispersion r e l a t i o n s describing the N-N interaction are transformed into those requiring knowledge cf 101,7X71, and eN interactions, but nothing of the actual N-N force i t s e l f . This method encounters d i f f i c u l t i e s at short range, owing to computational problems in including the exchange of systems of mass greater than two pions. To produce an " a l l radius" potential, the core region i s parametrized from N-N data, with the hope that this region (< 0.8 fm ) w i l l soon be calculable i n the theory of quantum chromodynamics (CCD). In t h i s approach, f i t s have been obtained to the data which are of comparable quality to those of the phenomenological phase s h i f t analyses (PSA). 4 '1-2 MOTIVATION FOR THE EXPERIMENT Information on the isospin dependence of the N-N force requires an examination of interactions of both the proton-proton (p-p) and neutron-proton (n-p) systems; the p-p case has access only to the 1=1 channel, whereas the n-p case involves both 1=0 and 1 = 1 channels. At the outset of this experiment, data for the p-p system were of adequate quality, while those f o r the n-p system i n the energy range 200 - 500 MeV were scarce and of low accuracy. Input of the data into the PSA gave ton-unique solutions for the parameters* 6. Furthermore, there were systematic disagreements between some of the data sets, especially around 300 MeV, e.g. the data from the Princeton-Pennsylvania A c c e l e r a t o r 1 7 (PPA) and L i v e r p o o l 1 8 . Dsing phase s h i f t analyses as a base, a s t u d y 1 9 was undertaken to assess the best set of experiments to perform i n order to maximize the resu l t i n g information. The procedure used was i t e r a t i v e , i n that "measurements" , with e r r o r s , of various observables were input to the analysis and the eff e c t observed. The r e s u l t of the study was that measurements of the following free, e l a s t i c n-p 5 observables were expected to be the to best improve the data set: Kolfenstein parameters D, B, A, D^ , B i r A^ 55°-125° CM ±0.03 Polarization P 55°-125<> CM ±0.02 d i f f e r e n t i a l cross section 5°-180° CM ±1% The error l e v e l shown was a r b i t r a r y , but t y p i c a l of that reguired. To date, the Wolfenstein parameters and polarization have a l l been measured, leaving only the d i f f e r e n t i a l cross section to f i n i s h the experimental program, aimed at f i x i n g a l l 1=0 phases to the same precision as the 1=1 phases. Measurement of the d i f f e r e n t i a l cross section to this l e v e l hecame possible with the advent of the high flux "meson f a c t o r i e s ' ^ " so that high i n t e n s i t y , nearly monoenergetic neutron beams became available, using deuterium targets for neutron production. .. Additionally, and perhaps most importantly, t h i s measurement of dtf /dJi-i s novel i n that i t i s the f i r s t i n the intermediate energy range 200-500 MeV to provide a d i s t r i b u t i o n over the entire angular range with a single normalization. Due to the kinematics of n-p scattering, the rate and 6 energy of scattered p a r t i c l e s decrease rapidly approaching 90° lab. Consequently, i t becomes impractical to detect the scattered neutrons over the entire angular range. In practice, only forward going, energetic p a r t i c l e s are detected: neutrons, to obtain the forward part; and forward scattered protons for the backward region. These measurements had previously always been done by separate methods and d i f f e r e n t experimental groups. Table 1 l i s t s the previously ex i s t i n g cross section data i n the v i c i n i t i e s of the energies 212 and 418 MeV. 1 - 3 DESCRIPTION OF THE EXPERIMENTAL HETHOD The technique used i n t h i s experiment was as follows (Fig 1). The neutron beam, monitored by an upstream detector, was incident on a proton target with the scattered neutrons observed by a neutron detector. As i s explained l a t e r i n the text, use of the technique of placing the detector in and out of the incident beam largely eliminated detector e f f i c i e n c i e s from the measurement, allowing calculation of d<T /dJl . The neutron detector was then calibrated absolutely by a conjugate p a r t i c l e method: scattered protons were counted i n one arm while some neutrons were detected at the kinematically 7 Neutron Center of Mass E n e r g y Angular Range Performed At (digl 46 '95.6 11 - 5) P P A 196 111 - 179 PPA 47 199 76 - 158 Rochester 48 2 0 0 6 - 180 D u b n a ^ 2 1 0 11 - 51 P P A 4 6 2 1 0 111 - 179 PPA Z f7 2 1 K 5 120 - 180 LAMPF** 2 2 '5 76 - 178 R o c h e s t e r ^ 224 1 1 1 - 1 7 9 PPA 4 7 224 11 - 51 P P A 46 390.2 1 1 - 5 3 PPA 4 6 -400 12 - 178 Carnegie 5 0 414 60 - 180 PPA 4 8 ^21 151 - 180 Sac lay Z , 3 428.9 118 - 180 LAMPF 42 T a b l e 1„ World data f o r the n-p 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 h i s Table l i s t s a l l the p r e v i o u s l y e x i s t i n g data on 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 near the energies 212 and 418 MeV. 8 NEUTRONS / MONITOR t\ HYDROGEN TARGET ! \ NEUTRON OR PROTON DETECTOR ( a ) \ \ NEUTRONS MONITOR RECOIL vy' PROTON DETECTOR HYDROGEN TARGET NEUTRON DETECTOR ( b ) Fig 1. Experimental configurations. ,, Fig(a) shows the setup used to measure the d i f f e r e n t i a l cross section. Fig(b) shows the setup for the c a l i b r a t i o n of the neutron monitors. conjugate angle by the neutron detector, giving the absolute e f f i c i e n c y of the detector. This information was used to cross-calibrate the upstream monitor, giving i t s e f f i c i e n c y f o r detecting neutrons. , Armed with t h i s information, measurement of the backward hemisphere could proceed..Scattered protons were detected with v i r t u a l l y 100% e f f i c i e n c y . With the number of incident neutrons known from the same monitor, the cross section was obtained, with the same normalization as the forward hemisphere. The object of th i s thesis i s to report on the measurement of d<f /aft. over the entire angular range at two energies, 212 and 418 HeV. The c a l i b r a t i o n of the neutron detector and monitor i s also discussed. F i n a l l y , the results of t h i s measurement are incorporated with the world data set on a l l N-N observables into a phase s h i f t analysis, completing this program of e l a s t i c n-p work. 10 I I . PRINCIPLE OP THE EXPERIMENT The interpretation of the n-p e l a s t i c d i f f e r e n t i a l cross section i s that i t i s the probability that a neutron incident upon a target proton w i l l scatter e l a s t i c a l l y into a s p e c i f i e d s o l i d angle. In p r i n c i p l e , i t can simply be determined by counting both the incident number of neutrons and the number scattered into the s o l i d angle of inter e s t . In pra c t i c e , however, the counting of neutrons is d i f f i c u l t due to the generally low and energy-dependent e f f i c i e n c i e s of a l l neutron detectors. For a detector with a small s o l i d angle of acceptance, d-fr, the number of neutrons scattered into i t , N s, i s given by * _f <kSl where n 0 i s the incident number of ne utrons n i s the density of target protons df /dj\- i s the e l a s t i c n-p 11 d i f f e r e n t i a l cross section (laboratory frame) i s the s o l i d angle subtended by the detector, and t i s the target thickness., With a neutron detector of f i n i t e size, e f f i c i e n c y £ , and a team monitor having e f f i c i e n c y ? J , the numbers of p a r t i c l e s detected are where Hp i s the number counted by the neutron detector, and N?*o«\ -*-s t n e number counted by the neutron monitor. The functional dependences of the variables should be noted here: 12 Here <x,y) correspond to coordinates describing the plane perpendicular to the scattered p a r t i c l e d i r e c t i o n ; E represents the kinetic energy of the p a r t i c l e ; and 0" the polar scattering angle. The (x'^y*) are the coordinates perpendicular to the incident beam d i r e c t i o n . Henceforth, the (x,y) variations s h a l l be neglected and considered only as corrections to the ide a l case of uniformity in spa t i a l coordinates. , The e f f i c i e n c i e s and t are generally unknown, but can be eliminated i f the measurements are made with the detector placed i n the incident neutron beam: both the detector and the monitor sample the same beam. , Hith E the energy of the incident beam. . Combining eg(1) and ( 2 ) , noting that in eg{1) £ (E )= £ ( E & ) , the scattered energy, one gets and 13 The monitor e f f i c i e n c y . T\ (E ') , h as cancelled out and cnly the r e l a t i v e energy e f f i c i e n c y variation of the neutron detector remains. Pig 2 shows a t y p i c a l plot of scattered p a r t i c l e k i n e t i c energy as function of laboratory scattering angle. The rate and energy of the scattered p a r t i c l e s drop rapidly as the angle approaches 90° lab.„It i s well known that neutron detector e f f i c i e n c i e s f a l l r a p i d l y with energy i n the range (100 - 500 MeV). I t i s p r a c t i c a l l y impossible to detect a single type of p a r t i c l e over the entire angular range and one must detect protons i n the range 0° - 50° (lab) to measure the backward angular d i s t r i b u t i o n of the scattered neutrons. With a proton detector one cannot simply move into the incident neutron beam to cancel out the monitor e f f i c i e n c y . . I t must he known absolutely a p r i o r i . ks has been described b r i e f l y i n the introduction, i t i s determined by c r o s s - c a l i b r a t i o n from the neutron detector e f f i c i e n c y , when i t i s also i n the neutron beam so that both the neutron detector and monitors sample the same neutron beam., Once ^ i s known, the number counted by the proton detector, of e s s e n t i a l l y unit e f f i c i e n c y , i s 14 ^ LAB Fig 2. ,. Scattered_nucleon kinetic energy  versus laboratory angle., The variation of the scattered nucleon's k i n e t i c energy with polar lab scattering angle i s shown for incident k i n e t i c energies of 215 and 42 0 MeV, 15 with ^< being the conjugate angle to & , and dtf" /d J l . the only unknown i n the eguation. To summarize, having measured the absolute e f f i c i e n c y cf the neutron monitor, the d i f f e r e n t i a l cross section i s obtained over the entire angular range with a single normalization. , 16 I I I . EXP EH MENTAL EQUIPMENT As discussed i n the previous chapter, the object of the measurements was to determine the number of neutrons incident on the target, and the number of neutrons (or protons) scattered into a given s o l i d angle. Fig 3 shows a schematic of the apparatus used to perform the measurement. Neutrons produced at the deuterium target scattered from the l i q u i d hydrogen (LH^ ) target. The scattered neutrons (or protons) were observed in a movable detector. III. 1 FIXED EQUIPMENT This section deals with the elements of apparatus which were fixed on the experimental f l o o r , i e . did not involve the movable neutron cr proton detectors. BEAM LINE 4A 17 MONITOR C CONVERTER 4AB2 DIPOLE ^/PROTON BEAM MONITOR 0° NEUTRON BEAM NEUTRON COLLIMATOR NEUTRON BEAM MONITOR CLEARING MAGNET AND COLLIMATOR I NEUTRON DETECTOR PV SCINTILLATOR CV MWPC PI SCINTILLATOR P2 SCINTILLATOR Fig 3. , Overview of apparatus used i n the measurements. Neutrons produced at the LD-2. target are collimated and then scatter i n the LH2. target into a movable detector. The neutron detector i s shown here.-18 I I I . 1. 1 The Cyclotron The primary proton beam was produced by the TBIOHF sector-focused c y c l o t r o n 2 1 . The protons, accelerated as H -ions, are extracted by a carbon or aluminium " s t r i p p e r " f o i l . The r a d i a l distance of the f o i l from the cyclotron determines the energy of the extracted beam, which i s variable from about 183-518 MeV. Two beams are t y p i c a l l y extracted (Fig 4) , one into the "proton" h a l l , and the other into the "meson" h a l l . As TBIOHF i s p r i n c i p a l l y a meson factory, proton currents of from 10-100 JJ< A are delivered to B11 f o r a high meson flux. The needs of the proton h a l l are i n the region of C.5yA.A, and for t h i s experiment, went as low as 2-5 nA. Consequently, much e f f o r t had been put into achieving large s p l i t r a t i o s between the extracted currents of BL1 and 4. I t has been found that r a t i o s of up to 1000: 1 can be maintained to about 5$., The proton currents required by t h i s experiment varied over a f a c t o r of about 100, so that techniques were required that would allow v a r i a t i o n of the beam int e n s i t y without change i n the other properties of the beam: s p a t i a l position, size and energy. .Simply reducing the ION SOURCE ACTIVATION ANALYSIS — » <£> ... y F i g k. The TRIUMF Fact 1 i ty Two independent beams are ex t r ac ted from the c y c l o t r o n . One goes to the proton h a l l f o r N-N and nuclear phys ics s tud ies and the other to the meson ha 11. 20 current in the ion source, which produces the H~ ions that are injected into the cyclotron, was inadequate as that procedure changed the emittance of the beam injected to the cyclotron. Three techniques were used at various times i n the data talcing: making use of a pulser on the ion source, which eliminated a given f r a c t i o n of the beam pulses; defocussing a lens element (the E i n z e l lens) on the inje c t i o n beamline to dump unwanted portions of the beam; and a l t e r i n g the v e r t i c a l p o sition of the stripper f o i l , to intercept a variable f r a c t i o n of the proton beam c i r c u l a t i n g i n the cyclotron tank. These three methods were found to be equivalent i n their a b i l i t y to allow low beam currents to be extracted without changing beam properties i n going from high currents. The cyclotron radio-frequency (8F) accelerating cavity operates at 23 KHz, and so every 43 ns a proton bunch, of up to 5 ns duration, i s extracted from the cyclotron tank. The bunch width could be varied down to about 2 ns through the use of a "buncher" and chopper on the i n j e c t i o n l i n e . The BE s i g n a l , available to the experiment, had a constant phase with respect to the proton bunch extraction 21 time. This s i g n a l served two purposes: i t gave a reference time with which to clock the a r r i v a l of p a r t i c l e s at the experimental station, allowing determination of the p a r t i c l e s ' energy by the time of f l i g h t 2 2 (TOF) method (which w i l l be described l a t e r in the text) ; and, permitted one to observe "decelerated" beam 2 3. Beam i n the cyclotron tank," which i s not stripped and extracted, i s accelerated to the outer edge of the tank where i t s l i p s cut of phase with the RF, i s decelerated back to the stripper f o i l and extracted. These protons would a r r i v e at the experiment at a time dif f e r e n t from, but with the same energy as, the main proton beam, which could cloud the results of the TOF method., Since the RF period was 43 ns, timings r e l a t i v e to the RF signal were modulo 43 as. P a r t i c l e s which took multiples of 43 ns to reach the experiment appeared to have i d e n t i c a l energy in the TOF method. To examine th i s e f f e c t , a "1:5 s e l e c t o r " 2 * was used to mechanically suppress four out of every f i v e proton bursts from the cyclotron, to a l e v e l of about 10 - 4. Data taken in this way could then be used to see whether there was any hydrogen-associated low energy background that "wrapped around" to be under the e l a s t i c neutron peak. The proton beam was transported to the neutron 22 production target using conventional magnetic elements, shown in Fig 5. The beam l i n e elements were c a r e f u l l y tuned to ensure that the beam properties were not affected by small d r i f t s in the settings of the elements. Several remotely insertable, g a s - f i l l e d , multi-wire proportional chambers were available along the beam line to check the s p a t i a l properties of the beam. Two, having 3 mm wire spacing, were located just upstream of the neutron production target. , The spot size of the beam on these monitors was t y p i c a l l y 5 x 5 mm2. . fts further checks, there were also a s p l i t plate monitor and a polarimeter upstream., III.1.2 Proton Polarimeter & twin double arm polarimeter (Fig 6) was mounted just upstream of the neutron production target. In previous experiments i t had been used to monitor the polarization of the proton beam i n the measurement of the free n-p Wolfenstein parameters. In t h i s experiment, i t was used as an intensity monitor and to check on the horizontal steering of the proton beam. The arms of the polarimeter were sat at the F i g 5• Beam 1ine kA Protons e x t r a c t ed from the c y c l o t r o n are t ransported to the experimental area v i a magnetic focus s ing and bending magnets. Downstream of t h i s experiment, the proton beam goes to a we l l sh ie lded dump. 24 1st LETTER 2nd LETTER SUBSCRIPT R RIGHT R RECOIL F FRONT L LEFT F FORWARD R REAR \ LR telescope Fig 6. Proton polarimeter., The proton polarimeter, upstream of the LB 2 target, detected l e f t - r i g h t asymmetries in e l a s t i c p-p scattering, by observing both protons i n two twin-arm counters. , 25 kineraatically conjugate angles for e l a s t i c p-p scattering from the 0.127 mm thick CH ^  target.. Any differences in the scattering rates between the l e f t and r i g h t arms indicated a horizontal mis-steering of the proton beam (mainly due to the rapid change of the proton-carbon d i f f e r e n t i a l cross section with scattering angle).. Due to requirements of other experimenters on the beam l i n e , the CR?. target was changed frequently so that the polarimeter could not be used as a long term intensity monitor. III.1.3 Neutron Production Target Neutrons were produced at zero degrees with respect to the incident proton direction by q u a s i - e l a s t i c scattering of the incident proton beam from a l i g u i d deuterium (ID^ ) t a r g e t 2 5 . Immediately downstream of the target a bending magnet was used to transport the remaining proton beam to the beam stop. On the way there, the beam was monitored by a secondary emission counter. The magnet also served to eliminate charged p a r t i c l e s coming from the target from the resulting neutron beam. , The target f l a s k , shown i n Fig 7, of length 203 mm by 26 JACK EDGE WELDED BELLOWS 20 K TRANSFER LINES STEEL SHIELDING H2/D2 GAS SUPPLY LINE 80 K COOLING LINE THERMAL SHIELD VACUUM VESSEL TARGET ASSEMBLY 20'-K COOLING COIL FLEXIBLE METAL HOSE VACUUM ONE METRE Fig 7. The l i q u i d deuterjam target. The deuterium i s held in the region denoted "target assembly". Three orientations are possible by moving the assembly up or down: a dummy c e l l , a carbon target, and the deuterium f l a s k . 27 51 mm diameter, held the l i q u i d deuterium. The target end windows were made of 50 j^m s t a i n l e s s s t e e l , while the target vessel was separated from the beam pipe vacuum by windows of 120 j^m thickness. , Target cooling was provided by a P h i l i p s A-20 cryogenerator with two cooling lines..The 20K l i n e fed the heat exchanger d i r e c t l y , while the 80K l i n e cooled the radiation s h i e l d . The target could be f i l l e d i n approximately twelve hours (most of this time required to cool the chamber) and emptied in about one hour. A hydrogen bulb thermometer and carbon r e s i s t o r s were used to monitor the flask's temperature and pressure. These quantities were interfaced into the cyclotron control system, giving access to them at any time. 28 III.1.4 Neutron Collimator A collimator was used to define the siz e of the neutron beam and shield the experimental area and equipment. I t could be used to look at any angle of scatter from the l i q u i d deuterium targe't from -3° to 30° in 3° steps..In t h i s experiment, only the 0° port H a s l e f t open, the others being f i l l e d with s t e e l plugs. At the upstream entrance, the s t e e l pipes were of 100 mm diameter and i n the center were of 125 mm diameter. They were placed between s t e e l plates, with the spaces between the pipes f i l l e d with lead. .The length of the 0° port was 3.3 m and i t s diameter was reduced to 3.81 cm by spec i a l l y made s t e e l plugs. 29 I I I . 1.5 Neutron Beam, Intensity Monitor The incident neutron flux was monitored by an assembly of counters, forming two independent monitors, placed upstream of the hydrogen target. These monitors had to deal with changes i n the neutron flux over two orders of magnitude., For th i s reason, they were b u i l t i n the configuration shown in F i g 8. The i n - l i n e counters, G1 and G2, were intended to work at low i n t e n s i t i e s , while the out-of-beam counters, CB and CL, placed at 29° to the incident neutron di r e c t i o n , were for high i n t e n s i t i e s . The two monitors provided i n t e r n a l consistency checks on each other, as well as for checking the beam conditions. a small f r a c t i o n of the neutron beam interacted in the 2.54 cm thick CH^ slab to produce charged p a r t i c l e s , which were detected by the monitor counters. The veto, CV, ensured that the neutral p a r t i c l e flux could be monitored. The CH slab was made larger than the collimator exit hole, making the monitors i n s e n s i t i v e to small s h i f t s i n the neutron beam shape. Copper plates eliminated some of the low energy background i n the out-of-beam monitor, at 212 MeV, 0.635 cm thick plate was used, while 1.91 cms 10 NEUTRON RANGER F i g 8 , Neutron beam in t e n s i t y monitors. , Neutrons interacted in the CH^ converter to produce charged p a r t i c l e s which were detected i n three counter arms. The two out-of-beam arms were summed to give one monitor, and the in-beam arm was the second monitor. Copper ranger was included i n the out-of-beam monitor to reduce the low energy background. 31 Counter Height (cm) CV CLl CL2 CRl CR2 Gl G2 25.0 20.3 15. 2 20.3 15.2 25.0 25.0 Width (cm) Th i ckness (cm) 25.0 20.3 15-2 20.3 15.2 25.0 25.0 0 . 3 0 0 . 3 2 0 . 3 2 0 . 3 2 0 . 3 2 0. 30 0 . 3 0 Table 2. Dimensions of the neutron beam monitor counters, , 32 sere used at 418 MeV..Table 2 gives the dimensions of the monitor counters. . III.1.6 Cleanup Collimatorfln d S weap_ gagn et A secondary collimator (Fig 9) was employed to reduce the neutral p a r t i c l e background from the main collimator and the monitors. I t was constructed of an aluminium frame f i l l e d with lead bricks and shot, placed between the pole faces of the sweep magnet. Emphasis was placed on shielding the angular region over which the detectors moved, and geometrically, the shielding r e s t r i c t e d the background to scattering angles of le s s than about 5°. The upstream bore of the collimator was 5.08 cm, and was 47 cm long. An inner helium bag was u t i l i z e d along the length of the secondary collimator to reduce scattering of the neutron beam i n the a i r upstream of the hydrogen target. The sweep magnet was used to remove charged p a r t i c l e backgrounds produced by the neutron beam upstream , as no veto counter was placed upstream of the target., I t was found that the veto introduced more background than i t eliminated, by converting a f r a c t i o n of the neutron beam without self-vetoing. The sweep magnet f i e l d was held at neutrons U C L A sweep magnet F i g 9 . C l e a n u p c o l l i m a t o r and sweep magnet* The s e c o n d a r y c o l l i m a t o r r e d u c e d t h e background f r o B the upstream m o n i t o r s and the l i p s o f t h e main c o l l i m a t o r . The sweep magnet removed any r e m a i n i n g c h a r g e d p a r t i c l e s . 34 10 kgauss throughout the experiment. III.1.7 Liquid Hydrogen Target The l i q u i d hydrogen {LH2 ) was contained in a mylar flask which, at room temperature, was 199.5 mm long with a 136.5 mm diameter (Fig 10). Cooling was provided by a S t i r l i n g cycle engine which could cool the target to l i q u i d in about twenty-four hours. Once cold, i t could be remotely emptied i n about eight minutes, leaving cold gas in the fl a s k , and f i l l e d in about two minutes. The density of the l i q u i d was most accurately determined by monitoring the pressure of the gas on the b o i l - o f f l i n e . The normal operating pressure was 17 psia, corresponding to a density of 0.0701 g/cm3,.. The ref r i g e r a t o r cut i n and out on pressure excursions of ± 0.25 psia variation from the operating point, while a 3 psia variation corresponded to a 1% change in the density. The temperature of the flask was monitored by a Cu/Constantan thermocouple attached to the center top of the f l a s k , and was continuously recorded. The t y p i c a l gas density was 5.4 • 10-* g/cm3. Knowledge of the empty target gas density was required i n order to correct the 35 F i g 10. The l i q u i d hydrogen t a r g e t . The t a r g e t f l a s k was surrounded by a gas b a l l a s t r e g i o n maintained at the same pr e s s u r e . The evacuated region o u t s i d e the gas b a l l a s t was surrounded by a spun aluminium dome. 36 empty target subtraction, as i s described l a t e r . , The length of a si m i l a r target was measured at both room and l i q u i d nitrogen temperatures, and was found to contract b j 0.4% of i t s magnitude., By l i n e a r extrapolation, t h i s gave a target length at l i q u i d hydrogen temperature of 198.5 mm, with 0.1 mm as an upper l i m i t on the error of the extrapolation. In the H 2, molecule, there are two possible orientations of the proton spins: p a r a l l e l (ortho-) and a n t i - p a r a l l e l (para-), which occur in the r a t i o of 3:1, and have d i f f e r e n t thermal p r o p e r t i e s 2 6 . To make the l i q u i d homogeneous, a catalyst was used to convert v i r t u a l l y a l l of the hydrogen molecules to the para state. The substance used was a n i c k e l s i l i c a t e having the brand name APACHI-1 produced by Houdry Di v i s i o n of A i r Products. The mylar end windows of the f l a s k were 0.Q13 cm thick. The f l a s k was covered with ten layers of 6. 3 JJ< m aluminized mylar ("superinsulation"), and was surrounded by a gas b a l l a s t region whose walls were 0.025 mm thick mylar. This region was i n contact with the l i g u i d , and so was maintained at the same pressure..The evacuated region, outside the gas b a l l a s t , was enclosed by a spun aluminium dome, 0.107 cm thick. This dome was found to be the main 37 contributor to background events. III.1.8 Downstream HeliumBag And Beam Dump A s e l f supporting helium bag, made of mylar, was placed downstream of the LH ^  target to reduce background from the neutron beam scattering from a i r i n t h i s region. The cylinder was 630 cm long by 36 cm diameter, strengthened by inner styrofoam rings and supported by two styrofoam stands. At the end of the 0° l i n e , a stack of concrete blocks supported two rows of 15x7.5x5 cm3 lead bricks. The bricks were placed to the l e f t of the incident beam so that when the detector was at a non-zero angle, the bricks were between the detector and the intersection point of the beam and the wall. 3 8 I I I . 1 . 9 Hydrogen Target Monitor A three counter telescope (Fig 11) was used to provide an additional monitor of the L H ^  target status. I t was placed at U5<> to the neutron beam, with the solid angle defining counter 70 cm from the center of the target. The telescope acceptance was limited to approximately the volume of the fl a s k . The placement and dimensions were chosen to optimize the constraints that the counting rate be higher than that of the detector at any angle; that i t accept charged p a r t i c l e s from the region of the f l a s k only; and that i t be out of the path of the detector. The counter dimensions are l i s t e d i n Table 3. This completes the discussion of the fixed equip ment. The remaining discussion of the apparatus w i l l deal with the neutron detector, used i n the forward hemisphere measurement, the r e c o i l arm, used to c a l i b r a t e the neutron detector, and, f i n a l l y , the proton detector used f o r the backward hemisphere data. 39 f i g 11 • Target monitor. , The s t a t u s of the LH2 t a r g e t was monitored by a three counter t e l e s c o p e a t 4 5 ° to t h e i n c i d e n t beam d i r e c t i o n . ho Counter Height Width Thi ckness (cm) (cm) (cm) TM1 6 . 0 6 . 0 0 .32 TM2 1 0 . 0 10 .0 0 .32 TM3 6 . 0 6 . 0 0 .32 Table 3. , Dimensions of the hydrogen target monitor counters. 41 III, 2 THE NEUTRON DETECTOR The p r i n c i p l e involved i n the neutron detector was to allow a neutral p a r t i c l e to impinge on a block of carbon, where there was a probability of interaction that resulted in charged p a r t i c l e s emerging from the block., These charged p a r t i c l e s were detected by s c i n t i l l a t i o n counters and indicated the int e r a c t i o n of a neutral par t i c l e i n the carbcn converter. , The apparatus used for the detector i s shown i n Fig 12. The carbon block was 53x53x9 cm3 and was followed by two tr i g g e r s c i n t i l l a t o r s , P1 and P2, which detected the converted charged particles,.The carbon block was 5.57 m from the target center. The detector was mounted on wheels and was attached to a center post, underneath the hydrogen target, by radius arms. The dimensions of a l l the s c i n t i l l a t o r s used are l i s t e d i n Table 4. An aluminium plate 1 cm thick was placed between the two s c i n t i l l a t o r s i n order to reduce the number of triggers from low energy background events. The plates were approximately one metre square i n area. NEUTRONS MWPC 2 (X) MWPC 4 (X) MWPC 6 (X) MWPC 8 (y) PV MWPC I (y) CARBON CONVERTER PI MWPC 3 (y) MWPC 5(y) MWPC 7(y) ALUMINUM SHEET P 2 F i g 12. Them neutron detector. Neutrons incident on the detector interacted i n the carbon converter to produce charged p a r t i c l e s which sere detected in the s c i n t i l l a t o r and MWPC array downstream of the converter. Charged p a r t i c l e s incident on the detector were vetoed by a combination of a s c i n t i l l a t o r and MWPC. *3 Counter Height Width Thickness (cm) (cm) (cm) P1 5 0 . 0 5 0 . 0 0.6k PV A-F Ik.k 3 6 . 5 0 . 3 0 PV G-H 1 0 0 . 0 1 5 . 0 0 . 3 2 P2 A-F ik.k 3 6 . 5 0 . 3 0 P2 G-H 1 0 0 . 0 1 5 - 0 0 . 3 2 Table 4. Dimensions; uof_ the neutron detector c i n t i l l a t o r s . . 44 III. 2. 1 The Trigger S c i n t i l l a t o r s P2 consisted of a hodoscope of s c i n t i l l a t i o n counters, shown Fig 13, to give the better timing resolution that can be obtained from smaller counters. P1 was made smaller i n area than the carbon block in an attempt to minimize edge e f f e c t s . To further reduce backgrounds, the P1 s c i n t i l l a t o r was viewed by two photomultipliers, one at the top, the other at the bottom. Requiring a coincidence between the two tubes eliminated seme of the background due to noise i n the tubes, and due to such phenomena as Cerenkov l i g h t from cosmic ray muons passing through either l i g h t guide. In an attempt to get the best timing from a l l the s c i n t i l l a t o r s on the detector, the l i g h t guides were made adiabatic, i n which the guides were segmented along the edge of the s c i n t i l l a t o r , joining at the c y l i n d r i c a l l i g h t guide base, the length of each segment being egual. , *5 Q Fig 13. S c he ma t i c _ of _ the,., P V a nd _ P2 s c i n t i l l a t o r arrays. The PV and P2 hodoscopes were i d e n t i c a l . The one meter-square area was covered by six s c i n t i l l a t o r s from above and below (A-F) overlapped i n the middle, and two s c i n t i l l a t o r s (G-H) covered the spaces between the others, 4 6 III.2. 2 The Veto Counters Two veto counters were used to ensure that only neutral p a r t i c l e s were able to trigger the detector: a s c i n t i l l a t o r hodoscope (PV) , i d e n t i c a l to P2 i n configuration; and a multi-wire proportional chamber (MWPC, to be described shortly) . The M8PC was used as a low mass device to pick up charged p a r t i c l e s missed by PV, or conversion of neutrals in PV. The need for very high vetoing e f f i c i e n c y i s best i l l u s t r a t e d by an example: with a detector having e f f i c i e n c i e s of 2% and 100%, respectively, f o r neutrons and charged p a r t i c l e s , a veto e f f i c i e n c y cf 99$ would resu l t i n a charged pa r t i c l e background of 50% f o r equal fluxes of both p a r t i c l e s . I l l . 2 . 3 The Multi-wire Proportional Chambers There were seven HWPC»s between Pi and P2 to reconstruct the tracks of the converted charged p a r t i c l e s through the detector. The p r i n c i p l e use of this information was to i d e n t i f y the location of the interaction in the carbon block. There were three MWPC*s giving horizontal coordinates and four giving v e r t i c a l coordinates. 47 The operational c h a r a c t e r i s t i c s of the MWPC's have been well described elsewhere 2 7. Consequently, only the properties important to this measurement are discussed here. The MWPC's were constructed with a wire spacing of 2 irm. To allow a saving on el e c t r o n i c s , they were operated in a mode which e l e c t r o n i c a l l y grouped the wires i n pairs, e f f e c t i v e l y reducing the resolution to 4 mm. This was achieved by summing the output from each pair of wires into an amplifier, instead of a single wire per amplifier. A pulse, induced on a wire by a charged p a r t i c l e traversing the chamber, was stretched out to l a s t 800 ns as a lo g i c pulse. I f the external trigger e l e c t r o n i c s determined that a pa r t i c l e of intere s t had passed by, a strobe pulse was sent to transfer a l l s i g n a l pulse's into latches. Data input was then inhibited while the latches were read sequentially., There was a one-to-one relationship between the latches and wire pairs, so that a set latch i d e n t i f i e d the f i r e d wire and MWPC. Once the reading was finished , an external reset re-enabled the MWPC system.. Readout cf a t y p i c a l event involved a dead time of about 5 msec, with the MWPC's having a memory time (the time i n which the p a r t i c l e ' s ion track remained i n the chamber) of about 150 ns, so that the rate l i m i t on a s the flwPC's was about 10 6 s e c - 1 . The MlfPC's used the "magic" 2 8 gas mixture of approximately SO % argon,bubbled through methylal, 0.4 % argon-freon 13B1, and 44 % isob utane . , This mixture has the property that the ions from the charged p a r t i c l e track diffuse to the nearest wire within 2 mm. The MWPC's (Fig 14) covered one metre square i n area and consisted of 20 yu. m sense wires sandwiched between high tension (HT) plane wires of 122 yx.m thick. , III . 4 APPARATUS FOR THE EFFICIENCY MEASUREMENT As previously discussed, the c a l i b r a t i o n of the neutron detector was achieved via the conjugate p a r t i c l e technigue. For t h i s an additional proton telescope was reguired to supplement the neutron detector. The proton ' telescope i s shown i n Fig 15, and was composed of three s c i n t i l l a t o r s , with copper plates between the l a s t two. The s c i n t i l l a t o r dimensions and placements were chosen to ensure that the conjugate neutrons passed through the neutron detector. The dimensions are l i s t e d in Table 5. The reasons f o r these choices are discussed l a t e r i n the text. US Fig 11. Multi-wire e r o p o r t i a l chambers. The MWPC's were composed of sense wires sandwiched between two HT planes. The "magic" gas mixture was enclosed i n the chamber by mylar windows and continuously c i r c u l a t e d , 50 Fig 15. The r e c o i l proton telescope. .. The r e c o i l protons i n the e l a s t i c n-p scatters were observed i n a three counter telescope. , Low energy pa r t i c l e s and pions were eliminated by copper ranger between BE2 and EE3.„ 51 Counter Height Width Thickness (cm) (cm) (cm) RE1 6.0 6.0 0.32 RE2 15.2 15.2 0.32 RE3 20.3 20 .3 1.11 counters. Table 5m Dimensions of the r e c o i l arm 52 III.6 THE PBOTON DETBCTOB Protons were detected for the measurement of the backward hemisphere of the d i f f e r e n t i a l cross section. The pri n c i p a l d i f f i c u l t y l i e s i n p a r t i c l e i d e n t i f i c a t i o n : there i s a variety of charged p a r t i c l e s , protons, pions and deuterons, which can trigger the detector. I d e n t i f i c a t i o n cannot be achieved by TOF alone - another independent kinematic guantity of the p a r t i c l e i s necessary. This point i s made clear by considering the standard r e l a t i o n s for a r e l a t i v i s t i c p a r t i c l e of momentum p and mass m £ s y -+ m -• r / f where >^ i s the velocity of the p a r t i c l e (c=1).,The TOF method yields j& , so that an independent measurement of p or E w i l l determine the mass of the p a r t i c l e . Partly because of the eguipment available to thi s experiment, momentum analysis was chosen for the second measure., The magnetic spectrometer used to determine the momentum i s shown i n Fig 16. The frame of the spectrometer was the same as f o r the neutron detector, and kept the S 2 counters at a radius of 2.317 m from the center of the 53 S I MWPC 2 ( y ) S2AD 4 m 6 ( x ) MWPC 8 ( y ) MWPC I ( x ) 3 ( X ) 5 ( y ) MAGNET MWPC 7 9 ( S ) (Ax) IO(X) I 2 ( x ) i K y ) P 2 Fig 16. The proton spectrometer. ; Scattered protons were detected i n a spectrometer array consisting of s c i n t i l l a t o r s to i d e n t i f y the passage charged p a r t i c l e s , a magnet to bend them, and HWPC's determine the path of the p a r t i c l e s through the system, P a r t i c l e i d e n t i f i c a t i o n was made by corre l a t i n g the TOF from S1 to P2 and the momentum for each p a r t i c l e . of to l i q u i d hydrogen target. The passage of charged p a r t i c l e s through the detector was signalled by coincidental f i r i n g s cf the s c i n t i l l a t o r s S1, S2 and P2. Si and S2 are described i n Table 6, while P2 i s the same counter used in the neutron detector., S2 was composed of four small counters, S2 A-D, side-by-side, so that the s o l i d angles of the angular bins defined by the counters would be determined by geometry. Six 1/2 m square HSJPC's, otherwise i d e n t i c a l to the previously described P P C s , were used to determine the p a r t i c l e ' s track before entering the magnet, and six 1-m square HWPC's were used a f t e r i t . Emphasis was placed on the p a r t i c l e s * horizontal bend so that four of each set of six chambers were cf horizontal readout. The remaining two were v e r t i c a l . , I d e ally, the v e r t i c a l component of the tracks would be unaffected by the v e r t i c a l f i e l d . This was l a t e r v e r i f i e d i n the analysis of the data. In order to allow a greater bend through the spectrometer, the front s c i n t i l l a t o r s and the magnet were offset to the right i n the detector..The magnet had a 10 cm pole gap, with the pole faces of S O cm diameter. The ^ B - d l was l i n e a r i n the e x c i t i n g current and was equal to 480.16 kG-cm at 1150 amps. A thick s c i n t i l l a t o r , S4, was i n s t a l l e d on the 55 Counter Height Width Thickness (cm) (cm) (cm) (cm) S1 25-0 25.0 0 .30 S2 A-D k.O 3.75 0.20 P2 A-F 7k.k 36 . 5 0.30 P2 G-H 100.0 1 5 .0 0.32 Sk ^Qi.O 15-0 10.0 Table s c i n t i l l a t o r s . 6. Dimensions of the spectrometer 56 spectrometer, which could be inserted immediately downstream of the S2 counters, S4 was used at large angles where i n e l a s t i c proton production was kinematically prohibited and the e l a s t i c a l l y scattered protons had t y p i c a l l y less than about 100 MeV. In these cases, the use of S4 eliminated the additional l o s s of protons i n the materials i n the spectrometer downstream of S2, The s c i n t i l l a t o r was 10 x 10 x 15 cm3. When not in use, S4 was s l i d to the side of the spectrometer frame,> It was important that the detection e f f i c i e n c y of the spectrometer be as close to unity as possible. The e f f i c i e n c i e s of the i n d i v i d u a l s c i n t i l l a t o r s were estimated by measuring the number of coincidences recorded by two counters on either side of the s c i n t i l l a t o r in guestion, and comparing that number to the number of three-fold coincidences. The e f f i c i e n c i e s were optimized to a l e v e l of better than 99.9% by adjusting the HT * s of the s c i n t i l l a t o r s . A s i m i l a r procedure was carried out for the HWPCs, using the s c i n t i l l a t o r trigger to determine the passage of charged p a r t i c l e s through the chambers. By adjusting the HWFC HT*s, t y p i c a l e f f i c i e n c i e s of about 99% were obtained. Due to the redundancy of the horizontal coordinate chambers, the expected f i t t i n g e f f i c i e n c y with 57 such i n d i v i d u a l e f f i c i e n c i e s was v i r t u a l l y 100%, so that u n - f i t events were probably due to had triggers, e.g. random coincidences i n the s c i n t i l l a t o r s . , III.7 ELECTRONICS The passage of p a r t i c l e s of i n t e r e s t through the various detectors ("events") was s i g n a l l e d by fast electronic l o g i c devices. The experiment was controlled by a PDP 11/34 computer, which communicated with the fast electronics through a CAHAC interface. An event triggered the computer by the f a s t e lectronics sending a pulse to (strobing) an EG5G C2 12 b i t pattern unit, which sent a Look-At-Me (LAM) i n t e r r u p t to the computer. This interrupt caused the computer to i n h i b i t the CAMAC and MWPC systems from recording further, and to proceed to record data for that event stored by the MWPC's, d i g i t a l counters (scalers), t i m e - t o - d i g i t a l converters (TDC's), analogue-to-digital converters (ADC's) , and the C212 b i t pattern unit. , The C212 also recorded the f i r i n g pattern of a l l non-monitor s c i n t i l l a t o r s . These data were transferred to 80 0 BPI magnetic tapes, and then used to form on-line histograms, which enabled experimenters to monitor the data as i t was 58 being taken. These were viewable on either a Decwriter II hardcopy terminal or a Tektronix 4010 graphics terminal. The CAMAC system was composed of two crates on a single branch. The f i r s t crate contained the C212, scalers, TDC's and ADC's, while the second contained the MWPC interfaces and a test c o n t r o l l e r (used to check the HHPC system) . as the el e c t r o n i c s configurations for the three measurements were very s i m i l a r , they w i l l be described together. The lo g i c devices used were NIM standard, and th e i r configurations are shown in Fig 17-Fig 20. Bandom coincidences in the various detectors were measured by u t i l i z i n g the periodic BF structure of the cyclotron..The probability of detecting p a r t i c l e s i n any beam burst i s assumed to be equal. Therefore, the coincidence rate of a count i n a detector with a count in a subsequent burst would be a measure of the coincidence rate in a single burst. It should be noted that the discriminator used f o r the monitor veto, CV, was used i n the burst guard mode, in which the l o g i c output pulse was extended u n t i l the input analogue pulse f e l l below the threshold l e v e l . This ensured that, for high rate conditions, multiple pulses in P R O T O N P O L A R I M E T E R 59 Out-of-beam and In-beam Monitors J C L | C L 2 C R | C R 2 C V ( C L+CR)Cv|^J Hydrogen Target Monitor TM, TMr TM Secondary Emission R P Monitor sine wove SE M T M T D C I : 4 stop TDC 2 :1 stop F i g 17, monitors. See Fig 19 for the legend, Electronics for the neutron 60 MWPC trigger F i g 1 8 . , E l e c t r o n i c s fpr„the.neutron d e t e c t o r . E l e c t r o n i c s f o r the r e c o i l arm, when used i n the c a l i b r a t i o n measurement are a l s o shown..See F i g 19 f o r the legend. \ 61 s I S 2 S 4 P2 A B C D ABCDEFGH I I I I ADC TDC I sian _ S,S2 S2 TDC 12 *top TDC II slop S|SgS4 "totol energy" trigger I l^2P2 sP e c , r o m e , e r trigger discriminator •D -j ^ logical "OR" to scaler input Legend JTYYY cable deloy r\j delayed by multiple of 43ns »— Inverted output M to C2I2 bit pattern unit spectrometer, Fig 19. Electronics f o r the proton 62 computer • trigger C 2 12 strobe ADC gate MWPC trigger computer busy dua gen. gate crote NIM inhibit /TTL busy clear from computer 32 ns scaler inhibit Fig 20. Electronics for the computer gating  and event readout. See Fig 19 f o r the legend. 63 the counter would be properly vetoed. , fill threshold l eve l s were set to - 1 0 0 mV and log ic pulse lengths l e s s than 4 3 ns were used to ensure that pulses from one beam burst could not overlap pulses due to an adjacent hurst.. 64 IV. ;AMALYSIS AND BBSOLTS Analysis of the data breaks naturally into three categories: the c a l i b r a t i o n of the neutron detector and monitor; the forward hemisphere data, taken with the neutron detector; and the backward hemisphere data, taken with the proton spectrometer. The data analysis consisted of taking the required information stored on data tapes, recorded durinq the experimental runs, f o r each event and reducing i t to obtain the d i f f e r e n t i a l cross section. The necessary computations were performed on the. University of B r i t i s h Columbia Amdahl 470/V6. IV.1 ANALYSIS OF NEOTBOH COPNTBB DATA As both the c a l i b r a t i o n and the forward hemisphere data were taken with e s s e n t i a l l y the same equipment, much of their description i s necessarily s i m i l a r . 65 IV.. 1.1 Event Selection An event was recorded by the neutron detector (Fig 21) whenever the s c i n t i l l a t o r s , P1 and P2, f i r e d coincidentally, while the veto s c i n t i l l a t o r , PV, did not. The p r i n c i p l e of t h i s d e f i n i t i o n was to require that a neutral p a r t i c l e be "converted" to charged p a r t i c l e s , i n the carbon, and be detected by Pi and P2. ,• There were several sources of background which were able to s a t i s f y t h i s c r i t e r i o n : (1) neutrons from hp —*• nnTf*" — * n PTT° (2) *s from np — * • np TT° 1—> y^r (3) cosmic rays which, for some reason, did not f i r e PV, and (4) random coincidences of P1 and P2. (note that processes (1) and (2) are not kinematically allowed at 212 BeV.) One of the primary tasks of the analysis was to separate the good, e l a s t i c n-p scattering events from the remainder of the data. The data which were av a i l a b l e for 66 BEAM LINE 4A MONITOR C CONVERTER 4 A B 2 DIPOLE 0° NEUTRON BEAM NEUTRON COLLIMATOR >y PROTON BEAM MONITOR NEUTRON BEAM MONITOR CLEARING MAGNET AND COLLIMATOR NEUTRON DETECTOR PV SCINTILLATOR CV MWPC PI SCINTILLATOR P2 SCINTILLATOR Fig 21. Measurement of the forward hemisphere of the d i f f e r e n t i a l cross section.; Forward scattered neutrons were detected i n t h i s measurement. 67 t h i s task were two tine of f l i g h t spectra, and the MWPC track f i t t i n g c a p a b i l i t y . IV. 1. 1. 1 Time Of F l i g h t This technigue i s used to determine the energy of a p a r t i c l e from the time i t takes to traverse a known distance. One has that * t - — -where s i s the distance ( i c metres) , Lt i s the t r a n s i t time (in ns), and A i s the ve l o c i t y of the p a r t i c l e . F ig 22 shows a plot of — * the change i n tit with dT kinetic energy, evaluated for protons, showing that as T increases, the resolution of the time of f l i g h t (TOF) method decreases rapidly. For example, at 200 MeV, a width of ±1 ns, over a distance of 10 m, corresponds to an energy spread of 18 HeV, while at 500 MeV, the spread i s 89 MeV, a change in resolution of from 9 to 18%. vAt these energies, TOF i s c l e a r l y not a high resolution technigue. fts mentioned previously, i t was possible to time the a r r i v a l of the events to the cyclotron BF s i g n a l . This es s e n t i a l l y gave the t o t a l t r a n s i t time for the neutron to travel from the LD« target to the detector. I t i s this 68 0' • : — > . : L _ 100 200 300 4 0 0 500 T(MeV) Fig 22. Besolution of the time of f l i g h t  measurement as a function of kinetic energy. The resolution increases rapidly with decreasing k i n e t i c energy, changing by more than a factor of s i x over the energy range of 100 to 500 HeV i n which the detector accepted neutrons. 69 guantity which was used to eliminate neutral p a r t i c l e s from background processes (1) and (2) . Fig 23 shows the calculated time difference between e l a s t i c a l l y scattered neutrons and the most energetic i n e l a s t i c neutrons possible, as a function of scattering angle. This i l l u s t r a t e s that the i n e l a s t i c s are well separated in time, and, as i s shown l a t e r , pose no problem., s i m i l a r fashion, since they t r a v e l so much more quickly than the e l a s t i c neutrons., Fiq 23 shows the time difference between these two sources of events also. A possible source of background was rescattering of neutrons from the f l o o r and a i r into the neutron detector. A s t e e l bar was placed between the hydrogen target and the detector to absorb almost a l l the neutrons coming d i r e c t l y from the target. A l l recorded events were then due to non-target associated sources. A contribution to these events from rescattered neutrons that had come from the l i q u i d hydrogen would show up i n a difference between target f u l l and empty rates. A measurement of t h i s effect yielded a n u l l r e s u l t , and so i t was neglected i n the analysis of of the data. The 43 ns period of the cyclotron introduced another The <2) can be eliminated i n a 70 Fig 23. Time difference_between e l a s t i c a l l y scattered neatrons and backgrounds. , The calculated time difference between e l a s t i c a l l y scattered neutrons and Q rays from the LH2, target shows that they are separable at a l l angles (ignoring the resolution of the TOF system and energy d i s t r i b u t i o n of the beam). Separation of e l a s t i c s and i n e l a s t i c s should be clean above 20° and good below. The contamination l e v e l s are discussed i n the text. 71 source of background to the measurement. As discussed previously, neutral particles a r r i v i n g at the detector a multiple of 4 3 ns after the e l a s t i c neutrons would be indistinguishable from the e l a s t i c s . The 1:5 selector was csed to investigate t h i s background, with the r e s u l t that no s t a t i s t i c a l l y s i g n i f i c a n t contamination of the e l a s t i c neutron peak resulted from t h i s low energy background,, The second piece of TOF information was the time reguired for the converted charged p a r t i c l e s to travel from P1 to P2. A t y p i c a l plot of the P1-P2 TOF i s shown in Fig 24. The smaller peak i n the plot corresponds to backward going p a r t i c l e s through the detector, allowing the elimination of those backward going cosmics which triggered i t . A narrow peak was found i n the backward region of the P1-P2 TOF spectrum, which was attributed to electronic r e f l e c t i o n s , though t h i s was never f u l l y v e r i f i e d . A l l of these "backward" going particles were cleanly eliminated by applying a cut, discarding a l l the events i n the smaller peak of the P1-P2 TOF plot.. I t was found that the number of e l a s t i c neutrons remaining was insensi t i v e to t h i s cut. 72 3000 neutrons I oo 2000h yrays O lOOOh "backward" going particles 0 O o 0 o o o 0 o o ° -o n " i o O O -O 1 20 30 40 50 60 70 P,-P 2 (chan) Fig 24, lime of f l i g h t of charged p a r t i c l e s  through the neutron detector. I cut was applied near channel 40 to eliminate "backward" going p a r t i c l e s . The y i e l d of e l a s t i c neutrons was inse n s i t i v e to reasonable variations of the cut., 73 IV. 1. 1. 2 MHPC Track F i t t i n g The procedure used to determine the charged p a r t i c l e tracks through the detector i s described i n some d e t a i l in Appendix a. , The primary uses of the track information were to i d e n t i f y the position of the interaction in the carbon, and the angle of the track on ex i t from the carbon. , The HWPC's were used to define a " f i d u c i a l " region of the carbon converter. This requirement was made to eliminate any e f f e c t s that might occur towards the edges. As an example, the probability of rescattering i n the converter was on the order of 10%. Therefore, at the edges, neutrons rescattering towards the center of the detector would stand a much better chance of triggering the detector, while those rescattering away from the center would be l o s t , causing a drop i n the detector*s ef f i c i e n c y at the edges. The f i d u c i a l region was (somewhat a r b i t r a r i l y ) defined to be 40 cms square, removing 6.5 cm from a l l edges. From purely geometrical considerations, i t can be seen that the e f f i c i e n c y of detection varies across the face of the carbon converter..The s o l i d angle subtended by P2 from any point on the converter i s not constant. In 74 addition, the angular d i s t r i b u t i o n of charged p a r t i c l e s observed i n n-C 1 2 scattering peaks near 20° lab, so that neutrons i n t e r a c t i n g i n the center of the carbon would be more l i k e l y to trigger P2 than those at the edges. The d i f f e r e n t i a l cross section i s independent of the azimuthal scattering angle, <J) , so that, to a good approximation, for 0 > 5 ° , the d i s t r i b u t i o n of events originating from the converter should be uniform i n the v e r t i c a l d i r e c t i o n , and should r e f l e c t i t s e l f i n a f l a t p r o f i l e of events, binned i n horizontal s t r i p s . Any deviation from flatness indicates a variation i n the e f f i c i e n c y , either due to geometry or eguipmental bias. Such a p r o f i l e i s shown in F i g 25, and shows d i s t i n c t drops towards the edges of the carbon. Only a central f i d u c i a l region of the carbon i s shown, to eliminate edge ef f e c t s . The p r o f i l e r e f l e c t s the geometrical drop-off in ef f i c i e n c y . A cut was made on the exit track angle of the scattered track, so that a l l events accepted at the converter would have an equal chance of triggering P2, regardless of the i r point of or i g i n within the f i d u c i a l region of the carbon. The choice of the maximum angle was determined by the geometry of the converter and P2, as shown i n Fig 26, and was set to 17°. A t y p i c a l v e r t i c a l 75 Fi g 25, V e r t i c a l p r o f i l e of events from the cartoon converter, with no exit track angle cut. The effect of the change of s o l i d angle subtended by P2 from points on the converter i s i l l u s t r a t e d i>y the f a l l i n g p r o f i l e away from the center. 76 Fig 26. Determination of the maximum allowable exit track angle from the converter. , The maximum angle was determined by the siz e of the " f i d u c i a l " region used on the carbon and the size of P2. The maximum angle chosen was 17°. 77 p r o f i l e , incorporating t h i s cut, i s shown i n Fig 27.„ The pro f i l e s were f l a t , within s t a t i s t i c s , i n d i c a t i n g that the i n e f f i c i e n c i e s were purely geometrical, and were eliminated by t h i s cut. Therefore, the ef f i c i e n c y was independent of the position of inter a c t i o n on the carbon converter, within the f i d u c i a l region. I t should be noted that the price paid for this cut was the l o s s of approximately half the recorded triggers that survived the other cuts. , The e f f i c i e n c y of track reconstruction was approximately 98% at non-zero angles and 99% a t zero degrees. The difference was attributed to a higher rate of tad triggers at non-zero angles, which were rejected by the MWPCs. Buns i n which the reconstruction e f f i c i e n c y varied by more than about 1% were rejected from the analysis. As discussed i n Chapter I I I , an MWPC was included behind PV to act as an additional veto counter, , I f a ve r t i c a l track, extrapolated to t h i s MWPC, came within 5 cm of a h i t wire, the event was rejected. The cut was made this loose as i t had been observed that protons frequently underwent small angle scatters in the carbon, so that in these cases, a tight requirement would have been in e f f e c t i v e . 78 160-140-120 -100-80 -60-40-20--200 -100 0 Y(mm) 100 200 P i g 27. V e r t i c a l p r o f i l e of events at the  carbon with an exit track angle cut of 17°., Sith a cut of 17or the p r o f i l e i s f l a t , showing that there are no geometrical or instrumental i n e f f i c i e n c i e s present in the neutron detector. 79 The track information was also found to be e s s e n t i a l in the elimination of three sources of background. The (beam off) cosmic ray runs had a very low f r a c t i o n of events with f i t t e d tracks ( " f i t t i n g e f f i c i e n c y " ) . Coupled with the requirements that tracks intersect the carbon and that the event not come in the "backward" region of the P1-P2 TOF spectrum, cosmic rays were, f o r a l l p r a c t i c a l purposes, completely eliminated as a source of background. This also implied that these u n f i t t a b l e events were primarily due to cosmic ray showers from above, a,nd not from p a r t i c l e s t r a v e l l i n g horizontally. , It was also noticed that up to 5-10% of the recorded events had no HWPC information associated with them at a l l . Investigations of the TOF and pulse height information for these events showed that they appeared to be ^ rays that were uniformly d i s t r i b u t e d i n time, i. e . they showed no correlation with the a r r i v a l times of normal events. I t was f e l t that they were perhaps due to thermal neutrons being captured in the carbon and releasing low energy If rays, which were incapable of trigg e r i n g the HWPC's. These events were discarded., The requirement that an event have a track f i t was also strong protection against random coincidences of the 80 El and P2 counters. IV. 1. 2 The Neutron Beam When the experiment began, i t was found that background coming from sources other than l i g u i d hydrogen was too severe. These sources were traced to i n s u f f i c i e n t secondary collimation of the incident neutron beam. Too many neutrons were scattering from the main collimator and monitors and causing a high background rate by rescattering from the aluminium target assembly. A secondary collimator was designed and placed inside the sweep magnet. F i g 28 shows p r o f i l e s of the neutron beam in the horizontal and v e r t i c a l d i r e c t i o n s . The p r o f i l e s were obtained ' by placing the neutron detector in the neutron beam, 5.57 m downstream of the LH^ target., Estimates of the beam properties at the l i q u i d hydrogen target were obtained by geometrical extrapolation, and are shown i n Table 7. The shape of the beam was not seen to change during the period of experimental running. From other measurements on production of neutron teams using deuterium t a r g e t s 2 9 , i t i s known that a nearly mono-energetic beam i s produced, with a narrow peak of about 1% dT/T which i s well separated from the lower 8 1 1000 100 1000 100 150 -100 -50 0 50 100 150 y (mm) l O L 150 -50 50 100 ISO x (mm) Fig 28. V e r t i c a l and horizontal p r o f i l e s of the neutron beam. ,. Reconstructions of the horizontal and v e r t i c a l d i s t r i b u t i o n of events at the carbon converter, 5,57 m downstream of the IH 2 target are shown. The wings of the team were at the 0.1% l e v e l 100 mm from the center of the beam. By geometrical extrapolation, t h i s corresponds to approximately 50 mm at the target. 82 Proton Beam Neutron Beam S p a t i a l S i z e Neutron Energy (MeV) Energy (MeV) FWHM (cm) Flux (n/sec/namp) 225 ± 1 21 2 + 2 2.5 8600 429 + 1 41 § + 2 2.5 6200 Table 7. Neutron beam properties 83 energy t a i l . The TOF measurement i s i n s u f f i c i e n t l y precise to check these properties on the neutron beam used i n this experiment., The average energy of the neutron beam was estimated ty accounting f o r energy loss of the primary proton beam to the center of the LD^ target, the 2.22 MeV binding energy of the deuteron, and an estimate of the energy taken up by the spectator proton in the deuteron., This was done by c a l c u l a t i n g the average momentum using Hulthen*s form of the deuteron wave function. The corresponding kinetic energy was 4 . 6 MeV. This was reduced by the f i n a l state i n t e r a c t i o n between the the two protons, which should be l e s s than the Fermi momentum, and greater than zero. The mean of these two values was taken. For completeness, the neutron production rates are shown i n Table 7 as well, calculated from estimates of the primary proton beam current and the absolute e f f i c i e n c i e s cf the monitors (described l a t e r i n the text). 84 IV.2 MEASUREMENT 0? THE ABSOLUTE EFFICIENCY OF THE HEPIRON DETECTOR IV. 2.1 Prin c i p l e And Requirements Of The Measurement The p r i n c i p l e of t h i s measurement i s simply stated: i f one has detected one of the two e l a s t i c a l l y scattered nucleons, then kinematics can be used to determine where the other member of the pair has gone.. The absolute e f f i c i e n c y of the neutron counter can then be obtained by detecting the e l a s t i c a l l y scattered protons, and then interogating the neutron detector as to whether a neutron had been observed (Fig 29) at the kine mat i c a l l y conjugate angle. There are several complications to t h i s ideal s i t u a t i o n , some of which are intimately related. /Put into two broad categories, they are: uncertainty of the paths of the two nucleons and possible losses; and background processes. These two categories can be dealt with separately. Both the incident neutron beam and the LH ^ _ target 85 | Cl to C7 MWPC'S P2 SCINTILLATOR Fig 29. Cal i b r a t i o n of the neutron detector. E l a s t i c a l l y scattered r e c o i l protons were observed i n the r e c o i l arm. The e f f i c i e n c y of the neutron detector was obtained by comparing t h i s number of protons with the number of coincidental!y observed neutrons in the neutron detector. 86 are of f i n i t e e xtent. As such, from geometry alone, there w i l l be a c o n s i d e r a b l e spreading of the "envelope" c o n t a i n i n g the s c a t t e r e d neutrons d e f i n e d by the proton arm, as i l l u s t r a t e d i n F i g 30. T h i s envelope i s most s e n s i t i v e to the l e n g t h of the t a r g e t , and, i n f a c t , i t was necessary t o r e s t r i c t the l e n g t h of t a r g e t from which protons were accepted by p l a c i n g a s m a l l counter, S 1 , up against the t a r g e t . , On the way to the r e c o i l arm, the protons undergo m u l t i p l e s c a t t e r i n g a f t e r the o r i g i n a l n-p c o l l i s i o n , p r i m a r i l y i n the l i q u i d hydrogen i t s e l f , and i n the aluminium surrounding the f l a s k . As a r e s u l t , t h e true, o r i g i n a l , d i r e c t i o n of the proton i s obscured and, consequently, the u n c e r t a i n t y i n the neutron d i r e c t i o n i s i n c r e a s e d . . M u l t i p l e s c a t t e r i n g i s a random process so that the amount of s c a t t e r can o n l y be p r e d i c t e d to w i t h i n a c e r t a i n p r o b a b i l i t y cf occurrence. The s o l u t i o n to both of these problems i s to b r i n g the neutron d e t e c t o r i n as c l o s e to the LH 2, t a r g e t as p o s s i b l e . T h i s must be o f f s e t by two f a c t o r s : the p h y s i c a l s i z e of the d e t e c t o r , as i t i s unwise to have i t i n the d i r e c t neutron beam; and the d e s i r e to match the running c o n d i t i o n s as c l o s e l y as p o s s i b l e to the data t a k i n g runs f o r d(f / d l l . , T h i s r e s t r i c t s the d i s t r i b u t i o n of incoming 87 Fig 30. Envelope of accepted neutrons determined by the r e c o i l arm. .  The envelope of protons accepted by the r e c o i l arm fixes the d i s t r i b u t i o n of neutrons at the neutron detector. To keep the s i z e of the neutron "beam" at the carbon smaller than the f i d u c i a l region, the detector was moved close to the target, and the target length was res t r i c t e d by a small trigger s c i n t i l l a t o r i n the r e c o i l arm up against the target. 88 neutrons to be approximately normally incident on the neutron detector.. The f i n a l compromise solution, s a t i s f y i n g these conditions, placed l i m i t s on the size of the r e c o i l arm counters, the proximity of both detectors to the target, and the angles of scatter to be used. Table 8 describes the configurations used in the measurement., Fig 31 shows a reconstruction of the horizontal and v e r t i c a l p r o f i l e s of the neutron envelope accepted at the carbon converter. I t v e r i f i e s that a l l the neutrons f e l l safely within the boundaries of the detector. The second category of complications involved background processes. In the processes np pp TT~ nn -n* The r e c o i l arm could have been triggered by any of the charged p a r t i c l e s . No i n e l a s t i c protons from the l i g u i d hydrogen were kinematically allowed at the angles defined by the r e c o i l arm, Pions were eliminated by TOF. .The *s that came within the same TOF window as accepted for e l a s t i c protons were eliminated by the use of copper plates, whose thicknesses were chosen to range out the pions. The amounts of copper used for each configuration 89 Pro ton Beam Energy (MeV) R e c o i l Arm A n g l e (deg) Neutron D e t e c t o r A n g l e (deg) Copper T h i c k n e s s in R e c o i l Arm (cm) 225 331 4 2 9 ^ 9 9 A99 51 51 ^9 48 60 35 35 35 35 25 0.64 0.64 1.27 0,64 Table - 8 . Recgil_arm and neutrondetector confiq urations. 90 8 0 -7 0 -6 0 5 0 -4 0 -30" -200 -too 0 y (mm) 100 2 0 0 8 0 70-6 0 -50 4 0 -30-2 0 10-- 2 0 0 -100 0 • (mm) 100 2 0 0 Fig 31. Horizontal and v e r t i c a l p r o f i l e s of neutrons at the carbon i n the c a l i b r a t i o n . , Ihe d i s t r i b u t i o n of events across the face of the carbon converter was e a s i l y contained within the f i d u c i a l region cf 4 0 cm sguare. , 91 are also l i s t e d in Table 8. The remaining sources of background are those not associated with the l i q u i d hydrogen, and sere primarily due to the target container. The e f f e c t s of these backgrounds can be well estimated by taking data with the IH ^ removed. This e f f e c t was greatly reduced by the small counter B1: the majority of possible background events, coming from the aluminium dome downstream of the flask, could not f i r e a l l three counters i n the r e c o i l arm. As a r e s u l t , the "empty target" rate was t y p i c a l l y less than 2% of the f u l l rate. IV. 2. 2 13at a Taking During the experimental running, an "event" occurred whenever a l l three s c i n t i l l a t o r s in the r e c o i l arm fi r e d in coincidence. At such a time, the on-line computer delayed i t s acceptance of further events and recorded the TOF and pulse height (ADC) information. .Furthermore, based on whether the neutron detector had also been triggered, i t read the flw"PC*s and set a b i t i n a pattern word. The philosophy i n analyzing t h i s data was to determine whether the TOF and ADC information v e r i f i e d 92 that the p a r t i c l e had indeed been an e l a s t i c a l l y scattered proton. If i t had been, then the information regarding the neutron detector was investigated: i f the pattern word bit had not been set, the neutron detector had missed the neutron; otherwise, the event was required to s a t i s f y three cuts before i t was classed as legitimate. , The 51-E2 TOF timing was required to be i n the forward region of the spectrum, a f i t was required for tracks through the HWPC's giving a l i n e intersecting the carbon converter, and the e x i t track polar scattering had to be l e s s than the same l i m i t as used in the d i f f e r e n t i a l cross section data. Fig 32 shows histograms of t y p i c a l TOF and ADC spectra for the r e c o i l arm. Tight cuts were made, as shown, with the philosophy that, as long as background events were excluded, any cuts were acceptable. , This was found to be the case upon varying the cuts., After a l l the cuts had been made on the r e c o i l arm and neutron detector events, the emphasis of the further analysis was to obtain the shape of the neutron detector e f f i c i e n c y as a function of energy for the forward hemisphere d i f f e r e n t i a l cross section data, and the absolute normalization of the e f f i c i e n c y to c a l i b r a t e the neutron beam monitors. 6 0 0 0 ; 4 0 0 0 f o „ „ (a) 2 0 0 0 - . p ° 9 ° , . % A . i _ 10 2 0 SO 4 0 5 0 6 0 70 6 0 9 0 FOO 110 3000} 2 0 0 0 (b) lOOOf I . 1 -o o — 8 - o 9 o o 170 « 0 190 2 0 0 210 2 2 0 2 3 0 2 4 0 2 5 0 P u l u (Might (Chan) 3 0 0 0 2 0 0 0 1 0 0 0 150 (c) t° 4 - a 0 160 170 180 T o F through r eco i l a r m (chon) ? o o o  190 XOF and A DC spectra j r tb~. Fig 32. ca l i b r a t i o n aeasurenent. Fig(a) shows the TOF through the r e c o i l arm. Fig(b) shows the TOF with respect to the BF, and Fig(c) shows the pulse height spectrue in BE3. The cuts applied are shown. 94 The data were analyzed i n two ways: with no exit track angle cut and with a cut of 17 <> on the angle. The two analyses were required to check the consistency of the data and to better determine the e f f i c i e n c y function with the cut applied, IV.2.3 Corrections To The Number Of Nucleons Incident On The Detectors The measurement of the absolute e f f i c i e n c y of the neutron detector meant that a beam of neutrons was defined by the protons accepted into the r e c o i l arm. Two ef f e c t s distorted the r e s u l t of the measurement: the neutrons were attenuated in the materials between the:point of scatter and the detector; and the protons multiply scattered into the r e c o i l arm such that the scattered neutrons were not necessarily directed towards the neutron detector. assuming that a l l interactions cause l o s s of the neutrons, the standard exponential loss c a l c u l a t i o n of exp(-n<f t) with n the number of scattering centers/cm 3, 95 <T the t o t a l cross section, and t the thickness of material yields an attenuation of about 2% f o r the neutrons i n approximately 0.8 g/cm3 of hydrogen equivalent material, as discussed in Appendix D. This must be corrected for those neutrons which scatter forward and are s t i l l within the detector acceptance. These corrections are l i s t e d i n Table 9. An error of about ±20% has been assigned to the calculation of t h i s correction due to uncertainty i n the shape of the d i f f e r e n t i a l cross section from nuc l e i , f i t t e d to existing data., At energies above 200 MeV, the multiple scattering corrections are small, as the number of protons scattering cut of the detector i s approximately egual to the number scattering i n . However, at lower energies, the cross section r i s e s sharply, enhancing the number of rescatters from those protons which had o r i g i n a l l y undergone a wide angle scatter over those which had scattered more forward. This gives more protons scattering i n from wider angles than scatter out from the nominal detector scattering angle. , This e f f e c t i s small for forward angles, and 5 6 C a l i b r a t i o n S e t t ing ( P r o t o n Beam Energy Neutron D e t e c t o r Angle) (MeV, deg) (220,35) (330,35) (429,35) (499,35) (499,25) A t t e n u a t ion o f Neutrons (*) 2.6 2.0 1.8 1.7 2.0 Double S c a t t e r ing o f Neutrons (%) 0.44 0.36 0.41 0.44 0.16 Double S c a t t e r i ng of P r o t o n s (%) 0.59 0.55 0.68 0.67 0.21 T o t a l C o r r e c t ion ( M u l t i p l i c a t i v e ) 1.036 1.029 1 .029 1.028 1.023 Table 9. Multiple scattering and attenuation corrections. The calculated values of the attenuation and multiple scattering of the neutrons on t h e i r way to the neutron detector, and of protons on t h e i r way to the r e c o i l arm are l i s t e d as a functions of scattering angle. , 97 approaches ^% at the aide angles. Table 9 also l i s t s t h i s correction to the data, and the ove r a l l correction applied. , IV.2.4 Analysis With No Exit Track Angle Cut A t y p i c a l histogram of the polar exit track angle from the carbon i s shown i n Fig 33..The e f f i c i e n c y with no cut on the angle was calculated by summing the entire range of t h i s histogram, the res u l t s of which are l i s t e d in Table 10, and plotted in Fig 34. I t was found that the data were well f i t by a l i n e a r function of the inverse kinetic energy of the neutrons incident on the detector. A least squares l i n e a r f i t to the functional form £,'(T)=m/T+b yielded the resu l t m = -4. 511 ± 0. 058 (HeV) b = 0.03978 ± 0.000 35 98 2000r 15001-1000 50 Oh 10 20 30 6 (deg) F i g 33. Exit track anale_distribution. Neutrons incident on the carbon interacted * to produce charged p a r t i c l e s which scattered according to t h i s d i s t r i b u t i o n , as measured by the fiWPCs. :'99 Neutron Energy E f f i c i e n c y Incident on the Detector e' (T) (MeV) 3 8 4 . 5 0 . 0 2 7 8 ±0 .0004 3 0 2 . 8 0 . 0 2 5 2 ± 0 . 0 0 0 3 2 6 1 . 3 0.0224 ± 0 . 0 0 0 3 2 0 3 . 3 0 . 0 1 7 6 ±0 .0004 1 3 7 . 2 0 . 0 0 6 9 2 ±0 .00014 Table 10, Neutron detector ef£ic iencies with out e x i t tr a ck_ cuts-. 100 3-Or f data linear fit in T to €' 2 0 I o x IO 0 8 T " ' ( l 0 ' 3 M e V ') F i g 34. Neutron d e t e c t o r e f f i c i e n c i e s without e x i t track c u t s . The uncut e f f i c i e n c y was w e l l f i t by a l i n e i n T _ 1 . T h i s f i t was used to o b t a i n values of £ (T) , u s i n g the 0° data. 101 with the error matrix for the f i t 1.263 * 10-7 -1.973 • 10-s -1.973 • 10-s 3.396 • 10~3 The f i t had a "X of 0.33 per point, showing that the form cf the f i t t i n g function well describes the data. IV.2.5 Analysis With A 17° Exit Track Angle Cut This e f f i c i e n c y was obtained by integrating the d i s t r i b u t i o n of Fig 33 up to angles less than 17°., As i s common i n scattering d i s t r i b u t i o n s , the exit track angle d i s t r i b u t i o n becomes more forward peaked with increasing k i n e t i c energy.. Consequently, the 17° cut i s energy dependent, as shown in Fig 35, where the r a t i o i s plotted, showing a 0 shape with a minimum around 260 HeV. The e x i t track angle d i s t r i b u t i o n i s described by f (0). This change i s most l i k e l y due to the onset of range e f f e c t s , where charged p a r t i c l e s produced near the upstream edge of the carbon do not have s u f f i c i e n t energy 102 TOO 200 300 400 500 T (MeV) Fig 35. Batip of e f f i c i e n c i e s wi th and without the exit track angle cut. The r a t i o shows that the 17<> exit track angle cut i s very energy dependent, and has a complicated form. I t i s this cut which complicates the form of £. (T). , 103 to trigger the remainder of the detector. As i s discussed l a t e r i n the text, data was taken with the neutron detector at zero degrees, sampling the neutron beam, at four energies: 212, 320 3 3, 418, and 490 3 3 MeV. The energies of 4 18 and 320 MeV were close to those c a l i b r a t i o n settings of (499 MeV,2 5°) and (429 MeV ,35°) , so that comparisons of the e x i t track angle d i s t r i b u t i o n s were possible. It was found that the values of B at approximately egual energies were the same, within s t a t i s t i c s , for the 0° and c a l i b r a t i o n data. This was possible since both data sets involved approximately the same area of the carbon converter, so that geometrical effects cancel., In addition, the e x i t track angle d i s t r i b u t i o n f e l l off quickly for angles greater than about 25°, so that effects due to the t a i l of the d i s t r i b u t i o n were minimized. Using the f i t for £*, the e f f i c i e n c y f o r the "cut" data £ , was obtained by £(T) = B(T) £» (T) Since the 0° data gave good agreement with the c a l i b r a t i o n data for B at two energies, i t was assumed to 104 also be the case for 490 MeV as well.,The 212 MeV 0° data was not used due to the f a i l u r e of P2E i n the forward hemisphere data at that energy. Ihe three values of B(T), also shown in Fig 35, were used to determine values of £. to augment those from the c a l i b r a t i o n in order to better determine the functional form of £» (T) at high energies, fill these points are shown i n F i g 36, and l i s t e d i n Table 11, i l l u s t r a t i n g a kink around 260 MeV. These data have been f i t to a cubic polynomial i n the inverse k i n e t i c energy £ (T) = a + B/T + C/T2 + D/T3 RHEBE .0269 ± .0013 B -7.85 ± 1.05 C 1169. ± 265. D -73317. ± 19900. 105 predicted from 0° data "r'ad^Mev"') Fig 36. Neutron detector efficiencies,, with exit track cuts. ,. The cut e f f i c i e n c y was well f i t by a cubic polynomial in T - i . , Data obtained from the 0° data was used to help determine the functional form at the higher energies. 106 Neutron Energy Inc ident on the Detector E f f i c i e n c y e(T) (MeV) 490.* 0.0151 ±0.0001 4 l 8 . * 0.0139 ±0.0001 384.5 0.0131 ±0.0004 320.* 0.0115 ±0.0001 302.8 0.0112 ±0.0002 261 .3 0.00976 ±0.00021 203.3 0.00788 ±0.00020 137.2 0.00337 ±0.00010 Table 11. KeutroD_detector_ej^iACA-|5ncies_with e x i t t r a c k c u t s . ~ l a t a marked by a * are f r o o 0 ° data. 107 The error matrix for the f i t was 0.167 «10-s -0.135 •10-3 0.333 -24.5 -0.135 « 10-3 1. 120 -277. 2.06 «10* I 0.333 -277. 7.00 »10* -5.25 • 1 0* -24.5 2.06 O O * -5.25 »10* 3.96 «108 -this functional form used four parameters to characterize eight data with a "X per point of 0.25. F i t s to lower order polynomials gave s i g n i f i c a n t l y higher X^. This form of £ (T) was used i n the analysis of the forward hemisphere. Ho model has been developed to describe this dependence, although- some work has shown that i t i s primarily due to the energy dependence of the n-C 1 2 cross section coupled with the range effects of the 9 cm thick block of carbon. 108 IV.2.6 Error Analysis No physically i n t u i t i v e explanations have been put forward to j u s t i f y the use of a l i n e a r f i t i n the inverse kinetic energy for the uncut c a l i b r a t i o n data, and a cubic polynomial f i t to the cut data. Consequently, i t i s necessary to explore the use of other, possibly equivalent, functional forms for these f i t s . Six f i t s were made i n order to estimate t h i s uncertainty. To test the assumption that £(T) could be obtained from £• was f i t to both linear and cubic polynomials i n T~*. This procedure changed the predicted values of £ from the 0° data by less than 1%. Furthermore, the e f f i c i e n c y £ , with the 17° exit track angle cut applied, was r e f i t to cubic polynomials in T~* and p-*, the inverse momentum. Each f i t was performed using the predicted 0° points from the two f i t s to £ • (T), hence four f i t s to £ (T) . The p-* f i t s both-gave higher Vy> than the T~ 1 f i t s . Most of the uncertainty i n the f i t to <£(T) was i n the energy region between 137 and 200 MeV, where there was no data. Using T~ 1, thi s region becomes elongated, making extrapolation over i t more questionable. I t i s i n this 1 0 9 area that the T~ 1 and p~ 1 f i t s show a different shape, and so affect the e f f i c i e n c y r a t i o s in the wide angle settings of the forward hemisphere data most seriously. The p~ 1 f i t s were assigned a lesser weight in estimating the errors involved due to the r e l a t i v e poorness of the"/^ {0.40 compared to 0.25 for T - 1 f i t s ) , ftll four f i t s were compared, and half the worst difference of the e f f i c i e n c i e s and for e f f i c i e n c y r a t i o s f o r the f i t s adopted, and the remaining three f i t s were taken to he a good estimate of the error incurred by choosing those f i t s , i . e . a l i n e a r polynomial i n T~l for L* (T) , and a cubic polynomial i n T~l for £(T). The r e s u l t s are shown i n Table 12, l i s t i n g the in the uncertain portion of the £ (T) curve., The 35° point was well constrained by the lowest energy c a l i b r a t i o n point for a l l f i t s . , a second error incurred i n the analysis was due to our knowledge of the incident neutron beam energy, which i s known to about ±2 HeV, due to the f i n a l state interaction of the protons i n the p(d,n)2p reaction. This e f f e c t becomes most serious for the low energy end of the £(T) curve. Using the T~* f i t for £{T), with an error dT cn the incident neutron beam energy, with B,= c{T3/£(T) 1 10 Error calculated Error due from Incident Neutron Beam Energy (MeV) Polar Scattering Angle (Lab) (deq) " F i t t i n g " Error (*) to Energy Uncertainty (*) Rfr.e) error matrix (%) Total Error 418±2 0 (0.5) (0.3) - (0.5) (0.77) 10 0.2 - 1.0235 0.10 0.22 12.5 0.1 0.01 1.0370 0.14 0.18 22.5 0.4 0.03 1.132 0.43 0.59 37.5 0.8 0.09 1.489 1.29 1.52 45 0.9 0.24 1.925 3.19 3.3 212±2 0 (0.3) (0.94) - (2.3) (2.5) 7.5 0.1 0.02 1.0193 0.18 0.28 15 0.5 0.12 1.0840 0.73 0.89 22.5 1.5 0.38 1.224 1.6 2.3 35 - 4.2 2.418 3.7 5.6 Table 12. Error e s t i m a t e s f o r the e f f i c i e n c y of the neutron detector. The estimated errors involved in B were the choice of the f i t t i n g function, the error calculated from the error matrix of the f i t , the error due to uncertainty i n neutron beam energy, and the t o t a l error are l i s t e d . The quantities i n brackets refer to the e f f i c i e n c i e s £ <T) calculated at 212 and 418 MeV. 111 the error i n R' i s 5 o> aft'jT. - a £ ( T ^ - 1±(t:) ^ where T 5 i s the scattered neutron k i n e t i c energy, 0 i s the scattering angle, and a i s the nucleon mass. The results for the e f f i c i e n c i e s at 212 and 418 Me?, and f o r B« corresponding to the forward hemisphere data are also l i s t e d i n Table 12. For a l l but the 35° point at 212 MeV, energy uncertainty contributes less than 0.5S error to B*. a t t h i s s e t t i n g , the error i s large- 4.2%, due to the low energy of the scattered neutrons at t h i s angle. These errors are systematic i n nature, and must be added i n to the errors calculated from the f i t f o r £(T) i t s e l f . The values f o r R * and the t o t a l error are also l i s t e d i n Table 12. with 3J 112 IV. 3 THE HEDT'ROK HQNITORS The purpose of these monitors, placed in the neutron learn, was to measure the flux of e l a s t i c neutrons incident on the l i q u i d hydrogen target, while either the neutron detector or proton spectrometer was downstream of the target measuring the number of scattered neutrons. ks such, the r e s u l t i n g cross sections depend heavily on the properties of the monitors. The monitors used for the cal c u l a t i o n of the d i f f e r e n t i a l cross section were the charged p a r t i c l e ones (CL+CR) and G1*.G2, since i t was f e l t unwise to base the monitors on the singles rate of the veto counter, CV., IV. 3. 1 Honitor S t a b i l i t y The data for the cross section measurements were taken over extended periods of time and often with very di f f e r e n t primary proton beam i n t e n s i t i e s . Consequently, the count rates were required to be stable with time and be li n e a r with the beam intensity. F i g 37 shows the r a t i o cf count rates of the in-beam neutron monitor to the out-of-beam monitor. This figure shows that these monitors 1 13 0-I40 0139 0138 0137 0 136 0135 0134 0 1331 2 10 230 920 940 960 980 1000 Run number 61 o i 6 0 (• 5 9 5-8h 400 440 480 810 830 650 1160 1200 1240 Run number Fig 37. Ratio of in-beam to out-of-beam  monitor counts as a function of time. The r a t i o , plotted against data run number, stayed constant to a l e v e l of about 1% over the entire running period. , The change in the r a t i o i s attributed to the s e n s i t i v i t y of the in-beam monitor to running conditions.. 114 sere stable to a l e v e l of 0.5% at 212 MeV and 1% at 418 MeV. The higher i n s t a b i l i t y at the higher energy i s most l i k e l y due to the increased f r a c t i o n of low energy background above the i n e l a s t i c threshold. t It was found that the in-beam monitor was very se n s i t i v e to the high tension (HT) applied to i t s photomultipliers, ft variation of 100 V gave about 15% var i a t i o n i n i t s count rate. This was due to the low energy components of the neutron beam incident on i t , as well as to conversions of neutrons to charged p a r t i c l e s in the monitor i t s e l f . Variations in the HT would indeed be expected to aff e c t the pulse heights of those p a r t i c l e s accepted by the discriminators for the counters i n the monitor. The out-of-beam monitor did not suffer from this problem, as copper plates were included to eliminate low energy background., Programmable power s u p p l i e s 3 0 were used to minimize the e f f e c t s of variations i n the HT. These supplies were able to hold the voltages to within about one volt of the nominal settings., This allowed the use of the in-beam monitor for analysis of adjacent runs where neither the HT cor the power supplies themselves might have been changed. 115 As both the P/S and HT's had been changed at certain times, i t would be incorrect to use t h i s monitor f o r the cross c a l i b r a t i o n of the monitors for the absolute normalization of the backward hemisphere data. IV.3.2 Monitor Linearity With Neutron Flux Fig 38 shows the variation of the monitor counts with those cf the proton polarimeter. Within the s t a b i l i t y of the polarimeter, there i s no var i a t i o n from l i n e a r i t y down to proton currents of about 50 nA. A deviation at low currents has been traced to the r a d i o a c t i v i t y of both the main collimator and the sweep magnet, having a half l i f e of about 30 - 60 min. In addition, the counters themselves exhibited an induced a c t i v i t y . These three sources contributed a constant background at equilibrium with the beam on, and a slowly decaying background with i t off. This e f f e c t showed up only for data taken with primary proton currents of a few nA: the zero degree runs taken for the forward hemisphere data, The corrections required were on the order of 6? for the in-beam monitor, and 3% for the out-of-beam one, and are l i s t e d i n Table 13. I t was found that the out-of-beam monitor was f a r less dependent on the previous history of beam current (which 116 Pig 3 8. Relation between the out-of-beam monitor and proton pclarimeter count rates. The l i n e a r i t y of the out-of-beam monitor with neutron int e n s i t y i s shown. The scatter in the points i s primarily due to the i n s t a b i l i t y of the polarimeter as an i n t e n s i t y monitor., 1 1 7 Neutron Beam Energy (MeV) 2 1 2 4 1 8 ( ea r l y runs) 4 1 8 ( l a t e runs) Mon i to r i n-beam out-of-beam i n-beam out-of-beam i n-beam out-of-beam "Beam O f f " Count Rate (sec -1) 1.29 ± 0 . 0 5 0.194 ± 0 . 0 1 9 1 7 . 3 ±0 .1 0 .311 ± 0 . 0 1 18.2 ± 0 . 2 0 . 4 5 5 ± 0 . 0 2 3 Table induced a c t i v i t y . 13. C o r r e c t i o n s to the monitors f o r 118 determined the l e v e l of a c t i v i t y ) than the in-beam monitor, making i t much more stable i n this respect. IV. 3. 3 Random Coincidences In The Monitors The count rates of the monitors were indeed rate dependent for large fuxes of neutrons. The probability that the coincidences were random (and not due to legitimate protons traversing the monitor) r i s e s with increasing f l u x . These e f f e c t s were measured in a l l runs by the fast electronics, as discussed previously. This was achieved by delaying the signal from one counter i n a coincidence by a multiple of the RF period. The random coincidence rate i n the in-beam monitor was about 2%. , This e f f e c t was neglig i b l e i n the out-of-beam monitor. ,• 1 1 9 IV, 4 ANALYSIS OF THE FORWARD HEMISPHERE DATA IV. 4. 1 Elimination Of Backgrounds As discussed i n Sec. IV. 1.1.1, tbe p r i n c i p a l sources of background from the hydrogen were neutrons and 7f rays from i n e l a s t i c reactions. These were separable from the e l a s t i c a l l y scattered neutrons by TOF with respect to the cyclotron RF. A t y p i c a l P1-RF TOF spectrum i s shown i n Fig 39. ,To better i l l u s t r a t e the hydrogen-associated events, an empty target subtraction has been performed on this data. The background T rays are o f f the high end of the scale, and the i n e l a s t i c s have no distinguishable onset. These backgrounds are well separated, as indicated by the fact that the r e s u l t s are i n s e n s i t i v e to reasonable variations in the cuts on the P1-RF TOF spectrum., This w i l l be dealt with l a t e r i n the error discussion.„ 120 2 4 0 r ° Target T u " ° x Target empty 200(-I60 oo I20 80 X X X X O v v O * r\ 4 0 " ° x x ° x x x o 9 X * x 6 x x X x g X ° 60 70 80 90 I00 II0 I20 I30 I40 P - r f (chan) Pig 39. Typical P1-BF TOP spectrum f o r the  neutron detector. > This data i s from a run at 418 HeV with the detector at 22.5°. The empty target background accounts for the t a i l s cf the peak, and the 7f rays are off the high end of the scale. 121 IV. 4. 2 Corrections Due To Equipment Problems When analyzing the data at 212 HeV, i t was found that a l l but one of the angular settings had been taken with the P2E counter almost inoperative. This introduced small errors i n the determination of d (T/dJl as the geometrical i n e f f i c i e n c y was s l i g h t l y d i f f e r e n t f o r the data taken at 0° and those taken at non-zero angles. & procedure was devised to cut out any tracks which intersected P2 i n the region of P2E, and then use a smoothing algorithm to f i l l i n the area, based on the remainder of the data. This procedure i s discussed i n some d e t a i l in Appendix B 3 1., B r i e f l y , the method can be described as follows. As mentioned previously, scattering cross sections depend only on the polar angle 0 , Therefore, the number of p a r t i c l e s at angle B i s assuming that the detector covers the entire 2"ft range in (j) for 0 . I f i t does not, for a l l events at 0 , the frac t i o n of 2 TC allowed can be calculated from the geometry of the detector. This data i s then weighted by that fraction to give the expected t o t a l number N( $ ). The f i n a l number of p a r t i c l e s detected i s then given by 122 The integration over G can be considered to have been evaluated by the d i s t r i b u t i o n i n 0 a n a " sum of the actual data, A region s l i g h t l y larger than P2E was excluded from the data, and then t h i s procedure was used to weight the data to account for the l o s s . In order to check the v a l i d i t y of the method, the unaffected setting at 212 MeV, and a set t i n g at 418 MeV were subjected to i t , i . e . the perfectly good data was a r t i f i c i a l l y removed and then replaced. In both cases the "before" and "after" r e s u l t s agreed to better than 0.251, giving confidence i n the correction for the remainder of the data. Approximately 10% of the data was affected by thi s correction. IV.4.3 Empty Target Subtraction As discussed i n Sec. IV.2, a s i g n i f i c a n t f r a c t i o n of the events accepted by the neutron detector originated in the material of the hydrcgen target. Since i t was a single arm detector, there was no r e c o i l coincidence test available to constrain the background. As a r e s u l t , background l e v e l s were on the order of that of the signal, Fig 39 showed a t y p i c a l pair of f u l l and empty runs, normalized to the same incident beam. This background 123 accounts for the large t a i l of the spectrum. IV.i*.4 Zero Degree Data In order to provide normalization to the forward hemisphere data, data was taken with the neutron detector at 0°. at t h i s position, i t sampled the same neutron beam as the monitors. Due to the length of the helium bag, i t was not placed between the L H ^ target and the neutron detector f o r t h i s measurement. The in t e n s i t y of the primary proton beam was reduced to a few nA for these runs, at which time the constant background from the a c t i v i t y around the monitors became s i g n i f i c a n t . As discussed previously, beam-off runs were taken to estimate the e f f e c t . Fig 4 0 shows a t y p i c a l P1-BF TOF spectrum of the neutron beam, i l l u s t r a t i n g the guasi - e l a s t i c neutron peak and a small, but long, low energy t a i l , and the If ray 0 peak (due to Tl production at the deuterium targe t ) . The effect of the t a i l i s to s h i f t the average incident neutron energy s l i g h t l y downward. The if peak i s cleanly separated from the e l a s t i c s . As the 1$ rays were separable from the e l a s t i c neutrons, and the out-of-beam 124 9 0 0 0 8 0 0 0 7 0 0 0 6 0 0 0 5 0 0 0 4 0 0 0 3 0 0 0 2 0 0 0 I 0 0 0 ^quas i -e las t ic y neutrons o o a y r Q y s o o o _ -cP-I 6 0 I 70 I 8 0 I 9 0 2 0 0 2 I 0 2 2 0 2 3 0 2 4 0 2 5 0 2 6 0 P - rf (chan) Fig 40. , Neutron beam HF time of f l i g h t spectrum., The~FF spectrum shows a narrow gu a s i - e l a s t i c neutron peak, a small but long low energy t a i l , and the *7f rays produced at the LD 2 target. The »s are well separated from the neutrons., 125 fficnitor was i n s e n s i t i v e to them, no absorber was placed in the neutron beam (upstream of the monitors) to eliminate "If rays, as had been done in other measurements of the n-p d i f f e r e n t i a l cross section. IV. 4.5 Time Of F l i g h t Cuts On The Data The events accepted by the neutron detector, f o r a l l the forward hemisphere data, was mono-energetic within the resolution of the TOF measurement. Therefore, the same cuts were applied with respect to the RF for the data at a l l angles. The cut used was ± 20 channels from the e l a s t i c peak. As i s discussed l a t e r i n the error analysis, the results were i n s e n s i t i v e to reasonable variations in th i s cut. It should be noted that t h i s RF width was almost e n t i r e l y due to the cyclotron bunch width and not the spread i n energy of the neutron beam. , 126 IV,4.6 Correct!ens To The Haw Data IV.4.6.1 Incident Beam Some of the 0° runs were taken with the hydrogen target f u l l . These were corrected, using the well-known values of the t o t a l cross section for free n-p scattering, to include them in the data set.,approximately 2-3% of the beam was attenuated by the hydrogen. ; ^ ^ ( n p ) i s known to about 335 at t h e s e 3 2 3 3 intermediate energies, so that the error on the correction was on the order of 0.05%, which i s completely n e g l i g i b l e . The number of neutrons accepted was corrected for attenuation i n the material downstream of the l i g u i d hydrogen i n the f l a s k . This increased the y i e l d by about 1%. . 127 IV,4.6,2 Data at Non-Zero angles Since the target was of non-zero length, the neutron beam was attenuated as i t passed through. On average, the neutron flux at the center of the target was reduced by tie value where the quantities refer to hydrogen. The number of events detected were scaled upwards to account for this l o s s , and amounted to corrections of 1.018 1.015 at 212 and 418 MeV respectively. ,. as discussed i n length previously for the c a l i b r a t i o n data, there was a correction to be applied f o r the multiple scattering of the incident beam neutrons and attenuation along the path to the neutron detector. The method of c a l c u l a t i o n was the same as previously, except for the dif f e r e n t geometry. The r e s u l t s are l i s t e d in Table 14 as a function of scattering angle. These corrections were t y p i c a l l y of the order of 1-2%. . 128 Neutron Beam 9* C o r r e c t i o n Energy (MeV) (degs) M u l t i p l i c a t i v e 212 101 1.034 20 1.015 301 1.015 40 1.014 50 1.014 60 1.013 70 1.013 80 1.013 418 10 1.024 20 1.011 30 1.010 40 1.010 50 1 .009 60 1.008 70 1 .006 80 1 .006 90 1.006 Table 14. Corrections to the forward hemisphere data. , The calculated corrections f o r attenuation and multiple scattering are l i s t e d . 129 As for the 0° data, when the target was empty, there was gaseous hydrogen in the flask. The density of the gas was determined by the measured temperature, and i s discussed in Appendix C. This gas caused some e l a s t i c scattering of neutrons into the neutron detector when i t was at non-zero angles. The number of neutrons was determined by the r a t i o of the densities of the l i g u i d and gas, giving a correction factor of 1.0 077 for a l l the f i n i t e angle settings. IV. 4.7 Parameters Needed To Calculate rff/dJL As discussed i n Chapter II, the d i f f e r e n t i a l cross section i n the forward region i s given by where d j l ^ / d j ^ ^ i s the Jacobian for the transformation to the center of mass frame. The quantities which remain to be given are the hydrogen target density and length, and the s o l i d angle subtended by the neutron detector. An i m p l i c i t quantity required i s the average angle of scatter i n t o the detector. 130 The density of the l i q u i d i s discussed in appendix C, and was 0.07005 ± 0.00040 g/cm . The target length was discussed i n Chapter III and Has 19.85 ± 0.01 cm. The s o l i d angle subtended by the detector i s given by integrated over the face of the detector, and over the sp a t i a l d i s t r i b u t i o n of the incident beam and volume of the target. However, since the detector i s so f a r from the target, this expression becomes the usual a/r* for a point source, to high accuracy. The average angle was calculated by evaluating where ( r , ^ ) are c y l i n d r i c a l coordinates about the incident beam axis, .1 represents the target length, and (x,y) cover the face of the neutron detector. The shape of 131 the beam i s taken as Gaussian with the measured width. <&> was found to equal the nominal scattering angle for a l l settings greater than a few degrees. Therefore, a l l average angles for the forward hemisphere data were taken to be the nominal angles. IV.4.8 Error Estimate Aside from the purely s t a t i s t i c a l errors i n making the measurements, some error i s incurred in applying the cuts to the data, selecting the e l a s t i c events. In addition, the monitor i n s t a b i l i t i e s and errors in geometrical and target parameters are involved i n the uncertainty of the f i n a l r e s u l t . The e f f e c t of possible j i t t e r i n application of the cuts on the data was simulated by varying the cuts over reasonable l i m i t s , and reanalyzing the data for each varia t i o n . The cuts made on the forward hemisphere data were on the e x i t track angle, the active area of the carbon, and the two TOF spectra. The error i n determining the exit track angle i s negligible, since the data i s always analyzed i n ratios. The determination of the active area also involves 132 negligible error, as binning e f f e c t s at the edges should cancel from blurring of the interaction points of p a r t i c l e s on either side of the cut. Table 15 shows a plot of the d i f f e r e n t i a l cross section for a variety of choices of these quantities. The cross section varies by about 1% f o r the values of t^. ^ shown. The e f f i c i e n c y function shape i s dependent on the choice of t h i s angle, so that the majority of t h i s variation i s most l i k e l y due to not having re-evaluated the e f f i c i e n c y as a function of energy f o r the choices of 0 . This error i s also taken to be ne g l i g i b l e . , Hithin s t a t i s t i c s , there i s no change in the d i f f e r e n t i a l cross section i n shrinking the active area of the carbon from 40 to 30 cm i n each plane. Table 15 also shows the variation i n the e l a s t i c neutron yield f o r d i f f e r e n t cuts on the TOF spectra. Even for large excursions of the P1-P2 TOF cut there i s less than a 0.2% change i n the s i g n a l . , A ±2 channel j i t t e r on the BF TOF gives a reasonable estimate of the possible error involved i n t h i s cut from run to run. Table 15 shows that an error of about 0.4% for non-zero angle data and 0.5% for 0° data i s introduced. Since a l l the neutron data was taken at about the same 133 ft max Cut RF TOF Cut dt/dSL (deg) (mb/sr) 17 4.73 + 0.12 16 4.78 16.5 4.78 17.5 4 . 7 2 18 4.70 l o se r l i m i t + x (chan) 0 2 4 6 -2 -4 -6 s i gna l (arb. un i t s ) 0.9177 + 0.0439 0.9152 0 . 9 0 5 6 0.9066 0.9213 0.9275 0.9256 Carbon A c t i v e Area x width y w idth d/f/dSV (cm) (cm) (mb/sr) P1-P2 TOF Cut 1owe r l i m i t +x (chan) d<T/dJU. (mb/sr) 40 40 4.73 0 4.73 35 40 4.76 3 4.74 30 40 4.74 5 4.73 40 35 4.75 40 30 4.73 Table 15. Variation of a<f/d$Vfor various choices of the outs f The s e n s i t i v i t y of the r e s u l t s to the choice of RF cuts, the active area of the carbon, the e x i t track angle cut, and the TOF through the detector are shown. 134 time, the same RF spectrum was used throughout. 5s discussed previously, the neutron beam monitor exhibited i n s t a b i l i t y at the 1% l e v e l at 418 MeV, and 0.5% at 212 MeV. The uncertainty i n the s o l i d angle was about 0.4%, and 0,5% for the target density. The error i n the target length was negligible., In summary, the only non-negligible sources of error in the c a l c u l a t i o n of the forward hemisphere d i f f e r e n t i a l cross section were the s o l i d angle, the target density, the RF cuts, and the monitor i n s t a b i l i t y . , added in guadrature, these errors t o t a l l e d 1.6% and 1.3% at 4 18 and 212 MeV, respectively. IV.4.9 angular Distributions The d i f f e r e n t i a l cross sections f o r the forward hemisphere at 212 and 418 MeV are l i s t e d i n Table 16. Qualitative aspects cf the d i s t r i b u t i o n s w i l l be discussed la t e r with the presentation of the backward hemisphere data. 1 35" Neutron 6 * dtf/dSI Energy (MeV) (deg) (mb/sr) 2 1 2 + 2 15.1 5.70 + 0.12 31.6 4 . 3 6+0.08 47.2 3-07 + 0.08 72.9 1.95 + 0.12 418+2 22.1 4 .66+0 . 0 8 27.5 4.29+0.10 49.2 2.96 + 0.06 80.6 1.69+0.04 95.8 1.37 + 0.06 Table 16. Results.fgr_the d i f f e r e n t i a l cross section at 212 and 418 MeV. 136 IV.4.10 Cross Calibration Of The Monitors IV, 4. 10. 1 A bsol at e Mo nit or Ef f i c ie nc ie s With the neutron detector at 0°, the number of neutrons detected i s r /vy where and £ are the absolute e f f i c i e n c i e s of the monitor and detector, respectively. A l l these quantities are evaluated at the same incident k i n e t i c energy T . N (0) has been determined i n the data analysis in a P fashion i d e n t i c a l to that in which the e f f i c i e n c y £ was measured. I t includes an RF cut of ± 20 channels from the e l a s t i c neutron peak. For the incident k i n e t i c energies 212 and 418 MeV, the values of ^ for the two neutron monitors are l i s t e d in Table 17. Note that the dependence on energy of the cut-of-beam monitor i s opposite to that of the in-beam monitor and the neutron detector. This i s due to the use cf d i f f e r e n t amounts of copper ranger in the out-of-beam monitor for the two energies. 137 Neutron Beam Monitor E f f i c i e n c y Energy (MeV) 212 in beam (0.604*0.034)x10" 2 out-of-beam (8.38-0.32)x10 _ l + 418 in-beam (1.22 -0.68)x10" 2 out-of-beam (7.32 1 6".23*)x1 0 _ Z f Table 17. , absolute_eff icienGJes of the neutron monitors. 138 The BF cut OB the 0° data determines the manner in which the backward hemisphere data i s to be analyzed: neutrons from the incident beam accepted i n that measurement must also come from a ± 20 channel window about the guasi-elastic neutron peak. This cut therefore determines the energy acceptance in the measurement., IV.10.2 Error Estimate The monitor e f f i c i e n c i e s are calculated from the r a t i o of the neutron detector e f f i c i e n c y and the guasi-elastic incident beam neutron y i e l d , normalized to the monitors, at 0°. The error introduced in the neutron y i e l d was due to the cuts applied to the data, monitor s t a b i l i t y , and s t a t i s t i c s . The sources of error on the determination of the detector .efficiency were the s t a t i s t i c s on the c a l i b r a t i o n data, the choice of the f i t t i n g function, and the energy resolution of the neutron beam. These errors are l i s t e d i n Table 12. There was a t h i r d source of error which became apparent i n the analysis of the backward hemisphere data. 139 This was change i n the shape cf the BF spectrum of the 0° neutron data from that of the proton data. This w i l l be discussed more f u l l y l a t e r i n the text. The conclusion reached was that allowance must be made for up to ±2.5% variations in the f i n a l r e s u l t s due to t h i s e f f e c t . The f i n a l errors and normalizations are l i s t e d in Table 17. It should be noted that the normalization errors guoted for the forward and backward hemisphere data are differ e n t . This i s mostly due to the fact that the forward hemisphere data was taken consecutively with the 0° data and, so, had the same BF d i s t r i b u t i o n . This eliminates the majority of the error assigned to the backward hemisphere data. , IV.5 ANALYSIS OF THE BACKWABD HEHISPHEBE DATA With the measurement of the absolute normalization of the neutron detector completed, the determination of the backward hemisphere of the n-p d i f f e r e n t i a l cross section became simple i n p r i n c i p l e : detection of e l a s t i c a l l y scattered proton (Fig 41), with 100% e f f i c i e n c y , gave the flux of scattered neutrons, while the neutron monitors gave the incident flux. 140 BEAM LINE 4A MONITOR 4 A B 2 DIPOLE 0° NEUTRON BEAM TRON LIMATOR >V PROTON BEAM / MONITOR NEUTRON BEAM MONITOR CLEARING MAGNET AND COLLIMATOR 51 SCINTILLATOR CI-C6 MWPC'S 52 A-D SCINTILLATORS ANALYZING MAGNET C7-CI2 MWPC'S P2 SCINTILLATORS Pig 41. Configuration f o r the backward hemisphere measurement., Scattered charged p a r t i c l e s sere detected i n a magnetic spectrometer., E l a s t i c protons were i d e n t i f i e d by TOF through the spectrometer and momentum, and by BF TOF., 141 This section discusses the methods used to select the e l a s t i c protons from the spectrometer data. IV.5.1 Selection Of Events The problem was one of s e l e c t i n g e l a s t i c a l l y scattered protons from the flux of charged p a r t i c l e s incident on the spectrometer. ,As discussed previously, the background cf p a r t i c l e s from non-hydrogen associated events was accounted for by the empty target subtraction. Of course, clean elimination of any of these backgrounds, by additional cuts on the data, would help reduce the dependence on the empty target subtraction. , The charged p a r t i c l e background was composed of the following: (i) deuterons from np —*- ~n° d r d in the allowed kinematic region of t y p i c a l l y less than 120 lab. ( i i ) pions from the reactions np —*• pp T\~ — » nnrr*" 142 ( i i i ) electrons from the decays of neutral pions np—1» 7T°d or —o i r ° np e + e _ (iv) i n e l a s t i c protons from the reactions n p —-> n p T f 0 —»> PP TT In the allowed kinematic region of t y p i c a l l y l e s s than 35° lab. There was no i n e l a s t i c production of nucleons from hydrogen at 212 SeV. The elimination of these backgrounds was achieved by independent measurements of the velo c i t y and momentum of each p a r t i c l e detected. The p a r t i c l e s 1 momenta were determined from the angle between the linear tracks before and afte r the magnetic f i e l d , as determined by the HWPCs, <6 c> with & & the angle between the tracks in radians. in units of kg-cm, and 143 p the momentum i n HeV/c,, In t h i s way, backgrounds frcm processes ( i ) , ( i i ) , and ( i i i ) were eliminated by corr e l a t i n g the TOF through the detector with the detector, as shown i n Fig 42. Ef f e c t i v e l y , t h i s was eguivalent to calcula t i n g the mass of the p a r t i c l e . The figure shows a clean separation between the protons and deuterons., I n e l a s t i c protons as well as pions and electrons, were eliminated by momentum analysis. Fig 43 shows the expected average momentum difference between the e l a s t i c and most energetic i n e l a s t i c protons energies, at each angle, neglecting energy losses i n the materials i n the par t i c l e s • paths. The elimination of the i n e l a s t i c s was complicated somewhat by the need to accept the same d i s t r i b u t i o n of the neutron beam as was accepted f o r the ca l i b r a t i o n of the monitcr. In the l a t t e r case, the energy determination was made via the. TOF technique, which allowed a certain f r a c t i o n of the t a i l of the neutron beam to be counted: consequently the TOF method was used to select the incident neutrons i n t h i s measurement. Thus, e l a s t i c scatters from these lower energy, but perfectly legitimate, neutrons could have been mistaken for i n e l a s t i c s from the e l a s t i c neutron peak i n the momentum analysis. This p o s s i b i l i t y was eliminated by co r r e l a t i n g 144 CUUMtS S C * L t U DU»N HT l / . t f O U O 3 C * L t U C O U N l S • 2 B l t , } * s I 1 B 0 . 0 1 1 6 0 . 0 1 1 « 0 . 0 1 1 * 0 . 0 I 1 0 0 . 0 tono.o I 0 * 0 . « l«'*J V . u i w o . u « » u . 0 •.MO.U 9*>U.U V » 0 . b 6 o U . u e u n . r •j* » *« . u »»UU.li 7 * 0 . 0 J b U . O r&u. o / w o . o 6 * n . 0 ftfcU. 0 * « u . u 0 e u u . v S h u . n S o C . o S « U . U • ng. a • 6 " . o • Cl « u o . n . 0 5 6 0 . 0 i f O . l t wo.o 3 0 0 . 0 ? A 0 . 0 ? 6 0 . 0 ? « 0 . 0 ??o. o 2 0 0 . 0 1 2 • a 2 1 1 1 e 1 6 •> 9 2 1 a 0 » 0 I i » 0 0 0 0 0 0 a 0 1 1 0 V 0 0 0 1 0 0 0 c 0 1 1 1 0 u V 1 2 1 2 1 0 0 0 0 1 I S a 2 1 u u 4 «* I* 1 1 . 2 u 1 a 21 2 " l u l o 2 0 1 « l a 1 . . 2 4 a 21 * 1 2 1 21 M 1 / 14 H 0 2 V / I v i as aO *t u 2 10 «s 02 zn 14 r . If 1 1 I o 2 » « 6 •>i 21 i 0 u 2 5 12 2 « 21 IS s u u 2 S 1 1 !•> 11 a u I 1 6 a B a u 0 0 1 « < ? a u 0 1 2 1 4 5 * 5 I 2 S a ! protons 7 T s 11 a I U II io i i a * 11 11 2 r 12 IP 2 7 a i i o o I 1 I I I I 2 2 2 1 ] a a a 2 a 1 i i s S a 2 4 0 a • a 4 • a a a a J 1 2 1 1 ) 0 a i « J / a a 1 0 1 1 o a a 1 i 2 0 1 2 0 a 1 1 0 a 0 1 1 a a 0 1 1 0 a 0 0 a deuterons l l a 11 i 0 1 n i 0 0 0 i 4 r 2 1 0 0 0 i 11 r a • 0 0 o o n - 2 1 1 a 1 0 if II 0 0 u ) u j a 1 1 0 0 0 0 i l u 1 / 6 2 1 0 0 u 0 i 2WU 6 / 1 1 0 0 0 l 100 6 a 2 a 0 0 u 0 0 0 l 111 } 4 a 1 I il II l 61 2 1 « 1 1 II 0 l «<* 1 1 1 1 2 2 1 0 0 a o l 10 It 1 2 1 2 2 1 1 0 0 0 0 0 1 l a 0 a 1 2 1 2 1 1 0 0 0 . 11 a 1 1 2 a a 2 2 1 0 0 1 1 « 0 0 2 1 a 4 1 0 0 0 1 In 0 0 2 a a a 2 1 0 0 1 1 / u o 0 1 1 4 a 1 1 1 0 0 t 16 0 0 1 2 } a i 1 1 a o o U 1 1 / 0 a 0 1 i 1 4 1 2 1 0 0 u 0 1 10 0 u 0 i 2 1 a 1 1 0 0 0 1 10 0 V 0 0 1 2 2 2 1 1 0 0 1 1« 0 0 0 2 2 2 1 0 0 0 0 0 1 il 0 0 u 0 a 0 1 1 1 0 0 0 0 • In 0 0 u 0 0 0 II 0 . 1 1 0 u 0 U 1 l a a a a 0 0 0 0 0 0 0 0 0 0 U 1 11 a u 0 0 0 0 0 0 0 01 10 2 0 0 0 0 0 0 01 ao 7 I 0 0 fl 0 0 0 0 01 a l 12 6 2 0 a 0 0 0 1 11 i i 11 a 2 I 1 u 0 0 01 ao a 13 12 / 2 1 0 ti a 0 1 a / 2 a 12 l u a a 2 0 a 0 0 0 1 a a 0 1 4 a 10 a a 2 I 0 o o a - i i a 0 1 2 a a » 4 i l » 0 0 0 1 / a a 1 1 a / a s a 2 1 0 0 0 0 0 1 11 0 a 0 1 i 5 a 0 2 1 0 0 0 0 0 0 1 21 a 0 0 1 1 4 a s 2 1 0 0 0 1 20 0 0 1 2 2 1 2 1 1 1 01 11 a a a a o 1 1 1 11 5 0 0 a 0 0 01 1 1 a 1 0 • 0 i i I 1 I i 1 2 2 2 I I 1 I I 2 2 2 2 7 7 a a a a a a a a 1 1 2 2 2 1 1 a a 2 a a a a 2 a 0 a s i a a a a 2 a 0 a ToF through spectrometer (chan) F i g 42. p a r t i c l e i d e n t i f i c a t i o n i n th1? spectrometer. Ihis data is taken frcir a run at 10° at a neutron beam energy of 4 1£ Mev. P a r t i c l e i d e n t i f i c a t i o n i s achieved by correlating the TOF through the spectrometer with the p a r t i c l e momentum. There are three bands apparent: pions, protons, and deuterons. 145 350h I i i 1— 0 10 20 30 o L A B (deg) F i g 43. .Homentam difference between e l a s t i c protons and most energetic i n e l a s t i c protons., The difference i s smallest near 0°, but i s greater than the resolution of the spectrometer, as i s discussed i n the text, the separation was very clean. \ 146 the time of a r r i v a l of the incident neutron at the l i q u i d hydrogen target with the momentum of the scattered p a r t i c l e , as shown in Fig 44, I t i s c l e a r l y shown that the t a i l of the beam separated from the i n e l a s t i c protons from the l i g u i d hydrogen. The MWPC's performed a cen t r a l role in the analysis of t h i s data: t h e i r information was used to determine the momentum of each p a r t i c l e , as well as i t s path through the detector. The usage of the MWPC's was i d e n t i c a l to that in the forward hemisphere measurement, except that the use of four MWPC*s to determine the incoming and outgoing tracks to and from the magnet ensured enough redundancy to permit a very high e f f i c i e n c y for f i t t i n g tracks, t y p i c a l l y 99,5%. Only horizontal coordinate information was used in the bulk processing; the v e r t i c a l was used only for checks. The path information i n the tracks helped eliminate three sources of background, as follows., P r o f i l e s of the l i q u i d hydrogen target were constructed with the front chamber data. As shown i n Fig 45, the p r o f i l e s were cf s u f f i c i e n t resolution, at wider angles, to show the good subtraction of the empty target background. Loose cuts were applied to the p r o f i l e s to eliminate obviously non-hydrogen associated events. 147 • »* F | „ » . . . . S C » l l t k n u l NU-atM I 5 ^ - „ , y 5 « u * l H l u m CIKINI5 S t « L t U O u -N 0, 2 2 . 0 0 0 0 S C * L t U C O u x I S . | « « 0 J , « P K U J t L l I U ' t 1 I I I 2 a a> n e o . o i 1 1 . 0 . 0 I 1 1 U U . o I 1 1 2 0 . 0 I 1 1 0 0 . 0 I 1 0 8 0 . 0 I 1 0 6 0 . 0 I 1 0 1 0 . 0 I I0<>0.0 I 1 0 0 0 . 0 • 9 6 0 . 0 I 9 6 0 . 0 I 9 . 0 . 0 I w g . t i 9 0 0 . 0 I B O O . O I 6 6 0 . 0 I e e o . o i B 2 0 . 0 I 6 0 0 . 0 -' " 0 . 0 I 7 6 0 . 0 I 7 4 0 . 0 I 7 2 0 . 0 I 7 0 0 . 0 I 6 1 0 . 0 I 6 6 0 . O I -6 0 0 . 0 1 6 2 0 . 0 I 6 0 0 . 0 -5 * 0 . 0 I S e O . O I ' 5 4 0 . 0 I 5 2 0 . 0 I 5 0 0 . 0 I 4 H 0 . O I • 6 0 . 0 I 4 0 0 . 0 t 0 2 0 . 0 I . 0 0 . 0 -1(10.0 I 1 6 0 . H O , 3 2 0 . 0 I i o o . o I 2 0 0 . 0 I 2 6 0 . 0 I 2 4 0 . 0 I 2 2 0 . 0 I 2 0 0 . 0 -I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 2 0 0 0 0 1 1 2 0 0 1 1 2 2 0 0 0 0 1 1 1 1 2 0 0 0 0 1 2 2 2 1 0 0 0 1 1 2 1 I 0 1 1 1 1 2 2 1 0 0 1 1 2 1 2 1 0 0 0 2 2 2 2 1 0 0 0 0 3 2 1 1 1 0 0 0 a 1 1 0 0 0 0 a 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 u 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 4 2 1 2 ; » a 1 5 4 0 2 6 I 3 2 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 2 1 0 1 1 4 4 2 0 1 6 13 1 3 5 1 . 2 10 26 2 9 13 2 0 4 17 42 5 « 2 7 7 0 0 5 21 47 6 3 46 10 1 5 2 2 S « 9 7 4 2 13 1 11 I S 4 5 76 50 11 2 a 12 SO 4 6 32 9 1 0 7 13 19 16 4 1 • 5 7 S 7 2 0 i 4 3 6 3 1 0 2 2 2 2 2 1 0 0 2 2 2 2 2 1 0 1 1 1 2 1 1 0 1 1 1 2 1 0 0 0 0 1 1 1 0 0 0 0 1 2 1 0 0 0 0 1 1 1 0 0 0 0 1 2 1 ] 0 0 0 1 2 2 t 0 0 0 0 1 I 1 1 0 0 0 0 I 2 2 1 0 0 0 1 2 2 1 0 0 0 0 0 1 2 2 t 0 0 0 0 0 u 1 2 2 1 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 1 1 i 1 0 0 0 0 0 I 2 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0. 0 0 0 0 'from the beam tail. neutron elastic proton peak •inelastic protons from the target area o o o o i i i i i i 3 1 i t i i / t 1 1 2 2 2 3 £ b 0 ti d 2 R F ToF (chan) Fig 4 4. Correlation of momentum and RF TOF. This data was taken at 10° and 418 MeV. The i n e l a s t i c t a i l of the beam can be seen from the low TOF end approaching the e l a s t i c peak., The i n e l a s t i c s from the LH come di r e c t l y down from the peak, with most of them being background events. t 148 • T A R G E T F U L L 8 0 0 r 0 T A R G E T EMPTY 70C4 60CH 5 0 C 4 400} 3 0 0 f Z00\ e l O O h . • 0 o 0 o e , oo oo»c...°»"°»''t''<"°°'»»''«N<.. - 3 0 0 - 2 0 0 - I 0 0 0 I 0 0 X (mm) Fig 45. P r o f i l e of events from the liqaid. hydrogen target* This p r o f i l e shows that the majority of the background events from the target are due to the aluminium dome. The empty target data accurately measures the contamination of the target f u l l data from t h i s source., 149 I t was a l s o p o s s i b l e t h a t p a r t i c l e s would i n t e r a c t i n the S2 c o u n t e r , s c a t t e r i n t o the magnet a t some d i f f e r e n t a n g l e of i n c i d e n c e , and g i v e a f a l s e i n d i c a t i o n of i t s momentum. In a u n i f o r m magnetic f i e l d , the i n c o m i n g and o u t g o i n g t r a c k s , when e x t r a p o l a t e d to the c e n t e r o f the f i e l d , would be very c l o s e t o i n t e r s e c t i o n , a t e s t o f t h i s g u a n t i t y would then i n d i c a t e whether the incoming p a r t i c l e had d e v i a t e d a f t e r the S2 c o u n t e r . A p l o t of t h i s i n t e r s e c t i o n i s shown i n F i g 46. I t was found t h a t t h e r e s o l u t i o n of the s p e c t r o m e t e r was a p p r o x i m a t e l y Q% FWHM. No improvement r e s u l t e d i n us ing the map of the magnetic f i e l d , so t h a t a " b l o c k f i e l d " a p p r o x i m a t i o n was made i n which the f i e l d was taken to be c o n s t a n t over the e n t i r e e f f e c t i v e l e n g t h . . I t was p o s s i b l e t o remove the t a i l of the i n c i d e n t n e u t r o n beam a r t i f i c i a l l y , v i a a BF TOF c u t , t o examine the i n e l a s t i c e v e n t s due to f u l l energy n e u t r o n s . , The momentum d i s t r i b u t i o n i s shown i n F i g 47, i l l u s t r a t i n g t h a t there i s adequate s e p a r a t i o n between the two t y p e s , e l a s t i c s and i n e l a s t i c s . The c a l c u l a t e d momentum was a l s o used t o c o r r e c t the BF TOP f o r time of f l i g h t of the protons from t h e l i q u i d hydrogen t a r g e t to the d e t e c t o r . T h i s was t o p e r m i t the c o n s i s t e n t usage o f the c a l i b r a t e d m o n i t o r s , i n t h a t the 150 o IOOOO 1000 I00 o I0L - 3 0 -20 -10 0 x (mm) 10 20 30 Fig 46. Intersection of tracks from the two  halves of the spectrometer at the magnet center. ; loose cuts M e r e applied to the intersection of the front and back tracks to eliminate events where the p a r t i c l e interacted between the front and back HHPCs, which would give an inaccurate measure of the momentum. The cuts sere applied at ±50 mm. , 151 I200I I 0 0 0 8 0 0 6 0 0 h o 4 0 0 2 0 O r - calculated three body threshold J o o o o o — Q — ° — 2 o 2 Q o—Lo o ° ° . o o 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 I 000 II00 Momentum MeV/c Fig 47. Momentam of the f a l l energy e l a s t i c protons. This data was taken at 10° and 418 MeV. The t a i l of the neutron beam was removed via an BF TOF cut, and a target subtraction was made to show the events coming from the l i q u i d hydrogen. There i s clean separation between the e l a s t i c and i n e l a s t i c protons. 152 TOF cut i n both cases referred to the incident beam d i s t r i b u t i o n only. IV.5.3 Total Energy Counter as discussed previously, f o r large angles, the t o t a l energy counter S4 was used. Due to problems with the IH target at 212 MeV and range cutoffs for the large angle settings at 418 MeV, only the 60° (lab) setting at 418 MeV was actually used. The only source of background from the l i g u i d hydrogen was due to pions, which were eliminated by correlating the pulse height i n S4 with the TOF from S1 to S2. Fig 48 shows a t y p i c a l scatter plot of these two quantities, i l l u s t r a t i n g the clean separation of the K 's from the protons. Fig 49 shows a t y p i c a l pulse height spectrum from S4. Only a small t a i l i s evident, predominantly due to nuclear reactions in the s c i n t i l l a t o r . 153 *.ILSI 2 2 2 i i i 4 4 1 o c o o CM CO i co" 2 2 " . t l I 2 2 0 . o I 2 2 2 . 0 I 2 2 0 . 0 I 2 1 0 . 0 I 2 1 6 . 0 I 2 1 0 . 0 I 2 1 2 . 0 I 2 1 0 . 0 -2 0 0 . 0 I 2 0 6 . 0 I 2 0 0 . 0 I 2 0 2 . 0 I 2 0 0 . 0 I 1 9 6 . 0 I 1 9 6 . 0 I 1 9 0 . 0 I 1 9 2 . 0 I 1 9 0 . 0 -I B B . O i 1 8 6 . 0 I 1 6 0 . 0 I 1 0 2 . 0 I l e o . o i 1 7 B . 0 I 1 7 6 . 0 I 1 7 0 . 0 I 1 7 2 . 0 I 1 7 0 . 0 • 1 6 0 . 0 I 1 6 6 . 0 t 1 6 0 . 0 I 1 6 2 . 0 I 1 6 0 . 0 I 1 5 0 . 0 I 1 5 6 . 0 I 1 5 0 . 0 I 1 5 2 . 0 I 1 S U . 1 * 7Ts~ deuterons protons 0 0 0 0 2 a 9 11 11 9 0 2 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 J e 1J IB 21 16 11 5 2 0 1 0 0 u 0 0 1 1 0 1 1 1 2 5 15 12 14 16 26 1 ' 10 0 1 1 0 0 0 0 0 0 1 t 1 2 1 1 2 1 I 6 11 12 50 70 60 40 10 15 1 2 1 0 0 U 0 0 1 2 1 2 1 1 ) i 1 } 0 10 27 51 01 41 00 64 11 16 6 0 1 u 0 II 1 1 t 1 2 2 1 2 2 | 4 4 8 IB 14 60 76 00 71 42 10 15 6 1 0 1 0 1 1 1 2 1 1 I 2 2 4 10 IB 15 06 40 o o 16 22 10 1 1 1 0 0 0; 0 1 1 0 1 1 1 1 1 2 1 4 4 12 20 22 20 16 6 a 1 0 0 0 0 0 0 0 1 1 0 1 1 2 2 0 0 7 7 7 4 1 1 1 0 0 0 « 0 0 1 1 I 1 1 2 1 1 1 2 1 1 2 2 1 0 0 0 1 0 0 1 2 2 2 2 2 1 1 0 0 0 0 0 0 0 0 0 1 1 2 2 2 1 1 1 0 0 0 0 0 0 0 0 0 1 I 2 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 • 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 i i - i o 6 i e i i i u*sr:»i to rivr w* i • HIGH. Y--t> i. o o o u U 0 0 0 I - - H K , T H l d ' i , 9 , <>UU 1 H l * l ** til** S. pulse height (chan) F i g 4 8. „ Correlation of pulse height _in_S4 with the TOF frota S1 to S2. 154 300 9> 200 00 o o - O - Q ^ O n Q p O O O o -o 100 o o CO S 4 Pulse height (chan) 2 0 0 protons.; F i g 4S. , Pulse h e i g h t i n S4 f o r f u l l energy ) 155 IV. 5.3 Seduction Of The Ban Data The angular d i s t r i b u t i o n s were measured i n 5° (lab) steps, from 2.5° - 60° at 418 MeV, and 5° - 55° at 212 BeV. Data runs which had known -equipment f a i l u r e s and errors i n the data taking were rejected i n the analysis. IV.5.4 Empty Target Data S certain f r a c t i o n of the events originated i n the vessel supporting the hydrogen, as discussed previously for the forward hemisphere data. To a very good approximation, the rate for these events was independent of whether there was l i g u i d i n the f l a s k or not. Fig 45 showed a t y p i c a l pair of runs, normalized to the same incident f l u x , for the f l a s k f u l l and empty. The r a t i o of the empty to f u l l rate was i n the range 10-20%. 1 5 6 IV. 5.6 Corrections To The Data Due To Equipment Aberrations In the early runs of the 118 HeV data, i t was found that the gas b a l l a s t region of the l i q u i d hydrogen target was p a r t i a l l y f i l l i n g with l i g u i d . The l i q u i d l e v e l varied with time, decreasing with the target empty and increasing with i t f u l l . Thus the empty target data i n those runs did not accurately measure the non-flask-hydrogen backgrounds which were present in the target f u l l runs. Once this problem had been diagnosed and corrected, much of the 418 HeV data was retaken. The variations in the target empty rates ranged from about 20-50??, and since this background formed about 10% of the s i g n a l , a 2-5% correction was required to account for the l i q u i d i n the b a l l a s t region. The e f f e c t was s i g n i f i c a n t only i n the angular range of about 30°-60° (lab), as data taking rates were lowest there. At small angles, the target was cycled often enough to erase the variation with time. The problem was i d e n t i f i a b l e by two c h a r a c t e r i s t i c s . Rhen the target was empty, the event rate decreased rapidly with time. Also, histograms of the horizontal 157 p r o f i l e of the LH target, from angles of greater than about 40 0 , showed a blurring of the events coming from the hydrogen, so that they appeared to merge with those from the aluminium dome. These two c r i t e r i a were used to determine whether the e f f e c t was present. I t was found that t h i s e f f e c t was not correctable. The settings which were affected were a l l of the t o t a l energy counter data at 212 MeV, and the f i r s t data sets of 30°, 35°, and 40° at 418 MeV. These data have been removed from the analysis. As the spectrometer was wheeled through the angular ranges for a l l the energies, the front of the detector became o f f s e t from the nominal scattering angles, by t y p i c a l l y 5 cm. This offset was measured at every angle, allowing c a l c u l a t i o n of the scattering angles. The e f f e c t cn the s o l i d angle of rotating the counters s l i g h t l y i n th i s way was completely negligible. , 158 IV.5.7 Corrections To The San Data The data represent the fra c t i o n of the incident neutron flux which was scattered into the spectrometer. As discussed previously for the c a l i b r a t i o n data, corrections were required for t h i s data to account f o r multiple scattering and attenuation of the protons. , These corrections are l i s t e d i n Table 18. On average, the spectrometer range cutoff was about 60-65 HeV, i . e . protons scattered from the center of the hydrogen target with less than about this value would have i n s u f f i c i e n t energy to reach P2., Bange cutoffs were calculated to begin at 73<> and 52° CE at 212 and 418 HeV, respectively, well beyond the range of data used i n this analysis. As for the forward hemisphere data, these data were corrected f o r attenuation of the neutron beam to the target center, and for gas i n the target when i t was nominally empty. 159 Neutron Beam 9* C o r r e c t i o n Energy (MeV) 212 418 (deg) (Mul t i p l ic. 60 0.995 70 0.986 8 0 0.985 9 0 0 . 9 9 0 100 0.995 110 0.999 120 1.0033 130 1.0064 140 1.0087 150 1.011 160 1 .012 170 1,014 180 1.016 50 1.0086 60 1.0018 70 0.998 8 0 0.995 § 0 0.995 100 0.993 110 O . 9 9 2 120 O . 9 9 8 130 1.003 140 1.008 150 1 . 0 1 1 160 1.014 170 1.017 180 1.019 Table 18. Calculated corrections to the data. The multiple scattering and attenuation corrections as functions of scattering angle f o r the spectrometer data are l i s t e d . , 160 IV.5.8 Parameters Needed To Calculate As discussed i n Chapter I I , the d i f f e r e n t i a l cross section i s calculated from the expression where the transformation to the center of mass has been The quantities remaining to be determined are &SI and <®>, the average laboratory scattering angle for each angular bin. The area density and length of the target has already been discussed. The angular binning of the data was determined by the geometry of the four S2 counters. This avoided the necessity of calculating the acceptance of the spectrometer, with the angles determined by the MWPC's. ,It introduced the problem of calcu l a t i n g the average scattering angles f o r each counter. The average angle was obtained by performing a s i m i l a r integration to that of the forward hemisphere data and i s shown as a function of Bominal angle i n Fig 50. The s o l i d angle subtended by the detector counters was calculated i n a s i m i l a r fashion to that f o r the made via the Jacobian djV/dyi . 161 Pig 5 0. average polar scattering angle, the average polar scattering deviates from the nominal scattering near 0°. This variation disappears above 5°. 162 forward hemisphere data. d J X was c l o s e l y A / r 2 , i . e. the s o l i d angle subtended by an area A at a d i s t a n c e r from a poi n t , and was c a l c u l a t e d to be 2.794 msr f o r each S2 counter. , IV.5.9 E r r o r E s t i m a t i o n As demonstrated i n the d i s c u s s i o n of the a n a l y s i s , p a r t i c l e i d e n t i f i c a t i o n and ' s e l e c t i o n of e l a s t i c a l l y s c a t t e r e d protons from l i q u i d hydrogen were unambiguously performed. As such, there was n e g l i g i b l e e r r o r i n v o l v e d i n those c u t s . As f o r the forward hemisphere data, the s o u r c e s of e r r o r were the BE cu t s , monitor s t a b i l i t y and the s o l i d angle d e t e r m i n a t i o n . Table 19 shows a p l o t o f the change i n the proton y i e l d f o r v a r i a t i o n s i n the BP c u t . An e r r o r cf about ±0.5% was a s s o c i a t e d with a ±2 channel j i t t e r on the c u t . Adding the three sources of e r r o r i n quadrature gives an e r r o r of 1,2% and 0.8% a t 418 and 212 fieV, r e s p e c t i v e l y . As w i l l be d i s c u s s e d l a t e r i n the t e x t , the phase s h i f t a n a l y s i s of the two 418 HeV data s e t s i n d i c a t e d t h a t the second s e t inv o l v e d more i n t e r n a l j i t t e r than was expected from the sources l i s t e d above. A f u r t h e r e r r o r o f 1% was added i n to t h i s data i n order to 163 RF TOF Cut s lower cu t l i m i t s i g n a l + x (chan) ( a r b . u n i t s ) 0 0.4949 + 0.0075 2 0.4911 4 0.4875 6 0.4824 •2 0.4979 -4 0.5000 -6 0.5021 Table 19. ., S e n s i t i v i t y of the^backward d i f f e r e n t i a 1 cross section.,to_the_.BF r mcuts. 164 reduce i t s " X v c l o s e to u n i t y i n the f i t . The 212 MeV data was a l s o found to r e g u i r e t h i s c o r r e c t i o n . The s o u r c e s of t h i s e r r o r remain unknown, although i t could well have been due to small i n s t a b i l i t i e s i n the c y c l o t r o n or the monitors. The BF d i s t r i b u t i o n was found to be the dominant source of e r r o r i n the n o r m a l i z a t i o n of the backward data. The 55° (lab) s e t t i n g s i n both data s e t s d i f f e r by about 1% i n n o r m a l i z a t i o n . , The only cause found f o r t h i s d i f f e r e n c e was a s l i g h t l y d i f f e r e n t shape of the BF d i s t r i b u t i o n s f o r the two data s e t s . , The phase s h i f t f i t s i n d i c a t e t h a t the two 418 MeV data s e t s have o v e r a l l n o r m a l i z a t i o n s that d i f f e r by about 2??. Removing t h i s 2%, and h a l v i n g the remainder of the d i f f e r e n c e y i e l d s an estimate of ±2.5% e r r o r i n the n o r m a l i z a t i o n to the EF d i s t r i b u t i o n . , 165 1V.5. 1 0 Angular Distributions The backward hemisphere r e s u l t s are l i s t e d in Tables 20 and 21, The f u l l angular d i s t r i b u t i o n s are shown i n Pigs 51 and 53, while the previous data are shown i n Figs 52 and 54, for 212 and 418 MeV, respectively. These data w i l l be discussed and compared in the next chapter. The d i s t r i b u t i o n s are asymmetric about 90° CM and show peaking i n the extreme forward and backward regions. In addition, structure can be seen in the backward hemisphere. The asymmetry i s due to the contributions of the 1=0 and 1=1 amplitudes. Were one absent, the d i s t r i b u t i o n s would be as those for i d e n t i c a l p a r t i c l e s - symmetric. The __. o peaking can be attributed to the exchange of pions: H in __ ^ the extreme forward peak, and Tl in the extreme backward (or charge exchange region). The structure in the backward region suggests the exchange of heavier mesons as the scattering becomes les s peripheral. 166 C OF E ANGLE 119. 2 121. 1 123. 1 125. 1 119.2 121. 1 123. 1 125. 1 129. 5 131. 4 133. 4 135. 4 140. 3 142. 2 144. 2 146.2 150.7 152.7 154. 7 156.7 16 1. 4 163.4 165. 4 167.4 171.8 173.7 175. 6 177.4 98.8 10C.7 102. 6 1C4.5 88. 6 90.4 9 2. 3 94.3 108. 8 110.7 112.7 114.7 CBOSS SECTION 3.054 3.306 3.344 3.466 2.786 3. 102 3. 256 3.397 3.916 4.104 4.250 4.411 5.002 5. 123 5. 34 1 5.608 5. 98 1 6.219 6. 396 6.680 7.49 1 7.857 8. 373 9.016 10.398 11.038 1 1.393 1 1.708 1. 876 1.925 1.980 2.080 1.608 1.589 1. 639 1.650 2.413 2.530 2. 649 2.738 EfifiCB 0.061 0.064 0.064 0.066 0. 058 0.061 0.062 0.065 0. 060 0.062 0.063 0. 065 0.076 0. 077 0.080 0. 083 0. 090 0. 093 0.095 0.093 0. 1 10 0. 115 0. 121 0. 130 0. 187 0. 197 0. 20 1 0.2 06 0.0 30 0.031 0.031 0.033 0. 034 0.034 0. 034 0.034 0. 041 0.042 0.044 0.044 Table 20. Backwardhemisphere d i f f e r e n t i a l  cross section a t 212 He?. 167 C CF I CEOSS EEEOE ANGLE SECTION 138.6 3.072 0.048 11.0. e 3. 255 0.049 112.7 3.416 0. 051 144. 6 3.61 1 0. 054 149.5 3.951 0.061 151.5 4. 144 0.063 153.6 4.304 0.065 155.7 4.54 1 0. 067 127.S 2.234 0.040 130.0 2.330 0.04 1 132.C 2.508 0.043 134.0 2.625 0.044 160.H 5.191 0. 075 162. 5 5.438 0.078 164. e 5.753 0.082 166. 6 6.46 1 0. 090 86. 5 1.489 0.042 88. 4 1.355 0.040 90.3 1.303 0.039 92.2 1.366 0.040 171.3 6.003 0. 132 173. 4 8.924 0. 144 175.4 9.688 0.153 177. 2 10.361 0. 161 66. S 1.997 0.042 68.7 1.943 0.041 70.5 1.838 0. 039 72. 4 1.750 0.037 57.3 2.413 0.045 59. 1 2. 346 0.044 60. S 2.350 0.043 62.7 2. 19 1 0.041 76.E 1.651 0.035 78.7 1. 575 0.035 80.5 1.534 0.034 82.4 1. 523 0.033 117.2 1.515 0.034 119. 2 1.648 0.035 121.2 1.788 0.037 123.2 1.808 0.037 106. 6 1.432 0.023 108.8 1. 483 0. 029 110.8 1.508 0.029 112.6 1.522 0.029 * 57.2 2.419 0.055 * 59.0 2.31 1 0.052 * 60.8 2.292 0.052 * 62.7 2. 163 0.049 C CF E CFOSS EBfiOE ANGLI SECTION 138.2 3.049 0.055 140. 2 3. 214 0. 058 142.3 3.371 0.059 144. 4 3. 673 0. 064 149.3 4.009 0.072 151. 3 4.228 0. 076 153.4 4.420 0.079 155. 5 4. 727 0.063 126.5 2.180 0.041 128. 9 2. 384 0.044 131.C 2.505 0.046 133.0 2.681 0.046 116.£ 1.613 , 0.032 118. 6 1. 73 1 0. 034 120.6 1.778 0.035 122. 6 1.921 0.036 106.5 1.396 0.028 108. 5 1. 412 0. 02b 110.4 1.505 0.029 112. 4 1. 498 0. 029 S5.7 1.367 0.027 2nd 97.6 1. 327 0. 027 99.5 1.390 0.027 b e L 101. 5 1.395 0.027 160.3 5.096 0.093 162. 4 5. 436 0.098 164.5 5.927 0.105 166. 5 6. 485 0. 1 13 165.7 6.135 0.121 167. 8 6.624 0. 129 169.6 7.774 0.148 171.9 8.451 0. 159 171.3 7.980 0.181 173. 4 6.740 0. 201 175.4 9.841 0.219 177.2 10. 137 0. 226 176. t 10.179 0.210 177. 9 10. 547 0. 2 16 176.4 10.010 0.207 65.S 2.174 0.046 67.7 2.083 0.044 69.5 2.000 0.043 71.4 1.925 0.041 Table 21. Backward hemisphere d i f f e r e n t i a l cross section at 418 MeV. The two sets of data taken at t h i s energy are shown. Data taken with the t o t a l energy counter are marked with a *. 1 6 8 12 10 7 X I E b cs T3 2I2 MeV $ neutron detector I spectrometer 3 0 6 0 9 0 I20 0* (deg) I50 I80 F i g 51. Backward hemisphere d i f f e r e n t i a l  c r o s s s e c t i o n a t 212 BeV. There was no o v e r l a p of the forward and backward hemisphere data s e t s due t o problems with the hydrogen t a r g e t . Phase s h i f t a n a l y s i s f i t s i n d i c a t e that the two se t s are c o n s i s t e n t i n t h e i r n o r m a l i z a t i o n . 169 12 10 9 8 i b CJ * I95-6 MeV PPA \ 200 MeV Dubno j 2 10 MeV PPA } 224 MeV PPA \ I99 MeV Rochester j \ 2II-8 MeV Lompf $ (normalized upwards ^ by III. See note ) ii i l 1 30 60 90 100 150 6 (deg) 180 Fig 52. Previous backward hemisphere d i f f e r e n t i a l cross section data near 212 BeY. Phase s h i f t analysis of the data set indicates that the r e l a t i v e l y normalized Lampf data should be renormalized upwards by 1155. , 170 1 2 IO E 6 7 3 5 4 I 8 MeV § neutron detector I spectrometer II, 3 0 6 0 9 0 I20 0*(deg) I50 180 Fig 53. Backward hemisphere d i f f e r e n t i a l cross section at 418 MeV. , Due to the amount of data in the backward hemisphere, only cne set of data i s shewn for each laboratory angle setting. There i s good overlap of the forward and backward hemisphere data sets. 171 I2r il I0 •Dl T3 5-4 -Y Lampf 4 2 9 MeV Saclay 4 2 1 MeV PPA 4.I4 MeV PPA 3 9 0 MeV Carnegie 4 0 0 MeV X o *° T * 4 o 0o A * 4 A A A A •2> 3 0 6 0 9 0 I20 0* (deg) I50 180 Fig 54. . Previous backward hemisphere d i f f e r e n t i a l cross section dafca near 418 MeV. The PPfi data at 414 MeV disagree strongly in shape and normalization with other data. They have been removed from the data set. 172 IV.6 IN RESTROPECT Looking back on the experiment, i t i s clear that there were features of i t which could have been improved. Overall, the results were limited by the s t a b i l i t y of the cyclotron and of the neutron beam monitors. The results depended on the constancy of the RF bunch widths between the forward and backward hemisphere data taking,.A competing factor here was the wide bunch width reguired for high intensity production of mesons on BL 1, so the solution to t h i s problem would probably l i e i n dedicated running for neutron experiments or the (doubtful) introduction of a medium in t e n s i t y beamline i n the meson h a l l so that running conditions would be well matched and allow a narrow, stable bunch width. The monitor s t a b i l i t y could l i k e l y be improved by including one or two more s c i n t i l l a t o r s in each arm. This would reduce the monitors 1 s e n s i t i v i t y to low energy backgrounds. An unfortunate drawback to the technigue used i n the forward hemisphere measurement was the very low e f f i c i e n c y of the neutron detector, which f e l l from about 1.4% at the highest energy to about 0,3% at the lowest. This as a factor 4 le s s than what was expected from the Los Alamos 173 data f o r a s i m i l a r s e t u p 3 * (on which the technique f o r t h i s experiment was based). The e f f i c i e n c y c o u l d be i n c r e a s e d by u s i n q a CH2. c o n v e r t e r , which p a r t i a l l y a v o i d s the "n u c l e a r s c r e e n i n g " of carbon nucleons by having the " f r e e " hydrogen. T h i s could give a f a c t o r 2-4 i n c r e a s e . , a s i g n i f i c a n t source of background i n the experiment o r i g i n a t e d from the aluminium dome surrounding the hydrogen t a r g e t . As shown with the spectrometer, most of the background of protons came from there. I f t h a t was a l s o t r u e f o r neutrons i n the forward hemisphere measurement, the removal of t h i s dome would g r e a t l y reduce the backgrounds., S e l f - s u p p o r t i n g mylar-and-styrofoara t a r g e t s are now a v a i l a b l e . n r . 7 COMPARISON OF EXPERIMENTAL TECHNIQUES -I t i s i n s t r u c t i v e to make a comparison of the technigues used i n the experiment with those p r e v i o u s l y used to perform s i m i l a r measurements. Previous measurements of the forward hemisphere used e i t h e r t h i c k s c i n t i l l a t o r s or a c o n v e r s i o n method, a s done here. Ose of s c i n t i l l a t o r s has two advantages: the d e t e c t i o n e f f i c i e n c y can be high ( t y p i c a l l y 20%) and i t 174 has only a slow variation with energy over the range 100-500 HeV. This i s to be contrasted with the low, very energy-dependent e f f i c i e n c i e s obtained with a converter. The converter method gains the overa l l advantage in other areas. The active area can be limited, eliminating edge e f f e c t s . This also gives an accurate determination of the s o l i d angle subtended by the counter. The active area can be measured to about ±1 mm, whereas by timing i n large s c i n t i l l a t o r s , accuracies of em's are obtained,, F i n a l l y , the t r i g g e r timing from the converted charged p a r t i c l e s w i l l have l e s s j i t t e r than from a large volume s c i n t i l l a t o r . Turning now to the detection of protons, the technigues used are either thick s c i n t i l l a t o r s , magnetic spectrometers, or range telescopes. Below the i n e l a s t i c threshold, a l l three technigues are comparable, though the s c i n t i l l a t o r s suffer somewhat from straggling and nuclear reactions. Above the threshold, the range technique f a i l s to provide p a r t i c l e i d e n t i f i c a t i o n and good energy resolution for selecting e l a s t i c protons. At high energies, the spectrometer i s best due to i t s s i m p l i c i t y . , 175 ?. INT .EB PH E T aTI0 N OF -THE DATA As discussefl i n the Introduction, information can be obtained on the N-N scattering amplitudes through phenomenological phase s h i f t analyses. This chapter w i l l describe the current state of the psa and the i n c l u s i o n of the data from t h i s experiment into the world data set. V. 1 PRINCIPLE OF PHaSE SHIFT ANaLYSIS The formalism cf scattering theory has been extensively d e s c r i b e d 3 5 , and an excellent summary of the formalism describing the E-matrix and N-N phase s h i f t s has been given in Bef.,36, i n which the possible t r a n s i t i o n s between the allowed states i n the N-N system i s parametrized by scattering phase s h i f t s . It i s convenient to describe the scattering theory in terms of an angular momentum expansion: a l l approximations are automatically unitary, and the expansion can be cut off at a given 1-value with the higher phases calculated from heavy boson exchange (HBE) t h e o r y 3 7 . 176 The Hamiltonian for N-N scattering conserves t o t a l angular momentum, parity,time reversal (TBI) and isospin, fls a consequence of these symmetries, i t follows that t o t a l spin i s conserved as well. From the extended Eauli exclusion p r i n c i p l e , the t o t a l wave-function for the N-N system must be t o t a l l y anti-symmetric, which leads to the condition (-0 - - 1 Coupled with the symmetries of the Hamiltonian, this equation gives the allowed states of the N-N system and the possible t r a n s i t i o n s . In spectroscopic notation these are, for 1-0 3 s , . , P , , ^ „ , K , 3 I > s . ' l : i , I 6 s > 4 , ! C - r ; H s , 5 T f / i t / j „ . . . and for 1=1 1 i c>., V ?, - \, ' f* .'*=«,' C-„ SH„ H^r, * tti, 'I,, The notation used i s with 1 = 0,1,2,3,4,5,... corresponding to S,P, D,F,G, H,. . . The allowed t r a n s i t i o n s are for the cases of 4 177 scattering of the state |pjls> into the state |p»jl's> of l ' = j < > l=j ; s=0 l»=j < > l=j ; s=1 l»=j±1 < > l=j±1 ; s=1 1' = j± 1 < > l=j + 1 ; s=1 The amplitudes for these l a s t two tr a n s i t i o n s are egual i f TBI holds. Furthermore, the l a s t four are not diagonal with respect to the angular momentum, 1, which results i n mixing of the states involved, i . e . those of egual j and s but unequal 1. Two new eigenstates can be generated by a unitary transformation, which involve a mixing parameter, £j , for each j v a l u e 3 8 . The phase s h i f t s describing the scattering are guoted in the same spectroscopic notation as f o r the states. The two new eigenstates are quoted by t h e i r 1* value of either j-1 or j * 1. Above the pion production threshold, there can be i n e l a s t i c scattering, which i s characterized by the phase s h i f t s becominq complex. As they are written as cS e when complex they become 178 where T h e r e f o r e , the N-N s c a t t e r i n g can be d e s c r i b e d by phase s h i f t s as i n the above n o t a t i o n , mixing parameters and i n e l a s t i c i t i e s . The most general form of the s c a t t e r i n g matrix s a t i s f y i n g the p r e v i o u s l y discussed symmetries can be wri t t e n i n the f o r m 3 9 where a,b,c,m, g and h are the complex H o l f e n s t e i n amplitudes, n, K, and P form an orthogonal v e c t o r s e t i n the center o f mass system, and vthe 0"^ are the P a u l i s p i n matrices. The amplitude b expresses the degree of i s c s p i n v i o l a t i o n i n the N-N system ( p r i m a r i l y due to electromagmetic e f f e c t s ) . floshizaki3 9 has compiled the formulae r e q u i r e d to c a l c u l a t e N-N observables using t h i s form o f El. The o b j e c t cf the phase s h i f t a n a l y s i s i s to c a l c u l a t e the observables from i n i t i a l guesses f o r the phase s h i f t s and i t e r a t e the guesses u n t i l the bes t f i t i s obtained f o r the 179 data. The f i t t i n g c r i t e r i o n i s the "Y, febich i s to be minimized. V.2 CDBRENT STATOS OF THE PHASE SHIFT ANALYSIS A phase s h i f t analysis has been developed to incorporate the TRIDHF N-N e l a s t i c scattering data into the world data set to determine the phase s h i f t s . Single energy analyses have been performed which group data around four energies in the energy range 200-500 MeV. The ones at 212 and 418 He? w i l l be described here. The de t a i l s of the analysis have been well described i n Refs 40 and 41, with the world data used l i s t e d i n Ref 41., The PPA*7 data at 414 HeV has been excluded since i t d i f f e r s s i g n i f i c a n t l y i n shape and normalization from those of Eonner et a l . * 2 and Bizard et a I * 3 , , Recent spin correlation data from S I N S S at 446 HeV has been added to the data set. The angular momentum expansion was cut off a t H saves for the 1=0 phases and I waves for 1=1. The higher waves were fixed at the prescription of Vinh Mau et a l . 3 7 , using OPE and HBE potentials. 180 At 212 HeV, below the i n e l a s t i c threshold, no i n e l a s t i c i t y was allowed. At 418 HeV using the isobar model-**, a l l i n e l a s t i c i t y i s assumed to be i n the 1=1 phases via delta production. Assuming that the delta and N are i n a r e l a t i v e s state, the lowest available N-N state which can couple to i t i s the 1 s t a t e . , I n e l a s t i c i t i e s it ' have neen calculated from the model of Green and S a i n i o * 5 . Only the ' D^ phase was allowed to have variable i n e l a s t i c i t y . I t has been found that i f more phases are permitted to have variable i n e l a s t i c i t y , the phase s h i f t analysis becomes unstable and cannot unravel the correlations between the various i n e l a s t i c i t i e s . ,, The phase s h i f t s which res u l t from this analysis are l i s t e d i n Table 22. The errors quoted are calculated from where *X ^ i s the "X per point of the f i t and £j'4'is the diagonal element of the error matrix for the j th parameter. , Since the "X \f of the f i t were always greater than unity, the errors in the parameters were increased to account for the quality of the f i t . The large values of "Xy suggest that there i s s t i l l some erroneous data i n the set. Note that using «£:•' gives only an estimate of the 181 212 MeV Phase I Value Phase I Value (deg) (deg) 3s , o 17.71*0.84 3PC 1 -1.83*0.56 4.08*0.49  lSD *• 53*0.59 >1 t -18.94-0.68 3P, -22.69-0.21 'p, -23.50± 0.89 3P2 16.18± 0.16 3 D 2 28.00+ 0.64 c 2 -2.87 ±0.10 30j 5.11 ± 0.42 3 F 2 1.03 ± 0.24 I 5.15 ± 0.27 ' P 2 7-34 ± 0.22 3 G 3 -3-05 ± 0.38 3 F 3 -2.66 ± 0.17 *F -2.27 ± 0.40 3 F ( ( 1.69 ± 0.13 4.91! ± 0.44 -1.17 ± 0.06 3 G $ 0.36 t 0.33 ^ 0.33 * 0.05 'G^ I.06 ± 0.08 3Hj -0.86 ± 0.05 3H f e 0.19 + 0.05 Phase 1 Value (deg) 3S, 0 -6.36 + 0.94 c1 7.33 + 0.63 3 " l -25.32 + 0.53 'p, -38.69 + 1.13 \ 22 . 64 + 0 . 71 \ 4.09 + 0.37 1 3 7.35 + 0.30 \ -4.88 + 0.42 \ -4.97 + 0.27 \ 6.78 + 0.51 \ -1.68 + 0.29 Phase I Value (deg) SP0 1 -20.35 +.0.58 'So -19.58 + 0.46 s p1 -35.85 + 0.30 3 P 2 18.26+0.17 e j -2.29 + 0.16 ,-, 3 p » 0.30 + 0.19 2,1-8 MeV 0.37 ? -P 2 11.61 + 0 . U J F j -2.60 + 0.19 3 C 3.5* + 0.10 E4 -1.68 +0.10 3« M4 0.75 + 0.07 B4 2.22 + 0.10 "5 -1.28 + 0.10 H6 0.66 + 0.07 Table 22. Phas€_shifts predicted frog the previous data at 212 and 418 HevT These analyses included a l l the BASQUE spin dependent data. 182 error. The errors also do not inconsistencies in the treatment of 418 MeV. V.3 NEW DATA 18 THE PHASE SHIFT ANALYSIS The phase s h i f t analysis of data provides not only an estimate of the phases, but also a quantitative comparison of the i n d i v i d u a l data sets used i n the analysis. This w i l l be used to discuss the the shape and normalization of the various cross section data near 212 and 418 MeV., V.2. 1 Data Near 212 MeV In the forward hemisphere alone, data i s from PPA*6 e n t i r e l y . In the backward hemisphere, there i s data from EPA*7, fiochester*8, and r e l a t i v e l y normalized data from Lampf*2. Over the entire range, there i s a measurement from Dubna*9, which was normalized to their measurement of the t o t a l cross section. In the analysis, data sets are assigned an o v e r a l l normalization (and error) which can be varied to give an overal l f i t to the data. From a calculation of the ^ of account f o r possible the i n e l a s t i c i t i e s at 183 individual data from the f i t , a quantitative measure of the agreement between the data sets i s obtained. Our forward and backward hemisphere data sets were put into the analysis with separate normalizations in order to ve r i f y that the f i t s would leave them egual, within the error l i m i t s set. i In the f i t , our backward hemisphere data had a \ ^ o f 1.3, i n d i c a t i n g that there was some j i t t e r i n the data not yet accounted for. The error bars were increased by 1$ to lower the "Xy*clcse to unity. Without our data, a l l the cross section data sets are in reasonable agreement, whereas the introduction of our data shows up disagreement with the two data sets which • cover the 75°-125° (cm) range. These are the data from Dubna and Rochester. The shape of our data i s i n good agreement with the Lampf data down to 120°, suggesting that the older data sets are faulty. This i s not surprising for the Dubna data where the separate measurements of the forward and backward hemisphere were made to be egual at 67°. Any error i n t h i s data would show up as a shape error i n t h i s region. The f i n a l phase s h i f t analysis at t h i s energy was performed leaving the Dubna data out e n t i r e l y , and 184 excluding the Bochester data in the 75°-125° range. Our recent measurement of the t o t a l cross section was also included. The f i t gave a "X.y of 1.6 for 271 data and 25 parameters, indicating that there are s t i l l some in t e r n a l iccocsistencies i n the data set. The t o t a l cross section provides a strong constraint on the normalizations of the d i f f e r e n t i a l cross section data, since the analysis wi l l attempt to s h i f t them so that the integrated d i f f e r e n t i a l cross section f i t s the measured value.,In order to do th i s , the analysis renormalized upwards a l l the ddVd/L data, by 3$ for the Bochester and PPA data, 111 f o r the r e l a t i v e l y normalized Lampf data, 1% f o r our forward hemisphere data, and UJL for our backward hemisphere data. Table 23 l i s t s the f i t t e d normalizations f o r each d i f f e r e n t i a l cross section data set. The normalizations obtained for our two data sets are in agreement, within the error l i m i t s set, and with the other absolutely normalized d i f f e r e n t i a l cross section data also. This lends good confidence to the normalization of our data. The phase s h i f t s which res u l t from the analysis are l i s t e d i n Table 24. Comparing these to the ones obtained from the previous analyses, one finds that there are some changes i n the phases by several quoted standard 185 Data Set Norma 1 izat ion BASQUE (forward data) BASQUE (backward data) PPA Dubna Rochester Lampf 1 .01 1 .Ok 1.10 1.00 (not f l oa ted ) 1.02 1.11 Table 23. , Fhase_shift_f itted_values_of_the normalizations f o r data near 212 MeV. The Dubna data was not included in the f i t . , 186 Phase Isospin Value D i f f e r - Phase Isospin Value D i f f e r -(deg) ence (deg) ence 5 S Q 0 17.14+0.69 0 .57 3 p 0 1 - 2 . 1 2 + 0 . 4 5 o : 2 9 £ 3.24+0.41 0.84 1 S Q 4 . 3 2 + 0 . 4 9 - 0 . 2 1 3 D 1 - 1 9 . 6 5 + 0 . 5 9 0.71 3 P , - 2 2 . 8 2 + 0 . 1 6 - 0 . 1 3 l p _25 .39+o .76 2.26 3 P 2 16 .22+0 .13 - 0 . 0 4 3 D 2 2 4 .76+0.63 3.24 <S 2 - 2 . 8 6 + 0 . 0 8 - o . 0 1 3 D 3 3.60+0.3** 1.51 3 l r 2 1 .07+0 .19 -0 . 04 £ 3 5 . 7 2 + O . I 9 - O . 5 7 1 D 2 7 . 4 1 + 0 . 1 8 - 0 . 0 4 3 G 3 -4 . 2 3+0.32 1 .18 3 F 3 - 2 .67+0 . 1 4 0 .01 1 F 3 - 3 . A 2 + 0 . 3 1 i . l 6 3 F j , 1 .71+0.11 - 0 , 0 2 3 G 2 ( 6 . 0 7 + 0 . 3 3 - 1 . 1 3 £ 4 - 1 . 1 8 + 0 . 0 1 o.O*1 01 3 G 5 0.45+0.30 . 0 > 0 g 3Hk 0.34+0.04 _ 0 > \ 1.06+0.07 0 > 0 3 H 5 -0.86+0.05 o o \ 0.20+0.04 _ Q > 0 1 Table 24, Phase s h i f t s from the current analysis at 212 HeV. The differences from the previous analysis are a l s o shown. 187 deviations., This points out the fact that the error bars do not yet accurately represent the true error i n the phases. The changes in the phases w i l l be discussed in more d e t a i l i n connection with t h e i r energy dependence. V. 2.2 Data Near U18 He? ftgain, a l l the data i n the forward hemisphere was performed at PPA4*. In the backward hemisphere, there are s t a t i s t i c a l l y precise measurements from Lampf*2 and Saclay* 3. These l a t t e r two sets were normalized to the deuteron production from neutrons, and, so, have ov e r a l l normalization uncertainties of about ±73. There i s also a ffeasurement from PPA*7 which has been found to disagree seriously with both the Lampf and Saclay r e s u l t s , and has been excluded from the analysis. F i n a l l y , there i s a measurement over the f u l l range from Carnegie 5 0. In addition to giving our forward and backward hemisphere data sets separate normalizations, the two backward sets were each given a separate normalization. The f i t t e d normalizations for a l l the d i f f e r e n t i a l cross section data are l i s t e d i n Table 25. Within the error l i m i t s , our three data sets agree i n normalization. 188 Data Set BASQUE (forward) BASQUE (backward, 1st set ) BASQUE (backward, 2nd set) PPA Carneg i e Saclay Lampf N o r m a l i z a t i o n 1.01 1.04 1.02 0.99 1.00 1.00 1.04 T a b l e 2 5 . . Phase s h i f t f i t t e d n o r m a l i z a t i o n s f o r data n e a r 4 18 MeV. The f i t t e d n o r m a l i z a t i o n s f o r each d i f f e r e n t i a l c r o s s s e c t i o n d a t a s e t a r e l i s t e d . 189 The 1st backward data set was well f i t i n the z analysis, having a h^of about 1, while the 2nd set showed v a much higher 'X v* of about 2. This indicates a source of i n s t a b i l i t y in this set which has not been accounted for in the error estimate. To account f o r thi s an error of 1% was added to bring the X»/ close to 1. u The 177 .990 point had a very bad i n d i v i d u a l 'X o f about 10, and was rejected from the data set on thi s basis. There i s mild disagreement of our data and those of lampf and Saclay at angles greater than 170°., Ho reason has been found for t h i s . The agreement among the data sets i s acceptable, with some small shape disagreements among the three s t a t i s t i c a l l y precise data sets, This i s an indication that the in t e r n a l consistency of the data has been overestimated. Most of the data l i e within one standard deviation of the f i t , while none l i e more than three standard deviations away. The t o t a l cross section was f i t to within one standard deviation of the value measured at 418 MeV. As f o r 212 MeV, the \ ^ of the o v e r a l l f i t was much larger than unity. The phase s h i f t s which result from the f i t are l i s t e d i n Table 26. They w i l l be discussed in 190 r e l a t i o n to the ones at other energies, V.3 ENEBGY DEPENDENCIES Using results from Bef. 33, d i f f e r e n t i a l cross section and phase s h i f t r e s u l t s at 3 25 MeV, the energy dependencies of these quantities can be shown. Previously, the phase s h i f t predictions for the d i f f e r e n t i a l cross section at forward angles did not show a smooth energy dependence., Fig 55 shows that t h i s situation has been remedied by our data. Figs 56 and 57 show the energy dependences of the phase s h i f t s that are l e f t free i n the analysis. Our data has l i t t l e e f f e c t on the 1=1 phases, and they are included only f o r completeness, showing the ef f e c t of the new p-p data. The results of the previous analysis i s also shown, indicating that the new data has improved the energy dependence of the £- mixing parameter and the G^phase. , The Fj phase shows a poor energy dependence and indicates that, as i n previous analyses, the r e a l part of the forward spin-averaged scattering amplitude w i l l have to be included to constrain the phase s h i f t f i t s a t 325 HeV. This amplitude w i l l have to be re-evaluated. 191 Phase Isospin Value D i f f e r - Phase Isospin Value D i f f e r -(deg) ence (deg) ence 0 - 4 . 7 8 + 0 . 7 7 - 1 . 5 8 X 7.05+0.51 0 . 2 8 X X -24 .77+0.41 - 0 . 5 5 X X -39.03+0.83 0 . 3 4 X X 22.62+0.49 0 . 0 2 t-l X 3.7^+0.36 0 . 3 5 X 8 .49+0 .20 - 1 . 1 4 X X - 5 . 4 8 + 0 . 3 1 0 . 6 0 X x - 5 . 1 2 + 0 . 1 8 . 0 . 1 5 X X 6.78+0.41 • : o . o x - 1 . 4 7 + 0 . 2 5 - - 0 . 2 1 X 1 -20.88+0.47 0,53 - 2 0 . 2 5 + 0 . 2 9 0 . 6 7 -34.76+0.22 - 1 . 0 9 18 . 31+0.14 -0.05 -2.11+0.13 -0.18 . O . 38+O . 15 -0.08 11 . 61+0.12 0.0 -2.99+0.13 0.39 3.^4+0.08 0.10 -1 .64+0.05 -0.04 0 . 80+0.06 -0.05 2 . 42+0.07 -0.20 3 H 5 -1.23+0.06 "0.05 3 H 6 0.65+0.05 0.01 Table 26. t Phase s h i f t r e s u l t s from the current analysis at 418 MeV. The differences from the previous analysis are also shown. 192 Fig 55. d i f f e r e n t i a l cross section. The extreme forward region of smooth energy dependence." Energy dependence of the the d i s t r i b u t i o n s now show a 193 | phases with new data included x,o previous phases (where different from new ones) 0 2 0 0 4 0 0 0 2 0 0 4 0 0 T (MeV) F i g 56. Energy dependence o f the 1=0 phase s h i f t s . • The dependence has improved over previous f i t s , e s p e c i a l l y f o r ? 3 and 3G 3. The r e s u l t s ! 3 of the P a r i s group's d i s p e r s i o n r e l a t i o n approach are a l s o shown. t phases with new data Included • previous phases (where different from new ones] — Paris potential predictions 194 0 -I - 2 0 T (MeV) 2 0 0 4 0 0 Fig 57. Energy dependence of the 1=1 phase s h i f t s . The 1=1 phase s h i f t s are v i r t u a l l y unaffected by our new data. They are shown to update those of Hef 4 1 , .with the new p-p data. The Paris group's r e s u l t s * 3 are also shown. 195 including the new values of the t o t a l n-p cross section in the intermediate energy region. This re-evaluation may affect the conclusion concerning the *G phase improvement, 3 however. V.4 CONCLUSION The shape of the n-p e l a s t i c d i f f e r e n t i a l cross section has been measured tc about 2%, with ov e r a l l normalizations of 3-4?S at 212 and 418 HeV, over the f u l l angular range. The energy dependence of dvVd5L in the extreme forward angles has become more reasonable than was previously indicated i n phase s h i f t analyses. Furthermore, the energy dependence of the phase s h i f t s has improved, notably those cf £, and G. ,. 1 z The BASQUE measurements of n-p e l a s t i c scattering observables have provided unambiguous information about the 1=0 N-N phase s h i f t s in the energy range 200-500 MeV. This t i e s in with the 1=1 phases which were already well determined to provide a good phenomenological description of the N-N in t e r a c t i o n in th i s energy region. This phenomenology can now be used t c compare with strong 196 interaction models, which, as yet, provide no theory. This information can also be d i r e c t l y applied to nuclear physics c a l c u l a t i o n s requiring knowledge of the H-N force. 197 REFERENCES 1. Chadwick J . Nature J_29, 312(1932) 2. Lock W.O., Measday D.F. Intermediate Energy Phy s i c s , Methuen,London, (1967) 3. Gammel J . L . , Tha le r R.M. Phys Rev 107, 291,1395(1957) 4. Heisenberg W. Z e i t F Phys 77, 1(1932) 5. Ke l logg J.M.B. Phys Rev 55_, 318(1939) 6. Wigner E. Proc Nat Acad Sc i U.S. 27, 281(1941) 7. Yukawa H. Proc Phys-Math Soc Japan 20, 720(1938) 8. La t tes C.M.G., Muirhead H., O c c h i a l i n i G.P.S., Powell C F . Nature 159, 69^ (19++7) Phys Rev C20, 555(1974) Phys Reports 13C, 5(1974) 11. MacGregor M.H., Stapp H.P., Moravcs ik M.J . 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Often several wires i n a chamber f i r e d , so that some procedure was required to determine which wires formed c l u s t e r s and which had f i r e d s i n g l y , as i t was quite possible to have more than one track going through the chambers. Groups of consecutive wires were treated in two says: i f three or less f i r e d adjacently, they were considered to have been due to a single track which had passed through the centre of the c l u s t e r . For greater than three, the entire c l u s t e r was passed on as single wires. No a p r i o r i decision could be made as to where, i n a large cluster, the track had passed. This decision was l e f t to the track f i t t i n g code. Once the number of discrete wire f i r i n g s i n each chamber had been determined, the granularity of the integral wire numbers was removed by randomizing the coordinate, using a square d i s t r i b u t i o n , over the 4 mm of the wire resolution. 20 2 To find whether an event had a fit-table track, the code t r i e d a l l combinations of wires f i r e d i n the KWPC's in each plane, eg. for three wires in each of three chambers,in one plane, f i t s to 27 l i n e s were attempted. For each set of wires a li n e a r least squares f i t was made, with the goodness of f i t reguirement based on the error of the intercept of the f i t t e d l i n e , which was proportional to the *)( of the f i t . Events where only two chambers f i r e d , i n any plane, were accepted on the condition that there was only a single c l u s t e r i n each chamber. Of course, a f i t was not required to obtain the eguations of these l i n e s , In the v e r t i c a l plane, where there were four chambers, i t was assumed that any one could misfire. I f no four-chamber f i t was obtained, a l l combinations of wires i n any three chambers were t r i e d to see i f an acceptable f i t could be found. In the case of multiple l i n e s f i t , rather than look for a vertex (in that plane) at the carbon, the l i n e with the - smallest X was taken as the best, and was the only one used to characterize the event. O r i g i n a l l y , a vertex c r i t e r i o n was used, but had a low success rate. The aWPCs were found to often f i r e wires close to each other, but 203 not adjacent. Frequently, l i n e s were f i t to a l l these wires, giving multiple l i n e s which diverged on t h e i r way to the carbon. The )C c r i t e r i o n was used to eliminate those l i n e s , rather than a test on the proximity of the c l u s t e r s . 204 APPENDIX E. CORRECTION FOB INCOMPLETE &ZIH0THAL ACCEPT & NCE OF DETECTORS This appendix describes an algorithm whose purpose i s to compensate for the limited azimuthal acceptance of detectors.. Consider a planar detector viewing p a r t i c l e s coming from a point source. As the polar angle & increases, there comes a value for ^ f o r which detection becomes a function of the azimuthal angle (j> , as well. For these values of 0 , only p a r t i c l e s having a r e s t r i c t e d range of values of (f) can be detected. This algorithm calculates the region of (f> accessible and then determines a factor 2 TV / (faf/^^ which i s used to weight the number cf detected p a r t i c l e s , eliminating the dependence on ^ , and so the dependence on the geometry of the detector. 205 E. 1 PBINCIPL E OF TJE 5LGOBITHM D i f f e r e n t i a l cross sections depend only on the polar angle of scatter, 0 . Therefore, the number of p a r t i c l e s cbserved by a detector i s where the azimuthal angle (£) i s integrated over a l l regions allowed for that value of 0 , as shown i n F i g B l . Define 1*4 - m f > I f the detector were of i n f i n i t e extent, there would be no l i m i t s on , and and so the true number of events scattered at angle would be 206 Fig B l . , allowed regions of the azimuthal  scatter ing angle. The amount of the azimuthal range ava i lab le depends on the polar scatter ing angle, being unrestr icted at small angles and zero at large angles. , 2 0 7 with the resu l t that a c a l c u l a t i o n of ft> would allow the determination of Mt from the data. , Consider now the case shown in Fig b2. ,&n incident p a r t i c l e whose dir e c t i o n i s { 0o t <$c) with respect to the 2 axis scatters at angle ( 0 , ^  ) into the detector. In general, the cone generated by rotating the scattered track about the incident one would intersect the detector forming an e l l i p s e . In order to determine the f r a c t i o n of the e l l i p s e circumference inside the detector, i t i s necessary to calculate the inte r a c t i o n points of the e l l i p s e with the detector boundaries. Define a coordinate frame based on the incident track 2 r £vw tf0 Cos <f) y • c ^  eo s q>0 ^ t oos 60 £ x = ? v j then i n t h i s frame, the major axis of the e l l i p s e w i l l intersect the cone at azimuthal angles 208 Fig B2. Geometry of the <g$i-S algorithm, fl t y p i c a l event i s characterized by a track incident on the carbon at {Qr (ft), with a scattered track at I £ , ) into P2. ° 209 One uses the transformation matrix H to go from the primed frame to the detector frame \ X 2: \ = n / x ' \ VI V A. end hack by Y 1 3 J V 4 a>*fa Note that for % =0 M reduces to the unit matrix as o expected. Bepeated use of these transformations yields the two points on the major axis of the e l l i p s e i n the detector frame: the distance between these two points gives the semi-major axis, and the average of the two gives the center of the e l l i p s e . Note that the center of the e l l i p s e 210 does not c o r r e s p o n d to the i n t e r s e c t i o n p o i n t o f the i n c i d e n t t r a c k with the d e t e c t o r . F o r an e l l i p s e with i t s major a x i s a long an a x i s x " , the e g u a t i o n of the e l l i p s e with semi-major and - m i n o r axes a and t , one has .it* „1 (K 1 V I f t h i s e l l i p s e i s r o t a t e d by an a n g l e ^ , a s i n F i g B3, then 4 " j Cotfa The miner a x i s i s o b t a i n e d i n a s i m i l a r f a s h i o n t o the major a x i s , & p o i n t on the cone i s chosen which l i e s cn the i n t e r s e c t i o n of t h e d e t e c t o r and the e l l i p s e , and i s t r a n f o r m e d back to the d e t e c t o r f r a m e . Then the c e n t e r p o i n t and t h i s p o i n t are t r a n s f o r m e d to the d o u b l e - p r i m e d frame where e g u a t i o n b. 1 h o l d s , so t h a t the minor a x i s can be s i m p l y s o l v e d f o r i n terms o f x'Vy" and the major a x i s . Upon t r a n s f o r m i n g e g u a t i o n b. 1 to the d e t e c t o r frame, 211 F i g B3. R o t a t i o n of t h e e x i t t r a c k e l l i p s e by the i n c i d e n t a z i m u t h a l a n g l e . The a z i m u t h a l angle of the i n c i d e n t t r a c k w i l l determine the amount of r o t a t i o n o f the e l l i p s e cn P2. 212 the eguation of the e l l i p s e becomes Z 1 with X^ 1 c \^Cosl(fo-k-' c\l s^X<<f)o r Sol? 40 ^G^Ui^ Given the eguation of the e l l i p s e , one can obtain the" eight possible intersection points (Fig B4 ) of the e l l i p s e and the four boundary l i n e s of the detector. These eight values are termed the 0_ . Transformation of these intersection points into the primed frame y i e l d s the azimuthal angles on the cone. Setting the angle to c / for a l l CJ)f ^  i ntersection points outside the boundaries, and to c 2 a l l those which did not have an intersection point, the weighting factor i s For every data point, with ( 0 , (j) ) , J? i s 213 Fig B4., D e f i n i t i o n of the eight possible intersections of the e l l i p s e and the detector boundaries. , Depending on the size of the e l l i p s e , there are eight possible intersections of the e l l i p s e and the detector boundaries., 214 calculated and used tc weight that point, compensating f o r the f i n i t e size of the detector. The data i t s e l f then acts as a Monte Carlo integration over the allowed polar angles E.2 J l P L I CaT IOH TO THE 8EUTB0N DETECTOR As discussed in Sec IV. , at 212 HeV the detector P2 developed a region of low e f f i c i e n c y , so that P2 e f f e c t i v e l y had a "hole" in the bottom. Hith a cut of 17° cn the polar angle, the only source of l o s s in <j"6 was in the i n e f f i c i e n t region, P2E. , There was no information on the incident neutron track, so that their origins were randomized over the target volume. ( 0O, (f)0) was then calculated using the reconstructed i n t e r a c t i o n point at the carbon converter. The (1) algorithm was used to calculate the allowed region cf (f) , |> so that weighting the data by the factor 1 . 1 ,t l - r ' corrected for the l o s s of P2E. The algorithm was tested on the 22.5° setting at 212 215 HeV, and 10° at 418 MeV. P2E was operational f o r both of these settings. The data was analyzed as usual, and with E2E a r t i f i c i a l l y removed using the MWPC's and then "replaced" by the algorithm. The agreement between the pairs was tet t e r than 0.25S. Fig B5 shows a s i m i l a r pair of histograms for a setting at 212 MeV in which P2E had f a i l e d . . This i s i l l u s t r a t e d by the d i s t i n c t slope in the p r o f i l e i n the uncorrected data. The slope i s removed by the algorithm, showing that no instrumental or geometrical i n e f f i c i e n c i e s remain. F i g B5. , V e r t i c a l p r o f i l e at the carbon with F2E f a i l e d . The v e r t i c a l p r o f i l e shows a d i s t i n c t r i s e from the bottom to the top of the carbon. This i s due to the f a i l u r e of F2E, which i s at the bottom of the P2E hodoscope., 217 APPENDIX C . DENSITIES OF LIPOID AND GASEOUS HYDBOGEN IN T h i s Appendix d e s c r i b e s the procedure used to determine the d e n s i t y of the p a r a - h y d r o g e n l i g u i d i n the t a r g e t when i t was f u l l , and of the gas when i t was n o m i n a l l y empty. The thermodynamic data used i n t h i s Appendix are from B e f 52. The p r e s s u r e o f the t a r g e t was m a i n t a i n e d at 1 7 . 0 0 ± 0 . 2 5 p s i a by the r e f r i g e r a t o r . A p l o t of vapour p r e s s u r e v e r s u s temperature i s shown i n F i g C I , i n d i a t i n g that t h e l i g u i d temperature was In F i g C 2 , a p l o t of temperature v e r s u s d e n s i t y i s shewn. The l i q u i d d e n s i t y was 0 . O 3 5 0 ± 0 . 0 0 0 2 g - m o l e / c m 3 , c o r r e s p o n d i n g to THE TABGET 218 IOr E o a> a. I 0 -> O l Fig C l . , Temperature of the .liquid, as a function of the pressure. , The data was taken from Bef 52.,The pressure was held constant by the r e f r i g e r a t o r , allowing the temperature to be determined. 219 0-05H Fig C2. Density of the l i q u i d hydrogen as a  function of temperature. ., The data was taken from Sef 52. Bote the units of g-mole/cm3. . 220 The temperature o f the t a r g e t was m o n i t o r e d by C u / C o n s t a n t a n t h e r m o c o u p l e s , w h i c h , u s i n g the l i g u i d temperature as a b a s e , gave a gas temperature o f P l o t s o f temperature a g a i n s t d e n s i t y were not a v a i l a b l e f o r the gas phase , and i n t e r m e d i a t e i s o t h e r m p l o t s of p r e s s u r e v e r s u s e n t r o p y and d e n s i t y versus e n t r o p y ( F i g C3) were u s e d . F i g C4 shows the r e l a t i o n between t h e t e m p e r a t u r e and gas d e n s i t y a t the c o n s t a n t pressure of 17 p s i a , y i e l d i n g T = 4 8 ± 8 K or A$ = ( 5 . 4 ± G . 2 ) * 10-* g / c m 3 221 F i g C3. Hydrogen qas pressure and density as  functions of entropy. , As data on gas density versus temperature were unavailable, intermediate plots of density and pressure against entropy were used to obtain the iso.bar.ic plot of density versus temperature. 222 Density gm-mole/cm3 Fig C4. Hydrogen gas density as a function of temperature,, Ihe'points below 50 K were obtained using Fig C 3 . ^ bove 50 K the hydrogen behaves as an,ideal gas, , 223 APPENDIX D. INVENTOBY OF MATERIALS This appendix deals with the amount of material between the point of scatter in the hydrogen target and the detectors. I t w i l l pertain s p e c i f i c a l l y to the spectrometer, with small changes required i n the length of air to describe the ether two configurations. This information i s required for the corrections applied for attenuation and multiple scattering, and to range-energy cutoffs in the spectrometer. Protons scattered out of the hydrogen target l o s t energy before they reached the spectrometer magnet, so that the measurement yielded a value l e s s than the true scattered momentum. , The energy l o s t by protons i n matter by Coulomb scattering from electrons has been well documented 5 3., The range of protons i n non-hydrogenous materials can be related to each other by 5* where the B*s are ranges (in g/cm2) i n the materials, and 224 the fl's the atomic .numbers. For s i m p l i c i t y , the thicknesses of a l l non-hydrogenous materials sere converted to carbon equivalent using the above r e l a t i o n . Table D1 l i s t s the materials between the hydrogen and the spectrometer magnet. The mean path length of the protons i n the hydrogen was calculated and i s shown i n Fig Dl. For scattering angles less than 34°, the curvature of the aluminium dome made i t normal to the proton t r a j e c t o r i e s , while above that angle, the thickness varied inversely with the sine of the angle. as a function of scattering angle, the material thickness was fo r 0"<34° t = d((7) (H) + 1.44 (C) (g/cm*) and for 8 >34<>, t = d(f}) (fl) +0.45/sin($) (C) +0.99 (C) (g/cm*) The guantities in brackets refer to either hydrogen or carton-equivalent materials, and d(0) i s the mean path 225 Ma te r i a l Th i ckness (g/cm ) Carbon-equ iva lent Thickness (g/cm^) mylar surrounding Q.053 the t a r ge t aluminium dome 0.274 a i r before magnet 0 .277 s c i n t i l l a t o r 0.50 MWPC wi res before 0 . 17 magnet mylar surrounding 0.21 MWPCs a i r a f t e r magnet 0.24 MWPC wires a f t e r 0 .17 magnet mylar surrounding 0.21 MWPCs a f t e r magnet 0.041 0.41 0.31 0.32 0.20 0 . 16 0 .27 0.20 0 .16 Tota l 2 . 0 7 Table D1. Thickness of materials between the hydrogen target and spectrometer. The materials are l i s t e d i n terms of l i n e a r dimensions and carbon-equivalent thickness. 226 d (cm) 8 10 2 0 3 0 4 0 e LAB 5 0 6 0 (deg) 7 0 80 Fig D1. , Bean, gat length,: of _scattered protons in hydrogen. The mean path length was calculated from the geometry of the apparatus and the d i f f e r e n t i a l cross section predicted from phase s h i f t analysis. length in hydrogen. 

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