Glonti, L N

Kazarinov, Yu M

Rozanova, A M

Silin, I N

CERN Document Server

CERN LIBRARIES, GENEVA CM-P00100690 JOINT INSTITUTE FOR NUCLEAR RESEARCH, DUBNA Report P1 - 5737 PHASE-SHIFT ANALYSIS OF pp SCATTERING AT 1 GeV L.N. Glonti, Yu.M. Kazarinov, A.M. Rozanova and I.N. Silin Dubna 1971 Translated at CERN by R. Luther (Original: Russian) Not revised by the Translation Service (CERN Trans. 71-39) Geneva September 1971 P1 - 5737 PHASE-SHIFT ANALYSIS OF pp SCATTERING AT 1 GeV L.N. Glonti*), Yu.M. Kazarinov, A.M. Rozanova and I.N. Silin Dubna 1971 *) Tbilisi State University Statement of the Problem The following assumptions were made when carrying out the phase-shift analysis: 1. A single-meson approximation is valid for the description of a pp interaction at 1 GeV in states with an orbital moment ℓ > 6. 2. Mesons are mainly produced from initial 3P0,1,2 1D2 and 3F2,3,4 states. 3. The energy dependence of the experimental data used can be ignored and they can be related to 1 GeV within the limits of error (viz. table 1). The applicability limit for a single-meson approximation is estimated on the basis of the results of the phase-shift analysis at 630 MeV/3/, allowing for variation in the impact parameter during the transition to 1 GeV. The assumption concerning the nature of the meson production processes was based on the fact that the angular distributions of the π- mesons produced in pp collisions at 1 GeV as well as at 650-660 MeV contain no terms higher than cos4 θ ( θ is the π-meson's emission angle). It is also known that, for an adequate description of the experiment during phase-shift analysis at 630 MeV, it is sufficient to allow for phase complexity only in P0,1,2, 1D2 and 3F2,3,4 states. The experimental data used for the phase-shift analysis are shown in table 2. In order to eliminate the possibility of systematic errors in the results obtained by the various authors, the data were processed first. The differential cross-sections for elastic pp scattering measured in/6-9/ were renormalized to the total cross-section for elastic scattering σ elas./tot. = 24.8 ± 0.9/15/. - 2 -The normalization factors are shown in the fourth column of table 2. To obtain corrected values for the differential cross-sections of the quantity d σ / d Ω , shown in the papers listed (table 1), it is essential to divide them into the appropriate norms. The interaction's total cross-sections measured in papers /12/ and /13/ at 1.03 GeV and 1.075 GeV were averaged out. The error in measuring the polarization of the primary beam (≈ 5%) is added quadratically to the results of the polarization measurements/12/. The data on differential cross-sections and polarization for angles θ > 90 were reduced to the range 0° ≤ θ ≤ 90° in terms of the known relations. It is easy to work out that 3lmax + 1 free parameters can be determined from the data in table 2 (σtot + 1 ; +1; P ( θ ) + l m a x + 1 ; σ i n e l a s t o t a l + 1 ( o r 21 parameters at lmax = 6).The number of phase-shifts to be determined at lmax = 6, if meson production from P, D and F states is taken into account, is 22. The single-meson approximation used to describe a pp interaction in states with high orbital momenta provides the missing equations and the problem seems to be solved. However, there will clearly be a large number of solutions (≈ 2m, where m is the required number of parameters/5/).In order to obtain some overdetermination, as is required with nonlinear problems solved by the maximum-likelihood method, the experimental data also included four points obtained by extrapolating the energy dependence of the depolarization factor Dpp measured in the lower energy region (400 - 630 MeV). The errors in the values extrapolated were such that this parameter was positively determined with 0,99 probability. The solutions were found from the functional minimum condition x2 η [Fexp-F(δ)]2i. wi, where Fexp is the value obtained by experiment, F (δ) is the calculated value of the quantity measured, Wi is the weight and n is the total number of experimental points used for the phase-shift analysis. The procedure used to search for solutions is described in detail in /19/. - 3 -Results The attempt to find a solution from random initial values and thus to verify that the solution to the problem was single-valued did not meet with success. It turned out that the errors in the parameters found by this method were so great (100% or more) that no distinction could be made between the solutions within the limits of error. It was therefore decided to obtain a set of phase-shifts describing the experimental data at 1 GeV by extrapolating the solution found at 630 MeV / 3 /. For this purpose, the phase shift values found in ' were taken as initial values and were determined more accurately in terms of the experimental data shown in table 2. During this process, measures were taken to ensure that the energy dependences of δ (Ε) were sufficiently smooth right up to 1 GeV. The solution obtained is shown in table 3. The table also shows the results of phase-shift analyses at 630 MeV/3/ and 1000 MeV/4/. A comparison of the set of phase-shifts thus obtained with the solution found previously at 630 MeV/3/ indicates that the experimental data at 1 GeV may be adequately described by assuming that there is a smooth dependence of phase-shifts on energy. There is no need to make any assumption about noticeable meson production from an initial1 So state, as the authors of paper/4/ had to do at 1000 MeV. The angular dependences of the values observed were calculated in terms of the set of phase-shifts obtained and are shown in figs. 1-6. The batched areas in figs. 1-3 are the error margins of the curves. The error margin of the curves in figs. 4-6 for the angular dependences of the Wolfenstein parameters is 100%. It clearly follows from this that at present the most useful information for determining the pp-scattering amplitude can be obtained only from experiments on triple scattering. - 4 -After this paper had been finished, fresh results concerning the measurement of differential cross-sections, polarization and depolarization were published (viz. table 1). Firstly, the Dpp depolarization at 90° (c.m.s.), measured at 984 MeV, unfortunately features an error of almost 100% and has virtually nothing new to offer in the way of information. The differential cross-sections and polarization measured in the 30° - 90° range correspond to previous data. In conclusion, the authors wish to thank S.I. Bilen'kaya for her help with this paper. _ 5 -Bibliography 1. M.H. MacGregor, R.A. Arndt, R.M. Wright. Phys.Rev., 173, 1272 (1968). 2. Z. Janout, Yu.M. Kazarinov, F. Lehar, A.M. Rozanova, Nucl.Phys., A127, 449 (1969). 3. S.I. Bilen'kaya, L.N. Glonti, Yu.M. Kazarinov, V.S. Kiselev. Zh.E.T.F. 59, 1050 (1970). 4. N. Hoshisaki, T. Kadota. Preprint NEAP, May 1969. 5. Ν.P. Klepikov. Zh.E.T.P., 44, 376 (1963). 6. W.K. MeFarlane, R.J. Homer, A.W. O'Dell et al. Nuovo Cim., 28, 943 (1963). 7. J.D. Dowell, W.R. Frisken, G. Martelli et al. Nuovo Cim., 18, 818 (1960). 8. L.W. Smith, A.W. McReynolds, G. Snow. Phys.Rev, 97, 1186 (1955). 9. T.A. Murray, L. Riddiford, G.H. Grayer et al. Nuovo Cim., 49, 261 (1967). 10. R.J. Homer, W.K. McFarlane, A.W. O'Dell et al. Nuovo Cim., 23, 690 (1962). 11. Y. Ducros. Rev. Mod. Phys., 39, 531 (1967); Phys. Rev., 164, 1672 (1967). 12. H.A. Neal, M.J. Longo. Phys. Rev., 161, 1374 (1967). 13. F.F. Chen, O.P. Leavit, A.M. Shapiro. Phys. Rev., 103, 211 (1956) 14. M.J. Longo, J.A. Helland, W.N. Hess et al. Phys. Rev. Lett., 3, 568 (1959). 15. D.V. Bugg, A.J. Oxley, J.A. Zoll et al., Phys. Rev., 133B, 1017 (1964). 16. G.H. Grayer, J.D. Dowell, C.J. Adams et al. Lett. Nuovo Cim., 3, 663 (1970). 17. M.G. Albrow, S.A. Anderson/Almened, B. Bonjakovic et al. Nucl.Phys., B23, 445 (1970). 18. D.V. Bugg, D.C. Salter, G.H. Stafford et al. Phys. Rev., 146, 980 (1966). 19. Yu. M. Kazarinov, I.N. Silin. Zh.E.T.F., 43, 692 (1962). - 6 -20. H.P. Stapp, T.Y. Ypsilantia, Ν. Metropolis. Phys. Rev., 105, 302 (1957). The document was received by the Publishing Department on 8 April, 1971 - 7 -Table 1. Experimental data on elastic pp scattering close to 1 GeV. E, θ° f ∆ source E, θ° f ∆f source MeV c.m.s. MeV c.m.s. PP total croos-section (mb) PP total cross-section (mb) 968 47,863 0,058 /18/× 970 22,48 0,8 /15/ 970 47,3 1,0 /15/ 1030 46,5 2,0 /12/ 1073 47,49 0,040 /13/ 1075 48,3 1,6 /18/× PP differential cross-section (mb/ster.) 950 35,90 6,71 0,50 /17/X 1000 36,5 5,66 0,10 / 8 / 38,73 6,30 0,51 / 41,3 4,54 0,10 43,12 4,76 0,25 53,7 2,44 0,07 49,45 3,51 0,23 64,0 1,33 0,05 54,55 2,58 0,17 77,0 0,79 0,05 58,67 2,26 0,18 90,0 0,62 0,05 62,62 1,65 0,11 1010 18,5 11,80 0,26 /17/× 67,05 1,45 0,12 24,6 10,40 0,33 70,12 1,08 0,09 30,7 7,89 0,18 73,74 1,00 0,08 36,7 5,76 0,09 77,88 0,99 0,08 41,5 4,11 0,09 81,95 0,65 0,05 48,5 2,718 0,051 86,55 0,73 0,06 60,0 1,546 0,041 89,43 0,78 0,10 71,1 0,922 0,029 970 12,30 19,600 1,200 /6/ 79,8 0,739 0,037 48,30 3,506 0,088 90,0 0,608 0,030 /17/× 59,73 2,037 0,070 1040 37,82 5,97 0,34 70,83 1,185 0,040 44,77 4,38 0,22 81,55 0,898 0,024 50,95 3,04 0,20 991 14,5 18,620 0,801 / 9 / 55,25 2,20 0,15 19,0 14,280 0,366 60,00 1,94 0,16 23,0 12,460 0,280 63,90 1,56 0,10 30,5 10,334 0,274 68,28 1,17 0,10 40,0 5,430 0,117 71,93 0,95 0,08 50,0 3,200 0,089 76,70 0,85 0,06 59,5 1,860 0,085 80,80 0,66 0,06 70,0 1,041 0,085 84,27 0,65 0,05 80,25 0,690 0,036 88,28 0,65 0,06 * not used in the search for solutions - 8 -Table 1 (Continued) Ε, )θ° f ∆f' source E, θ° f Δf source ΜeV c.m.s. MeV c.m.s. pp polarization P 9 5 0 2 9 , 5 5 0 ,41 0 ,03 / 1 7 / × 51,20 0 ,330 0,020 35 ,90 0 ,437 0,04 55 ,40 0 ,330 0,020 38 ,73 0 ,53 0 ,05 60,00 0 ,285 0 ,020 43,12 0,44 0 ,03 64,60 0 ,265 0,030 49 ,45 0 ,47 0,04 67 ,20 0 ,287 0 ,050 54 ,55 0 ,40 0,04 68,70 0 ,210 0 ,060 58 ,67 0 ,37 0 ,05 71 ,60 0 ,210 0 ,020 62,62 0 ,30 0 ,05 75 ,60 0 ,080 0 ,035 67,05 0 ,25 0 ,07 79 ,40 0,092 0 ,013 70,12 0 ,20 0 ,08 83 ,20 0 ,090 0,020 73,74 0 ,24 0 ,08 87 ,00 - 0 , 0 1 7 0 ,047 77 ,88 0,04 0 ,08 1 0 3 0 3 9 , 8 8 0 ,419 0 ,037 / 1 2 / 81 ,95 0 ,17 0 ,08 42 ,47 0 ,464 0 ,046 86,55 - 0 , 0 9 0 ,09 53 ,60 0 ,481 0 ,033 89 ,43 - 0 , 1 8 0 ,13 57 ,81 0 ,417 0 ,043 9 7 0 12,30 0 ,237 0 ,155 61,62 0 ,325 0 ,037 2 2 , 1 0 0 ,183 0 ,079 65,32 0 ,258 0,074 2 4 , 5 0 0,223 0 ,061 68,52 0 ,245 0 ,035 2 6 , 9 0 0 ,312 0 ,068 71 ,37 0 ,265 0 ,039 2 9 , 4 0 0 ,237 0,082 77 ,25 0 ,095 0,029 3 0 , 5 0 0,229 0 ,056 88 ,25 - 0 , 0 2 1 0,034 3 6 , 5 0 0 ,297 0 ,067 1 0 4 0 30 ,68 0 ,41 0,02 / 1 7 / × 4 8 , 3 0 0 ,386 0 ,070 37,82 0 , 4 7 0 , 0 3 59 ,70 0 ,334 0 ,083 44 ,77 0 , 3 8 0 ,02 70 ,80 0,169 0 ,067 50 ,95 0 ,46 0 ,04 81 ,60 0 ,063 0 ,066 55 ,25 0,32 0 ,04 1029 2 5 , 9 0 0 ,345 0 ,040 60 ,00 0 ,28 0 ,05 30 ,90 0 ,355 0 ,020 63 ,90 0 ,28 0 ,05 35 ,60 0 ,370 0 ,030 68 ,28 0 ,32 0 ,06 40 ,60 0 ,385 0 ,030 71 ,93 0,21 0 , 0 7 4 2 , 0 0 0 ,405 0 ,027 76 ,70 0 ,22 0 ,06 45 ,40 0 ,370 0 ,020 80 ,80 - 0 , 0 1 0 , 0 8 46 ,60 0 ,360 0 ,025 84 ,27 0,11 0 ,08 50 ,00 0 ,345 0 ,021 88 ,28 0 , 0 1 0 ,08 P P polarization correlation Cnn PP depolarization 9 7 8 4 2 , 0 0 ,70 0,19 / 1 1 / 984 9 0 , 0 0 ,65 0 ,56 / 1 6 / × 4 6 , 7 0,72 0 ,15 51,2 0 ,61 0 ,16 5 5 , 6 0,62 0 ,20 60 ,0 0 ,46 0 ,26 6 4 , 3 0 ,44 0 ,27 68 ,6 0 ,71 0 ,47 70 ,0 0,39 0 ,27 7 3 , 4 0 ,69 0 ,16 77 ,4 0 ,79 0 ,17 * not used in the search for solutions - 9 -Table 2 . Experimental data processed. exp.) value E, MeV no. of points norm x2 source remarks 9 7 0 1 0,003 / 1 5 / averaged 1030 1 0,054 / 1 4 / 1075 1 / 1 3 / 9 7 0 1 / 1 5 / 9 7 0 4 1,109 ± 0,044 4 , 8 / 6 / renormal lsed t o t o t a l i n e l a s t i c c r o s s - s e c t i o n 991 8 0 ,990 ± 0 ,038 20 ,1 / 9 / 1000 5 0 ,870 ± 0 ,034 7 , 6 / 8 / 1010 9 0,835 ± 0 ,031 1 3 , 0 / 7 / (24 ,8 ± 0 ,9 mb) Ppp 9 7 0 11 9 , 8 / / 1029 17 16,3 / 1 1 / 1030 10 1 5 , 6 / 1 2 / Cnn 9 7 8 10 0,82 / 1 1 / Dpp e x t r a p o l a t i o n Table 3 . P h a s e - s h i f t s in degrees (Stapp m a t c h / 2 0 / ) 630 MeV/3/ 1 GeV ( t h i s paper) 1 G e V / 4 / f2 0,076 ± 0 ,005 0 ,07 0 ,08 3S0 - 1 9 , 4 ± 3,4 - 5 , 0 - 3 0 , 0 - 2 0 , 7 ± 2 , 4 - 4 1 , 1 - 3 7 , 5 3P0 - 2 9 , 9 ± 2,2 - 1 7 , 6 - 7 1 , 5 3P2 3 4 , 7 ± 1,8 5 5 , 0 16,9 9,6 ± 1,6 11,8 11 ,3 ε2 2 , 9 ± 0 ,9 3 , 8 4 3 , 5 3 F 2 - 4 , 1 ± 0 , 6 - 6 , 6 - 1 3 , 7 3F3 0 , 7 ± 0 ,8 - 0 , 3 ( - 7 , 7 3 ) 3F4 3 , 8 ± 0 , 8 4,7 ( 6 , 5 0 ) 4G4 5,6 ± 0 ,7 6 , 4 ( 4 , 5 0 ) ε4 0 , 7 ± 0 ,8 - 2 , 5 3H4 - 2 , 3 ± 0 ,6 - 3 , 5 1 ( 1 , 1 0 ) 3H5 - 3 , 2 ± 0,8 4 1 , 5 ( - 2 , 0 0 ) 3H6 - 2 , 8 ± 0 ,5 - 3 , 7 ( 2 , 4 0 ) I6 single-meson - 3 , 2 ( 0 , 6 6 9 ) imaginary p a r t s of phase s h i f t s 4S0 - - 4 0 , 0 3P0 - 2 , 0 9 , 0 - 30,2 0 , 0 3P2 5 , 1 ± 1,5 5 , 4 16 ,0 4D2 10,9 ± 2 , 6 6 , 8 13,2 3F2 0 , 7 ±1 1 4 , 9 19,0 3F3 2 , 4 ± 1,5 9 , 4 18,0 3F4 4 , 0 ± 0 , 7 16,5 3 , 0 X2 88 52 η 82 62 - 10 -Fig. 1 Fig. 2 - 11 -F i g . 3 F i g . 4 - 12 -F i g . 5 F i g . 6 

Phase-shift analysis of pp scattering at 1 GeV

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