Scattering Phase Shifts at High Energies

Abstract

We evaluate the real and imaginary parts of the partial wave phase shifts for elastic pp, n±p and pp scattering from the experimental data on the total cross section, differential cross section and the ratio of the real to the imaginary of the forward scattering amplitude, assuming no spin dependence. In the case of pp scattering the calculated values of the ratio of the real to the imaginary of the forward scattering amplitude are used, because there are no experimental data available. The results obtained depend mainly on the contribution of the diffraction scattering, and it is shown that the contributions from the intermediate and large angle scattering are quite small numerically. It is also shown, by examining several reasonable forms of the t dependence of the ratio of the real to the imaginary of the scattering amplitude, that it does not affect the results appreciably. The results obtained are the following. The real parts of the partial wave phase shifts are, in all cases, negative and the absolute values decrease proportionally to (ln s) -l for PL210 GeV/c, up to an additive constant which is an integral multiple of n, where PL is the momentum of the incoming particle in the laboratory system. This additive constant is con­ sidered to be zero in the case of pp scattering according to the generalized Levinson's theorem. The reflection coefficients expressed. as a function of the impact parameter indicate the occur­ rence of strong absorption in the region where the impact parameter is nearly equal to or smaller than the nucleon Compton wave length for pL;;::;lO GeV/c, in contrast to the case for pL;;::;4 GeV/c where only peripheral absorption occurs. Therefore the real and imaginary parts of the scattering phase shifts obtained in this way suggest the existence of a certain critical energy in the region 5;S;pL;S;10 GeV/c, where their qualitative behavior changes drastically. The existence of a critical energy of this kind is in agreement with the results expected on a theory where a central part composed of many fermions is assumed to exist with a radius of the order of the nucleon Compton wave length.