Phenomenological Analysis of Pion Nucleon Scattering at High Energies

Abstract

Pion nucleon scattering in the multi-Ge V region is analyzed in a purely phenomenological way in the sense that any specific theoretical model is not introduced. The scattering amplitude including the spin flip part is appropriately parametrized and the numerical values of these parameters are determined. In particular, it is to be emphasized that the hitherto unknown parameter f3 (the real to imaginary ratio of the spin flip amplitude) is uniquely determined within the present experimental knowledge ((:W>=0.7 for the rc+p and sc->=0.8 for the re-p). Furthermore, an empirical formula for the scattering amplitude is proposed. This formula is valid for all angles and is able to explain most of the presently available data in the multi-Ge V region. For example, polarization data on elastic scattering are fairly well reproduced. Complete phase shift analysis is also performed and behaviours of the phase shifts and the absorption parameters are discussed. § l. Introduction Recently experimental data on the pion nucleon scattering' at high energies have been rapidly accumulated. 1 > Among these data the values of the recoil nucleon polarization for elastic rc+j), n-j) and charge exchange n-·p scattering 2 > enable us to discuss quantitatively a behaviour of the spin flip amplitudes for these processes. Furthermore, a very precise measuremene> of the real to im­ aginary ratios of the forward scattering amplitude gives also useful· information on the real amplitude. Nevertheless, the present experimental knowledge is still far from a complete determination of the whole scattering amplitude. It is, however, worthwhile for a further development of the theory to investigate to what extent we can get detailed information on the amplitude and to try to obtain an empirical expression for the amplitude at the present stage. Here we will, therefore, treat pion nucleon scattering in the multi-Ge V region purely phenomenologically. This means that in this paper we do not refer to any specific theoretical models such as the Regge theory, the statistical model, the quark model, etc. In § 2 the s-dependence of the amplitude at t = 0 is discussed by expanding the amplitude as a power series of 1/ Is (s and t are the usual Mandelstam vari­ ables, s = (centre-of-mass total energyy and t = (four-momentum transferY). Numerical values of the coefficients of the series are given to the order of 1/ vs- for the spin nonflip amplitude.