Scattering formalism for nonidentical spinor particles

Abstract

A detailed formalism for the elastic scattering of two spin 1/2 nonidentical particles is presented, reviewing known results and presenting some new ones where gaps existed. Parity conservation and time reversal invariance is assumed throughout. The formalism is applicable in particular to neutron-proton scattering when isospin invariance is not imposed, but also to e.g. hyperon-nucleon and lepton-nucleon scattering. Several different sets of 6 scattering amplitudes are introduced and related to each other (invariant c.m.s. amplitudes, helicity, transversity and singlet-triplet amplitudes, Lorentz covariant amplitudes). All 36 linearly independent experimental quantities in the c.m.s. and l.s. are expressed in terms of the scattering amplitudes. Relations between l.s. and c.m.s. quantities are established (taking all relativistic phenomena into account). All components of the polarization tensors are expressed in terms of the 36 pure c.m.s. or l.s. quantities. One photon exchange electromagnetic amplitudes taking the Dirac and Pauli form factors into account are presented for np scattering. The one pion exchange amplitudes for np scattering are calculated, accounting for the np and π± π0 mass differences and different nucleon-pion coupling constants. The article is mainly aimed at experimentalists measuring polarization phenomena and should be useful for planning and evaluating experiments and reconstructing amplitudes. It complements a recent article on nucleon-nucleon scattering by Bystricky, J., Lehar, F. and Wintemitz, P. (J. Physique 39 (1978) 1)