Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III: Integral Equation

Abstract

The practical theory of the four•nucleon scattering is presented by generalizing our formalism for the rank one separable potential to the rank n(;;:;;2) case. The Schmidt expansion is used to express the 3+ 1 and 2+2 subamplitudes at energies in the continuous spectrum region as an infinite series of separable terms. Employing the pole term decomposition for these subamplitudes in terms of the Schmidt expansion we can define, in conformity with Faddeev's residue prescription, respective four-nucleon amplitudes that describe elastic/rearrangement, partial breakup and full breakup scattering processes. Acquired simultaneous equations of these amplitudes take the form of multichannel two-particle Lippmann-Schwinger type equations. The four-nucleon binding energy and the nucleon-trinucleon elastic amplitude are obtained by numerical analysis of these equations for the Tabakin potential. Also was verified that this amplitude satisfies the unitarity relation.