Scattering between composite particles composed of Fermions in the one-dimensional delta-force model

Abstract

The general explicit formula of the exact amplitude of the composite particle scattering in the one-dimensional delta-force model is derived. The composite particles are composed of Fermions with an arbitrary SU h internal symmetry. The derivation is made by the use of the recoupling technique of the unitary group and by setting up the recurrence relation with respect to the Fermion number. The exact equivalent local potential which reproduces the exact scattering amplitude is constructed by the use of the soliton solutions of the Kortewegde Vries equation. In most cases the potential is energy-dependent. The accuracy of the time-dependent Hartree-Fock (TDHF) approximation for the composite particle scattering is investigated by comparing the TDHF scattering amplitude with the exact scattering amplitude. While at low energy limit the approximation is not good for small Fermion numbers, at high energy it is good for all Fermion numbers.