Solving three-body scattering problem in the momentum lattice representation

TL;DR

This paper introduces a novel wave-packet based momentum lattice method for solving three-body scattering problems, simplifying complex integral equations into manageable matrix equations and demonstrating accurate results for neutron-deuteron scattering.

Contribution

The paper presents a new wave-packet discretization approach that transforms three-body scattering problems into matrix equations on a momentum lattice, improving computational efficiency and accuracy.

Findings

Accurately computed phase shifts and inelasticity parameters for neutron-deuteron scattering.

Method effectively handles scattering above the breakup threshold with complex singularities.

Results agree well with previous benchmark calculations.

Abstract

A brief description of the novel approach towards solving few-body scattering problems in a finite-dimensional functional space of the $L_2$-type is presented. The method is based on the complete few-body continuum discretization in the basis of stationary wave packets. This basis, being transformed to the momentum representation, leads to the cell-lattice-like discretization of the momentum space. So the initial scattering problem can be formulated on the multi-dimensional momentum lattice which makes it possible to reduce the solution of any scattering problem above the breakup threshold (where the integral kernels include, in general, some complicated moving singularities) to convenient simple matrix equations which can be solved on the real energy axis. The phase shifts and inelasticity parameters for the three-body $nd$ elastic scattering with MT I-III $NN$ potential both below and above the three-body breakup threshold calculated with the proposed wave-packet technique are in a very good agreement with the previous accurate benchmark calculation results.