Three-body breakup within the fully discretized Faddeev equations

TL;DR

This paper introduces a new discretized Faddeev equation method using wave-packet basis to efficiently compute three-body breakup amplitudes and cross sections, simplifying calculations significantly.

Contribution

A novel discretization approach for three-body breakup calculations using wave-packet basis within the Faddeev framework, enabling more efficient and accurate results.

Findings

Accurate three-body breakup cross sections matching benchmark results.

Significant reduction in computational complexity and time.

Effective treatment of few-body continuum states as multi-channel scattering.

Abstract

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three- and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process $n+d\to n+n+p$ with non-local and local $NN$ interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.