Examination of the multiple-scattering expansion in the four-nucleon system

TL;DR

This study investigates the validity of multiple-scattering expansions in four-nucleon systems, specifically neutron-tritium elastic scattering, revealing their limitations at low energies and proposing a hybrid computational approach for practical calculations.

Contribution

It evaluates various truncation approximations of multiple-scattering series in four-nucleon systems and introduces a hybrid method combining exact and approximate calculations for efficiency.

Findings

Approximations fail at low energies but are somewhat accurate at small angles at higher energies.

All approximations fail at large scattering angles, highlighting the complexity of the scattering process.

A hybrid approach is proposed, combining exact low partial waves with approximate higher partial waves.

Abstract

The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into multiple-scattering series in terms of subsystem transition operators. Various approximations resulting from truncation of the series in different ways are evaluated and their validity is investigated. They fail at lower energies but at higher energies provide a rough reproduction of exact results at small scattering angles. In the large-angle region all approximations fail heavily, indicating that the scattering amplitude results from a delicate interplay of many multiple-scattering terms. The partial-wave analysis reveals that the developed approximations are reliable in higher partial waves, and for practical calculations an efficient ``hybrid'' approach is proposed, combining exact amplitudes in lower partial waves with approximations in higher partial waves. The implications for often used approximation of the first order in two-body transition matrix and development of microscopic optical potentials are discussed.