Breakup of three particles within the adiabatic expansion method

TL;DR

This paper develops a method using hyperspherical adiabatic basis to calculate three-particle breakup cross sections in $1+2$ reactions, addressing convergence issues with a new integral relation approach, demonstrated on neutron-deuteron scattering.

Contribution

It introduces an improved technique for calculating three-body breakup amplitudes that overcomes slow convergence problems in hyperspherical harmonic expansions.

Findings

Method accurately computes breakup cross sections for neutron-deuteron scattering.

The integral relation approach enhances convergence in challenging configurations.

Results agree with existing benchmark calculations.

Abstract

General expressions for the breakup cross sections in the lab frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The ${\cal S}$-matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe $1+2$ processes, there are nevertheless particular configurations in the breakup channel (for example those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations.