Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials

TL;DR

This paper extends integral relations and the adiabatic expansion method to describe 1+2 reactions above the breakup threshold, applying it to helium trimers with soft-core potentials and validating with benchmark data.

Contribution

It introduces a generalized approach combining integral relations and adiabatic expansion for reactions above breakup threshold, applied to helium trimers with soft-core potentials.

Findings

Method successfully describes helium trimer reactions above breakup threshold.

Results agree with previous three-body recombination and dissociation rate calculations.

Soft-core potentials with a three-body force effectively model helium interactions.

Abstract

The integral relations formalism introduced in \cite{bar09,rom11}, and designed to describe 1+$N$ reactions, is extended here to collision energies above the threshold for the target breakup. These two relations are completely general, and in this work they are used together with the adiabatic expansion method for the description of 1+2 reactions. The neutron-deuteron breakup, for which benchmark calculations are available, is taken as a test of the method. The s-wave collision between the $^4$He atom and $^4$He$_2$ dimer above the breakup threshold and the possibility of using soft-core two-body potentials plus a short-range three-body force will be investigated. Comparisons to previous calculations for the three-body recombination and collision dissociation rates will be shown.