Integral relations for three-body continuum states with the adiabatic expansion

TL;DR

This paper introduces a method using integral relations derived from the Kohn Variational Principle to efficiently compute accurate scattering phase shifts in three-body continuum states with the Hyperspherical Adiabatic expansion, overcoming slow convergence issues.

Contribution

It presents a novel approach employing integral relations to improve convergence and accuracy in three-body scattering calculations within the Hyperspherical Adiabatic framework.

Findings

Fast convergence of phase shifts using the new integral relations

Effective extraction of scattering amplitudes for three-body states

Enhanced computational efficiency over traditional methods

Abstract

Application of the Hyperspherical Adiabatic expansion to describe three-body scattering states suffers the problem of a very slow convergence. Contrary to what happens for bound states, a huge number of hyperradial equations has to be solved, and even if done, the extraction of the scattering amplitude is problematic. In this paper we show how to obtain accurate scattering phase shifts using the Hyperspherical Adiabatic expansion. To this aim two integral relations, derived from the Kohn Variational Principle, are used. The convergence of this procedure is as fast as for bound states.