General integral relations for the description of scattering states using the hyperspherical adiabatic basis

TL;DR

This paper develops general integral relations based on the hyperspherical adiabatic basis to describe scattering states in 1+2 reactions, applicable to multichannel processes and not limited to s-wave interactions.

Contribution

It introduces a set of integral relations derived from the Kohn variational principle for hyperspherical adiabatic expansion, applicable to multichannel and higher partial wave reactions.

Findings

Validated the method with a helium dimer collision model.

Analyzed convergence of the K-matrix with respect to adiabatic potentials.

Applied the approach to lithium-helium collision systems.

Abstract

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the ${\cal K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a $^6$Li and two $^4$He atoms (two channels open).