Three-body continuum wave functions with a box boundary condition

TL;DR

This paper demonstrates that discretized three-body continuum wave functions using a box boundary condition are fully equivalent to those with correct asymptotics, preserving all channel information even when asymptotic behavior is unknown.

Contribution

It proves the equivalence between discretized and asymptotic three-body wave functions, validating the use of discretization in complex interactions like Coulomb.

Findings

Discretized wave functions preserve full channel information.

The equivalence holds even with unknown asymptotic behavior.

Discretization is reliable for Coulomb interactions.

Abstract

In this work we investigate the connection between discretized three-body continuum wave functions, in particular via a box boundary condition, and the wave functions computed with the correct asymptotics. The three-body wave functions are in both cases obtained by means of the adiabatic expansion method. The information concerning all the possible incoming and outgoing channels, which appears naturally when the continuum is not discretized, seems to be lost when the discretization is implemented. In this work we show that both methods are fully equivalent, and the full information contained in the three-body wave function is actually preserved in the discrete spectrum. Therefore, in those cases when the asymptotic behaviour is not known analytically, i.e., when the Coulomb interaction is involved, the discretization technique can be safely used.