Green's function method for strength function in three-body continuum

TL;DR

This paper introduces new Green's function techniques for calculating dipole strength functions in three-body systems, comparing their effectiveness with existing methods like complex scaling and Lorentz integral transform.

Contribution

It develops novel Green's function methods that improve the calculation of strength functions in three-body continuum systems, offering practical alternatives to established techniques.

Findings

Green's function methods are comparable in accuracy to existing methods.

Lorentz integral transform is less practical due to inverse transform difficulties.

New techniques improve the correction of wave function tails in strength calculations.

Abstract

Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in a direct calculation of the strength function or by using a solution of a driven Schroedinger equation in a summed expression of the strength. They are compared with the complex scaling method and the Lorentz integral transform, also making use of a discretized continuum. Numerical tests are performed with a hyperscalar three-body potential in the hyperspherical-harmonics formalism. They show that the Lorentz integral transform method is less practical than the other methods because of a difficult inverse transform. These other methods provide in general comparable accuracies.