Anomaly-free singularities in the generalized Kohn variational method

TL;DR

This paper analyzes singularities in the generalized Kohn variational method for low-energy electron-H2 scattering, proposing two optimization approaches to avoid anomalies and demonstrating their effectiveness compared to the complex Kohn method.

Contribution

It introduces two novel optimization schemes for the generalized Kohn method to prevent anomalous singularities in scattering calculations.

Findings

Two optimization methods yield consistent results.

The methods produce results comparable to the complex Kohn approach.

Parameter variations can avoid certain anomalies.

Abstract

We have carried out an analysis of singularities in Kohn variational calculations for low energy e^{+}-H_{2} elastic scattering. Provided that a sufficiently accurate trial wavefunction is used, we argue that our implementation of the Kohn variational principle necessarily gives rise to singularities which are not spurious. We propose two approaches for optimizing a free parameter of the trial wavefunction in order to avoid anomalous behaviour in scattering phase shift calculations, the first of which is based on the existence of such singularities. The second approach is a more conventional optimization of the generalized Kohn method. Close agreement is observed between the results of the two optimization schemes; further, they give results which are seen to be effectively equivalent to those obtained with the complex Kohn method. The advantage of the first optimization scheme is that it does not require an explicit solution of the Kohn equations to be found. We give examples of anomalies which cannot be avoided using either optimization scheme but show that it is possible to avoid these anomalies by considering variations in the nonlinear parameters of the trial function.