Anomaly-free singularities in the generalized Kohn variational method

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.
Comment: 20 pages, 13 figures. Changes made in response to referees' comments. Significant improvements made to interpretation of results, necessitating a change of article title and abstract. Additional author added. This version of the article has been accepted for publication in Journal of Physics A: Mathematical and Theoretical (IOP)