Parameter-variation methods for elastic scattering calculations

Extensive Kohn calculations by Schwartz demonstrated the power of the method but also the presence of anomalies involving spurious rapid variations in tanη. Nesbet showed that anomalies result from the vanishing of a denominator, and he and others have proposed anomaly-free methods. Anomalies are analyzed herein by parametrizing the normalization of long-range expansion terms such that conventional direct and inverse Kohn methods are special cases. The functional dependence of the parametrized estimate on the normalization parameter is found to be of simple algebraic form. By appropriately averaging over this parameter, we obtain a generalized variational method which is anomaly free. Calculations for a simple model problem are used to test and illustrate properties of the several variational methods which are considered.