Variational methods in potential scattering

Abstract

A comparison of a variety of standard variational methods with a new method due to Harris is made with a view towards selection of the optimal method to be used in realistic many-body scattering calculations. Numerical results for two short-range potentials, the attractive exponential and the attractive Yukawa potential, are given and compared with exact results obtained analytically or by direct numerical integration. It is demonstrated by calculation that the source of an anomaly observed in earlier studies by Schwartz is not due to the attributed reason and, furthermore, we find the Kohn method significantly more accurate at the Harris eigenvalues than any of the other methods. Therefore, we propose the use of the Kohn method at the eigenvalues of the matrix Hamiltonian in the trial function subspace as the optimal method to be used in variational scattering calculations.