Variational Methods in Nuclear Collision Problems

Abstract

Variational methods, similar to the Rayleigh-Ritz method for bound state calculations, are developed for the phase shifts and elements of the scattering matrix in nuclear collisions. Numerical applications to neutron-proton and neutron-deuteron scattering involving trial functions with undetermined coefficients are described. Another variational principle, for scattering amplitudes, is shown to lead to the Born approximations and a formula recently derived by Schwinger. It may also be used in conjunction with the method of undetermined coefficients.