Comparison of nonperturbative variational approximations to the scattering amplitude for a Yukawa potential

Variational methods for calculating approximations to the scattering amplitude of a spinless particle from a Yukawa potential are compared. These arise from the variation of functionals that depend on trial forms of the Heitler operator K or the transition operator T. The trial forms are nonperturbative, and the variational principle is applied in the free particle and partial wave basis to obtain independent approximations. In addition, no artificial separability constraint is imposed on the momentum space representation of either the trial T or K. The full free particle Green's function is utilized without basis set truncation in all of the calculations. The different approximations provide a choice of technique in the event that one or the other variational method is unstable. The results at two representative energies are in good agreement with an exact calculation