Upper and Lower Bounds on Phase Shifts for Three-Body Systems:n−dScattering

Abstract

A variational-bound formulation of the three-body problem based on the Faddeev equations has been derived previously. This method involves a variational calculation of the exact effective potential between the incident particle and the bound two-body target. Variational upper and lower bounds on this effective potential are obtained by constructing approximate separable three-body Green's operators. The eigenphase shifts determined by using the effective potential in the two-body Lippmann-Schwinger equation are upper and lower bounds on the true eigenphases for energies below the three-body breakup threshold. The method is applied to the neutron-deuteron system, and a set of variationally converged phase shifts is obtained.