Solving a relativistic quasipotential equation for a sum of a nonlocal separable interactions

Abstract

Solving of the finite-difference quasipotential equation involving a total quasipotential simulating the interaction of two relativistic spinless particles of unequal masses is obtained. The total interaction consisting of the superposition of a local and a sum of a nonlocal separable quasipotentials is the spherically symmetric quasipotential and it admits one true bound state. The problem is investigated within the relativistic quasipotential approach to quantum field theory. Explicit expressions are obtained for the additions of the phase shift and their properties are investigated, theconditions under which bound states may exist are determined and the Levinson theorem is generalized.