Solving a Relativistic Quasipotential Equation for the Superposition of a Non local Separable Interaction and a Local Quasipotential not Admiting Bound States

Abstract

Within the relativistic quasipotential approach to quantum field theory, a method of solving a finite-difference quasipotential equation involving a non-local separable quasipotential simulating the interaction between two relativistic spin less particles of unequal masses is generalized to the сазе where the total interaction is the superposition of a nonlocal separable quasipotential and a local one. Besides, the local component of the total interaction is supposed to be known and that it can not admit bound states. This has permitted to find an explicit expression for the additional phase-shift, to determine the conditions under which bound states may exist, and to generalize the Levinson theorem.