Inverse-scattering theory at a fixed energy for the Klein-Gordon equation

The inverse-scattering theory at a fixed energy for the scattering of a par ticle by a potential in the Schrodinger equation formulated by Alam and Mal ik, which is based on the earlier work of Hooshyar and Razavy, is extended, in this paper, to the scattering of spinless particles at relativistic ene rgies governed by the Klein-Gordon equation. The differential equation is r eplaced by a set of difference equations. This reduces the inverse-scatteri ng problem to solving a continued fraction equation. The solution provides the values of the potential at a number of points which are equal to (one p lus the number of partial waves). The theory is tested for three widely dif ferent complex potentials, one of which is relevant to pion-nucleus scatter ing. The points of the potentials determined from the inverse-scattering fo rmalism are in accord with the actual ones in all three cases. Since the Kl ein-Gordon equation is effectively a Schrodinger equation with an energy-de pendent potential, the method may, in the appropriate cases, be suitable fo r the latter case. [S0556-2813(99)05502-8].