Reconstruction of the interaction potential in quasiclassical scattering

The reconstruction of a local spherically symmetric potential from scattering data is considered in the quasiclassical approximation for the case when the scattering data are known on some curve in the energy-angular momentum plane. In this plane a twoparameter family of curves is found for which the problem reduces to an Abel integral equation, and solutions are obtained that generalize the known solutions for constant energy and for constant angular momentum. It is shown that the solution of the quasiclassical inverse scattering problem is a combination of the solutions of two independent classical problems with different initial data – the scattering angle and the delay time. Cases are described in which the result can be represented in the form of an explicit function.