WKB Solution of Inversion Problems for Potential Scattering

Abstract

The construction of a local, not necessarily monotonic, potential is given in the WKB approximation for the two following sets of “input” information: (1) the phase shift as a function of impact parameter (or orbital angular momentum) at one energy; (2) the phase shift as a function of energy for one value of $l$ , plus the eigenvalues of the potential for this same $l$ . It is also shown that in the high‐energy WKB approximation (Eikonal approximation) the energy dependence of the total cross section can be inverted to obtain the potential. Procedures for constructing the classical deflection function (or, equivalently, the phase shift as a function of impact parameter) from the observed differential cross section are also discussed.