Semiclassical approach to dipole radial integrals for nonhydrogenic ions in supersymmetric quantum mechanics

Supersymmetric WKB (SWKB) wave functions diverging at the turning points and quantization relations up to the order (h) over bar(6) are derived directly from the supersymmetric partner Schrodinger equations. The resulting supersymmetric partner wave functions are used, without any Langer-type correction, for dipole radial integral calculations for bound-bound transitions in the Coulomb approximation To our knowledge, this is the first analytical calculation of matrix elements using SWKB wave functions. The bosonic SWKB partner wave function yields the WKB radial integral formula of Pankratov and Meyer-ter-Vehn which was derived by applying the Langer correction to the centrifugal potential The new dipole radial integral expression obtained from the fermionic SWKB partner wave function overestimates the oscillator strengths with respect to accepted values. However, we verify that in the classical limit both supersymmetric partner SWKB results converge to the same value.