Approximate penetration factor and reduced width for a diffuse edge well

The so-called anticlassical approximation for solutions of the radial Schroedinger equation with rapidly varying potentials U(r) for which vertical stroke (kU)-1 dU/drvertical stroke <<1 is worked out. With the diffuseness as a small parameter and using the method of matched asymptotic expansions the regular and irregular wave functions for the Woods-Saxon potential well with Coulomb and centrifugal barrier are obtained. The penetration factor and the reduced width are also deduced and used to express the resonance width. (orig.)