Approximate penetration factor and reduced width for a diffuse edge well

The so-called anticlassical approximation for solutions of the radial Schrödinger equation with rapidly varying potentialsU(r) for which ¦(kU)^–1 dU/dr¦ 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.Communicated by X. Campi