Approximate penetration factor and reduced width for a diffuse edge well

Abstract

The so-called anticlassical approximation for solutions of the radial Schrodinger equation with rapidly varying potentialsU(r) for which ¦(kU)−1dU/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.