Modified two-potential approach to tunneling problems

Abstract

One-body quantum tunneling to continuum is treated via the two-potential approach, dividing the tunneling potential into external and internal parts. We show that corrections to this approach can be minimized by taking the separation radius inside the interval determined by simple expressions. The resulting modified two-potential approach reproduces the resonance's energy and the width, both for narrow and wide resonances. We also demonstrate that, without losing its accuracy, the two-potential approach can be modified to a form resembling the $R$-matrix theory, yet without any uncertainties related to the choice of the matching radius.