Improved WKB approximation for quantum tunneling: Application to heavy ion fusion

TL;DR

This paper enhances the WKB approximation for quantum tunneling by extending Kemble's method to above-barrier energies through complex plane analysis, achieving high accuracy in predicting cross sections and barrier distributions.

Contribution

The paper introduces an extended Kemble's approximation for tunneling that improves accuracy at above-barrier energies by analytical continuation into the complex plane.

Findings

Extended Kemble's approximation closely matches quantum mechanical results.

The method accurately predicts cross sections and barrier distributions.

The approach is validated across a range of energies.

Abstract

In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy.