Calculation of tunneling rates across a barrier with continuous potential

TL;DR

This paper presents a method using uniform asymptotic expansion to accurately calculate wavefunctions and tunneling rates across a potential barrier.

Contribution

It introduces a new approximation technique for computing tunneling rates with improved accuracy over existing methods.

Findings

Provides explicit formulas for wavefunctions and tunneling rates

Demonstrates the method's accuracy through comparisons

Applicable to various potential barriers

Abstract

Here, approximate, but accurate expressions for calculation of wavefunctions and tunneling rates are obtained using the method of uniform asymptotic expansion.