Permeability of one-dimensional potential barriers

Abstract

A numerical method is described for computing the exact permeability (tunnelling probability) for any one-dimensional potential barrier. It is used to test the validity of the widely-used approximate formulae for the tunnelling factors for truncated parabolic barriers. The method is also used to calculate tunnelling factors for the H+H₂ exchange reaction, using the theoretical potential surface of Shavitt, Stevens, Minn and Karplus, and it is shown that standard Eckart and parabolic barrier approximations can yield considerable error.