Tunneling rates in bound systems using smooth exterior complex scaling within the framework of the finite basis set approximation

Abstract

A basis-set time-independent method to calculate tunneling rates in bound systems through a potential barrier is presented. The tunneling decay rates are associated with the imaginary parts of the complex eigenvalues of the Schrödinger equation where the reaction coordinate r′ is complex scaled such that, dr = dr′[1/cos θ(r′)]exp (iθ(r′)), where tan θ(r′) = tan θ∞g(r′). The function g(r′) fulfills 0 ≤ g(r′) ≤ 1 and shows a smooth transition from 0 to 1 near r′ = r0 which is the location of the top of the barrier. The value of θ∞ should be larger than a critical value for which a sharp transition from a real eigenvalue spectrum to a complex one is obtained. Illustrative numerical applications to two isomerization reaction models are given.