Assisted tunneling of a wave packet between square barriers

TL;DR

This paper analytically investigates how an external perturbation enhances the tunneling probability of a wave packet between square barriers, with exact calculations for a potential mimicking a time-dependent electric field, exemplified by nuclear alpha decay.

Contribution

It provides an exact analytical solution for assisted tunneling in a time-dependent potential, linking pole spectrum to decay times and demonstrating enhancement effects.

Findings

Tunneling probability is increased by external perturbation.

Pole spectrum determines decay time.

Analytical results applied to nuclear alpha decay model.

Abstract

The assisted tunneling of a wave packet between square one dimensional barriers is treated analytically. The tunneling rate is calculated exactly for a potential mimicking a constant electric field with arbitrary time dependence. The pole spectrum of the barriers determines the decay time. The tunneling probability is enhanced by the perturbation. The results are exemplified for a simplified model of nuclear $\ds \alpha$ decay.