Divergent perturbative series and Oppenheimer’s formula

Abstract

We present a derivation of the decay rate of a Hydrogen-type atom subjected to an external electrical field, the so-called Oppenheimer’s formula. The perturbative approach to this problem yields a divergent result, so we introduce the necessary mathematical tools to obtain a finite answer, and we illustrate them with two toy models. The result obtained agrees with the answer obtained originally by a WKB analysis.