The Hydrogen Atom in Strong Electric Fields: Summation of the Weak Field Series Expansion

TL;DR

This paper applies the order dependent mapping method to resum the perturbation series for the hydrogen atom's Stark effect, achieving accurate energy estimates in intermediate electric fields and capturing decay widths.

Contribution

It demonstrates the effectiveness of the order dependent mapping method for summing the perturbation series of the hydrogen atom in strong electric fields, extending previous applications.

Findings

Accurate energy estimates in the electric field range 0.03 to 0.25.

Reproduction of decay widths from standard perturbation series.

Excellent agreement with exact values up to the fiftieth order.

Abstract

The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a numerical experiment up to the fiftieth order of the perturbation expansion. A simple mapping suggested by the analytic structure and the strong field behavior gives an excellent agreement with the exact value for an intermediate range of the electric field, $0.03\leq E\leq0.25$. The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.