Highly accurate calculation of the resonances in the Stark effect in hydrogen

TL;DR

This paper presents three independent methods for accurately calculating resonances in the hydrogen Stark effect, with the Riccati equations method providing the most precise results and sharp resonances.

Contribution

The paper introduces a new high-accuracy approach using Riccati equations for calculating Stark resonances in hydrogen, complementing existing complex rotation methods.

Findings

Riccati equations method yields the most accurate resonances.

All three methods produce consistent results.

Sharp resonances are obtained with the Riccati approach.

Abstract

We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other one is based on the Riccati equations for the logarithmic derivatives of factors of the wavefunction (RPM). The latter approach enabled us to obtain the most accurate results and extremely sharp resonances.