On recent calculations of resonances for the Stark effect in hydrogen

TL;DR

This paper critically evaluates previous calculations of hydrogen Stark resonances, identifies inaccuracies due to imprecise matrix elements, and improves results using more accurate computational methods.

Contribution

It demonstrates that earlier results were less accurate than claimed and provides a more precise calculation method for hydrogen Stark resonances.

Findings

Previous results overestimated the imaginary part of the lowest resonance.

Improved calculations show better agreement with other methods.

Inaccuracy traced to imprecise matrix element calculations.

Abstract

We show that the resonances of the Stark effect in hydrogen reported in Phys. Rev. A \textbf{88}, 022509 (2013) are considerably less accurate than the number of digits appear to suggest. In particular, the imaginary part of the lowest resonance is several orders of magnitude greater than it should be. We compare the results of that paper with those provided by the Riccati-Pad\'{e} method, perturbation theory and an asymptotic expansion for the resonance width. The inaccuracy of those results can be traced back to the lack of precision in the calculation of the matrix elements of the secular equation. We carry out a more accurate calculation with the same method and show that the agreement with earlier results of other authors is greatly improved.