On recent calculations of resonances for the Stark effect in hydrogen

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-Padé 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.