Bound state properties and photodetachment of the negatively charged hydrogen ions

TL;DR

This paper derives an explicit formula for the photodetachment cross-section of negatively charged hydrogen ions, calculates these cross-sections with high accuracy for various isotopes, and introduces criteria to evaluate the quality of wave functions.

Contribution

It provides highly accurate photodetachment cross-sections for hydrogen ions and develops criteria for assessing wave function quality, including QED corrections and efficient integral calculations.

Findings

High-accuracy cross-sections for H$^{-}$ isotopes are determined.

Criteria for evaluating wave function quality are introduced.

Preliminary evaluations of photodetachment cross-sections are performed.

Abstract

Absorption of infrared and visible radiation from stellar emission spectra by the negatively charged hydrogen ions H$^{-}$ is considered. The explicit formula for the photodetachment cross-section of the negatively charged hydrogen ion(s) is derived. Photodetachemnt cross-sections of the ${}^{\infty}$H$^{-}$, ${}^{3}$H$^{-}$ (or T$^{-}$), ${}^{2}$H$^{-}$ (or D$^{-}$) and ${}^{1}$H$^{-}$ ions are determined to high accuracy and for a large number of photo-electron momenta/energies. We introduce criteria which can be used to evaluate the overall quality of highly accurate wave functions of the hydrogen ion(s). One of these criteria is based on highly accurate calculations of the lowest order QED corrections in the negatively charged hydrogen ions, including ${}^{1}$H$^{-}$ (protium), ${}^{2}$H$^{-}$ (deuterium), ${}^{3}$H$^{-}$ (tritium) and model ion with the infinitely heavy nucleus ${}^{\infty}$H$^{-}$. An effective approach has been developed to calculate three-body integrals with the Bessel functions of different orders. Some preliminary evaluations of the phototdetachment cross-sections of the negatively charged hydrogen ions are performed. Inverse bremsstrahlung in the field of the neutral hydrogen atom is briefly discussed.