On the absorption of radiation by the negatively charged hydrogen ion. I. General theory and construction of the wave functions

The absorption of infrared and visible radiation from stellar emission spectra by the negatively charged hydrogen ions H$^{-}$ is considered. We derive the explicit formulas for the bound-free absorption coefficient $a_{\nu}$ for the negatively charged hydrogen ion ${}^{\infty}$H$^{-}$ and its isotopes ${}^{1}$H$^{-}$ (protium) and ${}^{2}$H$^{-}$ (deuterium or D$^{-}$). The bound-free absorption coefficient $a_{\nu}$ is used to evaluate the actual absorption of infrared and visible radiation by the H$^{-}$ ion in photospheres of many cold stars with surface temperatures $T_s \le$ 8,250 $K$.