New method for highly accurate calculations of the photodetachment cross-sections of the negatively charged hydrogen ions

New approach to highly accurate calculations of the photodetachment cross-sections of the negatively charged hydrogen ions is developed. This effective, fast and numerically stable method is based on the use of the Rayleigh's formula for the spherical Bessel functions. Photodetachment cross-sections of the negatively charged hydrogen ion(s) ${}^{\infty}$H$^{-}$, ${}^{1}$H$^{-}$ (protium), ${}^{2}$H$^{-}$ (deuterium D$^{-}$) and ${}^{3}$H$^{-}$ (tritium T$^{-}$) are determined with the use of highly accurate, truly correlated, variational wave functions constructed for these ions. Our method allows one to investigate the problem of photodetachment of the negatively charged hydrogen ions completely, i.e. without any limitation by numerical values of the photo-electron momentum $p_e$.