Photodetachment cross-section of the negatively charged hydrogen ion

Photodetachment cross-section ${\sigma }_{ph}(p_e)$ of the negatively charged hydrogen ion H${}^{-}$ is determined with the use of highly accurate variational wave functions constructed for this ion. Photodetachment cross-sections of the H${}^{-}$ ion are also studied for very small and very large values of the photo-electron momentum $p_e$. Maximum of this cross-section and its location have been evaluated to high accuracy. In particular, we have found that $[{\sigma }_{ph}(p_e){]}_{\max }\approx$ 3.8627035742 $\cdot {10}^{-17}$ $c{m}^2$ at $p_e\approx$ 0.113206(1) $a\mathrm{.}u\mathrm{.}$ Our method is based upon the Rayleigh’s formula for spherical Bessel functions.