Elastic scattering of hydrogen atoms at low temperatures

Abstract

The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of ${\mathrm{H}}_{2}$. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41${\mathit{a}}_{0}$ for the singlet case and 1.91${\mathit{a}}_{0}$ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$, with a different fit to the triplet potential between 12${\mathit{a}}_{0}$ and 15${\mathit{a}}_{0}$. A more accurate triplet-state potential is needed at these separations.