Elastic scattering of hydrogen atoms at low temperatures

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 ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ 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×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ but it could be lower, at 4.8×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$, 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.