The effective range in the singlet electron-hydrogen system has been evaluated as 2.646±0.004 atomic units by using the asymptotic amplitude of the 202-parameter ${\mathrm{H}}^{-}$ wave function of Pekeris. This value of the effective range, together with the value of the electron affinity of ${\mathrm{H}}^{-}$, determines the scattering length in the singlet system as 6.167 atomic units. The effective range in the triplet system is calculated to be 1.219 atomic units by a Hartree-Fock approximation. It is shown that the effective-range approximation is very good for all energies at which only elastic scattering is allowed. The photo-ionization of ${\mathrm{H}}^{-}$ is briefly discussed on the basis of the effective-range theory.

• Received 23 October 1959

DOI:https://doi.org/10.1103/PhysRev.118.154