Photoionization of sodium atoms and electron scattering from ionized sodium

The polarized-orbital method [originally developed by A. Temkin, Phys. Rev. 107, 1004 (1957)] is used to calculate the photoionization cross sections of sodium atoms, from threshold to about 60 eV. The polarized orbitals are calculated from Sternheimer’s equation. The polarizability of ${\mathrm{Na}}^{+}$ is found to be 1.0914$a_0^3$, which is very close to the experimental value. The scattering equation is solved in the exchange, the exchange-adiabatic, and the polarized-orbital approximations. For consistency, both the bound-state and the continuum-state wave functions are obtained in the same approximation. In the calculation of these wave functions, all perturbed orbitals are taken into account in the direct polarization potential and only the perturbation of the very tightly bound 1s orbital is neglected in the exchange-polarization terms. The length form for the photoionization-cross-section formula is used and all terms are included in the photoionization matrix element. Our results are in good agreement with the many-body calculations of Chang and Kelly. However, no calculation to date, including this one, agrees well with experiment except at low energies. The phase shifts thus obtained for s, p, and d waves for the e+${\mathrm{Na}}^{+}$ system are used to calculate the differential cross sections; the phase shifts, as well as these cross sections, agree very well with other available results.