Two-photon excitation cross section in light and intermediate atoms in frozen-coreLS-coupling approximation

Using the method of explicit summation over the intermediate states two-photon absorption cross sections in light and intermediate atoms based on the simplistic frozen-core approximation and $\mathrm{LS}$ coupling have been formulated. Formulas for the cross section in terms of integrals over radial wave functions are given. Two selection rules, one exact and one approximate, valid within the stated approximations are derived. The formulas are applied to two-photon absorptions in nitrogen, oxygen, and chlorine. In evaluating the radial integrals, for low-lying levels, the Hartree-Fock wave functions, and for high-lying levels, hydrogenic wave functions obtained by the quantum-defect method have been used. A relationship between the cross section and the oscillator strengths is derived.