Calculation of He photoionization with excitation and de-excitation cross section

We present calculation results for photo-ionization with de- excitation of excited He and helium-like ions at high but non- relativistic photon energies $\omega$. The cross-section of this process is expressed in fact via integrals similar to that used already in description of two-electron ionization and ionization with excitation. In principle, the considered process can be separated pure experimentally from other two- electron processes, namely double ionization and ionization with excitation, if the photoelectrons's energy for a given incoming photon frequency $\omega$ is detected. Very accurate non-variation wave functions are used. As excited several lower $^{1}S$ and $^{3}S$ states are considered. We present the ratios $R^{+*}_{d}$ of the cross sections ``photo-ionization with de-excitation'' $\sigma ^{+*}_{(d)}(\omega )$ and ``photo- ionization with excitation'' $\sigma ^{+*}(\omega )$. It is shown how $R^{+*}_{d}$ depends upon the excitation of the target object and the charge of its nucleus.