Comparison of the random-phase approximation with the multichannel frozen-core Hartree-Fock approximation for the photoionization of ${\mathrm{N}}_2$

The photoionization of ${\mathrm{N}}_2$ leading to the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, ${\mathit{A}}^2$${\mathrm{\Pi }}_{\mathit{u}}$, and ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{N}}_2^{+}$ has been studied using the random-phase approximation (RPA) and the multichannel frozen-core Hartree-Fock (MCFCHF) approximation. The RPA has been implemented as a coupled-channel method with a set of open and closed channels corresponding to excitation operators and with a set of closed channels corresponding to deexcitation operators. Thus in the case of the photoionization of ${\mathrm{N}}_2$ there are 14 coupled channels. Both the RPA and MCFCHF were solved using the Schwinger variational method with Padé-approximant corrections. Good agreement was found between the RPA results and the MCFCHF results when the dipole-mixed form of the cross section was used. In comparison with experiment, both of these methods show qualitative improvements over previous computational results. These calculations give the correct behavior of the cross section in the 1${\mathrm{\pi }}_{\mathit{u}}$→k${\mathrm{\pi }}_{\mathit{g}}$ channel without ad hoc corrections needed in earlier calculations. Also both of these methods exhibit autoionizing resonances lacking in earlier results. However, there are still a number of discrepancies between theory and experiment, including the position and shape of the autoionization resonances, and the behavior of the photoelectron asymmetry parameters in the (2${\mathrm{\sigma }}_{\mathit{u}}$${)}^{\mathrm{-}1}$ ionization channel, which is strongly perturbed by the shape resonance in the (3${\mathrm{\sigma }}_{\mathit{g}}$${)}^{\mathrm{-}1}$ ionization channel.