Random-phase approximation with exchange for the inner-shell electron transitions

Abstract

We present our recently developed random-phase approximation with exchange (RPAE) method, which can be used to study the inner-shell electron transition in an open-shell atom. The expressions for the matrix elements of all terms of the dipole and Coulomb interactions have been derived and implemented in a computer program. The photoionization cross sections of the $4d$ giant resonances of ${\mathrm{Xe}}^{+}$, I, and ${\mathrm{I}}^{+}$ have been calculated. The results for ${\mathrm{Xe}}^{+}$ and ${\mathrm{I}}^{+}$ agree very well with the experimental data. However, the theoretical results for the I $4d$ cross section are still almost three to four times higher than the experimental data. We recommend a remeasurement of the I $4d$ giant resonance with a careful experimental arrangement.