DoubleK-shell electron capture for ion-atom collisions at intermediate energies

A three-state, two-center atomic expansion method is used to investigate double-electron capture from the $K$ shell of multielectron atoms to the $K$ shell of projectiles in the energy region where the projectile velocity is nearly equal to the orbital velocity of the target $K$-shell electron. By adopting an independent-electron approximation, the Coulomb interaction between the two electrons is replaced by monopole terms with a screening charge. The validity of this approximation is checked by comparing the cross sections for double capture in $p$-He and ${\mathrm{He}}^{++}$-He collisions obtained from this method with other theoretical calculations and experiments. Double-electron-capture cross sections from the $K$ shell of Ne atoms by ${\mathrm{F}}^{9+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{N}}^{7+}$ ions are then calculated; the results are shown to compare well with the neon Auger hypersatellite intensities measured by Woods et al.