Molecular-orbital theory forK-vacancy sharing in atomic collisions

We have calculated the projectile and target $K$-excitation cross sections and their ratio for a series of ion-target combinations using a basis of exact molecular eigenstates for a model system of one electron in the field of two effective nuclear charges. Except for very asymmetric high-velocity collisions, close agreement is found with Meyerhof's formula, which is based on an atomic two-state expansion. In this range, Meyerhof's formula may be considered an analytical fit to our ab initio results. We indicate that the apparent accuracy of Meyerhof's formula is due to mutual cancellation of effects arising from approximations and model assumptions used in his deduction of the cross-section ratio. The significant deviation found at high velocities results from interference between the coupling processes that govern $K$-vacancy production. This possibility was ruled out in Meyerhof's theory.