Role of outer shells in Born cross sections forK-shell ionization by charged particles

Many standard applications of the Born approximation to $K$-shell vacancy production apply first-order perturbation theory to the interaction between a projectile and an atomic target represented by a product wave function. It is shown that these standard Born predictions need not be restricted to one-electron ionization, but should be compared to experimental observations summed over all states corresponding to single-$K$-vacancy production to include multiple-vacancy production in other shells. These results are applicable to all targets in which the $K$ shell is weakly perturbed even though the other shells may be strongly perturbed.