High-energy calculation of K -shell ejection cross sections as a function of projectile charge

We present a high-energy calculation of the K -shell ejection cross section σ(Zₚ) as a function of projectile charge Zₚ. Charge-transfer effects are not included. The wave function for the heavy projectile is written as ${e}^{i{{{→}}{k}}₀•{}{{→}}{R}}F({-}in,1,i{k}ₑ|{{→}}{R}{-}{{→}}{r}|{-}i{{{→}}{k}}ₑ•{}({{→}}{R}{-}{{→}}{r})){Γ}(1+in){e}^{{{-}n{π}}{2}}$, as opposed to the Glauber approximation ${e}^{i{{{→}}{k}}₀•{}{{→}}{R}}exp({-}in{∫}{{-}{∞}}ZdZ{|{{→}}{R}{-}{{→}}{r}|}^{{-}1})$. These two approximations agree at large distances but differ as the electron and projectile approach closely to each other. A prediction is made that if ${T}ₘ$ (the maximum classical energy an electron at rest may receive) is much greater than ${I}K$ then ${r}₁₂$ will be less than unity. Here ${r}₁₂={{σ}({Z}₁){Z}₂²}{{σ}({Z}₂){Z}₁²}$, ${Z}₁>{Z}₂$. Higher-energy experiments are needed to confirm this theoretical result.