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

We present a high-energy calculation of the $K$ -shell ejection cross section $\sigma \left(Z_p\right)$ as a function of projectile charge $Z_p$. Charge-transfer effects are not included. The wave function for the heavy projectile is written as $e^{i{\overrightarrow{\mathrm{k}}}_0•\overrightarrow{\mathrm{R}}}\mathrm{F}(-in,1,i{k}_e|\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{r}}|-i{\overrightarrow{\mathrm{k}}}_{\mathrm{e}}•(\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{r}}\left)\right)\Gamma \mathrm{}(1+in)\mathrm{}{e}^{\frac{-n\pi }{2}}$, as opposed to the Glauber approximation $e^{i{\overrightarrow{\mathrm{k}}}_0•\overrightarrow{\mathrm{R}}}\exp (-in\int {-\infty }^Z\mathrm{dZ}{|\overrightarrow{\mathrm{R}}-\overrightarrow{\mathrm{r}}|}^{-1\mathrm{}})$. 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 $r_{12}=\frac{\sigma \left(Z_1\right)Z_2^2}{\sigma \left(Z_2\right)Z_1^2}$, $Z_1>Z_2$. Higher-energy experiments are needed to confirm this theoretical result.