Asymptotic Expression for the Stopping Power ofK-Electrons

An asymptotic form for the high energy stopping number of $K$-electrons (for any element) is determined by using the Born approximation expressions for the excitation and ionization probabilities of the $K$ shell. The stopping number takes the form $B_K(\theta ,\eta )=A\left(\theta \right)\ln \eta +B\left(\theta \right)+C\left(\theta \right)\left(\frac{1}{\eta }\right)+\cdots$, where $\eta$ is a dimensionless quantity proportional to the energy of the incident particle and $\theta$ is proportional to the observed ionization energy of the $K$ shell. Other results include the stopping number for hydrogen, obtained by sum-rule methods, to order ($\frac{1}{\eta }$), and results of M. C. Walske, obtained by numerical methods, for the low energy stopping number of $K$-electrons.