Tight-Binding Corrections of Stopping Powers

Theoretical tight-binding corrections for the stopping-power deficiency of inner-shell electrons at low particle velocities are compared with the experimental data measured by Burkig and MacKenzie for 20-Mev protons and by Bakker and Segrè for 300-Mev protons, with the following results. Walske's accurate tight-binding corrections for $K$ and $L$ shells are in complete agreement with experiment under conditions where only $K$ and $L$ shells are stopping-power deficient. If a larger fraction of the electron cloud of heavy atoms is deficient, extrapolations of Walske's corrections beyond their intended validity range underestimate the stopping-power deficiency. The stopping-power deficiency of heavy elements is well described by a cutoff approximation by Lindhard and Scharff of the tight-binding corrections of the statistical atom. "Best" tight-binding corrections are recommended and areas for further theoretical work indicated. After correction for valence and tight-binding effects, the mean excitation potentials $I_0$ from both sets of experimental data are in mutual agreement. The decrease of $\frac{I_0}{Z}$ with increasing $Z$ confirms the $Z^{-\frac{2}{3}}$ dependence of the exchange effects in the statistical atom.