Proton-stopping power of argon, krypton, and xenon

Parameters for the Bethe stopping-power theory for Ar, Kr, and Xe are obtained both via integration over optical oscillator strengths and from explicit plane-wave Born-approximation calculations. The former procedure produces a Bethe mean excitation energy ($I$) significantly lower than that measured, while the latter procedure produces $I$ values within 10 eV of the measured values for Ar and Kr. For Xe the experimental $I$ value lies midway between the two calculated $I$ values. Inner-shell corrections are obtained from the explicit calculations. The $K$-shell corrections ($C_K$) are a factor of 2 larger than those obtained from hydrogenic calculations. The total inner-shell correction ($\Sigma {\mathrm{nl}}^{}{C}_{\mathrm{nl}}$) is in qualitative agreement for Ar, Kr, and Xe with results from a statistical model. However, the quantitative difference between the two sets of inner-shell corrections leads to significant increases in $I$ values inferred from experimental measurements below 1 MeV proton energy.