Comparison of calculated atomic stopping-power oscillations with apparent fluctuations in measured nuclear lifetimes

Reported measurements by Broude et al. of the lifetime of the 3.34-MeV nuclear state in ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$, determined by Doppler-shift measurements on the $\gamma$ decay of the excited nucleus as it is slowed down by various absorbers, show an oscillatory structure that can be attributed to oscillations in the electronic stopping cross section ($S_e$) of the absorbers. Unlike previously observed oscillations in $S_e$, which were for channeled or forward-scattered particles, these are oscillations in the average value of $S_e$. We have considered the problem in terms of an extension of the Lindhard-Scharff-Winther (LSW) theory to low-velocity heavy ions. We find that in the LSW formalism the appropriate effective charge for the projectile is not simply related to conventional equilibrium charge distributions, for velocities corresponding to those in the nuclear lifetime measurements. Despite this, it is possible to obtain relative stopping powers, at a given velocity, which are strongly correlated with the apparent oscillations in the value of the nuclear lifetime.