Polarization effect in stopping of swift partially screened heavy ions: Perturbative theory

We report a calculation of the polarization correction - also called Barkas or Z₁ ³ effect - to the electronic energy loss of screened heavy ions above the Bohr velocity. For distant collisions we extend the classical calculation of Ashley et al. to a screened projectile, while for close collisions we make use of an argument by Lindhard. The variation of energy loss with impact parameter is illustrated for Li on C for different charge fractions and projectile velocities v. Stopping numbers are shown at fixed charge fraction as a function of velocity, and for a velocity-dependent equilibrium charge. The polarization correction is found to be sizable over most of the velocity range covered by Bohr theory (the classical regime), but for the three ions for which results are reported, Li, C and Ar, very similar curves are found when stopping numbers are plotted against the Bohr parameter mv³/Z₁e²ω, where ω is a characteristic resonance frequency of the target. The polarization correction is similar in magnitude to the leading term over a wide velocity range below mv³/Z₁e²ω≈3. Therefore the perturbative approach presented here, which includes only one order beyond the leading term, cannot be expected to deliver very accurate results. This work will therefore be followed up by a nonperturbative evaluation of the stopping cross-section.