Energy loss of heavy ions at high velocity

Abstract

The slowing down of heavy ions by electronic stopping at high velocity is discussed. The ions are nearly fully stripped and have a well defined charge with relatively small fluctuations. Owing to the large charge of the ions, the classical Bohr formula applies instead of the Bethe formula, which is based on a quantum perturbation calculation. It is essential to include the Barkas effect in the description since it becomes quite large for heavy ions, especially in high-Z materials. In Lindhard's treatment [Nucl. Instr. and Meth. 132 (1976) l], the Barkas correction is viewed as an effect of dynamic screening of the ion potential in the initial phase of a collision with an electron, which reduces the relative velocity and therefore enhances the cross section. With inclusion of this enhancement factor for all impact parameters, as evaluated by Jackson and McCarthy for distant collisions [Phys. Rev. B 6 (1972) 4131], the description reproduces within a few percent measurements for 15 MeV/u Br on Si, Ni, and Au and for 10 MeV/u Kr on Al, Ni, and Au. The procedure is shown also to apply at lower velocities near the stopping maximum, albeit with less accuracy. The straggling in energy loss has been analyzed for a measurement on Si and it is well described by a combination of about equal contributions from fluctuations in the number of violent collisions with single electrons (Bohr straggling) and from fluctuations in ion charge state.