Z3correction to the stopping power of ions in an electron gas

The $Z^3$ correction to the stopping power of an ion moving through a homogeneous electron gas is derived using a response-function formalism. An expression for the quadratic density response function which enters the stopping-power formula is obtained in the random-phase approximation and is evaluated in a limit appropriate to low ion velocities $\nu$. The equivalence of the responsefunction formalism and a scattering-theory approach is demonstrated in this limit and numerical results of the two approaches are compared as a function of the ion charge $Z$. The quadratic response theory is shown to be a reasonable approximation for high densities and low $Z$.