Eikonal approximation in the theory of energy loss by fast charged particles

Energy losses in fast charged particles as a result of collisions with atoms are considered in the eikonal approximation. It is shown that the nonperturbative contribution to effective stopping in the range of intermediate impact parameters (comparable with the characteristic sizes of the electron shells of the target atoms) may turn out to be significant as compared to shell corrections to the Bethe-Bloch formula calculated in perturbation theory. The simplifying assumptions are formulated under which the Bethe-Bloch formula can be derived in the eikonal approximation. It is shown that the allowance for nonperturbative effects may lead to considerable (up to 50%) corrections to the Bethe-Bloch formula. The applicability range for the Bethe-Bloch formula is analyzed. It is concluded that calculation of the energy loss in the eikonal approximation (in the range of impact parameters for which the Bethe-Bloch formula is normally used) is much more advantageous than analysis based on the Bethe-Bloch formula and its modifications because not only the Bloch correction is included in the former calculations, the range of intermediate impact parameters is also taken into account nonperturbatively; in addition, direct generalization to the cases of collisions of complex projectiles and targets is possible in this case.