BETHE THEORY OF STOPPING INCORPORATING ELECTRONIC EXCITATIONS OF PARTIALLY STRIPPED PROJECTILES

The Bethe theory for the energy loss of swift charged particles collid ing with atomic targets is extended to treat explicitly the case when the projectile has bound electrons. The theory is characterized by tak ing into account the excitation and ionizations (but not charge exchan ge) of both projectile and target. As a consequence of the Coulombic c haracter of the interaction between projectile and target, the electro nic stopping cross section S-e is split into contributions arising fro m the electronic structure of the projectile and of the target. In the lower part of the velocity region where this theory is applicable, th e electronic structure of the projectile makes an important contributi on, of the order 10-20 %, to S-e. At high projectile velocities, howev er, this contribution decreases, leaving only the standard Bethe term. The number of electrons bound to the projectile, N-1, as a function o f the velocity of the projectile is calculated using the adiabatic Boh r criterion in conjunction with the Thomas-Fermi model of the atom. We obtain an analytic expression for the total stopping cross section us ing the Bethe approximation, and we compare the results of calculation s of He, Li, and B ions on C and Al targets with experiment.