Bethe theory of stopping incorporating electronic excitations of partially stripped projectiles

The Bethe theory for the energy loss of swift charged particles colliding with atomic targets is extended to treat explicitly the case when the projectile has bound electrons. The theory is characterized by taking into account the excitation and ionizations (but not charge exchange) of both projectile and target. As a consequence of the Coulombic character of the interaction between projectile and target, the electronic stopping cross section S_e is split into contributions arising from the electronic structure of the projectile and of the target. In the lower part of the velocity region where this theory is applicable, the electronic structure of the projectile makes an important contribution, of the order 10–20%, to S_e. At high projectile velocities, however, this contribution decreases, leaving only the standard Bethe term. The number of electrons bound to the projectile, N₁, as a function of the velocity of the projectile is calculated using the adiabatic Bohr criterion in conjunction with the Thomas-Fermi model of the atom. We obtain an analytic expression for the total stopping cross section using the Bethe approximation, and we compare the results of calculations of He, Li, and B ions on C and Al targets with experiment.