Extension of the Brandt-Kitagawa model for Hartree-Fock electronic densities

An extension of the Brandt-Kitagawa model for the effective charge calculation is presented in the case of ions with atomic numbers from Z1 = 3 to 10. The Hartree-Fock method is used to provide electronic densities for projectiles with various charge states. The projectile screening lengths obtained using the Hartree-Fock method are larger than those calculated using the variational method as proposed in the Brandt-Kitagawa model. Differences between the effective charge calculated by the original method and the one presented here can be as high as 50% especially in the case of low charge states. With this alternative procedure, it is possible to input projectile shell effects in the stopping power such as Z1-oscillations. The differences between the present method and the original one are attributed to a poor description of the heavy ion screening length by the variational method assumed in the Brandt-Kitagawa model.