Slow projectiles nonlinear theory

In practice, one uses the Kohn-Sham scheme that consists in solving self-consistently the following one-electron equations [16]  

The electronic density n(r) is obtained from the sum over occupied states  

This sum includes a contribution originating from the occupied bound states and another one coming from the integration over the continuum up to 

One can also extract from this calculation the scattering phase shifts S/ for the conduction band. In this respect, a number of physical quantities can be expressed in terms of the phase shifts at the Fermi level which obey, 

At low velocities the stopping power can be written in terms of the transport cross-section at the Fermi level [34]  

---