Energy dependence of the real part of ion-ion interaction potential

A simple derivation for the energy dependence of the real part of ion-ion interaction potential is given in the framework of Brueckner's energy density formalism. This is based on the decreasing effect of antisymmetrization on the kinetic energy densities of the two ions which is studied in a Fermi gas model and tends to make the ion-ion potential more and more attractive with increasing relative energy $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$. On the other hand, the linear dependences of the kinetic energy densities and the momentum densities on $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$, through the effective mass term in the energy density, introduce a repulsion which increases directly as the relative energy. At low values of $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$ the first effect dominates over the second one, thereby making the ion-ion potential more and more attractive. However, at relatively high energies, the repulsion caused by the second effect dominates completely and makes the potential less and less attractive.