Density matrix approach to the complex heavy ion optical potential: Exchange part

We further analyse the validity of the density matrix expansion applied to the complex heavy ion optical potential by separately treating the direct and exchange contributions. We show that the discrepancies found previously when comparing the density matrix expansion optical potential with the exact one are mainly to be ascribed to the direct contributions. For the exchange part the density matrix expansion is nearly exact in the tail region and remains very good down to zero separation distance. The Campi-Bouyssy prescription for accelerationg the density matrix expansion convergence is also examined.