Density matrix approach to the complex heavy ion potential

We extend the applicability of the density matrix expansion to a complex effective interaction depending both on the density and the kinetic energy density. A detailed study of the kinetic energy density dependence of the density matrix expansion coefficients is given. The corresponding energy density has a parametrized form which is tested in the calculations of the optical potential of the 16O + 16O system at several energies. Exact results are well reproduced by the complex density matrix expansion.