The density matrix expansion method, together with three different effective nucleon-nucleon forces, is used to calculate the real part of the interaction potential between two 16O nuclei. The densities of the system are constructed using two different methods. In the first, a two-centre harmonic-oscillator potential is employed to construct the density and the kinetic energy density of the combined system and of the separated nuclei. In the second method, the density of the combined system is assumed to be the sum of the two separate densities and the kinetic energy densities are given approximately by the Thomas-Fermi approximation. The authors have found that the ion-ion potential derived using the second method shows a stronger energy dependence than that derived from the first. A comparison between the ion-ion potentials in the relevant tail region also showed that the second method includes, at zero energy, 30-60% of the exchange effects due to antisymmetrisation for the Negele force. At the same energy and for the Skyrme force the second method can be considered to be a very good approximation to the first.

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