The LOCV averaged two-nucleon interactions versus the density-dependent M3Y potential for the heavy-ion collisions

In order to have an effective two-nucleon potential based on the microscopic many-body calculations with a bare phenomenological nucleon–nucleon potential for the heavy-ion scattering calculations, the lowest order constrained variational (LOCV) method for the symmetric nuclear matter is applied to obtain the direct and the exchange parts of the averaged effective two-body interactions (AEI). The Reid68, the Reid  68-Δ, and the Av18Av18 interactions are used as the input phenomenological potentials. Then, it is tried to decompose the AEI into a radial and a density-dependent parts, such that the fitted LOCV AEI potentials give the same equation of state for the nuclear matter as the exact LOCV calculations. The results are compared with the various density-dependent M3Y potentials. It is shown that the direct and the exchange parts of the LOCV AEI   with different input potentials are reasonably in agreement with each other and besides the different behaviors of their direct terms at small relative distances (<0.6 fm), they also roughly have the same magnitude as the direct parts of those of M3YM3Y potentials. However, in contrast to the M3Y interaction, the exchange parts of the LOCV AEI have completely different behavior, i.e. their density dependence rises with increasing density. Finally, it is concluded that, since the direct and exchange parts of the LOCV AEI are constructed based on the many-body calculations with the phenomenological nucleon–nucleon potential, they are specially more trustable for the nucleus–nucleus collision calculations, in which the double-folding model is applied.