Approximate analytical solution for nuclear matter in a mean-field Walecka model and Coester line behavior

We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.