The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle B_A in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter. The results, obtained in the framework of the Brueckner-Hartree-Fock approximation with two- and three-body forces, confirm the well-known parabolic dependence on the asymmetry parameter β = (N ? Z)/A (β² law) that is valid in a wide density range. To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction, aside from the mean field approximation, the spin-isospin decomposition of B_A is performed. Theoretical indications suggest that the β² law could be violated at higher densities as a consequence of the three-body forces. This raises the problem that the symmetry energy, calculated according to the β² law as a difference between B_A in pure neutron matter and symmetric nuclear matter, cannot be applied to neutron stars. One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z = N nuclei and pure neutron matter.