Cold dilute nuclear matter with α-particle condensation in a generalized nonlinear relativistic mean-field model

We explore the thermodynamic properties of homogeneous cold (zero-temperature) nuclear matter including nucleons and alpha-particle condensation at low densities by using a generalized nonlinear relativistic mean-field (gNL-RMF) model. In the gNL-RMF model, the alpha particle is included as an explicit degree of freedom and treated as a pointlike particle with its interaction described by meson exchanges, and the in-medium effects on the alpha binding energy are described by density- and temperature-dependent energy shift with the parameters obtained by fitting the experimental Mott density. We find that below the dropping density n(drop) (approximate to 3 x 10(-3) fm(-3)), the zero-temperature symmetric nuclear matter is in the state of pure Bose-Einstein condensate (BEC) of alpha particles while the neutron-rich nuclear matter is composed of alpha-BEC and neutrons. Above the n(drop), the fraction of alpha-BEC decreases with density and vanishes at the transition density n(t) (approximate to 8 x 10(-3) fm(-3)). Above the n(t), the nuclear matter becomes pure nucleonic matter. Our results indicate that the empirical parabolic law for the isospin asymmetry dependence of the nuclear matter equation of state is heavily violated by the alpha-particle condensation in the zero-temperature dilute nuclear matter, making the conventional definition of the symmetry energy meaningless. We investigate the symmetry energy defined under parabolic approximation for the zero-temperature dilute nuclear matter with alpha-particle condensation and find it is significantly enhanced compared to the case without clusters and becomes saturated at about 7 MeV at very low densities (less than or similar to 10(-3) fm(-3)). The critical temperature for alpha condensation in homogeneous dilute nuclear matter is also discussed.