Nuclear condensation and symmetry energy of dilute nuclear matter: an S-matrix approach

Based on the general analysis of the grand canonical partition function in the S-matrix framework, the calculated results on symmetry energy, free energy and entropy of dilute warm nuclear matter are presented. At a given temperature and density, the symmetry energy or symmetry free energy of the clusterized nuclear matter in the S-matrix formulation deviates, particularly at low temperature and relatively higher density, in a subtle way, from the linear dependence on the square of the isospin asymmetry parameter $X=(\rho_n-\rho_p)/(\rho_n+\rho_p)$, contrary to those obtained for homogeneous nucleonic matter. The symmetry coefficients, in the conventional definition, can then be even negative. The symmetry entropy similarly shows a very different behavior.