Symmetry energy determination in heavy ion collisions

BEL~M(A,Z) = a,A asA2’3aJ2/A”3 + a,A“‘* asym (N-Z)2/A (1) where N, Z and A are the neutron, proton and mass numbers; a,, a, and a, are the volume, surface and Coulomb terms in the liquid drop model. aPA-“* is the pairing energy. The last term in Eq. (l), asym (N-Z)‘/A, accounts for the symmetry energy which favors nuclei with equal number of protons and neutrons. In most parametrizations, asym is a constant set to about 24 MeV. In this formulation, the symmetry energy is independent of the nucleon density. It has been pointed out by the study of Myers-Swiatechi [2] that the agreement of the calculated masses with experimental masses can be improved if the LDM formula includes corrections to the surface term due to asymmetry. The parametrization of the improved LDM formula is given in ref. [3]: fd$,mA,t (A,Z) = a,[l-k((A-2Z)/A)2]A a,[l-k((A-2Z)/A)2]A2’3 a, Z2/A”3 + aPA-“* + (2) where the extra Coulomb term CdZ2/A, neglected in most models, takes into account corrections to the Coulomb energy associated with the diffuseness of the nuclear surface. The symmetry terms in Eq. (2) can be regrouped in a form similar to Eq.(l)