Saturation properties of isospin asymmetric nuclear matter

The saturation properties of the isospin asymmetric nuclear matter, ANM, are studied microscopically using the density dependent M3Y-Paris and M3Y-Reid effective interactions in their CDM3Y-K versions. To do so, two-dimensional expansion of the energy per nucleon of ANM with respect to its density, ρ, and isospin asymmetry, I≡(ρn−ρp)/ρ, has been used within a suitable density range. Within this framework, the ANM saturation density, energy per nucleon and incompressibility as functions of the isospin asymmetry, I, up to its eighth order are derived in simple analytical formulas. These formulas link explicitly the ANM saturation properties to the CDM3Y-K density dependence forms through 24 characteristic quantities and coefficients which represent the different order partial derivatives of the energy with respect to ρ and I. The results show that the different terms up to I8, but with only 18 characteristic coefficients, are needed to describe reasonably the different ANM saturation properties. Up to four times the saturation density of nuclear matter, some properties such as the energy per nucleon of ANM and pure neutron matter are well expressed by their expansion up to only the quadratic term in I. Based on both Paris and Reid effective interactions and within the symmetric nuclear matter saturation incompressibility range of K0=220–250 MeV, the different coefficients of the ANM incompressibility are obtained with the values of K02=−348±57 MeV, K04=35±31 MeV and K06=4±13 MeV.