A Time Dependent Local Isospin Density Approximation Study of Asymmetric Nuclear Matter

The dynamic response of asymmetric nuclear matter is studied by using a Time-Dependent Local Isospin Density (TDLIDA) approximation approach. Calculations are based on a local density energy functional derived by an Auxiliary Field Diffusion Monte Carlo (AFDMC) calculation of bulk nuclear matter. Three types of excited states emerge: collective states, a continuum of quasi-particle-quasi-hole excitations and unstable solutions. These states are analyzed and discussed for different values of the nuclear density $\rho$ and isospin asymmetry $\xi=(N-Z)/A$. An analytical expression of the compressibility as a function of $\rho$ and $\xi$ is derived which show explicitly an instability of the neutron matter around $\rho\simeq 0.09 fm^{-3}$ when a small fraction of protons is added to the system.