Low densities in asymmetric nuclear matter

Asymmetric nuclear matter is investigated in the low-density region below the nuclear saturation density. Microscopic calculations based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach with realistic nucleon-nucleon potentials are used to adjust a low-density functional. This functional is constructed on a density expansion of the relativistic mean-field theory that allows a clear interpretation of the role of the mesons in the equation of state. It is shown that a correction term should be added to the functional to take into account the effects beyond the mean field. Two functionals with different corrections are obtained and their topological properties have been studied. Those functionals converge to predict a reduction of the spinodal zone in asymmetric nuclear matter by about 15–20% and an isoscalar unstable mode closer to the constant $Z/A$ direction than the functional without correction.

Figure 1

Comparison of several equations of state with the DBHF results. The DBHF calculations are represented by the stars, the variational calculations by the empty squares, the nonrelativistic Brueckner results by the dashed line, and two different relativistic mean-field parametrizations NL3 and DD-TW by dashed-dotted and dotted lines, respectively.

Figure 2

Representation of the different terms in the series expansion of the energy functional with respect to the baryonic density, up to 0.3 fm${}^{-3}$. The first three subsets show the fast convergence in symmetric nuclear matter (SNM) and the last subset (d) shows the contribution of the isovector mesons in pure neutron matter (PNM). To give an idea of the fast convergence, we have multiplied some of the terms by huge constants. The coupling constants (set A NL$\rho \delta$) obtained by Liu et al. [42] have been used.

Figure 3

Comparison between the best RMF adjustment and the scalar mass calculated with the DBHF approach. The asymmetry parameter $y={\rho }_p/{\rho }_B$ ranges from 0.5 to 0. It clearly shows a linear ($f_{\sigma }^2{\rho }_B$) and a quadratic ($f_{\sigma }^{\mathrm{nl}}{\rho }_B^2$) behavior in the baryonic density. The isospin asymmetry is also well reproduced by the linear term $f_{\delta }^2{\rho }_3$ in the asymmetry density ${\rho }_3$.

Figure 4

Comparison of the DBHF results (circle points) and the low-density functionals in asymmetric nuclear matter. On the top panels are shown the energy density and the binding energy for the parameters RMF; on the bottom panels are shown the binding energies for the corrected functionals RMF+C1 and RMF+C2.

Figure 5

Difference between the DBHF calculation and the low-density RMF fit (square symbols). The corrections (solid lines) are drawn for symmetric nuclear matter (left panel) and pure neutron matter (right panel).

Figure 6

Spinodal contour for the low-density RMF functional, RMF, RMF+C1, and RMF+C2.

Figure 7

Evolution of the unstable mode $\delta {\rho }_n/\delta {\rho }_p$ with the density for asymmetries ranging from $y=0.1$ to 0.5.