Perturbation theory of nuclear matter with a microscopic effective interaction

An updated and improved version of the effective interaction based on the Argonne-Urbana nuclear Hamiltonian, derived using the formalism of correlated basis functions and the cluster expansion technique, is employed to obtain a number of properties of cold nuclear matter at arbitrary neutron excess within the formalism of many-body perturbation theory. The numerical results, including the ground-state energy per nucleon, the symmetry energy, the pressure, the compressibility, and the single-particle spectrum, are discussed in the context of the available empirical information, obtained from measured nuclear properties and heavy-ion collisions.

Figure 1

Radial dependence of the spherically symmetric component of the bare AV6P potential (dashed line) and the CBF effective interaction (solid line) in the spin-isospin channel corresponding to $S=1$ and $T=0$. The effective interaction has been computed setting $\rho ={\rho }_0$.

Figure 2

Density dependence of the energy per nucleon of (a) PNM and (b) SNM. The dashed lines show the results obtained using Eqs. (14, 15, 16, 17) and the CBF effective interaction. The variational FHNC/SOC results are represented by the shaded regions, illustrating the uncertainty associated with the treatment of the kinetic energy [3], while the open circles of (a) correspond to the PNM results obtained using the AFDMC technique.

Figure 3

Energy per nucleon of nuclear matter, computed as a function of baryon density and proton fraction using Eqs. (14, 15, 16, 17) and the CBF effective interaction.

Figure 4

Density dependence of the symmetry energy of nuclear matter. The regions labeled ASY-EOS, Sn+Sn and IAS represent the results reported in Refs. [40], [41], and [42], respectively, while the symbols correspond to the analyses of Refs. [39] (cross with error bar), [43] (diamond), and [44] (square). The results of the present work are displayed by the dashed line.

Figure 5

Ground-state energy per nucleon of nuclear matter at baryon density $\rho ={\rho }_0$ and proton fraction $0\le x_p\le 0.5$. The diamonds represent the results obtained using Eqs. (14, 15, 16, 17) and the CBF effective interaction, while the solid line corresponds to the quadratic approximation of Eq. (18).

Figure 6

The dashed line illustrates the density dependence of the pressure of SNM obtained from the approach described in this paper. The shaded area corresponds to the region consistent with the experimental flow data reported in Ref. [45].

Figure 7

Momentum dependence of the single-nucleon energies, evaluated at $\rho ={\rho }_0$ within the Hartee-Fock approximation of Eq. (27). The solid and dashed lines correspond to PNM and SNM, respectively, whereas the dot-dashed and dotted lines represent the proton and neutron spectra in matter with proton fraction $x_p=0.1$. For comparison, the diamonds illustrate the results of a calculation of the single-particle spectrum of SNM at equilibrium density, carried out within the FHNC/SOC approach [51].

Figure 8

Density dependence of the ratio $m^{★}\left(k_F\right)/m$ for neutrons, computed using the Hartree-Fock spectra of Eq. (27). The solid and dashed lines correspond to PNM and SNM, respectively, while the dot-dashed and dotted lines represent the results obtained setting $x_p=0.1$ and 0.3, respectively.

Figure 9

Density dependence of the proton (p) and neutron (n) effective mass at the Fermi surface, computed setting the proton fraction to $x_p=0.1$.

Figure 10

Neutron energy at $k=k_F$ in (a) PNM and (b) SNM. The solid lines have been obtained by differentiating the ground-state energy per nucleon according to Eq. (24). Dashed lines and diamonds correspond to the results of calculations performed within the Hartree-Fock approximation of Eq. (27) and including the rerrangement term according to Eq. (29), respectively.