Nuclear matter equation of state including two-, three-, and four-nucleon correlations

Light clusters (mass number $A\le 4$) in nuclear matter at subsaturation densities are described using a quantum statistical approach to calculate the quasiparticle properties and abundances of light elements. I review the formalism and approximations used and extend it with respect to the treatment of continuum correlations. Virial coefficients are derived from continuum contributions to the partial densities which depend on temperature, densities, and total momentum. The Pauli blocking is modified taking correlations in the medium into account. Both effects of continuum correlations lead to an enhancement of cluster abundances in nuclear matter at higher densities. Based on calculations for $A=2$, estimates for the contributions with $A=3,4$ are given. The properties of light clusters and continuum correlations in dense matter are of interest for nuclear structure calculations, heavy-ion collisions, and astrophysical applications such as the formation of neutron stars in core-collapse supernovae.

Figure 1

Role of continuum correlations in the $d$ channel. Extended phase shifts, containing a contribution at negative intrinsic energies $E$ describing the bound state part, are presented for baryon densities of the nuclear medium $n_B=0.0001,0.003,0.01,0.03,0.1{\mathrm{fm}}^{-3}$ and $T=4$ MeV.

Figure 2

Baryon chemical potential $\overline{\mu }$ as function of the baryon density $n_B$ for symmetric matter ($Y_p=0.5)$. Isotherms are shown for $T=1,5,10,15$, and 20 MeV. The QS result (solid line) is compared with the RMF solution which considers only the contributions with $A=1$ in Eq. (4); see also Eq. (23) (thin line) and the ideal gas NSE solution (dashed). (Inset) Comparison with the QS calculations (Pauli blocking in uncorrelated matter) given in Ref. [8] (thin lines).

Figure 3

Free energy per nucleon $F_A$ as function of the baryon density $n_B$ for symmetric matter ($Y_p=0.5)$. Isotherms are shown for $T=1,5,10,15,20$ MeV. The QS result (solid lines) is compared with former QS calculations [8] neglecting continuum correlations (dashed lines).

Figure 4

Composition of symmetric matter ($Y_p=0.5$) at (a) $T=5$ MeV, (b) $T=10$ MeV, (c) $T=15$ MeV, and (d) $T=20$ MeV. The mass fraction $X_c$ is shown as a function of the density $n_B$. The QS solution (solid lines) is compared with the ideal gas NSE solution (dashed lines).

Figure 5

Composition of symmetric matter ($Y_p=0.5$) at $T=1$ MeV. The mass fraction $X_c$ is shown as function of the density $n_B$. The QS solution (solid lines) is compared with the ideal gas NSE solution (dashed lines). The mass fractions of $d,t,h$ are very small and are not seen here.

Figure 6

Composition of symmetric matter ($Y_p=0.5$) at $T=10$ MeV. The QS solution (solid lines), same as in Fig. 4, is compared with the solution (dashed lines), where the $\mathbf{P}$ dependence of the Pauli blocking for the residual continuum contributions [Eq. (51)] is taken into account.