Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory

Abstract

The isospin-asymmetry dependence of the nuclear matter equation of state obtained from microscopic chiral two-and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospinasymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.

Partial restoration of chiral symmetry in hot and dense neutron matter

“…2 the neutron matter thermodynamic equation of state (the free energy per particle as a function of temperature and density) obtained from the n3lo414 chiral two-and three-body potentials. The results are in good agreement with previous studies, 37,38 which employed the same two-and three-body potentials but included also self-consistent Hartree-Fock single-particle energies in the second-order diagrams. As we will show later, second-order perturbative contributions to the neutron matter equation of state and the chiral condensate are relatively small.…”

“…We start from a coarse-resolution chiral potential 34,35 with a momentum-space cutoff of Λ = 414 MeV, which has been shown to exhibit good convergence properties [34][35][36][37][38] in many-body perturbation theory calculations of infinite nuclear matter, comparable to low-momentum potentials constructed via renormalization group methods. 16,[39][40][41] In the present calculation the free energy per particle of pure neutron matter at finite temperature is computed in the imaginary-time Matsubara formalism.…”

Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

“…[30] together with the binding energies of doubly closed shell nuclei. We define the χ 2 minimization function:…”

Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy

“…Indeed, the quartic contribution to the kinetic symmetry energy contributes 5T/243=0.021T, about 2/3 of the missing amount. Most theoretical calculations of the potential contribution to the symmetry energy also find only small corrections beyond the quadratic term (Carbone et al 2014;Wellenhofer et al 2016). Recent calculations of neutron-rich matter (Drischler et al 2016b) have shown that up to densities approaching u∼1.5 the quadratic assumption is accurate to better than 1 MeV in the symmetry energy per particle for all values of x.…”

“…Studies suggest that these terms are small (Carbone et al 2014;Wellenhofer et al 2016). If the energy is divided into kinetic and potential contributions, then the kinetic energy of degenerate noninteracting fermions can be expanded as E u x m n u x x , 3 5 2 3 1 3 kin 2 2 0 2 3 5 3 5 3 …”