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Register a new userSymmetry energy of nuclear matter and isovector three-particle interactions
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We present a study of the symmetry energy (a_s) and its slope parameter (L) of nuclear matter in the general framework of the Landau-Migdal theory. We derive an exact relation between a_s and L, which involves the nucleon effective mass and three-particle Landau-Migdal parameters. We also present simple estimates which show that there are two main mechanisms to explain the empirical values of L: The proton-neutron effective mass difference in isospin asymmetric matter, and the isovector three-body Landau-Migdal parameter H_0. We give simple estimates of both effects and show that they are of similar magnitude.
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We derive from the subleading contributions to the chiral three-nucleon interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84, 054001 (2011)] their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter in an analytical way. For the variety of short-range and long-range terms that constitute the subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the results for 2-ring diagrams can be given in terms of elementary functions of the ratio Fermi-momentum over pion mass, one ends up in most cases for the closed 1-ring diagrams with one-parameter integrals. The same treatment is applied to the subsubleading chiral three-nucleon interactions as far as these have been constructed up to now.
We present a study of the skewness of nuclear matter, which is proportional to the third derivative of the energy per nucleon with respect to the baryon density at the saturation point, in the framework of the Landau-Migdal theory. We derive an exact relation between the skewness, the nucleon effective mass, and two-particle and three-particle interaction parameters. We also present qualitative estimates, which indicate that three-particle correlations play an important role for the skewness.
The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state (EOS), which is commonly assumed to be almost quadratic. In this work, we confront this standard quadratic expansion of the EOS with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective field theory. We study, in particular, the importance of non-quadratic contributions to the symmetry energy, including the non-analytic logarithmic term introduced by Kaiser [Phys.~Rev.~C textbf{91}, 065201 (2015)]. Our results suggest that the quartic contribution to the symmetry energy can be robustly determined from the various Hamiltonians employed, and we obtain 1.00(8) MeV (or 0.55(8) MeV for the potential part) at saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We finally employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a small 5% correction.
Working on the framework of Relativistic Mean Field theory, we exposed the effect of nonlinear isoscalar-isovector coupling on G2 parameter set on the density dependence of nuclear symmetry energy in infinite nuclear matter. The observables like symmetric energy and few related coefficients are studied systematically. We presented the results of stiff symmetry energy at sub-saturation densities and a soft variation at normal densities. Correlation between the symmetric energy and the isoscalar-isovector coupling parameter fully demonstrated for wide range of density. The work further extended to the octet system and showed the effect of coupling over the equation of state.
Adopting hyperon-nucleon and hyperon-nucleon-nucleon interactions parametrized in chiral effective field theory, single-particle potentials of the $Lambda$ and $Sigma$ hyperons are evaluated in symmetric nuclear matter and in pure neutron matter within the framework of lowest order Bruckner theory. The chiral NLO interaction bears strong $Lambda$N-$Sigma$N coupling. Although the $Lambda$ potential is repulsive if the coupling is switched off, the $Lambda$N-$Sigma$N correlation brings about the attraction consistent with empirical data. The $Sigma$ potential is repulsive, which is also consistent with empirical information. The interesting result is that the $Lambda$ potential becomes shallower beyond normal density. This provides the possibility to solve the hyperon puzzle without introducing ad hoc assumptions. The effects of the $Lambda$NN-$Lambda$NN and $Lambda$NN-$Sigma$NN three-baryon forces are considered. These three-baryon forces are first reduced to normal-ordered effective two-baryon interactions in nuclear matter and then incorporated in the $G$-matrix equation. The repulsion from the $Lambda$NN-$Lambda$NN interaction is of the order of 5 MeV at the normal density, and becomes larger with increasing the density. The effects of the $Lambda$NN-$Sigma$NN coupling compensate the repulsion at normal density. The net effect of the three-baryon interactions to the $Lambda$ single-particle potential is repulsive at higher densities.
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