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Register a new userSkewness of nuclear matter and three-particle correlations
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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.
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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.
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.
The present work starts by providing a clear identification of correlations between critical parameters ($T_c$, $P_c$, $rho_c$) and bulk quantities at zero temperature of relativistic mean-field models (RMF) presenting third and fourth order self-interactions in the scalar field $sigma$. Motivated by the nonrelativistic version of this RMF model, we show that effective nucleon mass ($M^*$) and incompressibility ($K_o$), at the saturation density, are correlated with $T_c$, $P_c$, and $rho_c$, as well as, binding energy and saturation density itself. We verify agreement of results with previous theoretical ones regarding different hadronic models. Concerning recent experimental data of the symmetric nuclear matter critical parameters, our study allows a prediction of $T_c$, $P_c$ and $rho_c$ compatible with such values, by combining them, through the correlations found, with previous constraints related to $M^*$ and $K_o$. An improved RMF parametrization, that better agrees with experimental values for $T_c$, is also indicated.
We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($chi$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $chi$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $chi$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.
We present a new technique for observing the strange quark matter distillation process based on unlike particle correlations. A simulation is presented based on the scenario of a two-phase thermodynamical evolution model.
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