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Register a new userEnergy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions
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N. Kaiser
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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.
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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.
The long-range terms of the subleading chiral three-nucleon force [published in Phys.,Rev.,C77, 064004 (2008)] are specified to the case of three neutrons. From these $3n$-interactions an effective density-dependent neutron-neutron potential $V_text{med}$ in pure neutron matter is derived. Following the division of the pertinent 3n-diagrams into two-pion exchange, two-pion-one-pion exchange and ring topology, all self-closings and concatenations of two neutron-lines to an in-medium loop are evaluated. The momentum and $k_n$-dependent potentials associated with the spin-operators $1,, vecsigma_1!cdot!vecsigma_2,, vecsigma_1!cdot!vec q, vecsigma_2!cdot!vec q,, i( vecsigma_1!+!vecsigma_2)!cdot ! (vec q!times ! vec p,),, (vecsigma_1!cdot!vec p,vecsigma_2!cdot!vec p+vecsigma_1!cdot!vec p,, vecsigma_2!cdot!vec p,)$ and $ vecsigma_1!cdot ! (vec q!times ! vec p,)vecsigma_2!cdot ! (vec q!times ! vec p,)$ are expressed in terms of functions, which are either given in closed analytical form or require at most one numerical integration. The subsubleading chiral 3N-force is treated in the same way. The obtained results for $V_text{med}$ are helpful to implement the long-range chiral three-body forces into advanced neutron matter calculations.
We present a family of nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to N3LO in the chiral expansion that provides an accurate ab initio description of ground-state energies and charge radii up to the medium-mass regime with quantified theory uncertainties. Starting from the NN interactions proposed by Entem, Machleidt and Nosyk, we construct 3N interactions with consistent chiral order, non-local regulator, and cutoff value and explore the dependence of nuclear observables over a range of mass numbers on the 3N low-energy constants. By fixing these constants using the 3-H and 16-O ground-state energies, we obtain interactions that robustly reproduce experimental energies and radii for large range from p-shell nuclei to the nickel isotopic chain and resolve many of the deficiencies of previous interactions. Based on the order-by-order convergence and the cutoff dependence of nuclear observables, we assess the uncertainties due the interaction, which yield a significant contribution to the total theory uncertainty.
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 existence of superfluidity of the neutron component in the core of a neutron star, associated specifically with triplet $P-$wave pairing, is currently an open question that is central to interpretation of the observed cooling curves and other neutron-star observables. Ab initio theoretical calculations aimed at resolving this issue face unique challenges in the relevant high-density domain, which reaches beyond the saturation density of symmetrical nuclear matter. These issues include uncertainties in the three-nucleon (3N) interaction and in the effects of strong short-range correlations -- and more generally of in-medium modification of nucleonic self-energies and interactions. A survey of existing solutions to the gap equations in the triplet channel shows that the separate or combined impacts of 3N forces, coupled channels, and mass renormalization range from moderate to strong to devastating, thus motivating a detailed analysis of the competing effects. In the present work we track the effects of the 3N force and in-medium modifications in the representative case of the $^3P_2$ channel, based on the Argonne V18 two-nucleon (2N) interaction supplemented by 3N interactions of the Urbana IX family. Sensitivity of the results to the input interaction is clearly demonstrated, while consistency issues arise with respect to the simultaneous treatment of 3N forces and in-medium effects. We consider this pilot study as the first step towards a systematic and comprehensive exploration of coupled-channel $^3P F_2$ pairing using a broad range of 2N and 3N interactions from the current generation of refined semi-phenomenological models and models derived from chiral effective field theory.
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