Chiral three-nucleon forces and neutron matter (0911.0483v2)

Abstract: We calculate the properties of neutron matter and highlight the physics of chiral three-nucleon forces. For neutrons, only the long-range 2 pi-exchange interactions of the leading chiral three-nucleon forces contribute, and we derive density-dependent two-body interactions by summing the third particle over occupied states in the Fermi sea. Our results for the energy suggest that neutron matter is perturbative at nuclear densities. We study in detail the theoretical uncertainties of the neutron matter energy, provide constraints for the symmetry energy and its density dependence, and explore the impact of chiral three-nucleon forces on the S-wave superfluid pairing gap.

• The paper derives density-dependent two-body interactions from chiral three-nucleon forces to model neutron matter properties.
• It employs renormalization group methods to smooth energy predictions and reduce cutoff sensitivities in many-body calculations.
• The study shows that repulsive 3N forces decrease the neutron superfluid pairing gap, influencing neutron star models.

Insights into Chiral Three-Nucleon Forces and Neutron Matter

The paper "Chiral Three-Nucleon Forces and Neutron Matter" by Hebeler and Schwenk focuses on elucidating the role of chiral three-nucleon (3N) forces within neutron matter and provides comprehensive calculations to understand these effects. Notably, the investigation centers on the long-range $2\pi$-exchange interactions of leading chiral 3N forces, deriving new insights into the neutron matter system, which is pivotal in nuclear theory and astrophysics.

The authors begin by deriving density-dependent two-body interactions from chiral 3N forces at next-to-next-to-leading order (N$^2$LO) within neutron matter. They focus on summing the third nucleon over occupied states in the Fermi sea. The paper presents strengths of chiral 3N contributions, highlighting their effect in suggesting the perturbative nature of neutron matter at typical nuclear densities. Convergence is achieved through the evolution of interactions to low momenta using the renormalization group (RG), thereby softening short-range forces and improving the precision of many-body calculations.

One of the significant outcomes presented is the energy predictions for neutron matter. The second-order results are contrastingly smooth due to the RG-evolved interactions, exhibiting minimal cutoff dependence, suggesting the interactions' sufficiency in encapsulating many-body contributions without significant accuracy loss. It is emphasized that the chiral N$^2$LO interactions provide a notably repulsive contribution, predominantly due to the central components of the derived density-dependent two-body interaction, $V$.

An essential aspect addressed is the theoretical uncertainty due to variations in the low-energy constants $c_1$ and $c_3$. The energy calculations show sensitivity primarily to these parameters, advocating for improved determinations of these coefficients due to their critical contribution to the energy band, influencing the uncertainty in symmetry energies crucial for developing accurate nuclear matter equations of state.

The paper also explores the implications of chiral 3N forces on neutron superfluidity. It extends the analysis to the $^1$S$_0$ superfluid pairing gap, revealing a reduction in the gap when 3N forces are incorporated, attributable to the repulsive interaction in the relevant channels. These results collaborate with previous findings underlining the relevance of three-body forces in adjusting predictions for pairing gaps, pertinent for understanding neutron star crusts and cooling rates.

Overall, the work yields significant theoretical contributions to nuclear many-body physics, particularly relevant in the astrophysical context of neutron stars. Future developments could further refine low-energy constant calibrations, elucidate higher-order contributions and extend these computational techniques to broader nuclear systems, thereby enhancing predictive capabilities across nuclear physics and astrophysics. The methodology and results serve as a prototype for employing chiral effective field theory combined with RG in tackling complex nuclear systems, heralding further advancements in bridging nuclear theory and machine learning to better emulate nuclear interactions in dense astrophysical environments.