Improved nuclear matter calculations from chiral low-momentum interactions (1012.3381v2)

Abstract: We present new nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force contribution that includes a corrected combinatorial factor beyond Hartree-Fock that was omitted in previous nuclear matter calculations. We find realistic saturation properties using parameters fit only to few-body data, but with larger uncertainty estimates from cutoff dependence and the 3NF parametrization than in previous calculations.

• The paper introduces an innovative method for treating three-nucleon forces beyond Hartree-Fock to naturally achieve empirical saturation properties.
• It employs chiral EFT-derived low-momentum interactions softened through renormalization group techniques for rapid convergence in many-body calculations.
• The study’s approach enhances nuclear modeling, with implications for density functional theory and astrophysical applications like neutron star structure.

Improved Nuclear Matter Calculations from Chiral Low-Momentum Interactions

The research paper titled "Improved nuclear matter calculations from chiral low-momentum interactions" presents an innovative approach to nuclear matter calculations by utilizing low-momentum interactions derived from chiral effective field theory (EFT) potentials. The authors, Hebeler et al., aim to improve the treatment of three-nucleon force (3NF) contributions beyond the Hartree-Fock approximation, an aspect often simplified in previous studies. Their methodology is significant for yielding realistic saturation properties consistent with empirical data, achieving this without parameter adjustments based on nuclear potentials.

The authors employ soft Hamiltonians informed by interactions fitted solely to few-body data (A ≤ 4). This paper particularly leverages recent advancements in chiral EFT, renormalization group (RG) techniques to soften repulsive short-range interactions, and an innovative procedure for fitting 3NF to the $^4$He radius rather than its binding energy. These methodological enhancements allow for a more rapid convergence of many-body calculations. The low-momentum interactions are systematically derived using chiral EFT and subsequently softened through RG evolution, a strategy that enhances computational feasibility and precision.

Notably, this research emphasizes the intricate role of 3N forces in achieving saturation at nuclear matter densities. It contrasts with historical methods that imposed empirical saturation properties by artificially adjusting short-range three-body forces. The current approach allows the properties of symmetric nuclear matter to emerge naturally from the theoretical framework, thereby bolstering the predictive power of the chiral EFT framework. The manuscript demonstrates reasonable saturation at the expected Fermi momentum and density, alongside uncertainties arising primarily from cutoff dependencies and the parameterization of the 3NF.

The findings underscore the perturbative nature of nuclear matter interactions when using low-momentum interactions, especially in the particle-particle channel. This supports the prospect that nuclear forces, when adequately evolved, adhere to predictable behavioral patterns across various systems, from few-body to infinite matter scenarios. The authors present results that show energy calculations of symmetric matter based on different approximations—Hartree-Fock, second-order, and third-order expansions—that incorporate progressively more complex interaction terms.

The implications of this work are profound for nuclear theory, as it paves the way for improved density functional theory (DFT) calculations that can encapsulate nuclear properties across a range of nuclei. The close agreement with empirical saturation properties, achieved without reliance on finely tuned parameters, suggests that these theoretical models may be adept at predicting properties of finite nuclei with significant accuracy in the future. The findings also hold potential relevance for astrophysical applications, such as modeling the structure of neutron stars, given the close relation between dense matter calculations and neutron star equations of state.

While the authors acknowledge that further refinements—including higher-order many-body corrections and thorough explorations of chiral Hamiltonians—are necessary to enhance the accuracy and reliability of their predictions, this paper constitutes a solid step toward a unified understanding of nuclear forces across different contexts. Future developments may see reduced uncertainties with the inclusion of more sophisticated many-body interactions and broadened EFT order expansions, enhancing the impact of this approach in nuclear structure and reaction predictions.