An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order (1303.4674v1)

Abstract: We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next- to-leading order. The resulting new chiral force NNLOopt yields \chi^2 \approx 1 per degree of freedom for laboratory energies below approximately 125 MeV. In the A = 3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLOopt to study properties of key nuclei and neutron matter, and demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.

• The paper refines NN interaction parameters with derivative-free optimization, achieving a χ² near one for energies below 125 MeV.
• It employs chiral effective field theory and the POUNDerS algorithm to accurately fit experimental phase shifts.
• The optimized model precisely predicts nuclear properties such as binding energies, radii, and subsaturation neutron matter behavior without additional three-nucleon forces.

Optimized Chiral Nucleon-Nucleon Interaction at NNLO

The paper "An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order" addresses a salient aspect of nuclear physics: the parametrization and optimization of nucleon-nucleon (NN) interactions within the framework of chiral effective field theory (ChEFT) at next-to-next-to-leading order (NNLO). The authors present significant refinements in the NN interaction model by employing advanced optimization techniques, achieving a $\chi^2$ value approximating one per degree of freedom for laboratory energies below 125 MeV, greatly improving upon previous models.

Chiral effective field theory utilizes the symmetries and framework of quantum chromodynamics (QCD) to describe low-energy nuclear interactions. In this paradigm, the exchange of pions accounts for long-range nuclear forces, while short-range interactions are characterized by contact terms. Parameters, or low-energy constants (LECs), are fitted to experimental data to optimize the accuracy and predictive power of the interaction model. Traditionally, the NNLO level encapsulates three-nucleon forces (3NFs), and the rigorous optimization of LECs has been instrumental in the accurate reproduction of nuclear phenomena.

In their approach, the authors utilize the Practical Optimization Using No Derivatives (for Squares) algorithm, known as POUNDerS, to perform a derivative-free optimization of the chiral NN interaction. This systematic optimization targets the fit to experimental phase shifts derived from the Nijmegen partial wave analysis. Uniquely, the optimization constraints focus on both peripheral waves and central $P$-waves, demonstrating improvements over earlier parametrizations by Entem and Machleidt.

The paper reports that the optimized chiral force, referred to as {}, delivers observables consistent with experimental data across a range of key nuclear systems, including $A=3,4$ nuclei. Strikingly, the implications extend to the precise determination of binding energies and radii, eschewing the complex contributions of 3NFs that some previous models required. This streamlined approach of utilizing a two-body component primarily resonates in its success in accurately predicting nuclear structure.

In the paper of medium-mass isotopes of oxygen and calcium, previous N$^3$LO interactions demonstrated deficiencies, necessitating the inclusion of 3NFs to align with experimental drip lines and shell closures. However, the refined NNLO interaction described in this paper reproduces experimental data without additional forces, notably reaffirming the magic nature of $^{48}$Ca and predictive subshell closures in $^{52,54}$Ca. Moreover, it competently models neutron matter at subsaturation densities, which is pivotal for understanding the equation of state (EOS) in astrophysical scenarios.

Looking forward, the work propels further exploration into the role of 3NFs in larger nuclear systems, setting a foundation for future enhancement at subsequent orders in ChEFT. It indicates a vital pathway for incorporating precise variance analysis across interaction parameters that will refine the landscape of nuclear theory. This paper serves as a beacon for future endeavors that aim to extend the reach of chiral EFT, consolidate theoretical uncertainties, and develop finely-tuned, robust nuclear models.