Accurate nuclear radii and binding energies from a chiral interaction

Abstract: With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLO$_{\rm sat}$, yield accurate binding energies and radii of nuclei up to $^{40}$Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low-lying collective $J^\pi=3^-$ states in $^{16}$O and $^{40}$Ca are described accurately, while spectra for selected $p$- and $sd$-shell nuclei are in reasonable agreement with experiment.

• The paper introduces an optimized chiral interaction that simultaneously fits 2N and 3N forces to accurately predict nuclear radii and binding energies.
• It employs coupled-cluster calculations to yield results consistent with empirical saturation and collective excitation data for nuclei up to 40Ca.
• The study advances nuclear structure models, offering actionable insights for applications in astrophysics and the research of exotic nuclei.

Insights into Nuclear Radii and Binding Energies Through Chiral Interaction

The paper "Accurate nuclear radii and binding energies from a chiral interaction" presents an advanced investigation into nuclear structure calculations emphasizing the significance of chiral effective field theory (EFT) interactions. The authors introduce an optimized interaction for the simultaneous description of light and medium-mass nuclei, achieving a significant level of accuracy for nuclear radii and binding energies, up to $\mathrm{^{40}Ca}$.

Methodological Foundation

The authors utilize chiral EFT to derive two-nucleon (2N) and three-nucleon (3N) forces. The optimization of these chiral interactions encompasses low-energy nucleon-nucleon scattering data in addition to binding energies and radii for few-nucleon systems and specific isotopes, notably those of carbon and oxygen. This approach stands out for its simultaneous optimization of 2N and 3N forces, deviating from traditional strategies which often optimize these forces separately and only adjust 3N forces using few-nucleon data.

Computational Techniques

The research employs coupled-cluster (CC) calculations, renowned for their proficiency in handling both few-body and medium-mass nuclear systems effectively. Through CC methods, the study yields nuclear properties consistent with the empirical saturation point of nuclear matter. The validation of their results includes a suite of spectroscopic predictions in $\mathrm{^{16}O}$ and $\mathrm{^{40}Ca}$, which exemplify the interaction’s capability in accurately describing collective excitation modes within these nuclei.

Numerical Findings and Implications

Critically, the numerical outcomes presented feature a substantial concordance with observed nuclear properties. The calculated binding energies and charge radii align closely with experimental data across a range of nuclei, from the lightest systems like $\mathrm{^3H}$ and $\mathrm{^4He}$ to the medium-mass $\mathrm{^{40}Ca}$. The satisfactory handling of the empirical saturation point, a long-standing challenge in nuclear theory, is a notable achievement.

The positive results in describing collective states, such as the $3^-$ phonon states in $\mathrm{^{16}O}$ and $\mathrm{^{40}Ca}$, underscore the robustness of the developed interaction model. The successful reproduction of such nuclear excitations suggests the improved modeling of long-range and medium effects, inherent to chiral approaches, has substantial merit.

Theoretical and Practical Implications

From a theoretical perspective, this work advances the frontier of chiral nuclear forces by demonstrating their applicability across a greater range of nuclei than previously feasible. The implications for nuclear physics are profound, as the study suggests a comprehensive model that can be utilized not only for light nuclei, once the domain of few-body techniques, but also for nuclei approaching the medium-mass regime.

Practically, these findings could inform further studies on nuclear matter properties, such as neutron-rich systems and isotopic chains, with relevance to understanding neutron star crusts and rare isotopes. The cross-validation with nuclear matter properties also addresses a key challenge in bridging finite nuclei studies with infinite matter descriptions, potentially benefiting both nuclear structure research and astrophysical applications.

Future Directions

This research opens doors for future investigations into extrapolating these interactions to heavier and more exotic nuclei. The quest for a unified nuclear interaction applicable across all mass numbers remains demanding, yet this study marks a significant stride towards that goal. Additionally, the extension of such methodologies within quantum many-body computations could parallel advances in other domain-specific applications of CC methods, potentially enhancing the precision in other correlated matter studies.

In conclusion, while the optimization of nuclear interactions from chiral EFT represents a technically challenging task, its execution as demonstrated here reveals promising results. This work contributes meaningfully to the repertoire of predictive nuclear models, further cementing the relevance of EFT within the nuclear theory landscape.