Three-body forces and the limit of oxygen isotopes

Abstract: The limit of neutron-rich nuclei, the neutron drip-line, evolves regularly from light to medium-mass nuclei except for a striking anomaly in the oxygen isotopes. This anomaly is not reproduced in shell-model calculations derived from microscopic two-nucleon forces. Here, we present the first microscopic explanation of the oxygen anomaly based on three-nucleon forces that have been established in few-body systems. This leads to repulsive contributions to the interactions among excess neutrons that change the location of the neutron drip-line from $<sup>{28}$O to the experimentally observed $<sup>{24}$O. Since the mechanism is robust and general, our findings impact the prediction of the most neutron-rich nuclei and the synthesis of heavy elements in neutron-rich environments.

• The paper demonstrates that incorporating Fujita–Miyazawa three-nucleon forces explains the shift of the neutron drip-line from 28O to the experimentally observed 24O.
• It employs chiral effective field theory and single-particle energy analysis to reveal the limitations of traditional two-nucleon force models.
• The findings improve predictions of nuclear binding energies and offer insights into nucleosynthesis in neutron-rich astrophysical environments.

Three-body Forces and the Limit of Oxygen Isotopes

The paper under discussion presents a pivotal study on the anomalous positioning of the neutron drip-line in oxygen isotopes, a key topic in the domain of nuclear physics. The neutron drip-line is an essential concept that signifies the limit at which adding one more neutron results in an unbound nucleus, thereby elucidating the stability of neutron-rich isotopes. The anomaly noted in oxygen isotopes poses a significant challenge, as traditional shell-model calculations based on two-nucleon (NN) forces fail to replicate this behavior, whereas three-nucleon (3N) forces present a plausible explanation.

The authors introduce the role of three-nucleon forces derived from few-body systems as a crucial component in addressing this anomaly. Their research leverages the established Fujita-Miyazawa (FM) 3N forces, grounded in the excitation of one nucleon to a $\Delta(1232 MeV)$ resonance. This approach extends the nuclear interaction forces beyond the conventionally considered two-body limits, offering repulsive contributions that crucially adjust the nuclear binding energies. The study rigorously discusses how these forces accurately predict the transition of the neutron drip-line from $^{28}$O to the experimentally observed $^{24}$O, offering a compelling theoretical elucidation for this specific anomaly.

The research traces the effect of these 3N forces in chiral effective field theory (EFT), emphasizing that these forces naturally emerge under this framework via pion exchanges and shorter-range interactions. This systematic expansion, which considers interactions of increasing complexity, inherently includes the $\Delta$ excitations prominent in 3N forces. These interactions impact the nuclear architecture, shifting the binding mechanics of isotopic sequences.

Analyzing the single-particle energies (SPE) of additional neutrons in the oxygen isotopes, the authors identify the flaws in existing NN potential models, specifically the inadequately predicted bound state at $^{28}$O due to overly attractive monopole components. When the FM 3N forces are incorporated, there occurs a notable redirection of SPE trends, aligning predictions with experimental observations. The robustness of these 3N forces proves crucial in reproducing the experimental gas, particularly at $N=16$, which substantiates the existing boundaries at $^{24}$O.

Quantitative review of the ground-state energies further corroborates the central claim. The inclusion of 3N forces in shell-model calculations markedly alters the landscape of binding energies for the observed isotopes, a factor unexplained by NN forces alone. Notably, the 3N theories exhibit a substantive shift in predictive success for unstable nuclei, aligning closely with empirical data.

The implications of these findings are profound, not only do they improve the accuracy of drip-line predictions, but they also enhance our understanding of rare isotopic formations. Furthermore, 3N forces are anticipated to play a pivotal role in assessing nuclear structures far from stability, potentially impacting the understanding of astrophysical nucleosynthesis in neutron-rich environments.

Future research directions might focus on integrating these 3N mechanisms into broader nuclear models and exploring their ramifications in higher-mass isotopes, potentially influencing both theoretical and practical applications in nuclear physics. Moreover, further investigation into the role of 3N forces could refine computational models, aiding in the comprehension of forces at nucleonic boundaries, and contributing to the overarching synthesis of elements within stellar phenomena.