Ab Initio Calculations of the Carbon and Oxygen Isotopes: Energies, Correlations, and Superfluid Pairing
Young-Ho Song, Myungkuk Kim, Youngman Kim, Kihyeon Cho, Serdar Elhatisari, Dean Lee, Yuan-Zhuo Ma, Ulf-G. Meißner
TL;DR
The paper advances ab initio calculations of neutron-rich carbon and oxygen isotopes using nuclear lattice effective field theory (NLEFT) with chiral interactions up to next-to-next-to-next-to-leading order ($O(Q^4)$, i.e., N3LO). Energies of the isotopes are computed and show good agreement with experiment, validating the lattice approach and the high-fidelity chiral interactions up to $O(Q^4)$. A model-independent framework is developed to quantify two-nucleon correlations by introducing short-range perturbations and tracking changes in scattering phase shifts $\Delta\delta(p)$, aided by an isospin diagnostic based on the $T_z$-linearity relation $f(1)=2f(0)-f(-1)$. The results reveal universal patterns: in the $^1S_0$ channel, paired neutrons interact with both their partner and the core, while unpaired neutrons couple primarily to the core; other partial waves exhibit smoother neutron-number dependence, and $T=0$ versus $T=1$ S-wave correlations remain comparatively similar due to a hidden spin-isospin exchange symmetry. These insights, grounded in a robust, operator-based framework, are readily transferable to other ab initio methods and may inform future studies of charge radii and other observables in neutron-rich nuclei.
Abstract
We perform \textit{ab initio} nuclear lattice calculations of the neutron-rich carbon and oxygen isotopes using high-fidelity chiral interactions. We find good agreement with the observed binding energies and compute correlations associated with each two-nucleon interaction channel. For the isospin $T=1$ channels, we show that the dependence on $T_z$ provides a measure of the correlations among the extra neutrons in the neutron-rich nuclei. For the spin-singlet S-wave channel, we observe that any paired neutron interacts with the nuclear core as well as its neutron pair partner, while any unpaired neutron interacts primarily with only the nuclear core. For the other partial waves, the correlations among the extra neutrons grow more slowly and smoothly with the number of neutrons. These general patterns are observed in both the carbon and oxygen isotopes and may be universal features that appear in many neutron-rich nuclei.