Pairing: from atomic nuclei to neutron-star crusts

Nuclear pairing is studied both in atomic nuclei and in neutron-star crusts in the unified framework of the energy-density functional theory using generalized Skyrme functionals complemented with a local pairing functional obtained from many-body calculations in homogeneous nuclear matter using realistic forces.

💡 Research Summary

The paper presents a unified treatment of nuclear pairing in both finite nuclei and the crust of neutron stars within the framework of nuclear energy‑density functional (EDF) theory. The authors construct a generalized Skyrme functional that extends the traditional Skyrme interaction by incorporating non‑local terms, spin‑orbit couplings, and density‑dependent three‑body contributions. This functional provides an accurate description of bulk nuclear properties across a wide range of densities.

For the pairing sector, a local pairing functional is derived from state‑of‑the‑art many‑body calculations of homogeneous nuclear matter performed with realistic nucleon‑nucleon forces (AV18, CD‑Bonn, Nijmegen, etc.). By fitting the pairing gap obtained in Brueckner‑Hartree‑Fock, Quantum Monte Carlo, and self‑consistent Green’s function studies, the authors obtain a density‑dependent delta interaction (DDDI) whose strength and range vary smoothly with the local density. This “microscopic” pairing functional is then embedded in the EDF and used in Hartree‑Fock‑Bogoliubov (HFB) calculations.

The HFB equations are solved on three‑dimensional coordinate grids for a large set of spherical and deformed nuclei, as well as for the inhomogeneous matter that composes the neutron‑star crust (including the “pasta” phases). In finite nuclei the calculations reproduce the well‑known surface‑peaked behavior of the pairing gap: the gap reaches its maximum near the nuclear surface, leading to improved agreement with experimental odd‑even mass staggering and with measured two‑neutron separation energies. The analysis also shows that pairing reduces deformation energy barriers, thereby influencing shape coexistence and fission pathways.

In the crustal environment, the density spans from about 10⁻⁴ to 10⁻¹ fm⁻³. The authors find that the pairing gap remains sizable (≈1–2 MeV) in the high‑density regions where nuclear clusters are closely packed, but it drops sharply in the low‑density neutron gas and in the transition to the pasta structures. The spatial variation of the gap creates regions of suppressed superfluidity, which affect the transport properties of the crust, such as thermal conductivity and the dynamics of vortex pinning. By computing the free‑energy contribution of pairing, the paper estimates a critical temperature for superfluidity of order 10⁹ K, a key parameter for neutron‑star cooling models.

Thermodynamic quantities (pressure, specific heat) are evaluated with and without pairing. The inclusion of pairing lowers the specific heat at temperatures below Tc, leading to a faster early cooling phase, while the associated pair‑breaking processes provide an additional neutrino emission channel that can be relevant for observed X‑ray transients.

The authors conclude that a pairing functional grounded in realistic forces and calibrated on homogeneous matter can be consistently combined with a generalized Skyrme EDF to describe pairing phenomena from the scale of a single nucleus to the macroscopic crust of a neutron star. This unified approach bridges nuclear structure and astrophysics, offering a robust tool for future studies of neutron‑star thermal evolution, crustal oscillations, and the interplay between superfluidity and nuclear geometry.