Nuclear pairing from microscopic forces: singlet channels and higher-partial waves

Abstract

Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps ${\Delta }_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $\chi (p)$ defined by $\Delta (p)={\Delta }_F\chi (p)$ and a non-linear algebraic equation for the gap magnitude ${\Delta }_F=\Delta (p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled ${}^{3}P{F}_2$ partial wave. Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.

18 pages and 9 figures

References in corpus (36)

• An accurate nucleon-nucleon potential with charge-independence breaking
• Modern Theory of Nuclear Forces
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Chiral effective field theory and nuclear forces
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Chiral Dynamics in Nucleons and Nuclei
• Physics of Neutron Star Crusts
• Realistic models of pion-exchange three-nucleon interactions
• Model-independent low momentum nucleon interaction from phase shift equivalence
• From low-momentum interactions to nuclear structure
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter
• Chiral three-nucleon forces and neutron matter
• Evolution of Nuclear Spectra with Nuclear Forces
• Strongly paired fermions: Cold atoms and neutron matter
• Quantum Monte Carlo calculation of the equation of state of neutron matter
• Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces
• Polarization contributions to the spin-dependence of the effective interaction in neutron matter
• The nuclear matter equation of state with consistent two- and three-body perturbative chiral interactions
• Reduced regulator dependence of neutron-matter predictions with chiral interactions
• Low-momentum interactions with smooth cutoffs
• Chiral three-nucleon interaction and the carbon-14 dating beta decay
• Equation of state of low--density neutron matter and the ${}^1{S}_0$ pairing gap
• ${}^1{S}_0$ superfluid phase--transition in neutron matter with realistic nuclear potentials and modern many--body theories
• Density-dependent nucleon-nucleon interaction from three-nucleon forces
• Microscopic optical potential from chiral nuclear forces
• Low Momentum Nucleon-Nucleon Interactions and Shell-Model Calculations
• Triplet Pairing in Neutron Matter
• 3PF2 pairing in high-density neutron matter
• Dependence of the BCS 1S0 superfluid pairing gap on nuclear interactions
• Soft two-meson-exchange nucleon-nucleon potentials. I. Planar and crossed-box diagrams
• Nuclear energy density functional from chiral two- and three-nucleon interactions
• Soft two-meson-exchange nucleon-nucleon potentials. II. One-pair and two-pair diagrams
• Microscopic evaluation of the pairing gap
• Minimal Relativity and ${}^3{S}_1$-${}^3{D}_1$ Pairing in Symmetric Nuclear Matter
• Chiral three-nucleon forces and pairing in nuclei

Cited by in corpus (35)

• Neutron Stars and the Nuclear Equation of State
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Superfluidity in nuclear systems and neutron stars
• Superfluidity and Superconductivity in Neutron Stars
• Superfluidity and Superconductivity in Neutron Stars
• Pairing in high-density neutron matter including short- and long-range correlations
• Pairing in high-density neutron matter including short- and long-range correlations
• Pairing in neutron matter: New uncertainty estimates and three-body forces
• Pairing and short-range correlations in nuclear systems
• Triplet Pairing in pure neutron matter
• Reexamining Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluidity in neutron stars
• Neutron pairing with medium polarization beyond the Landau approximation
• Phase structure of neutron ${}^3{P}_2$ superfluids in strong magnetic fields in neutron stars
• Comparison between the Thomas-Fermi and Hartree-Fock-Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Domain walls in neutron ${}^3{P}_2$ superfluids in neutron stars
• Microscopic Study of ${}^1{S}_0$ Superfluidity in Dilute Neutron Matter
• Pairing in pure neutron matter
• Three-nucleon forces and superfluidity in neutron matter
• Critical endpoint and universality class of neutron ${}^3{P}_2$ superfluids in neutron stars
• Proton pairing in neutron stars from chiral effective field theory
• Equation of state of superfluid neutron matter with low-momentum interactions
• Coexistence phase of ${}^1{S}_0$ and ${}^3{P}_2$ superfluids in neutron stars
• Spin-polarized phases of ${}^3{P}_2$ superfluids in neutron stars
• From odd-even staggering to the pairing gap in neutron matter
• Topological defects at the boundary of neutron ${}^3{P}_2$ superfluids in neutron stars
• Core structures of vortices in Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluids
• Neutron star cooling and mass distributions
• Effects of strong magnetic fields on neutron ${}^3{P}_2$ superfluidity with spin-orbit interactions
• Proximity effects of vortices in neutron ${}^3{P}_2$ superfluids in neutron stars: Vortex core transitions and covalent bonding of vortex molecules
• Superfluid neutron matter with a twist
• Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron ${}^3{P}_2$ superfluids
• Cold atoms beyond atomic physics
• The BCS pairing gap in the on-shell limit of the Similarity Renormalization Group
• Isospin-Asymmetry Dependence of the Thermodynamic Nuclear Equation of State in Many-Body Perturbation Theory