Local Density Approximation for proton-neutron pairing correlations. I. Formalism

Abstract

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.

22 RevTeX pages

References in corpus (8)

• Pairing in nuclear systems: from neutron stars to finite nuclei
• Pairing Interaction and Self-Consistent Densities in Neutron-Rich Nuclei
• Group theoretical analysis of symmetry breaking in two-dimensional quantum dots
• Nuclear Pairing in the T=0 channel revisited
• Interpretation of the Wigner Energy as due to RPA Correlations
• The T=0 neutron-proton pairing correlations in the superdeformed rotational bands around 60Zn
• Cranking in isospace - towards a consistent mean-field description of N=Z nuclei
• Alpha decay and proton-neutron correlations

Cited by in corpus (133)

• Nuclear Energy Density Optimization
• Nuclear energy density optimization: Large deformations
• The tensor part of the Skyrme energy density functional. I. Spherical nuclei
• Microscopic Theory of Nuclear Fission: A Review
• Axially Deformed Solution of the Skyrme-Hartree-Fock-Bogolyubov Equations using The Transformed Harmonic Oscillator Basis. The program HFBTHO (v1.66p)
• Nuclear energy density optimization: Shell structure
• The TDHF Code Sky3D
• Shell Structure of Exotic Nuclei
• One-quasiparticle States in the Nuclear Energy Density Functional Theory
• Particle-Number Projection and the Density Functional Theory
• Self-Consistent Description of Multipole Strength in Exotic Nuclei I: Method
• Particle-Number Restoration within the Energy Density Functional Formalism
• Tensor part of the Skyrme energy density functional. II: Deformation properties of magic and semi-magic nuclei
• Toward ab initio density functional theory for nuclei
• Towards the global description of nuclear charge radii: exploring the Fayans energy density functional
• Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations
• Local nuclear energy density functional at next-to-next-to-next-to-leading order
• Description of Induced Nuclear Fission with Skyrme Energy Functionals: I. Static Potential Energy Surfaces and Fission Fragment Properties
• Global description of beta-minus decay in even-even nuclei with the axially-deformed Skyrme finite amplitude method
• Broyden's Method in Nuclear Structure Calculations
• Low-Energy Heavy-Ion Reactions and the Skyrme Effective Interaction
• Self-interaction errors in nuclear energy density functionals
• Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals
• Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations
• Effective pseudopotential for energy density functionals with higher order derivatives
• Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory: Global, Regional and Local Comparisons
• Variation after Particle-Number Projection for the HFB Method with the Skyrme Energy Density Functional
• Solution of the Skyrme HF+BCS equation on a 3D mesh. II. A new version of the Ev8 code
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): a new version of the program
• Finite Amplitude Method for Charge-Changing Transitions in Axially-Deformed Nuclei
• The tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin
• The unrestricted Skyrme-tensor time-dependent Hartree-Fock and its application to the nuclear response from spherical to triaxial nuclei
• Dependence of single-particle energies on coupling constants of the nuclear energy density functional
• Linear response of homogeneous nuclear matter with energy density functionals
• Density-functional theory for fermions in the unitary regime
• Beta decay of deformed r-process nuclei near A = 80 and A= 160, including odd-A and odd-odd nuclei, with the Skyrme finite-amplitude method
• Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms
• Finite amplitude method applied to giant dipole resonance in heavy rare-earth nuclei
• Error Analysis in Nuclear Density Functional Theory
• Symmetry energy in nuclear density functional theory
• Pairing renormalization and regularization within the local density approximation
• Nuclear response for the Skyrme effective interaction with zero range tensor terms
• Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: II. Time-reversal symmetry breaking
• The Skyrme Tensor Force in Heavy Ion Collisions
• Nuclear Halos and Drip Lines in Symmetry-Conserving Continuum HFB Theory
• Nuclear response for the Skyrme effective interaction with zero-range tensor terms. II. Sum rules and instabilities
• Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations
• Spectroscopic properties of nuclear Skyrme energy density functionals
• Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications
• Breaking and restoring symmetries within the nuclear energy density functional method
• Density Matrix Expansion for Low-Momentum Interactions
• Constraining the surface properties of effective Skyrme interactions
• Nonlocal energy density functionals for low-energy nuclear structure
• Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using N2LO Skyrme pseudo-potential in spherical symmetry
• Ab Initio Derivation of Model Energy Density Functionals
• Toroidal high-spin isomers in the nucleus ${}^{304}120$
• Global nuclear structure effects of tensor interaction
• Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h): a new version of the program
• Large-Scale Self-Consistent Nuclear Mass Calculations
• Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory
• Collective inertia of Nambu-Goldstone mode from linear response theory
• Symmetry restoration in the mean-field description of proton-neutron pairing
• Self-consistent symmetries in the proton-neutron Hartree-Fock-Bogoliubov approach
• Energy-density-functional calculations including the proton-neutron mixing
• Nonlocal energy density functionals for pairing and beyond-mean-field calculations
• Isospin-invariant Skyrme energy-density-functional approach with axial symmetry
• Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei
• Symmetry interaction and many-body correlations
• The neutron polaron as a constraint on nuclear density functionals
• Microscopic origin of reflection-asymmetric nuclear shapes
• Pauli energy contribution to nucleus-nucleus interaction
• What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}
• Extended Skyrme pseudo-potential deduced from infinite matter properties
• Neutron-Proton pairing revisited
• The nuclear energy density functional formalism
• A quartet BCS-like theory
• Enhanced Tensor-Force Contribution in Collision Dynamics
• Complex-energy approach to sum rules within nuclear density functional theory
• Iterative approaches to the self-consistent nuclear energy density functional problem. Heavy ball dynamics and potential preconditioning
• Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms
• The Negele-Vautherin density matrix expansion applied to the Gogny force
• An introduction to Bootstrap for nuclear physics
• Extrapolating from neural network models: a cautionary tale
• Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals
• Comparison between the Thomas-Fermi and Hartree-Fock-Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations
• Possibility of Electron Pairing in Small Metallic Nanoparticles
• Systematic analysis of inner crust composition using the extended Thomas-Fermi approximation with pairing correlations
• Shape co-existence and parity doublet in Zr isotopes
• Natural Units For Nuclear Energy Density Functional Theory
• Instabilities in the Nuclear Energy Density Functional
• High-spin intruder states in the fp shell nuclei and isoscalar proton-neutron correlations
• Model nuclear energy density functionals derived from ab initio calculations
• Tools for incorporating a D-wave contribution in Skyrme energy density functionals
• Entrainment effects in neutron-proton mixtures within the nuclear-energy density functional theory. I. Low-temperature limit
• Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
• Nuclear matter response function with a central plus tensor Landau interaction
• Isospin effects in N~Z nuclei in extended Density Functional Theory
• Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation
• Linear Response Theory with finite-range interactions
• Building Surrogate Models of Nuclear Density Functional Theory with Gaussian Processesand Autoencoders
• Density-functional theory for the pairing Hamiltonian
• Cluster model of 12C in density functional theory framework
• A first step in the nuclear inverse Kohn-Sham problem: from densities to potentials
• Calibration of Energy Density Functionals with Deformed Nuclei
• Contradicting effective mass scalings within the Skyrme energy density functional method
• Pairing properties of superheavy nuclei
• Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT
• Nuclear Energy Density Functionals Constrained by Low-Energy QCD
• Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N${}^2$LO
• Visualization of nuclear many-body correlations with the most probable configuration of nucleons
• Nucleon localization function in rotating nuclei
• Statistical learnability of nuclear masses
• Energy-weighted sum rule for nuclear density functional theory
• Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange
• Nuclear structure far from stability
• Local alpha-removal strength in the mean-field approximation
• Two-body weak currents in heavy nuclei
• Microscopic Description of Induced Fission
• Isospin mixing of isospin-projected Slater determinants: formalism and preliminary applications
• Triplet-odd pairing in finite nuclear systems: Even-even singly closed nuclei
• Extending pairing energy density functional using pairing rotational moments of inertia
• Precision of finite-difference representation in 3D coordinate-space Hartree-Fock-Bogoliubov calculations
• Landau parameters for energy density functionals generated by local finite-range pseudopotentials
• Multipole responses in fissioning nuclei and their uncertainties
• A Bayesian Analysis of Nuclear Deformation Properties with Skyrme Energy Functionals
• Shape polarization in the tin isotopes near $N=60$ from precision $g$-factor measurements on short-lived $11/2^{-}$ isomers
• Electromagnetic moments in the Sn-Gd region determined within nuclear DFT
• Reflection-asymmetric nuclear deformations within the Density Functional Theory
• Spatial symmetries of the local densities
• Quadrupole Strength in Isobaric Triplets
• Two-center harmonic oscillator basis for Skyrme-DFT calculations (I): formalism and Proof of Principle
• The Quest for Superheavy Nuclei: A Theoretical Perspective
• Skyrme pseudopotentials at next-to-next-to-leading order Construction of local densities and first symmetry-breaking calculations