From finite nuclei to the nuclear liquid drop: leptodermous expansion based on the self-consistent mean-field theory

Abstract

The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A^{-1/3} (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10^6. The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.

arXiv comment13 pages revtex4, 7 eps figures, submitted to Phys. Rev. C

References in corpus (19)

• Nuclear Ground-State Masses and Deformations
• A New Parameterization for the Lagrangian Density of Relativistic Mean Field Theory
• Shell structure of superheavy nuclei in self-consistent mean-field models
• Asymmetric Nuclear Matter from Extended Brueckner-Hartree-Fock Approach
• Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model
• Asymmetric nuclear matter:the role of the isovector scalar channel
• Shell Corrections of Superheavy Nuclei in Self-Consistent Calculations
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. II: Role of the effective mass
• Systematics of Fission Barriers in Superheavy Elements
• Relativistic Point-Coupling Models as Effective Theories of Nuclei
• Fitting theories of nuclear binding energies
• Asymmetric semi-infinite nuclear matter: surface and curvature properties in relativistic and non-relativistic models
• Vacuum Nucleon Loops and Naturalness
• Shell corrections for finite depth potentials: Particle continuum effects
• Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method
• The Skyrme Energy Functional and Naturalness
• Consequences of the center-of-mass correction in nuclear mean-field models
• Calculation of exciton densities in SMMC
• Critical densities for the Skyrme type effective interactions

Cited by in corpus (74)

• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Nuclear Energy Density Optimization
• Nuclear energy density optimization: Large deformations
• The Skyrme Interaction in finite nuclei and nuclear matter
• Error Estimates of Theoretical Models: a Guide
• The tensor part of the Skyrme energy density functional. I. Spherical nuclei
• Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei
• Symmetry Energy II: Isobaric Analog States
• Electric dipole polarizability and the neutron skin
• Symmetry Energy I: Semi-Infinite Matter
• The equation of state for dense nucleonic matter from a metamodeling. I. Foundational aspects
• The Compression-Mode Giant Resonances and Nuclear Incompressibility
• The neutron skin thickness from the measured electric dipole polarizability in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb
• Nuclear energy density optimization: Shell structure
• The TDHF Code Sky3D
• Review on the progress in nuclear fission
• Electric Dipole Polarizability in ${}^{208}$Pb: insights from the Droplet Model
• Unified treatment of sub-saturation stellar matter at zero and finite temperature
• Theory of Nuclear Fission
• Surface Symmetry Energy of Nuclear Energy Density Functionals
• Energy density functional for nuclei and neutron stars
• Electron and Nucleon Localization Functions of Oganesson: Approaching the Thomas-Fermi Limit
• Properties of the nuclear medium
• Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory: Global, Regional and Local Comparisons
• Parking-garage structures in astrophysics and biophysics
• Nuclear matter symmetry energy and the symmetry energy coefficient in the mass formula
• A Minimal Nuclear Energy Density Functional
• Neutron skin uncertainties of Skyrme energy density functionals
• Surface properties of neutron-rich exotic nuclei: A source for studying the nuclear symmetry energy
• Central depression in nucleonic densities: Trend analysis in nuclear density-functional-theory approach
• Beyond the charge radius: the information content of the fourth radial moment
• Symmetry energy in nuclear density functional theory
• Nuclear charge and neutron radii and nuclear matter: trend analysis
• Testing the density matrix expansion against ab initio calculations of trapped neutron drops
• Nucleus-nucleus potential with shell-correction contribution
• Triaxiality and shape coexistence in Germanium isotopes
• Statistical aspects of nuclear mass models
• Insights into nuclear saturation density from parity violating electron scattering
• Densities and energies of nuclei in dilute matter
• Constraining the surface properties of effective Skyrme interactions
• Lightweight self-conjugate nucleus ${}^{80}$Zr
• In-medium nuclear cluster energies within the Extended Thomas-Fermi approach
• Origin of symmetry energy in finite nuclei and density dependence of nuclear matter symmetry energy from measured alpha-decay energies
• The impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals
• Large-Scale Self-Consistent Nuclear Mass Calculations
• Sensitivity of the fusion cross section to the density dependence of the symmetry energy
• Properties of nuclear matter from macroscopic-microscopic mass formulas
• Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter
• Many-body correlations in Semiclassical Molecular Dynamics and Skyrme interaction
• Volume and surface contributions to the nuclear symmetry energy within the coherent density fluctuation model
• What can be learned from binding energy differences about nuclear structure: the example of delta V_{pn}
• Mass dependence of symmetry energy coefficients in Skyrme force
• Symmetry energy of warm nuclear systems
• Empirical information on nuclear matter fourth-order symmetry energy from an extended nuclear mass formula
• Temperature dependence of volume and surface symmetry energy coefficients of nucle
• Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions
• Estimating the relevance of predictions from nuclear mean-field models
• A Bayesian mixture model approach to quantifying the empirical nuclear saturation point
• New method for calculating shell correction
• Symmetry energy of hot nuclei in the relativistic Thomas-Fermi approximation
• Energy systematics of heavy nuclei -- mean field models in comparison
• The phonon-coupling model for Skyrme forces
• Thermal Fluctuations in Nuclear Pasta
• Compressibility and equation of state of finite nuclei
• Study of hot thermally fissile nuclei using relativistic mean field theory
• Triaxial nuclear models and the outer crust of nonaccreting cold neutron stars
• Global analysis of Skyrme forces with higher-order density dependence
• Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT
• A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach
• Occupation number-based energy functional for nuclear masses
• Skyrmion crystals stabilized by $\omega$-mesons
• Impact of choices for center-of-mass correction energy on the surface energy of Skyrme energy density functionals
• Many-body correlations in Semiclassical Molecular Dynamics and Skyrme forces for symmetric Nuclear Matter
• Impact of nuclear masses on r-process nucleosynthesis: bulk properties versus shell effects