Second and fourth moments of the charge density and neutron-skin thickness of atomic nuclei

Abstract

A method is presented to extract the neutron-skin thickness of atomic nuclei from the second and fourth moments of the electric charge distribution. We show that the value of the proton fourth moment must be independently known in order to estimate the neutron skin thickness experimentally. To overcome this problem, we propose the use of a strong linear correlation among the second and fourth moments of the proton distribution as calculated with several energy density functionals of common use. We take special care in estimating the errors associated with the different contributions to the neutron radius and show, for the first time, the analytic expressions for the spin-orbit contribution to the charge fourth moments of neutrons and protons. To reduce the uncertainty on the extraction of the neutron radius, two neighboring even-even isotopes are used. Nevertheless, the error on the fourth moment of the proton distribution, even if determined or assumed with large accuracy, dominates and prevents the present method from being applied for a sound determination of the neutron skin thickness.

arXiv comment19 pages, 3 figures, 3 tables

References in corpus (52)

• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• The Nuclear Equation of State and Neutron Star Masses
• Equation of state and neutron star properties constrained by nuclear physics and observation
• Constraints on the symmetry energy and neutron skins from experiments and theory
• Reaction Dynamics with Exotic Beams
• Accurate Determination of the Neutron Skin Thickness of ${}^{208}$Pb through Parity-Violation in Electron Scattering
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering
• Nuclear Energy Density Optimization
• Nuclear energy density optimization: Large deformations
• The maximum mass and radius of neutron stars and the nuclear symmetry energy
• Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment
• Intermediate-Energy Semileptonic Probes of the Hadronic Neutral Current
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• The Nuclear Symmetry Energy
• GW170817: constraining the nuclear matter equation of state from the neutron star tidal deformability
• Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter
• A Coherent Interpretation of the Form Factors of the Nucleon in Terms of a Pion Cloud and Constituent Quarks
• Nuclear energy density optimization: Shell structure
• Weak charge form factor and radius of 208Pb through parity violation in electron scattering
• Giant Quadrupole Resonances in 208Pb, the nuclear symmetry energy and the neutron skin thickness
• A new Skyrme interaction with improved spin-isospin properties
• Survey of nucleon electromagnetic form factors
• Neutron skins of atomic nuclei: per aspera ad astra
• Defining the Proton Radius: a Unified Treatment
• Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances
• Density dependence of the symmetry energy from neutron skin thickness in finite nuclei
• Neutron skin thickness of heavy nuclei with $\alpha$-particle correlations and the slope of the nuclear symmetry energy
• Probing the Nuclear Symmetry Energy with Heavy Ion Collisions
• Electroweak Measurements of Neutron Densities in CREX and PREX at JLab, USA
• Electromagnetic form factors of the nucleon: new fit and analysis of uncertainties
• First elastic electron scattering from ${}^{132}$Xe at the SCRIT facility
• Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): a new version of the program
• Constraining the symmetry energy with heavy-ion collisions and Bayesian analyses
• Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii
• Effect of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei
• Electromagnetic form factors of the nucleon in relativistic baryon chiral perturbation theory
• Parity-Violating Electron Scattering and the Electric and Magnetic Strange Form Factors of the Nucleon
• Beyond the charge radius: the information content of the fourth radial moment
• Impact of spin-orbit currents on the electroweak skin of neutron-rich nuclei
• Symmetry energy at supra-saturation densities via the Gravitational Waves from GW170817
• Model dependence of the neutron-skin thickness on the symmetry energy
• From the microscopic to the macroscopic world: from nucleons to neutron stars
• Neutron rich matter in the laboratory and in the heavens after GW170817
• The effect of realistic nuclear charge distributions on isotope shifts and towards the extraction of higher order nuclear radial moments
• Correlation of the neutron star crust-core properties with the slope of the symmetry energy and the lead skin thickness
• Probing Matter Radii of Neutron-Rich Nuclei by Antiproton Scattering
• Effects of the Neutron Spin-Orbit Density on Nuclear Charge Density in Relativistic Models
• Sensitivity of isotope shift to distribution of nuclear charge density
• Effects of finite nucleon size, vacuum polarization, and electromagnetic spin-orbit interaction on nuclear binding energies and radii in spherical nuclei
• Utility of antiproton-nucleus scattering for probing nuclear surface density distributions

Cited by in corpus (14)

• Charge radii in covariant density functional theory: a global view
• Prediction of Nuclear Charge Density Distribution with Feedback Neural Network
• Probing new bosons and nuclear structure with ytterbium isotope shifts
• Comparative study on charge radii and their kinks at magic numbers
• Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness
• Local variations of charge radii for nuclei with even $Z$ from 84 to 120
• Constraining the relativistic mean-field models from PREX-2 data: Effective forces revisited
• Revisiting the extraction of charge radii of ${}^{40}$Ca and ${}^{208}$Pb with muonic atom spectroscopy
• Towards accurate nuclear mass tables in covariant density functional theory
• Exploring sensitivity of charge-exchange ($p,n$) reactions to the neutron density distribution
• Impact of intrinsic electromagnetic structure on the nuclear charge radius in relativistic density functional theory
• Implication of odd-even staggering in the charge radii of calcium isotopes
• Charge symmetry breaking effects of $\omega$-${\rho }^0$ mixing in relativistic mean-field model
• Comprehensive table of calculated Huff factors