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.

19 pages, 3 figures, 3 tables

References in corpus (14)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Accurate Determination of the Neutron Skin Thickness of ${}^{208}$Pb through Parity-Violation in Electron Scattering
• Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Giant Quadrupole Resonances in 208Pb, the nuclear symmetry energy and the neutron skin thickness
• A new Skyrme interaction with improved spin-isospin properties
• Defining the Proton Radius: a Unified Treatment
• Neutron skin thickness of heavy nuclei with $\alpha$-particle correlations and the slope of the nuclear symmetry energy
• Electromagnetic form factors of the nucleon: new fit and analysis of uncertainties
• Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii
• 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
• Neutron rich matter in the laboratory and in the heavens after GW170817
• Utility of antiproton-nucleus scattering for probing nuclear surface density distributions

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• 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