Symmetry Energy from Two-Nucleon Separation Energies of Pb and Ca Isotopes

Abstract

We investigate the symmetry energy in relation with the two-proton and two-neutron separation energies using different nuclear mass data. For this aim, we exploit the deformed relativistic Hartree-Bogoliubov theory in the continuum (DRHBc), FRDM2012 and AME2020 data. First, we study the two-proton and two-neutron separation energies in Pb and Ca isotopes by subtracting the contribution of Coulomb energy. They show a strong correlation with neutron number as well as with the neutron skin thickness. By taking the relative difference of both separation energies, we derive the symmetry energy from Ca and Pb isotopes. Since the nuclear surface contributes to the symmetry energy, we deduce the volume symmetry energy by subtracting the surface contribution using several mass models. The obtained symmetry energy coefficient, $a_{sym}$, is 20.0 $\sim$ 22.7 MeV for Pb isotopes and 18.7 $\sim$ 19.3 MeV for Ca isotopes from the DRHBc mass table data, while the results from other mass tables are 19.6 $\sim$ 22.1 (20.7 $\sim$ 22.3) MeV for Pb isotopes and 18.9 $\sim$ 19.0 (19.6 $\sim$ 19.7) MeV for Ca isotopes from AME2020 (FRDM2012) data. The volume contribution to the asymmetry coefficient, $a_{sym}^v$, which depends on the ratio of the surface to the volume energy coefficients, $a_s/a_v$, is also provided for each mass model. Since the ratio $a_s/a_v$ is neither determined by nuclear theory, nor by experimental data, we have investigated $a_{sym}^v$ by using the ratio $a_s/a_v$ as a free parameter, and have obtained $a_{sym}^v=$ 27.0 MeV, almost irrespective of nuclear model and isotopic chain, with the ratio $a_s/a_v$ constrained as $a_s/a_v=1.10\sim 1.13$.

References in corpus (27)

• Nuclear ground-state masses and deformations: FRDM(2012)
• New parametrization for the nuclear covariant energy density functional with point-coupling interaction
• Accurate Determination of the Neutron Skin Thickness of ${}^{208}$Pb through Parity-Violation in Electron Scattering
• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• A finite range pairing force for density functional theory in superfluid nuclei
• DIRHB -- a relativistic self-consistent mean-field framework for atomic nuclei
• Neutron halo in deformed nuclei
• Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
• Nuclear Equation of State from ground and collective excited state properties of nuclei
• The limits of the nuclear landscape explored by the relativistic continuum Hatree-Bogoliubov theory
• Spherical Relativistic Hartree theory in a Woods-Saxon basis
• Deformed relativistic Hartree Bogoliubov theory in continuum
• Nuclear landscape in covariant density functional theory
• Shrunk halo and quenched shell gap at $N=16$ in ${}^{22}$C: Inversion of $sd$ states and deformation effects
• Deformed relativistic Hartree-Bogoliubov theory in continuum with point coupling functional: examples of even-even Nd isotopes
• Quasi-free Neutron Knockout Reaction Reveals a Small $s$-orbital Component in the Borromean Nucleus ${}^{17}$B
• Pairing and rotational properties of actinides and superheavy nuclei in covariant density functional theory
• Predictive power for superheavy nuclear mass and possible stability beyond the neutron drip line in deformed relativistic Hartree-Bogoliubov theory in continuum
• Study of ground state properties of carbon isotopes with deformed relativistic Hartree-Bogoliubov theory in continuum
• Possible bound nuclei beyond the two-neutron drip line in the $50⩽Z⩽70$ region
• Nuclear symmetry energy from the Fermi-energy difference in nuclei
• Neutron drip line in the deformed relativistic Hartree-Bogoliubov theory in continuum: Oxygen to Calcium
• Shape coexistence and neutron skin thickness of Pb isotopes by the deformed relativistic Hartree-Bogoliubov theory in continuum
• Angular momentum projection in the deformed relativistic Hartree-Bogoliubov theory in continuum
• Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction
• Multipole expansion of densities in the deformed relativistic Hartree-Bogoliubov theory in continuum
• Extraction of the symmetry energy coefficients from the masses differences of isobaric nuclei

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