Novel ansatz for charge radii in density functional theories

Abstract

Charge radii are one of the most fundamental properties of atomic nuclei characterizing their charge distributions. Though the general trend as a function of the mass number is well described by the $A^{1/3}$ rule, some fine structures, such as the evolution along the calcium isotopic chain and the corresponding odd-even staggerings, are notoriously difficult to describe both in density functional theories and ab initio methods. In this letter, we propose a novel ansatz to describe the charge radii of calcium isotopes, by adding a correction term, proportional to the number of Cooper pairs, and determined by the BCS amplitudes and a single parameter, to the charge radii calculated in the relativistic mean field model with the pairing interaction treated with the BCS method. The new ansatz yields results consistent with data not only for calcium isotopes, but also for ten other isotopic chains, including oxygen, neon, magnesium, chromium, nickel, germanium, zirconium, cadmium, tin, and lead. It is remarkable that this ansatz with a single parameter can describe nuclear charge radii throughout the periodic table, particularly the odd-even staggerings and parabolic behavior. We hope that the present study can stimulate more discussions about its nature and relation with other effects proposed to explain the odd-even staggerings of charge radii.

6 pages, 5 figures

References in corpus (5)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Surface diffuseness correction in global mass formula
• Improved nuclear matter calculations from chiral low-momentum interactions
• Accurate nuclear radii and binding energies from a chiral interaction
• Cooper pairs in atomic nuclei

Cited by in corpus (12)

• Proton distribution radii of ${}^{16-24}$O: signatures of new shell closures and neutron skin
• Improved phenomenological nuclear charge radius formulae with kernel ridge regression
• Nuclear charge radius predictions by kernel ridge regression with odd-even effects
• Constraining nuclear symmetry energy with the charge radii of mirror-pair nuclei
• Improved description of nuclear charge radii: Global trends beyond $N=28$ shell closure
• Local variations of charge radii for nuclei with even $Z$ from 84 to 120
• Charge radii of Ca isotopes and correlations
• Potential signature of new magicity from universal aspects of nuclear charge radii
• Correlation between the charge radii difference in mirror partner nuclei and the symmetry energy slope
• The charge radii of calcium isotopes within relativistic density functional theory: nucleon's finite-size and quadrupole shape fluctuation effects
• Implication of shell quenching in scandium isotopes around N=20
• Implication of odd-even staggering in the charge radii of calcium isotopes