Isospin-symmetry breaking in masses of N≃Z nuclei

Abstract

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N = Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T = 1 2 doublets and T = 1 triplets, and TDEs for the T = 1 triplets. Relative strengths of the obtained isospinsymmetry-breaking terms are not consistent with the differences in the NN scattering lengths, a nn , a pp , and a np . Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.Keywords: nuclear density functional theory (DFT), energy density functional (EDF), proton-neutron mixing, isospin symmetry breaking (ISB), mirror displacement energy (MDE), triplet displacement energy (TDE) AbstractEffects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the N = Z line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the T = 1 2 doublets and T = 1 triplets, and TDEs for the T = 1 triplets. Relative strengths of the obtained isospinsymmetry-breaking terms are not consistent with the differences in the NN scattering lengths, a nn , a pp , and a np . Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.Keywords: nuclear density functional theory (DFT), energy density functional (EDF), proton-neutron mixing, isospin symmetry breaking (ISB), mirror displacement energy (MDE), triple displacement energy (TDE) This Supplemental Material explains technical aspects of the method presented in the Letter and provides numerical results that complement those

Isobaric multiplet mass equation within nuclear density functional theory

“…Small differences with respect to the values obtained in Ref. [17] are due to a slightly different dataset used now. Table 1, and all obtained results are plotted in Fig.…”

“…The goal of the present Letter is twofold: First, we extend the formalism of Ref. [17] from the leading-order (LO) zero-range class II and III interactions to the analogous next-to-leading-order (NLO) terms. We show that the agreement with data improves, correcting for the deficiencies of the LO ISB DFT approach identified in [17].…”

“…[17] from the leading-order (LO) zero-range class II and III interactions to the analogous next-to-leading-order (NLO) terms. We show that the agreement with data improves, correcting for the deficiencies of the LO ISB DFT approach identified in [17]. Second, we compare our DFT results with those obtained [20,21] using an ab initio Green Function Monte Carlo (GFMC) approach.…”

“…are the isotensor and isovector operators. Similarly as at LO [17], the spin-exchange terms are redundant and could be omitted. The NLO extension brings to the formalism four additional adjustable low-energy coupling constants (LECs): t II 1 , t II 2 , t III 1 , and t III 2 .…”

“…Then, the difference of BICs ‡ In this Letter, we corrected a numerical error of estimating statistical uncertainties that was present in Ref. [17]. (circles) functionals, in comparison with experimental data (squares) [24,25].…”