Isospin-symmetry breaking in masses of $N\simeq Z$ 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 $T=\frac{1}{2}$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets. Relative strengths of the obtained isospin-symmetry-breaking terms {\em 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.

Letter 20 pages, 4 figures, Supplemental Material 11 pages, 6 figures; important bug corrected & conclusions modified; submitted to Physics Letters B

References in corpus (8)

• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): a new version of the program
• Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei
• Error analysis of nuclear mass fits
• Identification of the Lowest $T=2$, $J^{\pi =}{0}^{+}$ Isobaric Analog State in ${}^{52}$Co and Its Impact on the Understanding of $\beta$-Decay Properties of ${}^{52}$Ni
• Simple regularization scheme for multi-reference density functional theories
• High-precision mass measurements for the isobaric multiplet mass equation at A = 52
• Realistic calculations for $c$-coefficients of the isobaric mass multiplet equation in $1p0f$ shell nuclei
• Mirror and triplet displacement energies within nuclear DFT: numerical stability

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