Pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-coreconfiguration-interaction formalism rooted in multi-reference density functional theory is presented. After successful test performed for 6 He→ 6 Li β-decay, the model is applied to compute MEs in the sd-and pf -shell T =1/2 mirror nuclei. The calculated GT MEs and the isospin-symmetry-breaking corrections to the Fermi branch are found to be in a very good agreement with shell-model predictions in spite of fundamental differences between these models concerning model space, treatment of correlations or inclusion of a core. This result indirectly supports the two-body current based scenarios behind the quenching of axial-vector coupling constant.PACS numbers: 21.10. Hw, 21.60.Jz, 21.30.Fe, 23.40.Hc, 24.80.+y The atomic nuclei are unique laboratories to study fundamental processes and search for possible signals of new physics beyond the Standard Model in ways that are complementary or even superior to other sciences. This is due to enhanced sensitivity of specific isotopes to fundamental symmetries caused, in particular, by intrinsic-symmetry-related or purely accidental (near-)degeneracies of nuclear states. For example, parity doublets caused by stable octupole deformation increase sensitivity to search for the violation of CP-symmetry which is responsible for matter over anti-matter dominated Universe [1]. Accidental near-degeneracy of 3/2 + and 5/2 + levels in 229 Th, which are separated only by 7.6±0.5 eV, opens up a possibility for high-precision measurement of the temporal variation of fine-structure constant with much higher sensitivity as compared to the atomic transitions [2]. Last but not least, nuclear physics input is critical in an ongoing hunt for a weakly-interacting massive particle (WIMP), a candidate for dark matter, in direct detection experiments measuring the recoil energy deposited when WIMP is scattered off the nucleus, see [3] and refs. quoted therein.Traditionally, the atomic nuclei are used to study the weak interaction. A flagship example is the superallowed I=0 + →I=0 + β-decay among the members of the isobaric triplets T =1. With small, of order of a percent, theoretical corrections accounting for radiative processes and isospin symmetry breaking (ISB), these semileptonic pure Fermi (vector) decays allow to verify the conserved vector current (CVC) hypothesis with a very high precision. In turn, they provide the most precise values of the strength of the weak force, G F , and of the leading element, V ud , of the Cabbibo-Kobayashi-Maskawa (CKM) matrix, see [4] for a recent review.The T =1/2 mirror nuclei offer an alternative way to test the CVC hypothesis [5]. These nuclei decay via the mixed Fermi and Gamow-Teller (GT) transitions. Hence, apart from the radiative and the ISB theoretical corrections, the final values of G F and V ud depend on the ratio of statistical rate functions for the axial-vector and vector interactions, f A /f V , and the ratio of nuclear matrix elements ρ ≈ λM GT /M F where ...

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

We describe the new version (v2.73y) of the code hfodd which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between hfbtho and hfodd, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particlenumber corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.

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We extend the nuclear Density Functional Theory (DFT) by including proton-neutron mixing and contact isospin-symmetry-breaking (ISB) terms up to next-to-leading order (NLO). Within this formalism, we perform systematic study of the nuclear mirror and triple displacement energies, or equivalently of the Isobaric Multiplet Mass Equation (IMME) coefficients. By comparing results with those obtained within the existing Green Function Monte Carlo (GFMC) calculations, we address the fundamental question of the physical origin of the ISB effects. This we achieve by analyzing separate contributions to IMME coefficients coming from the electromagnetic and nuclear ISB terms. We show that the ISB DFT and GFMC results agree reasonably well, and that they describe experimental data with a comparable quality. Since the separate electromagnetic and nuclear ISB contributions also agree, we conclude that the beyond-mean-field electromagnetic effects may not play a dominant role in describing the ISB effects in finite nuclei.