No-core configuration-interaction model for the isospin- and angular-momentum-projected states

Abstract

[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Methods] The method is based on solving the Hill-Wheeler-Griffin equation within a model space built of linearly-dependent states having good angular momentum and properly treated isobaric spin. The states are generated by means of the isospin and angular-momentum projection applied to a set of low-lying (multi)particle-(multi)hole deformed Slater determinants calculated using the self-consistent Skyrme-Hartree-Fock approach. [Results] The theory is applied to calculate energy spectra in N~Z nuclei that are relevant from the point of view of a study of superallowed Fermi beta-decays. In particular, a new set of the isospin-symmetry-breaking corrections to these decays is given. [Conclusions] It is demonstrated that the NCCI model is capable to capture main features of low-lying energy spectra in light and medium-mass nuclei using relatively small model space and without any local readjustment of its low-energy coupling constants. Its flexibility and a range of applicability makes it an interesting alternative to the conventional nuclear shell model.

13 pages, 10 figures

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• Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei
• Dispersive formalism for the nuclear structure correction ${\delta }_{\mathrm{NS}}$ to the $\beta$ decay rate
• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Nuclear charge radius of ${}^{26m}$Al and its implication for V${}_{ud}$ in the quark-mixing matrix
• Gamow-Teller response in the configuration space of DFT-rooted no-core configuration-interaction model
• Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$
• Configuration interaction projected density functional theory: effects of four-quasiparticle configurations and time-odd interactions
• Mirror energy differences in T=1/2 f7/2-shell nuclei within isospin-dependent DFT
• Efficient computation of matrix elements of generic Slater determinants
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Precision calculation of isospin-symmetry-breaking corrections to T=1/2 mirror decays using multi-reference charge-dependent density functional theory
• The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model