Precision calculation of isospin-symmetry-breaking corrections to T=1/2 mirror decays using multi-reference charge-dependent density functional theory

Abstract

We present systematic study of isospin impurities (${\alpha }_{\mathrm{ISB}}$) to the wave functions of $T=1/2$, $11\le A\le 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections (${\delta }_{\mathrm{ISB}}^{\mathrm{V}}$) to their ground state vector $\beta$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of ${\alpha }_{\mathrm{ISB}}$ and ${\delta }_{\mathrm{ISB}}^{\mathrm{V}}$ as compared to the results obtained within MR-DFT that uses Coulomb interaction as the only source of ISB. This, in turn, increases a central value of the $V_{\mathrm{ud}}$ element of the CKM matrix extracted from the $T=1/2$ mirrors bringing it closer to the value obtained form the purely vector superallowed $0^{+}\to 0^{+}$ transitions. In order to compute the value of $V_{\mathrm{ud}}$, we performed precision calculation of the Fermi matrix elements in $A=19,21,35$, and 37 mirror nuclei using DFT-rooted configuration-interaction model that includes all relevant axially-deformed particle-hole configurations built upon Nilsson orbitals originating from the spherical $sd$ shell. Our calculations yield $|V_{\mathrm{ud}}|=0.9736(16)$.

arXiv comment8 pages, 6 figures

References in corpus (25)

• Quantum Monte Carlo methods for nuclear physics
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• Tests of the standard electroweak model in beta decay
• Superallowed 0+ --> 0+ nuclear beta decays: 2014 critical survey, with precise results for Vud and CKM unitarity
• New physics searches in nuclear and neutron $\beta$ decay
• Isobaric multiplet yrast energies and isospin non-conserving forces
• Determination of |Vud| from nuclear mirror transitions
• Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches
• Ft values of the T = 1/2 mirror beta transitions
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.38j): a new version of the program
• 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 mixing in nuclei within the nuclear density functional theory
• Microscopic calculations of isospin-breaking corrections to superallowed beta-decay
• Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei
• The nuclear symmetry energy and the breaking of the isospin symmetry: how do they reconcile with each other?
• Precision measurement of the $\beta$-asymmetry in spin-polarized ${}^{37}\mathrm{K}$ decay
• Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications
• No-core configuration-interaction model for the isospin- and angular-momentum-projected states
• Isospin-symmetry breaking in superallowed Fermi beta-decay due to isospin-nonconserving forces
• High-Precision Measurement of the 19Ne Half-Life and Implications for Right-Handed Weak Currents
• Isobaric Multiplet Mass Equation within nuclear Density Functional Theory
• Measurement of the half-life of the T=$\frac{1}{2}$ mirror decay of ${}^{19}$Ne and its implication on physics beyond the standard model
• Beta-decay study within multi-reference density functional theory and beyond
• Gamow-Teller response in the configuration space of DFT-rooted no-core configuration-interaction model
• Mirror energy differences in T=1/2 f7/2-shell nuclei within isospin-dependent DFT

Cited by in corpus (1)

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