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Register a new userIsospin mixing within the multi-reference nuclear density functional theory and beyond - selected aspects
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W. Satula
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The results of systematic calculations of isospin-symmetry-breaking corrections to superallowed beta-decays based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT) are reviewed with an emphasis on theoretical uncertainties of the model. Extensions of the formalism towards no core shell model approach with basis cutoff scheme dictated by the self-consistent particle-hole DFT solutions will be also discussed.
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We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and charge-independence-breaking studies offered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.
Pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multi-reference density functional theory is presented. After successful test performed for 6He -> 6Li beta-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.
The conventional Skyrme interaction is generalized by adding zero-range charge-symmetry-breaking and charge-independence-breaking terms, and the corresponding energy density functional is derived. It is shown that the extended model accounts for experimental values of mirror and triplet displacement energies (MDEs and TDEs) in sd-shell isospin triplets with, on average, about 100~keV precision using only two additional adjustable coupling constants. Moreover, the model is able to reproduce, for the first time, the A=4n versus A=4n+2 staggering of the TDEs.
Within the nuclear density functional theory (DFT) we study the effect of reflection-asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver AxialHFB that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even-even isotopes of radium and thorium.
Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T=1/2 --> I,T=1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.
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