Isospin Mixing Within the Symmetry Restored Density Functional Theory and Beyond

Abstract

We present results of systematic calculations of the isospin-symmetrybreaking corrections to the superallowed I=0 + , T =1 → I=0 + , T =1 βdecays, 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-independencebreaking studies offered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.

Symmetry energy in nuclear density functional theory

“…Although at present the calculations can be realized only for the SkV EDF, the preliminary results [94] are encouraging, as shown in fig. 8.…”

Beta-Decay Studies in N ≈ Z Nuclei Using No-Core Configuration-Interaction Model

“…The formalism, dubbed static, was specifically designed to treat rigorously the conserved rotational symmetry and, at the same time, tackle the explicit breaking of the isospin symmetry due to the Coulomb field. Recently, by allowing for mixing of states that are projected from self-consistent Slater determinants representing low-lying (multi)particle-(multi)hole excitations, we have extended the model to the so-called dynamic variant [5]. The model belongs to the class of the no core configuration-interaction approaches, with the two-body short-range (hadronic) and long-range (Coulomb) interactions treated on the same footing.…”

“…The first applications of the model to the low-lying spectra in 32 Cl and 32 S have been published in [5]. Hereafter, we focus on nuclei relevant to high-precision tests of the weak-interaction flavor-mixing sector of the Standard Model.…”

Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model

“…Bally and coworkers proposed a DFT-NCCI framework involving a Skyrme superfluid functional and applied it successfully to compute spectra and electromagnetic transition rates in 25 Mg [4]. Our group has developed a variant involving an unpaired Skyrme functional and a unique combination of angular-momentum and isospin projections and applied to calculate the spectra and β-decay rates in N ≈ Z nuclei from p-shell to medium mass nuclei around 62 Zn [5][6][7][8]. Recently, the DFT-NCCI method was applied to calculate spectra in neutron-rich 44 S and 64 Cr nuclei with the Gogny force [9,10], within the relativistic framework [11] in 54 Cr, or within the pairing-plus-quadrupole model in the magnesium chain [12].…”