β-decay study within multireference density functional theory and beyond

Abstract

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 ...

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

“…The flagship example concerns physical origin of the quenching effect of the weak axial coupling constant [for free-neutron decay g A = −1.2701 (25)], a subject of intense discussion since the first Gamow-Teller (GT) β-decay calculations were performed. The DFT-NCCI calculations in T = 1/2 mirror nuclei [8] somewhat contradict the statement that the quenching has its roots in a model space, and therefore support the two-body current based explanation, put forward in Refs. [13,14]; see also [15][16][17][18].…”

“…and 8 Li, 2 + g.s. β decays, paying special attention to the physical interpretation of particular peaks.…”

“…In this section we will investigate the structure and β-decay properties of very light nuclei 8 Be, 8 Li, and 8 He by using the DFT-NCCI framework. The p-shell nuclei offer an excellent playground to test, in particular, a configurationspace dependence of our scheme.…”

“…[8,35]. In order to account for β-decay strength distribution, the MR-DFT concept needs to be extended by including the states (1) projected from many Slater determinants ϕ j corresponding to different (multi)particle-(multi)hole excitations.…”

“…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].…”