$\beta$-decay study within multireference density functional theory and beyond

A pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multireference density functional theory is presented. After a successful test performed for ${}^6\mathrm{He}\to {}^6\mathrm{Li}\beta$ 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 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 the axial-vector coupling constant.

Figure 1

GT ME for $\beta$ decay of ${}^6\mathrm{He}$ as a function of a number of configurations taken in the NCCI calculations in ${}^6\mathrm{Li}$ and ${}^6\mathrm{He}$. Solid line shows the experimental value of Ref. [25].

Figure 2

Theoretical binding energies of $T=1/2$ mirror nuclei calculated using the NCCI framework. The results are shown relative to the experimental data.

Figure 3

Excitation energies of the lowest $3/2^{+}$ and $5/2^{+}$ states in $sd$-shell $T=1/2$, $T_z=1/2$ nuclei ranging from $A=19$ to 33. The calculated (experimental) levels are marked by thick solid (dashed) lines. The calculated states come from MR-DFT. Theoretical energies have been normalized to the experimental ground states.

Figure 4

Gamow-Teller matrix elements calculated using the MR-DFT (triangles) and NCCI (diamonds) approaches in comparison with experimental data (dots) taken from Ref. [3] ($sd$ shell) and Refs. [4, 27] ($pf$ shell).

Figure 5

GT MEs calculated using the NCCI model (triangles) in comparison to the NSM results of Ref. [3] ($sd$ shell) and Refs. [4, 27] ($pf$ shell).

Figure 6

Ikeda sum rule for the GS of ${}^{39}\mathrm{Ca}$. Thick horizontal lines indicate the theoretical (solid) and experimental (dashed) total BEs of the GS in ${}^{39}\mathrm{Ca}$ and the lowest $1/2^{+}$, $3/2^{+}$, and $5/2^{+}$ states in ${}^{39}\mathrm{K}$. The numbers over the arrows indicate the total calculated GT strength for each $I$. Multiple arrows and shadowing indicate that the strength is distributed over several states.