In the present work, we report a comprehensive theoretical study of the $\log ft$ values for the allowed and forbidden $\beta^-$ decay transitions of $^{ 46}$K and $^{ 47}$K corresponding to recently available experimental data from the GRIFFIN spectrometer at TRIUMF-ISAC [Phys. Rev. C { \bf 100}, 054327 (2019); Phys. Rev. C { \bf 102}, 054314 (2020)]. We perform the nuclear shell-model calculation in $sdpf$-valence space, with the SDPF-MU interaction, to calculate low-lying energy spectra of $^{ 46,47}$K and $^{ 46,47}$Ca. For further investigation, we also calculate spectroscopic properties of $^{ 46,47}$K, $^{ 46,47}$Ca and compare the results with the experimental data. We suggest spin-parity of several levels, which were previously tentative, in both the calcium isotopes. Based on the energy and $\log ft$ values, we conclude that the state at 3.984 MeV in $^{ 46}$Ca could be either $3^{ -}$ or $2^{ +}$ and a state at 4.432 MeV might be $3^{ -}$. The spin-parity of the states at 2.875, 3.951 and 4.453 MeV are predicted to be $1/2^-$, $3/2^-$ and $1/2^-$ or $1/2^+$, respectively, in $^{ 47}$Ca. We also give the confirmation to spin-parity of 2.850, 3.889 and 4.606 MeV states for $^{ 47}$Ca. Our results of level schemes of $^{ 46,47}$K are in a reasonable agreement with the experimental data, while the agreement of calculated $\log ft$ values for the $\beta^-$ decay with the experimental data is limited.
Categories: nucl-th