Structure of $^{46,47}$Ca from the $\beta^-$ decay of $^{46,47}$K in the framework of nuclear shell model

TL;DR

This study uses nuclear shell-model calculations to analyze the energy spectra and beta decay properties of calcium isotopes $^{46,47}$Ca and potassium isotopes $^{46,47}$K, providing insights into their structure and decay characteristics.

Contribution

The paper applies the shell-model with SDPF-MU interaction to predict energy levels and beta decay properties, refining spin-parity assignments and comparing with experimental data.

Findings

Predicted spin-parities for several calcium states.

Reasonable agreement of level schemes with experiments.

Limited agreement of calculated $eta$-decay $ m log ft$ values with data.

Abstract

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.