The anomalous $^{14}$C-dating $\beta$ decay problem revisited

TL;DR

This study revisits the anomalous inhibition of $^{14}$C beta decay using shell-model calculations, revealing the key role of tensor force-induced configuration mixing and identifying limitations in realistic interactions.

Contribution

It demonstrates that the decay inhibition is mainly caused by configuration mixing induced by the tensor force, and highlights issues in realistic Hamiltonians' monopole component description.

Findings

Decay inhibition is dominated by configuration mixing of specific states.

Tensor force significantly influences the mixing effect.

Realistic calculations struggle to reproduce the inhibition due to monopole component issues.

Abstract

The anomalous inhibition of $^{14}$C-dating $\beta$ decay rate is restudied in terms of shell-model calculations in the $jj$ coupling scheme with both realistic and empirical Hamiltonians. It is seen that the accidental cancellation of the decay strength is dominated by the mixing effect of two configurations of the final state wave function, $|0p^{-2}_{1/2}>$ and $|0p_{3/2}^{-1}0p_{1/2}^{-1}>$. By decomposing the effective interactions into different tensor components, it is clearly seen that the mixing is largely induced by the tensor force. The failure of realistic calculations in reproducing the inhibition may be related to its ill description of the monopole component rather than the tensor force.