Origin of the Anomalous Long Lifetime of ${}^{14}\mathrm{C}$

We report the microscopic origins of the anomalously suppressed beta decay of ${}^{14}\mathrm{C}$ to ${}^{14}\mathrm{N}$ using the ab initio no-core shell model with the Hamiltonian from the chiral effective field theory including three-nucleon force terms. The three-nucleon force induces unexpectedly large cancellations within the $p$ shell between contributions to beta decay, which reduce the traditionally large contributions from the nucleon-nucleon interactions by an order of magnitude, leading to the long lifetime of ${}^{14}\mathrm{C}$.

Figure 1

Excitation spectrum of ${}^{14}\mathrm{N}$ obtained in the no-core shell model using chiral interactions as a function of basis space cutoff $N_{\max }$, the number that labels the columns. $(J^{\pi },T)$ values are in the legend. The center column displays the experimental spectrum for ${}^{14}\mathrm{N}$. Columns to the right are obtained with the chiral $NN$ interaction alone, while those on the left are obtained with the chiral $NN+3\mathrm{NF}$ by using $c_D=-0.2$ (solid lines) and $c_D=-2.0$ (dashed lines). The baseline is the $(1^{+},0)$ ${}^{14}\mathrm{N}$ ground state.

Figure 2

Contributions to the ${}^{14}\mathrm{C}$ beta-decay matrix element as a function of the HO shell in which they are evaluated when the nuclear structure is described by the chiral interaction. The top panel displays the contributions with (two right bars of each triplet) and without (leftmost bar of each triplet) the 3NF at $N_{\max }=8$. All contributions are summed within the shell to yield a total for that shell. The bottom panel displays the running sum of the GT contributions over the shells included in the sum. Note the order-of-magnitude suppression of the $p$-shell contributions arising from the 3NF.