Neutron Drip Line in the Ca Region from Bayesian Model Averaging

The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around ${}^{60}\mathrm{Ca}$ O. B. Tarasov et al. [Phys. Rev. Lett. 121, 022501 (2018)] and the experimental determination of masses for ${}^{55–57}\mathrm{Ca}$ S. Michimasa et al. [Phys. Rev. Lett. 121, 022506 (2018)] provide unique information about the binding energy surface in this region. To assess the impact of these experimental discoveries on the nuclear landscape’s extent, we use global mass models and statistical machine learning to make predictions, with quantified levels of certainty, for bound nuclides between Si and Ti. Using a Bayesian model averaging analysis based on Gaussian-process-based extrapolations we introduce the posterior probability $p_{\mathrm{ex}}$ for each nucleus to be bound to neutron emission. We find that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predict that ${}^{68}\mathrm{Ca}$ has an average posterior probability $p_{\mathrm{ex}}\approx 76\%$ to be bound to two-neutron emission while the nucleus ${}^{61}\mathrm{Ca}$ is likely to decay by emitting a neutron ($p_{\mathrm{ex}}\approx 46\%$).

Figure 1

One-neutron separation energy for ${}^{55,57}\mathrm{Ca}$ (left) and two-neutron separation energy for ${}^{56}\mathrm{Ca}$ (right) calculated with the nine global mass models with statistical correction obtained with GP trained on the AME2003 ($\mathrm{GP}+2003$) and AME2016* datasets. The recent data from Ref. [8] (RIKEN2018) and the extrapolated AME2016 values [40] are marked. The shaded regions are one-sigma error bars from Ref. [8]; error bars on theoretical results are one-sigma credible intervals computed with GP extrapolation.

Figure 2

Extrapolations of $S_{1n}$ and $S_{2n}$ for the Ca chain corrected with GP and one-sigma CIs, combined for three representative models. The solid lines show the average prediction while the shaded bands give one-sigma CIs. The insert shows the posterior probability of existence for the Ca chain. The $p_{\mathrm{ex}}=0.5$ limit is marked by a dotted line. For the Ti-chain plot, see the SM [43].

Figure 3

Posterior probability of existence of neutron-rich nuclei in the Ca region averaged over all models. Top: Uniform model averaging. Bottom: Averaging using posterior weights [Eq. (1)] constrained by the existence of ${}^{52}\mathrm{Cl}$, ${}^{53}\mathrm{Ar}$, and ${}^{49}\mathrm{S}$. The range of nuclei with experimentally known masses is marked by a yellow line. The red line marks the limit of nuclear domain that has been experimentally observed; nuclei to the right of the red line await discovery. The estimated drip line that separates the $p_{\mathrm{ex}}>0.5$ and $p_{\mathrm{ex}}<0.5$ regions is indicated by a blue line.