Quantified limits of the nuclear landscape

Background: The chart of the nuclides is limited by particle drip lines beyond which nuclear stability to proton or neutron emission is lost. Predicting the range of particle-bound isotopes poses an appreciable challenge for nuclear theory as it involves extreme extrapolations of nuclear masses well beyond the regions where experimental information is available. Still, quantified extrapolations are crucial for a wide variety of applications, including the modeling of stellar nucleosynthesis.

Purpose: We use microscopic nuclear global mass models, current mass data, and Bayesian methodology to provide quantified predictions of proton and neutron separation energies as well as Bayesian probabilities of existence throughout the nuclear landscape all the way to the particle drip lines.

Methods: We apply nuclear density-functional theory with several energy density functionals. We also consider two global mass models often used in astrophysical nucleosynthesis simulations. To account for uncertainties, Bayesian Gaussian processes are trained on the separation-energy residuals for each individual model, and the resulting predictions are combined via Bayesian model averaging. This framework allows to account for systematic and statistical uncertainties and propagate them to extrapolative predictions.

Results: We establish and characterize the drip-line regions where the probability that the nucleus is particle bound decreases from 1 to 0. In these regions, we provide quantified predictions for one- and two-nucleon separation energies. According to our Bayesian model averaging analysis, 7759 nuclei with $Z\le 119$ have a probability of existence $\ge 0.5$.

Conclusions: The extrapolation results obtained in this study will be put through stringent tests when new experimental information on existence and masses of exotic nuclei becomes available. In this respect, the quantified landscape of nuclear existence obtained in this study should be viewed as a dynamical prediction that will be fine-tuned when new experimental information and improved global mass models become available.

Figure 1

The quantified landscape of nuclear existence obtained in our BMA calculations. For every nucleus with $Z,N\ge 8$ and $Z\le 119$ the probability of existence $p_{\mathrm{ex}}$ (8), i.e., the probability that the nucleus is bound with respect to proton and neutron decay, is marked. The domains of nuclei which have been experimentally observed and whose separation energies have been measured (and used for training) are indicated. To provide a realistic estimate of the discovery potential with modern radioactive ion-beam facilities, the isotopes within FRIB's experimental reach are marked. The magic numbers are shown by straight (white) dashed lines, and the average line of $\beta$-stability defined as in Ref. [51] is marked by a (black) dashed line. See text for details. This figure (without the FRIB range), in PDF format, can be downloaded from Ref. [32].

Figure 2

The quantified separation energy landscape in the neutron drip-line region obtained with the BMA($n$) model averaging. The color marks the “probability of existence” $p_{\mathrm{ex}}$ of neutron-rich nuclei, i.e., the probability that these nuclei are bound with respect to neutron decay. For each proton number, $p_{\mathrm{ex}}$ is shown along the isotopic chain versus the relative neutron number $N-N_0\left(Z\right)$, where $N_0\left(Z\right)$, listed in Table 2, is the neutron number of the heaviest isotope for which an experimental one- or two-neutron separation energy value is available. The domain of nuclei that have been experimentally observed is marked by stars. To provide a realistic estimate of the discovery potential with modern radioactive ion-beam facilities, the isotopes within FRIB's experimental reach are delimited by the shadowed solid line. See text for details. This figure (without the FRIB range), in PDF format, can be downloaded from Ref. [32].

Figure 3

Posterior distributions of the number of particle-bound nuclei. The histograms show the posterior densities for each model: the peaks correspond successively to HFB-24, FRDM-2012, D1M, BCPM, SLy4, SkP, SV-min and UNEDF2, UNEDF0, UNEDF1, and $\mathrm{SkM}{}^{*}$. The lines shows the BMA posterior densities (multiplied by a constant factor 6.3 to facilitate presentation).