Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the protondrip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protonsfrom escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of protonemitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear densityfunctional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two- protonseparation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two- proton decaystudies have been identified. The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantificationof theoretical predictions.