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

Abstract

Background: The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters 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.Purpose: 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.Methods: Separation energies were computed within nuclear density functional 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. Results:We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one-and two-proton separation 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 decay studies have been identified. Conclusions:The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions.

Quantified limits of the nuclear landscape

“…We have found in a previous study [26] that Gaussian processes overall outperform Bayesian neural networks, achieving similar rms deviations with a more faithful uncertainty quantification and considerably fewer parameters. We have also demonstrated [30,31] that the parameters θ are well constrained and fairly uncorrelated. It is worth noting that a non-zero value of the GP mean prediction µ allows to reproduce more consistently the extrapolative data.…”

“…Our methodology follows closely our previous work [26,30,31] in which we combined the current theoretical and experimental information using Bayesian simulations to arrive at informed predictions.…”

“…For each model, the mass table of even-even nuclei was computed self-consistently by solving the Hartree-Fock-Bogoliubov (HFB) equations as described in Refs. [5,26,30,31]; masses of odd-Z and odd-N systems were then extracted using computed pairing gaps [30,41].…”

“…Still, the rms mass deviations are reduced to similar values across models following statistical treatment, as demonstrated in Refs. [26,31].…”

“…In this study, we combine results of several global mass models and information contained in experimental masses to make a quantified assessment of proton and neutron separation energies and drip lines. To this end, we employ the technique of Bayesian model averaging (BMA) [27][28][29], which has recently been adopted to provide quantified predictions for both neutron-rich nuclei in the Ca region [30] and two-proton emitters [31].…”