Neutron Drip Line in the Ca Region from Bayesian Model Averaging

Abstract

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 Ca [1] and the experimental determination of masses for 55−57 Ca [2] 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 Gaussianprocess-based extrapolations we introduce the posterior probability pex 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 Ca has an average posterior probability pex ≈ 76% to be bound to two-neutron emission while the nucleus 61 Ca is likely to decay by emitting a neutron (pex ≈ 46%).

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].…”

“…For prediction purposes, we use the full mass dataset for training -the performance of the statistical model was assessed in previous work [26,30,31] -and carry out calculations based on a large set of nuclei for which raw theoretical separation energies are not too negative; this includes all proton-bound nuclei. Nuclei with negative experimental separation energies, e.g., narrow groundstate proton resonances, have not been used for training.…”

“…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].…”