Nuclear Mass Models with Deformation Optimized and Diagnosed by Bayesian Analysis with Markov Chain Monte Carlo

Abstract

We employ a full Bayesian analysis with adaptive Metropolis-Hastings Markov chain Monte Carlo (BA-MCMC) sampling to systematically study the posterior probability distributions of the strengths of energy terms in optimized nuclear mass models of Bethe-Weizsäcker variants. Strong correlations of some energy terms for some mass models are revealed through the parameter degeneracy diagnosis. We analyze selected refined models to determine parameter degeneracies while proposing a new macroscopic-microscopic mass model, BWL, which considers quadrupole and high-multipole deformation and shell corrections. All mass models in this work are analyzed and optimized through the BA-MCMC method. Compared with 2242 precise experimental binding energies of AME2020, BWL produces a root-mean-square deviation of 759 keV, particularly improving the description of masses in the light-nuclei and actinide regions. BA-MCMC offers robust inference on parameter degeneracy while providing an optimization method for future nuclear mass models.

Accepted by Chinese Physics C on 7 Sep 2026 with minor revision, finalized version, 24 pages, 7 main figures (colorblind-friendly colors), 12 tables, data availability: this https URL{https://zenodo.org/records/21988436}