Novel Bayesian neural network based approach for nuclear charge radii

Abstract

Charge radius is one of the most fundamental properties of a nucleus. However, a precise description of the evolution of charge radii along an isotopic chain is highly nontrivial, as reinforced by recent experimental measurements. In this paper, we propose a novel approach which combines a three-parameter formula and a Bayesian neural network. We find that the novel approach can describe the charge radii of all $A\ge 40$ and $Z\ge 20$ nuclei with a root-mean-square deviation about 0.015 fm. In particular, the charge radii of the calcium isotopic chain are reproduced very well, including the parabolic behavior and strong odd-even staggerings. We further test the approach for the potassium isotopes and show that it can describe well the experimental data within uncertainties.

13 pages, 4 figures, to appear in Physical Review C

References in corpus (11)

• Accurate nuclear radii and binding energies from a chiral interaction
• Nuclear Charge Radii of Be-7,9,10 and the one-neutron halo nucleus Be-11
• Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
• Nuclear charge radii: Density functional theory meets Bayesian neural networks
• Probing the N = 32 shell closure below the magic proton number Z = 20: Mass measurements of the exotic isotopes 52,53K
• Laser spectroscopy of neutron-rich ${}^{207,208}$Hg isotopes: Illuminating the kink and odd-even staggering in charge radii across the $N=126$ shell closure
• Nuclear liquid-gas phase transition with machine learning
• Bayesian evaluation of charge yields of fission fragments of 239U
• The Proton Radius from Bayesian Inference
• Novel ansatz for charge radii in density functional theories
• Mean-field calculations of charge radii in ground and isomeric states of Cd isotopes

Cited by in corpus (17)

• Improved phenomenological nuclear charge radius formulae with kernel ridge regression
• Nuclear charge radius predictions by kernel ridge regression with odd-even effects
• Constraining nuclear symmetry energy with the charge radii of mirror-pair nuclei
• Decay of superheavy nuclei based on the random forest algorithm
• Global prediction of nuclear charge density distributions using deep neural network
• Calibration of nuclear charge density distribution by back-propagation neural networks
• Improved description of nuclear charge radii: Global trends beyond $N=28$ shell closure
• Constraining the Woods-Saxon potential in fusion reactions based on the neural network
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation
• Local variations of charge radii for nuclei with even $Z$ from 84 to 120
• Evolution of nuclear charge radii in copper and indium isotopes
• Potential signature of new magicity from universal aspects of nuclear charge radii
• Machine learning the deuteron: new architectures and uncertainty quantification
• Implication of shell quenching in scandium isotopes around N=20
• Predictions of charge density distributions for nuclei with $Z\ge 8$
• Bayesian model mixing with multi-reference energy density functional
• Implication of odd-even staggering in the charge radii of calcium isotopes