A Bayesian Analysis of Nuclear Deformation Properties with Skyrme Energy Functionals

TL;DR

This study demonstrates that Gaussian Process emulators can quantify and propagate uncertainties in Skyrme EDF-based nuclear deformation energies, enabling Bayesian inference of EDF parameters from fission observables. Focusing on $^{240}$Pu, the authors emulated the one-dimensional potential energy curve $E(q)$ across a restricted six-parameter neighborhood of the unedf1$_{ m HFB}$ functional, and used a truncated normal likelihood with MCMC to obtain posterior parameter estimates. The results show strong constraints on a couple of surface-related couplings, while others remain near priors, and reveal that calibrating only a few observables can meaningfully reshape the entire deformation-energy landscape and potentially impact predicted fission lifetimes. The work highlights both the promise and limitations of emulation for high-cost nuclear DFT calculations and points toward extending the approach to higher-dimensional collective spaces and alternative observables or matrix elements to improve predictive power.

Abstract

In spite of numerous scientific and practical applications, there is still no comprehensive theoretical description of the nuclear fission process based solely on protons, neutrons and their interactions. The most advanced simulations of fission are currently carried out within nuclear density functional theory (DFT). In spite of being fully quantum-mechanical and rooted in the theory of nuclear forces, DFT still depends on a dozen or so parameters characterizing the energy functional. Calibrating these parameters on experimental data results in uncertainties that must be quantified for applications. This task is very challenging because of the high computational cost of DFT calculations for fission. In this paper, we use Gaussian processes to build emulators of DFT models in order to quantify and propagate statistical uncertainties of theoretical predictions for a range of nuclear deformations relevant to describing the fission process.

Figures (7)

• Figure 1: Deformation energy curves in $^{240}$Pu as a function of the axial quadrupole moment $q\equiv \langle \hat{Q}_{20} \rangle$ for a training set of 60 different parametrizations of the Skyrme edf. The rectangular grid guides the eye.
• Figure 2: Leave-one-out residuals $\epsilon_{\rm GaSP} = E(q) - E_{\rm GaSP}(q)$ (in MeV) for the gasp emulator as a function of the axial quadrupole moment.
• Figure 3: Expectation value $\braket{\hat{Q}_{22}}$ (triaxial quadrupole) and $\braket{\hat{Q}_{30}}$ (axial octupole) of the multipole moments as a function of the axial quadrupole moment $q\equiv \braket{\hat{Q}_{20}}$.
• Figure 4: Centered potential energy curves with gasp predictions. Dashed lines represent the mean prediction of the gasp model, and shaded areas represent 95% credible intervals. The solid lines represent the simulated values.
• Figure 5: Boxplots overlaying violin plots for the leave-one-out prediction error for the location of the scission point, the number of protons in the heavy fragment (ZH) and the number of particles in the heavy fragment (AH)