Statistical uncertainty quantification for multireference covariant density functional theory

TL;DR

This paper develops a Bayesian framework to quantify statistical uncertainties in covariant density functional theory for nuclear matter and finite nuclei, using extensive parameter sampling and a subspace-projected approach.

Contribution

It introduces a novel Bayesian method combined with a subspace-projected approach to propagate uncertainties in covariant density functional calculations.

Findings

Low-lying states in deformed nuclei are well reproduced with uncertainty quantification.

Near spherical nuclei remain challenging to describe accurately.

The framework can be extended to include quasiparticle excitations for better results.

Abstract

We present a theoretical framework to quantify statistical uncertainties in covariant density functional theory (CDFT) for both nuclear matter and finite nuclei, based on a relativistic point-coupling energy density functional (EDF). By sampling approximately one million parameter sets, with nine parameters varied around their values in the PC-PK1 functional, we construct a probability density function for nuclear matter properties. Incorporating empirical values of nuclear matter at saturation density and those of predictions from chiral nuclear forces, and measured $B(E2)$ values of finite nuclei, we infer posterior distributions for the model parameters within a Bayesian framework. These posterior distributions are then propagated to the low-lying states of finite nuclei using the newly developed subspace-projected (SP)-CDFT approach, in which the wave functions of target EDF parameter sets are expanded in a subspace spanned by low-lying states obtained from a set of training parameterizations. We find that the observables of low-lying states in deformed nuclei $^{150}$Nd and $^{150}$Sm are well reproduced once statistical uncertainties are taken into account. In contrast, those of near spherical nuclei $^{136}$Xe and $^{136}$Ba remain difficult to describe within the present framework, a limitation that is expected to be alleviated by extending the model space to include quasiparticle excitations.