J. McDonnell

Nuclear energy density optimization: Shell structure

Background: Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. Purpose: In this work, we propose a new parametrization unedf2 of the Skyrme energy density functional. Methods: The functional optimization is carried out using the pounders optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parametrization unedf1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. Results: The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting unedf2 parametrization is comparable with unedf1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous unedf parametrizations, the parameter confidence interval for unedf2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. Conclusions: unedf2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits, and significant changes to the form of the functional are needed.

Uncertainty quantification for nuclear density functional theory and information content of new measurements

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

Error analysis in nuclear density functional theory

Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the formation of elements in the universe or the mechanisms that power stars and reactors. The predictive power of the theory depends on the amount of physics embedded in the energy density functional as well as on efficient ways to determine a small number of free parameters and solve the DFT equations. In this article, we discuss the various sources of uncertainties and errors encountered in DFT and possible methods to quantify these uncertainties in a rigorous manner.

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model

Uncertainty quantification and propagation in nuclear density functional theory

\eta(\theta)

Microscopic Description of Nuclear Fission: Fission Barrier Heights of Even-Even Actinides

where

Nuclear Energy Density Optimization: UNEDF2

\theta

Third Minima in Thorium and Uranium Isotopes in a Self-Consistent Theory

denotes the uncertain, best input setting. Hence the statistical model is of the form

Quantification of Uncertainties in Nuclear Density Functional Theory

y = \eta(\theta) + \epsilon

Uncertainty Quantification for Nuclear Density Functional Theory

, where