FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

We describe the software package FELIX that solves the equations of the time-dependent generator coordinate method (TDGCM) in N-dimensions (N $geq$ 1) under the Gaussian overlap approximation. The numerical resolution is based on the Galerkin finite element discretization of the collective space and the Crank-Nicolson scheme for time integration. The TDGCM solver is implemented entirely in C++. Several additional tools written in C++, Python or bash scripting language are also included for convenience. In this paper, the solver is tested with a series of benchmarks calculations. We also demonstrate the ability of our code to handle a realistic calculation of fission dynamics.

Uncertainty Quantification and Propagation in Nuclear Density Functional Theory

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better root nuclear DFT in the theory of nuclear forces [see Duguet et al., this issue], energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in finite nuclei. In this paper, we review recent efforts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.

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.

Broydens Method in Nuclear Structure Calculations

Broydens method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broydens method a tool of choice for large-scale nuclear structure calculations.