News & Announcements

March 5, 2012

"Finding functionals for fission"

Media Contacts: Gail Pieper, Argonne National Laboratory

Understanding of the fission process is crucial for many areas of science and technology—for example, for the deployment of safe and efficient advanced nuclear reactors. Accurately estimating the stability of a heavy nucleus against fission in its ground state is, however, a complex mathematical problem involving hundreds of strongly interacting protons and neutrons moving in a splitting nucleus. Only recently, with the advent of high-performance computers and state-of-the-art optimization techniques, have scientists begun to unlock the secrets of fission.

Under the DOE-funded Universal Nuclear Energy Density Functional (UNEDF) SciDAC collaboration, researchers have been conducting a study of nuclear fission, based on nuclear density functional theory (DFT) and its extensions. The goal is to deliver fission models capable of providing nuclear data not only of a high quality but also with quantified uncertainties.

The quality of a DFT calculation relies on the form and parameterization of an underlying energy density functional. Since the functional’s parameters cannot be derived or computed, the usual approach is to select parameters; compute observables (such as binding energy) of hundreds of nuclei; and compare the results with experimental values. The process is then repeated with a new set of parameters. The challenge is to obtain an optimal fitting with a minimal number of runs.

Researchers at Argonne National Laboratory now have successfully met this challenge. The key to their success was threefold: their new algorithm POUNDERS  (Practical Optimization Using No Derivatives (for Squares), techniques to parallelize key computational bottlenecks, and use of high-performance computing.

Building on earlier optimization results (UNEDF0), the researchers enlarged the dataset by adding ground-state masses of three deformed actinide nuclei and excitation energies of fission isomers in three nuclei. For the parameter set they also performed a sensitivity analysis, using an optimal finite-difference procedure to obtain information about the standard deviations and correlations among the parameters.

POUNDERS ran 218 simulations for each nucleus in the dataset, using 80 compute nodes on Argonne’s Laboratory Computing Resource Center cluster, for a total of 5.67 hours. The sensitivity analysis revealed the importance of states at large deformations in driving the parameterization of the functional. Good agreement was achieved with the experimental data on masses and separation energies. Moreover, the POUNDERS optimization required 10 times fewer runs than are needed with traditional methods; a similar optimization could previously have consumed a month of computations.

But the most striking feature of the new UNEDF1 functional is its ability to reproduce the empirical fission barriers in the actinide region: the quality of UNEDF1 predictions for inner and outer fission barriers is comparable to that obtained in more phenomenological models. Indeed, UNEDF1 gives a much-improved description of the fission barriers in Pu-240 and neighboring nuclei.