Argonne National Laboratory

Mysteries of the nuclear landscape

By Eleanor TaylorSeptember 1, 2010

Approximately 3,000 nuclei are already known, and twice as many could, in principle, still be discovered experimentally. Providing a comprehensive and unified description of all these nuclei is the goal of the Department of Energy-funded Scientific Discovery through Advanced Computing (SciDAC-2) project, “Low-Energy Nuclear Physics National HPC Initiative: Building a Universal Nuclear Energy Density Functional” (UNEDF).

Energy density functional theory (DFT) has been applied successfully in other fields, such as chemistry, and is one of the main tools now used for studying complex nuclei. But searching for optimal DFT parameters is computationally expensive. For example, each simulation of a single nucleus at a particular parameter set can consume up to 0.3 CPU-hours. Hence, improving the efficiency of this optimization is a key step to the eventual goal of optimization across the entire nuclear table.

To this end, a team of applied mathematicians in Argonne’s Mathematics and Computer Science division recently added to their computer code POUNDERS (Practical Optimization Using No DERivatives for Sums of squares) the ability to restrict the search space to finite ranges for some of the parameters. The results have been excellent.

“We’ve obtained good fits to diverse data on 72 nuclei in much shorter times than with traditional approaches,” said Stefan Wild, an Argonne Director’s Postdoctoral Fellow and leader of the UNEDF optimization team at Argonne. “And the POUNDERS algorithm has also proved significantly better than standard optimization methods in terms of reliability, accuracy, and precision,” he said.

The Argonne team is also developing sensitivity analysis procedures for quantifying the uncertainty due to the data, model, and underlying parameters. With these new procedures, the researchers have successfully computed 11-dimensional correlations using 5,616 cores of the Cray supercomputer Franklin at the National Energy Research Scientific Computing Center — in the same wall-time as a single nucleus simulation.

Moreover, the approach can use even more cores as the number of nuclei and parameters grows.

With collaborators at the University of Tennessee, Oak Ridge National Laboratory, Warsaw University, and the Bulgarian Academy of Sciences, the Argonne researchers have tested their optimization and sensitivity analysis methods on other EDF fitting problems. The results are in good agreement with experimental masses, radii, and deformations and appear to be free of finite-size instabilities.

Optimization has become a central part of the UNEDF effort and continues to provide valuable insights into next-generation functionals. “Our tests have revealed the need to incorporate richer sets of observables — pairing and excited states, for example — in order to obtain EDF parameterizations expected to apply to nuclei across the mass table,” said Wild.

The research is reported in the August 2010 issue of Physical Review C, 82, no. 2.