In 2017, the Oak Ridge Leadership Computing Facility celebrated 25 years of leadership in high-performance computing. This article is part of a series summarizing a dozen significant contributions to science enabled by OLCF resources. The full report is available here.

In 2012, an ORNL and University of Tennessee team used the Cray XK6 Jaguar supercomputer to calculate the number of isotopes allowed by the laws of physics.

The team, led by Witold Nazarewicz, applied a quantum approach known as nuclear density functional theory (DFT) to six leading models to determine that there are about 7,000 possible combinations of protons and neutrons allowed in bound nuclei with up to 120 protons.

Most of these nuclei have never been observed experimentally. Of the total, about 3,000 have been found in nature or produced in a lab. Many others are expected to be created in massive stars and violent stellar explosions.

By carrying out large-scale computations, the team provided nuclear physicists with a more detailed roadmap that marks the so-called “drip lines,” the boundaries of nuclear existence. This guide lends insight to researchers exploring exotic, weakly bound nuclei that directly impact the way elements are produced in stars. Additionally, the calculations point toward unexplored regions of the nuclear chart that may contain isotopes with properties useful in health care, material science, and nuclear power, among other applications.

The Science

An illustration of the nuclear landscape, with isotopes arranged by an increasing number of protons (up) and neutrons (right). The dark blue blocks represent stable isotopes. The lighter blue blocks are unstable isotopes that have been observed. The gray blocks are bound isotopes that have not been observed. Nuclear existence ends at the drip lines (orange clouds), where there is no longer enough binding energy to prevent the last nucleons from dripping off (floating blocks).

For each number of protons in a nucleus, there is a limit to how many neutrons are allowed. For example, a helium nucleus, which contains two protons, can hold no more than six neutrons. If another neutron is added, it will simply “drip” off. Likewise, there is a limit to the number of protons that can be added to a nucleus with a given number of neutrons. The closer the isotope is to one of the drip lines, the faster it decays into more stable forms.

Identification of the drip lines for heavier elements is based on theoretical predictions well beyond the reach of experiment and is, therefore, uncertain. Nazarewicz’s team carried out calculations based on the microscopic forces that cause neutrons and protons to cluster into nuclei to predict where exotic nuclei might exist. The calculations themselves were massive, with each set of nuclei taking about 2 hours on the 244,256-processor Jaguar system.

Applying DFT to six nuclear energy density functionals, the team found its results to be surprisingly consistent across models. By using several models, theorists were able to quantify uncertainties for the predicted drip lines for the first time, a measurement that gauges the accuracy of the predictions. The accomplishment served as one of the capstones of a 5 year multi-institutional collaboration under the DOE Office of Science’s Scientific Discovery through Advanced Computing (SciDAC) program to develop a predictive theory to determine the properties of atomic nuclei using petascale systems.

“Over the years we’ve tried to improve the models of the nucleus to include more and more knowledge and insights. We are building a nuclear model based on the best theoretical input guided by the best experimental data.” —Witek Nazarewicz, Michigan State University

The Legacy

The team’s nuclear landscape study represented a milestone in the nuclear physics community with regard to both its scale and its scope. Since 2012, other groups have followed in the Nazarewicz team’s footsteps, producing similar findings. Additionally, the team pioneered the practice in nuclear physics of providing theoretical predictions with an estimated error range, an idea that is becoming standard in the field.

As more powerful particle accelerators come online, the simulation results will continue to guide scientists’ efforts to confirm the existence of exotic isotopes through experiment. This coupling hastens the discovery process and could lead to new “designer nuclei” with advantageous properties for humans. Examples of such nuclei existing today include terbium-149, which has shown an ability to attach to antibodies and irradiate cancer cells without affecting healthy cells, and radium-225, which could help scientists understand why there is more matter than antimatter in the universe.

Related Publication: Erler, J., et al. (2012), The Limits of the Nuclear Landscape, Nature. Volume: 486, no. 7404.