Nuclei by the numbers

Interactions between the neutrons and protons, quarks and gluons that make up what we see might answer some of nature’s biggest questions: How do subatomic particles make the matter that forms our universe? How does matter organize itself based on interactions between these particles? Do we fully understand how these particles interact?

These questions drive the work of Gaute Hagen, a researcher in the Physics Division at Oak Ridge National Laboratory. Approaching such fundamental concepts – which literally lie at the heart of everything around us – relies on a trio of disciplines: nuclear physics, applied mathematics and computational science.

Although Hagen calls himself a good mix of those components, his team also includes experts in each field. This diverse group is out to tackle what he describes as “trying to build the nucleus from scratch, and trying to understand how the nucleons – protons and neutrons – interact with each other” to do so.

In particular, Hagen wants to understand properties of medium-mass matter, such as elements with a mass number of 40 to 60, especially when there’s a sizeable excess of neutrons. Some of these nuclei lie at the edges of the nuclear chart that defines the limits of matter as we know it. “What are the properties of neutron-rich matter created in, say, a supernova explosion?” Hagen asks.

The stability of the nucleus largely determines which matter survives. Some numbers of nucleons – two, eight, 20 and others – bond more strongly than others. Under the nuclear shell model, these are so-called magic numbers of protons or neutrons that fill particular energy levels. For example, the calcium in our bones consists of 20 protons and 20 neutrons, making up a mass number of 40. Both hit a magic number, which makes this nucleus doubly magic. But what about unbalanced calcium isotopes at the edges of the nuclear chart? Do these isotopes follow nuclear shell model rules?

‘Better algorithms and more computing power are really driving this work.’

By solving a knotty quantum mechanical many-body problem, Hagen’s team computed the characteristics of Ca-54, with a nucleus comprised of 20 protons and 34 neutrons. The computational results, published in Physical Review Letters in 2012, revealed that this isotope is not as magic as its cousins Ca-40 or Ca-48.

Later, experiments at Japan’s RIKEN research institute confirmed Hagen’s Ca-54 findings. “The results fell right on top of our predictions,” Hagen says. “This illustrates the value of providing accurate calculations.” Such computational results can be used as input to experiments, to suggest specific experiments or to help explain empirical findings.

To create these atomic structures from scratch, Hagen turns to NUCLEI: the Nuclear Computational Low Energy Initiative. Hagen and other scientists working on this SciDAC (for Scientific Discovery through Advanced Computing) project hope to expand our knowledge of neutron-rich matter beyond Ca-54. Understanding such exotic nucleonic matter could further our comprehension of things like neutron stars, for example, Hagen says. In addition, “NUCLEI is essentially making a third leg of nuclear physics, by adding a computational side to theory and experiment.”

As an illustration, Hagen cites a 2014 DOE Office of Science highlight describing some of his research on nuclear forces. In this work, Hagen and his colleagues explain some of the interactions between nucleons and how that knowledge affects complex calculations of nuclei. “We showed that the role of the so-called three-nucleon force could be more complicated than previously thought.” For example, Hagen and his colleagues used this new information to calculate the masses of oxygen isotopes. The results produced much more accurate numbers, compared to experimentally measured masses, than previous theories.

“Better algorithms and more computing power are really driving this work,” Hagen says. “It also requires us to be able to understand the physical problems and put the codes on the supercomputers.” The algorithms behind Hagen’s work require complex programming, and the task grows even more complicated when trying to optimize that code across hundreds of thousands of processors. “It’s not trivial to figure out how to make the code efficient.”

For the most part, Hagen runs his simulations on Oak Ridge’s Titan supercomputer, a Cray XK7 consisting of 299,008 computing cores accelerated with graphics processing units (GPUs). The Office of Science’s INCITE (Innovative and Novel Computational Impact on Theory and Experiment) program provides the project with about 100 million CPU hours per year on Titan, but that’s devoured faster than someone might expect. A full simulation of Ca-54, for example, uses about 1 million CPU hours. The data generated include the energy of the atom’s ground and excited states, the density distribution of the charge and more.

By combining Hagen’s inherent curiosity about the universe’s fundamental features with high-performance computers, advanced applied mathematics and computer programming, scientists can start to unravel the forces and structures that turn subatomic particles into the matter that forms elements.

That knowledge can help us understand anything from a desk holding a computer to an exploding star hundreds of light years away.