National Center for Computational Sciences

Physicists explore what makes carbon-14 tick

Carbon-14 allows us to put a timeline on our unwritten history.

When, in 1994, researchers discovered the Chauvet Cave in southern France filled with Stone Age artwork, carbon-14 told them the charcoal drawings on the cave walls were 31,000 years old, more or less. Earlier, in 1988, when scientists examined the Shroud of Turin, carbon-14 analysis indicated the relic—a linen cloth believed by many to have been placed over Jesus’s body at the time of his burial—was actually created more than a millennium later, in the Middle Ages.

For the past half-century, carbon-14 has allowed scientists to date the flotsam of human history: skeletons, ruins, anything that was once part of a plant or body. By existing in all living things and decaying at a steady rate, carbon-14 gives researchers the ability to look at a long-abandoned community, tool, or other artifact and tell us how old it is. And because—for reasons not yet understood—carbon-14 decays far more slowly than most isotopes in its weight class, it allows researchers to confidently date items as far back as 60,000 years.

Now a team led by David Dean of Oak Ridge National Laboratory (ORNL) is using the unprecedented computing power of ORNL’s petascale Jaguar supercomputer to examine the carbon-14 nucleus. The team, which includes Hai Ah Nam of ORNL, James Vary and Pieter Maris of Iowa State University, and Petr Navratil and Erich Ormand of Lawrence Livermore National Laboratory, hopes to both explain carbon-14’s long half-life—about 5,700 years—and advance our understanding of what holds all nuclei together.

“Carbon-14 is interesting to us because the physics says it should decay quickly; however, the measured half-life is much longer than expected,” explained Nam, who is a physicist with ORNL’s National Center for Computational Sciences. “The theoretical models people have been using to describe light nuclei such as lithium, with six particles, or boron, which has ten, have been getting some pretty good results. But carbon-14, also a light nucleus, has been elusive, and the existing theoretical models don’t do so well at coming up with the same value as what’s measured experimentally. That means we’re not capturing all of the physics.”

Carbon-14 has three qualities that make it a boon to archeologists. First, new carbon-14 is constantly being produced. Cosmic rays bombard the atmosphere and set in motion a process that turns an occasional atom of nitrogen-14 into an atom of carbon-14. As a result about one of every trillion carbon atoms in the atmosphere is carbon-14. Second, plants use carbon dioxide in photosynthesis, exchanging carbon, including carbon-14, with the atmosphere throughout their lifetimes. Animals, including humans, participate in this process by eating plants. When a plant, animal, or human dies, however, this exchange ends. We are assumed to die with our bodies containing the same ratio of carbon-14 to total carbon atoms as the atmosphere, say one in a trillion. Third, carbon-14 decays at a constant rate. If at the time of your death, one carbon atom per trillion in your body is carbon-14, you can assume that the proportion will drop to one per two trillion after 5,730 years, one per four trillion after 11,460 years, and so on.

Carbon is carbon because its nucleus contains six protons. Carbon-14, with eight neutrons, is one of three naturally occurring carbon isotopes and the only one subject to radioactive decay, in this case through a process known as beta decay. Through beta decay carbon-14 emits a negatively charged electron and an antineutrino; at the same time an uncharged neutron becomes a positively charged proton and the atom itself goes back to being nitrogen-14.

Parsing the nuclear attraction

An isotope’s half-life, then, is the time it takes half the atoms in a sample to decay. For most light isotopes the half-life is typically minutes or even seconds, so carbon-14, with a half-life pushing 6,000 years, is an anomaly. A simulation that can make us understand why the half-life of this isotope is so long has the potential to illuminate all half-lives, long and short, and help us better understand how we and the observable matter in the universe around us are put together.

The task is especially challenging because we don’t quite know how an atom’s nucleus is held together. We know that the nucleus is made up of protons and neutrons, known generically as nucleons. We know further that these nucleons are made up of even smaller particles known as quarks and gluons, which hold together through the “strong force,” the strongest known to physics.

The tail of the strong force yields interactions among nucleons that hold the nucleus together. A holy grail of nuclear physics, then, is to theoretically describe the properties of all nuclei, stable and unstable, mundane and exotic, large and small.

Dean and his colleagues have an allocation of 30 million processor hours on Jaguar to dissect the secrets of carbon-14 with an application known as Many Fermion Dynamics, nuclear (MFDn), created by Vary at Iowa State. According to Nam, MFDn is an especially good code for this application because it scales very well. Dean’s team will be using nearly 150,000 of Jaguar’s more than 180,000 computing cores on the project (the entire XT5 partition of the machine), and the application is ready to scale to even more cores as they become available.

The team is using an approach known as the nuclear shell model to describe the nucleus. Analogous to the atomic shell model that explains how many electrons can be found at any given orbit, the nuclear shell model describes the number of nucleons that can be found at a given energy level. Generally speaking, the nucleons gather at the lowest available energy level until the addition of any more would violate the Pauli exclusion principle, which states that no two particles can be in the same quantum state. At that point nucleons occupy the next higher energy level, and so on. The force between nucleons complicates this picture and creates an enormous computational problem to solve.

Using the power of the petascale

Jaguar’s unprecedented power allows the team to depart from other nuclear structure studies in a variety of respects. For one thing the project takes a microscopic look at the nucleus, working from its smallest known constituents. Nuclear models have been moving in this direction for seven decades, from the liquid drop model of Niels Bohr, which treated the nucleus as a single drop of nuclear fluid, to models that looked at the protons and neutrons separately. Now, the team is able to go even deeper, taking an ab initio (or first principles) approach, working from the strong-force interactions of the quarks and gluons within each nucleon. In addition, Dean’s team takes a “no-core” approach that incorporates all 14 nucleons—without assuming an inert set of particles—and includes more energy levels in the model space. And lastly, the simulations go beyond two-body forces, which include the interaction of every nucleon with every other nucleon two at a time, to incorporate three-body forces.

“Previously we could only consider two-nucleon interactions because the number of combinations needed to describe all the different interactions is really big, even for only two particles at a time,” Nam explained. “And while two-particle interactions are the dominant way that these particles interact, there are some nuclear phenomena, like the half-life of carbon-14, that can’t be explained using a two-nucleon interaction only. Three-particle interactions or higher can also be at play.

“So this project is probing whether these two approaches—using the ab initio methods and the higher number of interactions—will better describe why carbon-14 has such a long half-life and in general explain how all nuclei are put together.”

Jaguar makes these calculations possible not only because it is capable of up to 1.6 thousand trillion calculations a second, making it the world’s fastest scientific supercomputer, but also because, at 362 terabytes, it has three times more memory than other system on the planet. Before the system was installed in late 2008, such a simulation of the carbon-14 nucleus working from its smallest known constituents would have been unthinkable.

“These types of calculations for carbon-14 were previously not possible because it’s a memory-intensive calculation,” explained Nam. “Accounting for the three-nucleon force amounts to storing tens of trillions of elements … that’s hundreds of terabytes of information.”

By making use of Jaguar’s power, the team hopes to push us a little closer to an understanding of the atom’s nucleus. In doing so it will make carbon-14 an even bigger star than it already is.

–by Leo Williams