• Number 397  |
• September 16, 2013

Protons and neutrons get social in the nucleus

When you post a joke, picture or link on Facebook, you have the option of sharing not only with your friends, but also with their friends, or "friends of friends." It turns out that something similar occurs inside the nucleus of the atom. 

A new, robust calculation shows that "friends of friends" sharing by protons and neutrons in the carbon nucleus plays a significant role in its structure. Carbon is an essential ingredient for all life on Earth, as well as the sixth most abundant element in the universe. Its nuclei are among the most popular with physicists, who are studying them to unlock the secrets of the sub-atomic world. 

At DOE's Jefferson Lab, scientists bombard carbon nuclei with electrons in experiments to probe protons and neutrons and how they combine to form the nucleus. The data from these experiments are then compared to theoretical models that have been developed by theorists. The models are based on theoretical insights into the nature of nuclear interactions and on inputs from decades of experiments on proton and neutrons – collectively called nucleons – and how they interact.

With six protons and six neutrons, the carbon 12 nucleus has recently become something of a Goldilocks nucleus for physicists to study. It's neither so small that its structure fits neatly into the theoretical models of how nuclei are put together, nor so large that more complicated models for describing its structure are too complex to calculate.

Rocco Schiavilla, a theorist who holds a joint appointment at Jefferson Lab and Old Dominion University, recently worked with his colleagues to perform the most detailed theory calculation yet of the structure of the carbon nucleus. The result was recently published in Physical Review Letters.

"These calculations are very computationally intensive, so we have to use a big computer. It was a collaborative effort," he says. 

He and his colleagues performed the calculations on the world's fifth-most-powerful computer, Argonne National Laboratory's IBM BlueGene/Q (Mira). The calculations required the compute power of Mira, because they are the first to take into account this concept of "friends of friends" sharing.

In calculating the structure of the carbon nucleus, one of the things that theorists were really trying to calculate is the so-called binding energy. The binding energy is a measure of how strongly the nucleons are interacting. It's generated by the forces that hold the nucleons together. 

In the past, theorists were only capable of calculating the binding energy of carbon by simplifying their calculations somewhat. For instance, they'd limit the calculations related to how a single nucleon in a nucleus interacts with a so-called mean field generated by all the other nucleons, in a type of model called a shell model. But in the carbon nucleus, tightly packed with 12 nucleons, such calculations simply don't describe the nucleus very well.

"As a matter of fact, if you want to reproduce the empirical binding energy of a nucleus, you need two-nucleon and three-nucleon interactions. With just two nucleon potentials only, you get less binding than is observed," Schiavilla explains. 

The new calculation is the first to take into account a nucleon's interactions with multiple other nucleons in the nucleus at a time - a concept that can be thought of as "friends of friends" sharing. When compared to the actual binding energy of carbon-12, which has been experimentally measured, the new calculation was spot on.

"It turns out, these two- and three-body forces reproduce verywell the binding energy of carbon 12, and in fact, all nuclei in between,from helium 3 to boron 10," Schiavilla says.

Another aspect of the new calculation involves how the nucleus responds to electromagnetic fields. As mentioned earlier, Jefferson Lab uses its Continuous Electron Beam Accelerator Facility to hurl electrons at atomic nuclei. Most of the electrons will pass on through the atom, completely missing the nucleus at its heart. But sometimes, the electrons will come close enough to the positively charged nucleus to interact with it via the electromagnetic force. 

These experiments can have two outcomes: either they leave the nucleus intact, yielding the nucleus' form factor, which is related to its size and the distribution of the protons inside it; or they smash the nucleus into pieces, yielding a measurements of its "inelastic response." 

The theorists found that for these quantities, too, "friends of friends" sharing was a very important factor. They found that while the electron probe often interacts with just one nucleon in the nucleus, it can also interact with multiple nucleons.

Or, as Schiavilla puts it, "If you want to describe in a quantitative way the response of a nucleus to electromagnetic probes, you need to include not just the coupling of this probe to single nucleons, but also to pairs of nucleons."

In fact, the "friends of friends" sharing aspect of the calculation accounted for as much as half of the inelastic response. And, for the first time, the total response that was calculated by the theorists matched that obtained in experiments.

"It gives us the confidence that we have an understanding of the structure of carbon 12 and of the dynamics of the nucleons inside it," he says. 

Now, Schiavilla and his colleagues have turned their attention to other facets of their calculations. It turns out that the calculation may clear up a mystery in another realm of subatomic physics. Neutrinos are ghostly particles that are produced as a byproduct of the nuclear fusion that powers the sun. They are ghostly particles that can float through stars and planets relatively unhindered. Experimenters studying neutrinos directed a beam of the particles at carbon nuclei. The result had seemed to indicate that the carbon nucleus was more responsive to neutrinos than theorists' calculations predicted.

According to Schiavilla, once this new calculation is taken into account, that discrepancy might largely disappear. He and his colleagues will soon complete a study of the response of the carbon 12 nucleus to the weak force, its so-called weak interaction, which is being probed in the aforementioned neutrino experiment.

The research was conducted by scientists at three DOE National Labs: Jefferson Lab, Argonne National Laboratory and Los Alamos National Laboratory; and two universities: Middle Tennessee State University and Old Dominion University. You can learn more about the computational resources at the Energy Department's National Labs in the Supercomputers: Extreme Computing at the National Labs blog.

Submitted by DOE’s Thomas Jefferson Accelerator Facility