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It Takes Three to Tango

An accurate picture of the carbon14 nucleus must consider the interactions among protons and neutrons both in pairs (known as the twobody force, left) and in threes (known as the threebody force, right). 
OAK RIDGE, Tenn.,
July 12, 2011
—
The nucleus of an atom, like most everything else, is more complicated than we first thought. Just how much more complicated is the subject of a Petascale Early Science project led by Oak Ridge National Laboratory's David Dean.
According to findings outlined by Dean and his colleagues in the May 20, 2011, edition of the journal Physical Review Letters, researchers who want to understand how and why a nucleus hangs together as it does and disintegrates when and how it does have a very tough job ahead of them.
Specifically, they must take into account the complex nuclear interactions known as the threebody force.
Nuclear theory to this point has assumed that the twobody force is sufficient to explain the workings of a nucleus. In other words, the halflife or decay path of an unstable nucleus was to be understood through the combined interactions of pairs of protons and neutrons within.
Dean's team, however, determined that the twobody force is not enough; researchers must also tackle the far more difficult challenge of calculating combinations of three particles at a time (three protons, three neutrons, or two of one and one of the other). This approach yields results that are both different from and more accurate than those of the twobody force.
Nuclei are held together by the strong force, one of four basic forces that govern the universe. (The other three are gravity, which holds planets, solar systems, and galaxies together and pins us to the ground, the electromagnetic force, which holds matter together and keeps us from, for instance, falling through the ground, and the weak force, which drives nuclear decay.)
The strong force acts primarily to combine elementary particles known as quarks into protons and neutrons through the exchange of force carriers known as gluons. Each proton or neutron has three quarks. The strong force also holds neighboring protons and neutrons together into a nucleus.
It does so imperfectly, however. Many nuclei are unstable and will eventually decay, emitting one or more particles and becoming a smaller nucleus. While we cannot say specifically when an individual nucleus will decay, we can determine the likelihood it will do so within a certain time. Thus an isotope's halflife is the time it takes half the nuclei in a sample to decay. Known halflives range from an absurdly small fraction of a second for beryllium8 to more than 2 trillion trillion years for tellurium128.
One job of nuclear theory, then, is to determine why nuclei have different halflives and predict what those halflives are.
"For a long time, nuclear theory assumed that twobody forces were the most important and that higherbody forces were negligible," noted team member and ORNL computational physicist Hai Ah Nam. "You have to start with an assumption: How to capture the physics best with the least complexity?"
Two factors complicate the choice of approaches. First, twobody interactions do accurately describe some nuclei. Second, accurate calculations including threebody forces are very difficult and demand stateoftheart supercomputers such as ORNL's Jaguar, the most powerful system in the United States. With the ability to churn through as many as 2.33 thousand trillion calculations each second, or 2.33 petaflops, Jaguar gave the team the computing muscle it needed to analyze the carbon14 nucleus using the threebody force.
Carbon14, with six protons and eight neutrons, is the isotope behind carbon dating, allowing researchers to determine the age of plant or animalbased relics going back as far as 60,000 years. It was an ideal choice for this project because studies using only twobody forces dramatically underestimate the isotope's halflife, which is around 5,700 years.
"With Jaguar we are able to do ab initio calculations, using threebody forces, of the halflife for carbon14," Nam said. "It's an observable that is sensitive to the threebody force. This is the first time that we've demonstrated at this large scale how the threebody force contributes."
The threebody force does not replace the twobody force in these calculations, she noted; rather, the two approaches are combined to present a more refined picture of the structure of the nucleus. In the carbon14 calculation, the threebody force serves to correct a serious underestimation of the isotope's halflife produced by the twobody force alone.
Dean and his colleagues used an application known as Many Fermion Dynamics, nuclear, or MFDn, which was created by team member James Vary of Iowa State University. With it, they tackled the carbon14 nucleus using an approach known as the nuclear shell model and performing ab initio calculationsâ€”or calculations based on the fundamental forces between protons and neutrons.
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 protons and neutrons 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, some nucleons bump up to the next higher energy level, and so on. The force between nucleons complicates this picture and creates an enormous computational problem to solve.
The carbon14 calculation, for instance, involved a billionbybillion matrix containing a quintillion values. Fortunately, most of those values are zero, leaving about 30 trillion nonzero values to then be multiplied by a billion vector values. As Nam noted, just keeping the problem straight is a phenomenally complex task, even before the calculation is performed; those 30 trillion matrix elements take up 240 terabytes of memory.
"Jaguar is the only system in the world with the capability to store that much information for a single calculation," Nam said. "This is a huge, memoryintensive calculation."
The job is even more daunting with larger nuclei, and researchers will have a long wait for supercomputers powerful enough to compute the nature of the largest nuclei using the threebody force. Even so, if the threebody force gives more accurate results than the twobody force, should researchers be looking at four, five, or more nucleons at a time?
"Higherbody forces are still under investigation, but it will require more computational resources than we currently have available," Nam said.
