It takes three to tango: Nuclear analysis needs the three-body force

Jul 13, 2011 by Leo Williams
It takes three to tango: Nuclear analysis needs the three-body force
An accurate picture of the carbon-14 nucleus must consider the interactions among protons and neutrons both in pairs (known as the two-body force, left) and in threes (known as the three-body force, right).

(PhysOrg.com) -- 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 , 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 three-body force.

Nuclear theory to this point has assumed that the two-body force is sufficient to explain the workings of a nucleus. In other words, the half-life 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 two-body 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 two-body 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 , which holds matter together and keeps us from, for instance, falling through the ground, and the , which drives nuclear decay.)

The strong force acts primarily to combine known as quarks into protons and neutrons through the exchange of force carriers known as gluons. Each proton or neutron has three quarks. The 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 half-life is the time it takes half the nuclei in a sample to decay. Known half-lives range from an absurdly small fraction of a second for beryllium-8 to more than 2 trillion trillion years for tellurium-128.

One job of nuclear theory, then, is to determine why nuclei have different half-lives and predict what those half-lives are.

"For a long time, nuclear theory assumed that two-body forces were the most important and that higher-body 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, two-body interactions do accurately describe some nuclei. Second, accurate calculations including three-body forces are very difficult and demand state-of-the-art 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 carbon-14 nucleus using the three-body force.

Carbon-14, with six protons and eight neutrons, is the isotope behind carbon dating, allowing researchers to determine the age of plant- or animal-based relics going back as far as 60,000 years. It was an ideal choice for this project because studies using only two-body forces dramatically underestimate the isotope's half-life, which is around 5,700 years.

"With Jaguar we are able to do ab initio calculations, using three-body forces, of the half-life for carbon-14," Nam said. "It's an observable that is sensitive to the three-body force. This is the first time that we've demonstrated at this large scale how the three-body force contributes."

The three-body force does not replace the two-body 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 carbon-14 calculation, the three-body force serves to correct a serious underestimation of the isotope's half-life produced by the two-body 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 carbon-14 nucleus using an approach known as the nuclear shell model and performing ab initio calculations—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 carbon-14 calculation, for instance, involved a billion-by-billion 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, memory-intensive 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 three-body force. Even so, if the three-body force gives more accurate results than the two-body force, should researchers be looking at four, five, or more nucleons at a time?

"Higher-body forces are still under investigation, but it will require more computational resources than we currently have available," Nam said.

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User comments : 17

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Adam
5 / 5 (1) Jul 13, 2011
Ow my aching head! Trying to compute those dratted 3-body forces! No wonder three's a crowd!
gwrede
not rated yet Jul 13, 2011
Humbling news. This means that mankind will never see the day when we can precisely compute the state of a glass of milk.

I guess I needed that for reading Kurzweil and feeling that we'll conquer the Universe in no time. :-)
Jarek
1 / 5 (2) Jul 13, 2011
2 or 3 body interaction is only approximation: effective description of field dynamics with e.g. singularities like charge (of electric field, resulting in Coulomb force).
Shell models represents extremely complicated structure of nucleus through simple probability cloud - it only shows averaged situation (is thermodynamical model).
To really understand what's happening there, we need to search for its spatial structure: field configuration behind with mechanisms leading to what we effectively observe (like here: http://www.scienc...__590130 )
jscroft
1 / 5 (1) Jul 13, 2011
@qwrede: Not NO time. LOGARITHMIC time. Just hold your horses and try to keep breathing.
frajo
4 / 5 (2) Jul 13, 2011
Humbling news. This means that mankind will never see the day when we can precisely compute the state of a glass of milk.

The n-body-problem is a difficult mathematical problem, but progress is being made. Thus we cannot exclude the possibility of finding methods to get exact solutions some day in the future.
Nik_2213
3 / 5 (2) Jul 13, 2011
Uh, I can't find any hint of how much their mega-calculation improved on the 'simple' version...
hush1
1 / 5 (1) Jul 13, 2011
"You have to start with an assumption: How to capture the physics best with the least complexity?" - ORNL computational physicist Hai Ah Nam

"The n-body-problem is a difficult mathematical problem" - frajo

Well Nature has some pretty cool mathematics. I bet we are using the wrong expression or at least we haven't recognized an expression that Nature uses.
jscroft
4 / 5 (4) Jul 13, 2011
@hush1: The n-body problem is INTRINSICALLY difficult, because it involves recursive nonlinearities that generate chaotic attractors and other exotic animals. When your best model involves sensitivities to initial conditions and measurement errors down to the zillionth decimal place, you're allowed to make the distinction.
hush1
1 / 5 (1) Jul 13, 2011
@jscroft

The only known way that a top quark can decay is through the weak interaction producing a W-boson and a down-type quark (down, strange, or bottom). Because of its enormous mass, the top quark is extremely short lived with a predicted lifetime of only 5×1025 s.

To compute this decay takes longer than the process itself.
Obviously the computation model used to express this process and the process event itself differ.

Of course the n-body problem is intrinsically difficult.
Nature obviously 'computes' this differently if the n-body problem is the appropriate description of the process.

hush1
not rated yet Jul 13, 2011
typo correction:
"...5x10-25 s."
Ober
not rated yet Jul 13, 2011
I think this is why Quantum Computers are a necessity.
These little babies should be able to simulate Quantum physics by actually dong it, and allowing us to read out the results!!!

Hurry up and get these Quantum Comps going wil ya!!!!!!
Science will be revolutionised by them.
SemiNerd
not rated yet Jul 13, 2011
Uh, I can't find any hint of how much their mega-calculation improved on the 'simple' version...

They stated that a 2 body approach yielded a value widely shy of the value established by experiment. A 3 body approach gave results almost spot on. And you didn't see that the more complex calculation improved the simple one?
lomed
5 / 5 (1) Jul 14, 2011
The associated arxiv paper seems to be: http://arxiv.org/pdf/1101.5124 . As for the 2-body value of the half-life, eq. 1 in the paper gives the half-life in terms of known and calculable parameters. The value they have improved is M[SUB]GT[/SUB], they say the expected (2-body) value would be 0.275 one while the observed value (which can be obtained in their model using certain values of the adjustable parameters) is 2x10[SUP]-3[/SUP]. Assuming the latter gives exactly 5730 years and all the other constants are the same, the 2-body value would be ~111 days (~0.303 years, ~18900 times smaller).
Callippo
1 / 5 (1) Jul 16, 2011
The n-body-problem is a difficult mathematical problem, but progress is being made. Thus we cannot exclude the possibility of finding methods to get exact solutions some day in the future.
The question is, why we should attempt for it, if the particle simulations are done routinely for nearly unlimited particles already. If someone wants to find some ultimate equation for it, he shouldn't be payed for it from public taxes, because of apparent ineffectiveness of such approach from practical perspective.
ScienceLust
not rated yet Jul 17, 2011
Not sure I get it. Carbon-14 is still made of 14 red and blue balls right?
lomed
not rated yet Jul 17, 2011
Yes, that is to say, this article is not about a new experimental finding and C-14 still is made up of 6 protons and 8 neutrons. This article is saying that we can now account for the half-life of C-14 theoretically (so presumably we now understand it, and many other nuclei, better).
bbbeard
not rated yet Jul 18, 2011
The n-body problem is different from 3-body forces. In the n-body problem, there are n particles interacting via 2-body forces, that is, the potential energy has a bunch of terms V(x[i],x[j]) for i,j in 1:n. In the case of this C14 calculation, there are 14 particles interacting via both 2-body forces and 3-body forces, i.e. potentials V(x[i],x[j],x[k]).