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). Image: Oak Ridge National Laboratory |
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 (ORNL) David Dean.
According to findings outlined by Dean and
his colleagues in 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 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 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 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 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,” notes 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 supercomputers such as ORNL’s Jaguar. 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 says. “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 notes; 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. Nam notes, 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.
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
says.