As a rapidly rotating gemanium-72 nucleus gets hotter, pairing among the protons and neutrons within the nucleus tends to decrease steadily. At one critical temperature, however, the pairing spikes back up, as represented in the center illustration. This odd behavior marks a phase transition within the germanium-72 nucleus. Image: Andy Sproles, ORNL |
There’s a lot we don’t know about the atomic
nucleus, even though it was discovered a century ago this year.
We have, of course, learned much. We can get
energy by splitting the nucleus in a process known as fission or smashing
nuclei together in a process known as fusion. While we can’t say exactly when
an unstable nucleus will decay on its own—spontaneously transforming from one
isotope to another—we can say how fast a large group of nuclei will do so. In
fact, we can confidently determine the half-life of a nucleus—the time in which
50% will decay—even in cases in which that half-life is greater than the age of
the universe. The nucleus displays oddities the understanding of which will
help explain our world. One of these is the tendency of protons and neutrons
that make up the atomic nucleus—known collectively as nucleons—to bond together
in pairs.
Physicists from Oak Ridge National
Laborator, the Univ. of Tennessee, and Germany’s GSI in Darmstadt recently used
ORNL’s Jaguar supercomputer to explore the pair bonding of neutrons in one
uncommon isotope—germanium-72. In doing so they discovered that changes in
temperature and rotation take the nucleus through at least two physical phases.
Their work, which offers the first realistic description of this kind of phase
transition in an atomic nucleus, was featured in Physical Review Letters.
In our mundane lives we witness phase
transition anytime we see water chill into ice or boil into steam. Those three
states of water are the three phases, and the transitions depend on both
pressure and temperature. In the concealed quantum world of the atomic nucleus,
however, phase transitions are more subtle.
Germanium-72 has 32 protons (like all
germanium isotopes) and 40 neutrons. Those 40 neutrons pair off strongly when
the nucleus is cold and calm, but pairing weakens as you increase the
temperature or rotation. What the team discovered, however, was that the
relationship is not straightforward. When rotation is high, the pairing weakens
as temperature rises, spikes back up at one small range of temperatures, and
then weakens as temperature continues to rise. That spike indicates the
transition between phases.
“The phase transition is an outgrowth
of the pairing, the rotation, and the temperature,” noted team member Hai
Ah Nam
of ORNL. “What we saw was that at the highest rotation, there was a
critical temperature where all of a sudden pairing was favored again. That was
interesting.”
She said the discovery is exciting in part
because the phase transition is reminiscent of the change undergone by
ferromagnetic superconductors. In that case electrons in the superconducting
material pair off into Cooper pairs below a critical temperature, allowing the
material to conduct electricity without loss.
“At this temperature, pairing was
reintroduced,” Nam
said of neutrons in the germanium isotope. “It went through this phase
transition. It’s like superconducting, where you have to be a certain
temperature for the Cooper pairs to form. And that results in the
superconducting phenomenon.”
The team simulated germanium-72 on Jaguar
using a statistical technique called Shell Model Monte Carlo, pioneered at
CalTech in the 1990s by a collaboration that included team members David Dean,
now of ORNL, and Karlheinz Langanke, now of GSI. In the nuclear shell model,
protons and neutrons occupy successively higher energy levels, with a limited
number of nucleons able to occupy each level. So, for instance, two neutrons
can sit in the lowest energy level, four in the one above that, two more in the
one above that, and so on.
The computational technique looks at protons
and neutrons in each of these energy levels. To avoid having to look at every
possible configuration of the 72 nucleons—a trillion trillion configurations in
all—the technique calculates properties of the nucleus using a quantum
statistical average. This approach gives the team a highly accurate answer combined
with a known uncertainty.
Even with this sampling technique, the
calculation used 80,000 of Jaguar’s 240,000 processor cores for four hours to
study a single nucleus.
“Jaguar’s impact in solving these
calculations is tremendous,” Nam said. “Finding this same
amount of information used to take months to complete a decade ago. Now we are
able to conduct the computational research on a supercomputer in a week.”
The team plans to continue this research to
see whether the effect is present in isotopes other than germanium-72. The
researchers have also suggested a way to compare the theoretical results to
experiment. Initial results indicate that the phase transition seen in
germanium-72 may be unique.
“In continuing studies we will look at
a dozen or more medium-mass nuclei within this range to see if we can get the
same effect,” Nam
said. “Because Jaguar is such a formidable resource, we can delve in
deeper and essentially perform more ‘experiments’ in a short period of time to
gain a better understanding of the science. The speed at which we can look at a
large range of nuclei would have been impossible when David first started
this.”
One advantage of the Shell Model Monte Carlo
technique, she noted, is that it predicts consequences of the phase transition
that can be experimentally verified. In this case the amount of energy needed
to raise the temperature of the material—known as the specific heat—drops
noticeably at the critical temperature.
Nam said the team has
been contacted by experimentalists interested in verifying the result, a
daunting but doable task. Researchers have been able to examine the specific
heat of nuclei in the past, but so far no one has taken a close look at
germanium-72.
So what does it mean that at least some
nuclei go through this type of phase change? Nobody’s sure. The result is very
new, and the implications will take time to become clear.
“The competition between
superconductivity, rapid rotation, and temperature is a fascinating topic that
can be studied in diverse physical systems, including tiny atomic nuclei and
macroscopic-scale ferromagnets,” said team member Witold Nazarewicz, a
physicist at the University of Tennessee-Knoxville and Poland’s Warsaw University,
as well as scientific director of ORNL’s Holifield Radioactive Ion Beam
Facility. “We were happy to find out that our theoretical model can offer
the first realistic description of an elusive phenomenon of successive pairing
phase transitions in nuclei.”
“So what is the physical
impact of learning that germanium has a phase change? Well, phase changes are
certainly exploited in many engineering practices,” said Nam. “For
now, these results get us one step closer to understanding the atomic nucleus.”
