Scientists at Lawrence Berkeley National Laboratory believe they have solved a mystery concerning atomic nuclei that's persisted for several decades. Taking a new approach to the analysis of existing experimental data, the researchers found the strongest evidence to date that atomic nuclei can be made to undergo a "phase transition" and change from a liquid to a vapor state.

"The question has been whether the nucleus can be treated as a liquid drop, for which we can generate a phase diagram showing its transition from a liquid to a vapor," says Luciano Moretto, a chemist and coleader of this study. "We've shown the answer to this question is yes."

The team that uncovered nuclear phase changes: (from left, front) Luciano Moretto and Larry Phair, (back) Dimitry Breus, Gordon Wozniak, and Jim Elliott

The findings of the study were reported in the January 14, 2002, issue of Physical Review Letters. In addition to Moretto, Berkeley Lab authors were Gordon Wozniak, the study's coleader, and James Elliott and Larry Phair, all with the Nuclear Science Division. Nine authors were also cited from the ISiS Collaboration led by Vic Viola of Indiana University.

Understanding the nature of matter requires knowing the boundary between its different phases, and how it changes from one phase to another. For example, imagine trying to understand the nature of water without knowing that under the right conditions it can be transformed into ice or steam. To understand the nature of atomic nuclei, scientists have long treated the nuclei as tiny drops of liquid, for which the physical properties and behaviors have been well-characterized.

If this "liquid drop model" is accurate, scientists believed that under the right conditions — such as in the fireballs of particle accelerator collisions — the protons and neutrons inside an atomic nucleus should behave like ordinary molecules, and the nuclei should change from liquid to vapor phases. However, until now no one has been able to demonstrate that such a transition occurs.

	Schematic diagram of the collision stages in reactions between a 5 GeV hydrogen ion and a gold nucleus: in the initial stage, heat is deposited in the nucleus, accompanied by the knockout of several fast particles. The hot nucleus then thermalizes and expands, eventually undergoing a "soft explosion," or multifragmentation. During this process, the nucleus acts like a molecule that is going from the liquid to the vapor state. (Image courtsey of Vic Viola, University of Indiana.

"One problem is that the nuclear matter inside atomic nuclei consists of only scores of neutrons and protons compared to the 10-to-the-24th molecules in a glass of ordinary liquid," says Wozniak. "Furthermore, in order to observe nuclei change from liquid to vapor, temperatures of nearly one hundred billion degrees Celsius are required. No container is available, and the vaporization must occur in vacuum."

The Berkeley Lab scientists succeeded where others before them had not, by departing the beaten nuclear science path of identifying critical components, caloric curves, and negative heat capacities.

"We borrowed from the materials scientists and treated the multiple fragments of nuclei emerging from relativistic heavy ion collisions as aggregates or clusters of molecules," says Phair.

Treating the fragments of nuclei as clusters of matter brings into play mesoscopic (intermediate scale) physics, sufficiently well understood to generate a nuclear liquid-to-vapor phase diagram. When the Berkeley Lab researchers did this, they produced a curve that matched the predictions of theoretical models.

"It was the signature we were looking for," Phair says, "a curve that describes the process by which excited nuclei undergo a liquid-to-vapor phase transition."

The Berkeley researchers worked with data from two major experiments, the ISiS (Indiana Silicon Sphere) collaboration experiments of 1997, and the EOS (Equation of State) collaboration experiments of 1990-1992. The ISiS experiments involved the multifragmentation of gold nuclei, and the EOS studies involved multifragmentation of gold, lanthanum, and krypton.

"Recent experiments have made advances towards proving that nuclei undergo a liquid-to-vapor phase transition, but these efforts suffered from incomplete knowledge of the location of the nuclear fluid in density/pressure space," says Moretto. "By taking a cluster approach to the data, measurements of the nuclear fluid's location in density/pressure space could be made. More importantly, a phase diagram of finite-charge nuclear matter could be mapped."

Says Elliott, "We analyzed both the ISiS and EOS data sets in order to survey an experimentally based Mason-Dixon line between nuclear liquid and gas on a pressure-versus-temperature plot. This represents the first experimental measurement of any phase diagram not bound together by electromagnetic forces."

With their phase diagram, the Berkeley Lab researchers say that, given the size of the fragmented nuclei and the energy that was used to fragment them, they can predict the temperatures and pressures under which the nuclei will change from the liquid to the vapor phase.

As with materials scientists, the next step for nuclear scientists will be to determine how the properties of atomic nuclei clusters compare to the properties of bulk nuclear matter.

Says Elliott, "The resemblance of the alien form of nuclear matter we mapped in our phase diagram to the ubiquitous bulk nuclear matter supported by electromagnetic forces is highly significant. It could mean that the behavior of matter is determined by its form rather than by the origin of the force that holds it together."

Additional information:

• More about nuclear phase changes in Physical Review Letters
• More about ISiS, the Indiana Silicon Sphere experiment
• More about EOS, the Equation of State collaboraton