Nuclei Go Through Phases

For the first time, scientists have staked out, in the form of a diagram, how nuclear matter goes from the liquid phase to the gas phase. Liquid-gas phase diagrams are a staple of chemistry, where they anatomize the energy frontier between, say, liquid water and water vapor. Altering the pressure or the temperature can send one back and forth across the two forms of existence.

Do the protons and neutrons sheltering together inside a nucleus act like molecules in an ordinary gas or liquid? Theorists have thought as much, but it's been hard to prove owing to the extreme finiteness of a nucleus (with perhaps 100-200 constituent protons and neutrons) compared to a macroscopic liquid (with 10²⁴ or more molecules).

In an experiment at Brookhaven 8 GeV pions are slammed into gold nuclei. What happens next can be compared to the evaporation or boiling processes in chemistry. First, some nucleons are ejected, leaving behind an agitated nucleus; it now casts off more fragments of various sizes and can be said to possess a virtual "vapor pressure."

By looking at collisions of various degrees of violence, and by counting the number and size of fragments thrown off, an equivalent nuclear "pressure" and "temperature" can be calculated for these events (see sequence of figures).

Such an experiment has been carried out at Brookhaven with the Indiana Silicon Sphere (ISiS) detector as the thermometer and pressure gauge. The ISiS scientists (Indiana/Laval/Los Alamos/Simon Fraser/Texas A&M/Maryland; contact Vic Viola, viola@indiana.edu, 812-855-6537) have collaborated with two different teams of scientists, one at LBNL (contact James Elliott, jbelliott@lbl.gov, 510-486-7962,) and one at Michigan State University (Wolfgang Bauer, bauer@pa.msu.edu, 517-353-8662) to survey, for the first time, an experimentally based Mason-Dixon line between nuclear liquid and vapor on a previously uncharted pressure-vs-temperature plot. Indeed this represents the first time an experimentally derived phase diagram has ever been made for a system of particles that wasn't held together by the electromagnetic force.

It is interesting to note that the vapor from an excited nucleus, if you take into account the sticky interactions among nucleons, behaves approximately like an ideal gas (loosely conforming to Boyle's law: PV=nRT). While the absolute scales of the nuclear and atomic forces are quite different, the shape of these two types of interactions (repulsive at very short range, attractive at longer range) are qualitatively similar.

Just to appreciate the difference in scales being compared here, take the case of a group of krypton atoms and a krypton nucleus. For the atoms, the critical temperature (boiling point) is 209 K and the critical density about 0.01 moles per cubic cm. For the nucleus, the critical temperature would be about 7 MeV, or 8*10¹⁰ K, and the critical density about .05 nucleons per cubic fermi, or 8*10¹³ moles/cm³. Finally, the experiment is germane to astrophysics since the opposite of nuclear boiling-namely nuclear condensation-is what happens during a supernova when a neutron star forms. (Two papers in Physical Review Letters for: Elliott et al. (LBNL) 28 January 2002; and Berkenbusch et al. (MSU) in the 14 Jan 2002 issue; for the ISiS experimental results see Lefort et al., Physical Review C, 1 December 2001.)