# Focus: In Search of Boiling Nuclei

Phys. Rev. Focus 1, 13

A “liquid” of neutrons and protons should boil at sufficiently high temperature, but observing this proposed phase transition has been tricky. The biggest problem is finding an accurate thermometer. Three years ago the international ALADIN collaboration caused a stir by publishing a “caloric curve” that seemed to show nuclear matter reaching a constant temperature as more energy was added, just as a boiling tea kettle remains at a steady 100 degrees Celsius. In the 4 May PRL, the same group directly compares their previous thermometer with a more conventional one and finds a disagreement–but they ascribe the different temperatures to different parts of the nuclear reaction.

Many condensed matter physicists, who often describe the collective properties of ${10}^{23}$ atoms, find it incredible to apply thermodynamic concepts such as equilibrium and temperature to systems as small and short-lived as colliding nuclei. But considerable experimental and theoretical evidence supports the limited use of thermodynamics for the 394 nucleons in ALADIN’s collision of two gold nuclei, for example. Nuclear physicists hope to explore the various states (or “phase diagram”) of nuclear matter, which is bound by the strong force and fundamentally different from normal matter, which is held together by electromagnetic forces. Theorists predict the “boiling” of an infinite mass of uncharged nuclear matter, but they are less certain about a phase transition in real nuclei.

To look for the liquid/gas transition, the standard experiment involves slamming one heavy nucleus into another, which causes a compression, followed by an expansion that reduces the density to perhaps half or a third of the normal nuclear density. Like a large drop of water forced to expand, the nuclear conglomeration eventually fragments into large chunks, but not before reaching a certain degree of equilibrium, according to many in the field, and perhaps achieving “coexistence” between liquid and vapor phases. In the previous ALADIN paper, the team used a “thermometer” based on ratios of the yields of helium and lithium isotopes–hotter nuclear matter should produce more of the less-stable isotopes than cooler matter would. With increasing input energy, they found a plateau in the temperature at about 5 MeV (about $6x{10}^{10}$ K), not very far from the predicted transition temperature, but many questions have been raised about the reliability of the method.

In their latest work, the ALADIN group compared their previous thermometer with a more conventional one, the “excited state” temperature. This method relies on reconstructing the short-lived excited states of unstable light nuclei, such as ${}^{5}L\phantom{\rule{0}{0ex}}i$, and assuming they were populated according to a Boltzmann distribution. Although the two methods agree at the lowest beam energies, the team found that the isotope temperature increases, while the excited state temperature remains at a constant 5 MeV over the entire range of beam energies (50 to 200 MeV per nucleon). Their interpretation is that the known unstable excited states, which are normally measured with isolated light nuclei, form only at the surfaces of the large fragments, at a relatively late, cooler stage of the reaction. A simple “blast wave” model of a large exploding nucleus agrees roughly with the isotope method, and the authors associate that thermometer with an earlier, more central temperature of the combined nuclei, before fragmentation.

Wolfgang Trautmann, of the Institute for Heavy Ion Research (GSI) in Darmstadt, Germany, is one of the ALADIN collaborators. He admits the methods have many difficulties that require further study and that alternative explanations for the discrepancy exist. But he’s determined to push the methods as far as possible, in hopes of confirming the liquid/gas transition in nuclear matter. Betty Tsang, of Michigan State University in East Lansing, has complete confidence in the ALADIN data but believes they may be misinterpreting the isotope temperature. “As with all interesting physics,” she says, “in the beginning there’s a lot of controversy, and we don’t know who’s right yet.”

Nuclear Physics

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