Nuclear Physics II

The Phases of Nuclear Matter

A liquid-to-gas transition is what we observe every day when we boil water. The average distance between water molecules is of the order of 0.1 nm as a result of an attractive interaction at large distances and a strong repulsion at short distances. The underlying potential is shown in as a function of the distance (see Figure).

When we heat water by transferring energy to its molecules the temperature increases until we reach 100 °C. At this point the temperature stays constant although we keep transferring energy. This energy is used to break the bonds between the water molecules; thereby water is converted to vapor. The temperature increases again only after all water has been evaporated.

The force between two nucleons in a nucleus shows a very similar dependence on the distance. The scale is however changed by 5 orders of magnitude leading to a density which is almost 15 orders of magnitude higher than that of normal matter. If one would compress the earth to nuclear matter density it would easily fit into a sphere with a radius of about 200 m; just to give you a feeling what nuclear matter density means.

Nuclei in their ground state thus behave very similar to a liquid. A liquid-to-gas transition of nuclear matter was indeed observed at GSI.

The figure shows the experimental data of the ALADIN collaboration. When one heats nuclear matter in a nuclear collision one first observes an increase of the temperature followed by a plateau-like behavior corresponding to the breaking of bonds between nucleons, i.e. one observes the evaporation of nuclear matter. Only after completion of the evaporation process the temperature rises again.

This is an excellent example how analogies between different areas of physics help to understand the underlying generic process, in this case the breaking of bonds between constituents.

Hadrons in the Nuclear Medium

Having discussed the liquid-to-gas phase transition we come to the properties of hadrons in the nuclear medium at high densities (hadrons are strongly interacting particles). Nuclear matter can be compressed in nucleus-nucleus collisions. The high energy density in the collision zone is also used to produce new particles like, e.g., positively and negatively charged kaons.

The complex evolution of a nuclear collision in space and time is described with so-called transport model calculations. There are theoretical predictions which are related to the restoration of chiral symmetry - one of the fundamental symmetries of Quantum-Chromodynamics (QCD), the theory of strong interactions - which say that the mass of particles is modified in compressed nuclear matter.

The central diagram in the Figure shows in a schematic way the predicted change of the K+ and K- mass as a function of nuclear density (density 1 corresponds to normal nuclear matter density). How can this be verified experimentally?

K+ and K- production was studied in elementary proton-proton collisions as a function of collision energy and the K- yield was always found to be at least one order of magnitude smaller than the K+ yield. In contrast, in heavy-ion collisions studied at the KAOS spectrometer at GSI the production probability for K+ and K- particles was found to be nearly the same when plotted as a function of the available energy (see plot on the right part of the Figure). Compared to the elementary reaction the K- production is thus enhanced in nucleus-nucleus collisions.

How can we understand that? If the mass of the K- meson is indeed lowered in the compressed nuclear medium, as theoretically predicted, then it takes of course less energy to produce such a K- meson and for a given available energy one can produce more of the K- particles compared to the proton-proton collision; this can explain the equal production probabilities for K+ and K- mesons in nucleus-nucleus collisions as actually confirmed in detailed calculations. This experimental result is therefore taken as evidence that the kaon masses are indeed modified in dense nuclear matter.

It is of importance for understanding fundamental features of the strong interaction but the importance of this result goes far beyond that: e.g., it has a bearing on the question how massive neutron stars can be, before collapsing to a black hole.

Transition to the Quark-Gluon-Plasma

If we further increase the temperature in nucleus-nucleus collisions, we expect - according to our present knowledge of the theory of strong interaction - that nuclear matter undergoes another phase transition to the so-called quark-gluon plasma. If one performs heavy-ion collisions at ultrarelativistic energies then energy densities in the collision zone may reach values sufficiently high that quarks and gluons are liberated forming a plasma of quasi-free moving particles.

The quasi-free quarks and gluons in the collision zone show their color charges while in the periphery of the collision the energy density is not sufficient for quark-gluon plasma formation. Here the nucleons remain intact. In the final phase of the reaction one can determine the temperature and density of the matter.

While the extracted temperatures and densities for experiments at SIS (GSI) are clearly below the phase boundary, the data are close to this boundary for nucleus- nucleus collisions at AGS (Brookhaven) and SPS (CERN). Various results obtained in SPS experiments indicate that in the initial phase of the collision the phase boundary was surpassed.

Again this observation is of utmost relevance for understanding the strong interaction, but it also provides an important contribution to our understanding of the evolution of the universe which started with the Big Bang. Ever since the universe expands and cools down from this initial phase of near infinite energy density and temperature. A few microseconds after the Big Bang the whole universe was a quark-gluon plasma until in the millisecond range quarks and gluons were confined and formed nucleons and later on nuclear matter.

In experiments one has now managed to go backward in this evolution and a detailed investigation of the questions related to the evolution of the early universe will be the research line at the relativistic heavy-ion collider RHIC and at LHC with the ALICE detector.

The close link between nuclear and particle physics and cosmology was explicitly emphasized in the exhibition 'Reise zum Urknall' in Berlin which was one of the events of the '2000 - the Year of Physics' initiative initiated by the Federal Ministry for Education and Research and the German Physical Society (see also GSI-brochure 'Journey to the Big Bang').