The Phase Diagram of Nuclear Matter

Physical systems consisting of many particles can come about in different phases, depending on conditions such as temperature or pressure: Water can be solid, fluid, or gaseous, and matter made up of atoms with magnetic moments can show spontaneous magnetisation. These different properties are represented in phase diagrams. Now, at the heart of every atom, there is an atomic nucleus built up of protons and neutrons, which again consist of quarks kept together by gluons. Thus, it is natural to ask if there is a phase diagram of nuclear matter, and how it may look like.

And indeed, there is a phase diagram of nuclear matter. Here it is, in a schematic representation, as it shows up in nearly every talk about quark matter and the quark-gluon plasma:


Source: Compressed Baryonic Matter (CBM) Experiment at the Facility for Antiproton and Ion Research (FAIR), GSI, Darmstadt, Germany.

The horizontal axis shows density (that's different from the phase diagram of water we have seen before) - to be precise, net baryon density, i.e., the density of protons and neutrons (which are both baryons) minus the density of antibaryons. Under usual conditions, there is not much antimatter around, and net baryon density is just the density of protons and neutrons. However, in more extreme conditions, for example if the temperature is sufficiently high, thermal energy may materialise in particle-antiparticle pairs, and then, it becomes important to properly distinguish baryon density and net baryon density. The scale for net baryon density is set by the density of nuclear matter in the ground state: atomic nuclei of the different atoms in the periodic system have all the same density of about 10¹⁸ kg m^-3, or 10¹⁵ times the density of water - this value corresponds to a net baryon density of 1 on the horizontal axis.

The vertical axis gives temperature, as in the phase diagram of water. However, as for density, the scale is vastly different. Via Boltzmann's constant, temperature is equivalent to energy - for example, room temperature corresponds to an energy of 1/40 electron volt (eV). In the phase diagram of nuclear matter, temperature is measured in million electron volt, or MeV - that's an enormous temperature scale: 100 MeV correspond to a temperature of about 1.2×10¹² K, or 100 000 times the temperature at the centre of the Sun. On that scale, normal nuclear matter is quite cool - it's represented by the black dot in the lower left corner of the phase diagram at density 1.

Normal nuclear matter consists of neutrons and protons, which are classified as baryons, and more generally as hadrons. In hadrons, the elementary constituents of quarks and gluons are packed together in well-defined bags, made up of three quarks for baryons, and a quark and an antiquark for mesons (the other class of particles among the hadrons). Quarks and gluons are said to be confined in hadrons. The range of density and temperature where this confined phase prevails is shown in the light shade in the lower left part of the phase diagram.

However, if temperature or density, or both, increase, confinement eventually can break down, and quarks and gluons are set free - that's the deconfinement of hadrons to the quark-gluon plasma. At the same time as becoming deconfined, the mass of quarks drops to to a few MeV, which is called the chiral transition. In the phase diagram, the quark-gluon plasma occupies the region shaded in orange.

Deconfinement at high density is believed to happen in the interior of neutron stars, where nuclear matter is compressed under the star's own weight to up to 10 times the normal nuclear density. Deconfinement by heating up nuclear matter is achieved by colliding heavy nuclei at enormous energies, for example at the Relativistic Heavy Ion Collider (RHIC), or at the planned heavy-ion program at the Large Hadron Collider LHC. The red line indicates how nuclear matter is heated up at these collisions and reaches the region of deconfinement.

At this point, it should be clear that it is not possible to explore the phase diagram of nuclear matter in the same way as it can be done with, say, water. We cannot take a chunk of nuclear matter, heat it up or compress it in a controlled way and study its properties. Instead, we have to smash together heavy nuclei, and to rely entirely on the analysis of the fragments that emerge from these collisions to reconstruct the evolution of density and temperature during the event. If deconfinement has occurred in the collision has to be deduced by circumstantial evidence - there are never free, deconfined quarks measured in the detector.

For this reason, the exact details of the phase diagram of nuclear matter are not known yet, and all qualitative features so far are deduced from the fundamental theory of nuclear matter, quantum chromodynamics (QCD). That's why the phase diagram of nuclear matter is usually also called the phase diagram of QCD. Analysing QCD on a space-time lattice using computers, current knowledge suggests that the transition from hadrons to the quark-gluon plasma is of first order at high net baryon density - meaning that there is latent heat, a surface tension, and that the transition occurs via the formation of bubbles - and has a critical point somewhere around a temperature of 150 MeV and a bit above nuclear density. This is completely analogous to the vapour line in the phase diagram of water, which separates fluid from gas and ends in the critical point. The line of the first-order transition is shown in the diagram in yellow.

As a curious consequence of the location of the critical point, when in the very early universe quarks and gluons condensed into hadrons for the first time, this transition was very smooth and gentle - it is what is called technically a cross-over. This is because in the hot early universe, a lot of antimatter was still around, and hence, the net baryon density was very close to zero. For some time it had been thought that the hadronisation transition in the early universe may be responsible for the seeds of structure formation in the universe - with the smooth transition of a cross-over, this cannot be the case.

Of course, it would be very interesting to check the predictions of QCD for the phase diagram in experiment. For example, one could try to identify signals of the first-order transition, or even better, of the critical point. At a critical point, all kinds of fluctuations grow large, and that may yield a good signal. So far, there are very few, and inconclusive data. One problem is, for example, that heavy ion collisions at RHIC are too high in energy and explore high temperatures at low net baryon density, i.e. the cross-over region of the phase diagram. However, starting in 2012, a new experiment at a collider currently under construction at the GSI in Darmstadt, Germany, will hopefully be able to find answers to this issue: The Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) will achieve higher net baryon densities at moderate temperatures, and hopefully cross the first-order transition and get close to the critical point.

So, in ten years form now, we may know a bit more details about the phase diagram of nuclear matter.

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A very general introduction to heavy ion physics and the phase diagram of QCD is given on the pages of CBM and FAIR.

For more on QCD in general, see e.g. QCD Made Simple by Frank Wilczek, Physics Today 53, August 2000, page 22. For heavy ion physics at RHIC, check out What Have We Learned From the Relativistic Heavy Ion Collider? by Thomas Ludlam and Larry McLerran, Physics Today 56, October 2003, page 48, and The First Few Microseconds by Michael Riordan and Bill Zajc, Scientific American, May 2006.

The status of the phase diagram as seen by Lattice QCD is described, e.g., in Exploring the QCD phase diagram by Owe Philipsen, arXiv:0710.1217v1.

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This post is part of our 2007 advent calendar A Plottl A Day.