Wednesday, December 05, 2007

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.

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.

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


  1. The foamy visible mass distribution of the cosmos arising from hadron critical point opalescence has a certain elegance. Computable theory, too.
    multiple reactive component example

  2. For me the lay person, it has always been important to me, that the experimental process be married with current dynamics going on within the formation of our universe. It had to make sense.

    Why I ask what value of gravity at the heart of collision processes. There is "that point" where they are all united.

    Cosmic ray collisions? Ice Cube? Neutrinos

    Where are such examples developing that we could say "that here" within this part of the universe such a formation "is the beginning" and becoming?

    So we have followed this back to the QGP state. Wonderful.

    So from a microperspective could such examples in microstate blackholes show relevance to the gravitational collapse(heat generation from decreasing spherical size) seen in the blackholes in our universe have motivation for universe expansion, to hold entropic designed products, just as particles do from.... some asymmetry breaking aspect developed from the perfect fluid???

  3. G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1).

    Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

    The universe in expression?

    "Nothing to me would be more poetic; no outcome would be more graceful ... than for us to confirm our theories of the ultramicroscopic makeup of spacetime and matter by turning our giant telescopes skyward and gazing at the stars," Brian Greene

    Even the String theorists had to turn their views to the heavens. Bring the Heavens down to earth. Now they see the landscape of the universe(gravity) in terms of the Lagrangian?

  4. Stephan

    I'm a non-scientist. Here is a my question:Can a free quark be crushed down to a smaller diameter than it normally has? Do the laws of physics allow this? Can a single quark be crushed and squeezed into a black hole? Can a quark be torn apart in a black hole or is this unknowable because the laws of physics break down at the singualrity?

    Have a nice day

  5. 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.

    Where did the antimatter disappear without annihilating the matter in the process?

  6. Hi Anonymous:

    The intersection between the quantum field theories in the standard model and general relativity that one needs to describe black holes is so far not very well understood. What you would need to know to answer your question is how to treat black holes and their formation in quantum field theory, including the strong interaction of particles. Regarding the first part of you question: one typically associates a size to objects depending on the energy at which they can be resolved. If you go to higher energies (collider) you can resolve smaller distances. Such, we were eventually able to find the proton has a substructure of three (valence) quarks. This scale at which you start seeing them isn't something that can be changed. If you were to go to higher energies (smaller distances) you would however 'see' a lot of virtual (see) quark-antiquark pairs, gluons etc. In a certain sense you might say these are 'smaller'.

    Roughly speaking I think the problem goes back to us talking about elementary 'particles' that one might imagine like a small ball, while the 'stuff' that we are made of is actually a quantum field. Does that help?


  7. Bee

    Yep, helps a bit. The idea that point particles at certain energy scales becomes a meaningless concept(not sure if your saying this) seems interesting. Thanks

  8. Feynman's Quantum Electrodynamics (QED) actually requires electrons to be point particles, a notion that has already been wrestled with since shortly after Natural Philosophy professor J.J. Thomspon discovered the electron in 1898.

    Long before one gets down to a Planck length, there should be some deviations from QED -- I think around 10^-15 cm.

    I turn now to an expert.

    F. Rohrlich, "The Theory of the Electron", 31st Joseph Henry Lecture, read before the Society 11 May 1962.

    Rohrlich (the #1 authority on the history of the theory of the electron) gives a replacement for the Dirac equation, namely an
    integro-differential equation of the 2nd order whose solutions are exactly consistent with an extension of the principle of equivalence
    to eletromagnetic systems. It avoids non-physical "run-away
    solutions" that I addressed in my paper on Higher Order Terms in
    Maxwell's Equation, and other problems.

    "This leads to an apparent contradiction with energy conservation.... Here an essentially new feature emerges, a feature which was not expected and does not fit into the concepts of classical physics of
    which this theory is part: the new equation of motion has a non-local
    behavior in time, a certain lack of instantaneity which brings with itself a lack of causality over time intervals of the order of tau_0. In particular, energy conservation is no longer satisfied at every instant of time, but is spread out over a time interval of about
    tau_0... given in terms of the electron's mass and charge as

    tau_0 = (2/3) (r_0)/c = (2/3) e/mc^3 = 6 x 10^-24 sec

    Clearly such time intervals are entirely outside the domain of
    competence of classical physics..."

    Prof. Jonathan Vos Post

  9. Nice summary. The feasibility of a search for the critical point at RHIC from AGS-SPS-RHIC energies is underway. The accelerator has already been tested down to a CMS energy of 9 GeV.

    If all goes well, the plan is to have this energy scan in 2010.

  10. Hi Oxo,

    Where did the antimatter disappear without annihilating the matter in the process?

    Well, the antimatter did annihilate the matter in the process... At the time of the hadronisation transition, the total number of quarks + antiquarks was enormously bigger than the net number of quarks (quarks - antiquarks) - sorry, I am not sure about actual numbers.

    The big problem, then, is of course, how comes that there have been some more quarks than antiquarks, so that not all matter has been annihilated. There is no conclusive answer yet to this question, which runs under the name of baryogenesis. For more about this, you may find this article helpful: The Mystery of the Matter Asymmetry by Eric Sather (PDF file).

    Best, Stefan

  11. Hi terry,

    thanks for the update about RHIC!

    I guess this is a rare case where tuning an accelerator for energies lower than originally scheduled may yield cool physics results ;-) ... and 2010 would be before FAIR...

    Best, Stefan

  12. Hi Stefan,

    It will be an interesting time at RHIC, that's for sure. Hopefully some questions will be answered, such as whether the famous peak/"horn" in the K+/pi+ ratio observed at SPS is actually there.

    From the experimental side, performing this energy scan in a collider environment with the same detectors will assist in getting a good handle on systematic errors. For example, the corrections for detector acceptance are much more straightforward in a collider than for fixed target experiments.

    FAIR will be able to study the low energy arena in much more detail. I hope they remain on schedule.

  13. What about the lower right corner: color super conductivity? What is the status of that?

  14. Dear Bee,

    about colour superconductivity - good question! I am not aware of concrete plans how this could be tested in heavy-ion collision experiments. I remember some ideas that the quark pairing may show up in enhanced pentaquark production, but as the pentaquark is more or less dead... Colour superconductivity could also be play a role for neutron stars, but I am not so sure about the status.

    Maybe one of our readers knows more?

    Best, Stefan


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