The “double folding” approach. Notice the famous “nuclear rainbow,” and the rainbow's end!  In the diagram R + r1 - r2 is the distance between interacting nucleons. The convolution theorem for Fourier transforms makes this kind of nested integral doable.

Very, very little is known experimentally about the equation of state of nuclear matter, for the simple reason that all nuclei have the same density. Physicists realized in the 1970s that the only hope of observing any kind of phase transition experimentally was to collide the heaviest possible nuclei head-on at the largest possible center-of-momentum energy. Popular systems are gold on gold, lead on lead and uranium on uranium. The Relativistic Heavy Ion Collider's STAR detector on Long Island, NY, and the LHC's ATLAS and ALICE detectors have been used to study such collisions, and experiments are still ongoing. The basic problem is that the collision results in complete hadronization, so that one has to be able to detect, identify and analyze many, many thousands of outgoing particles simultaneously. We'll discuss these efforts later in the course. If you wonder what Color Superconductivity is, QCD predicts that at high density in nuclear matter, quarks can form Cooper Pairs, analogous to the electron pairs that cause one kind of superconductivity in solids.   According to the standard current cosmological parameter set, Lambda-CDM, the entire infinite universe was in the form of a quark-gluon plasma when it was a millionth of a second old.  The local expert on nucleus-nucleus collisions at relativistic energies is Prof. Christina Markert.

We shall see later that the question of whether there is a critical point, and a true first-order phase transition between hadronic matter and a quark-gluon plasma is still very much an open experimental question.