[Source: Kay Königsmann: Radiative decays in the Ψ family, Physics Reports 139, Issue 5, June 1986, Pages 243-291, Fig. 5.]
One may wonder, is there a similar phenomenon for bound systems between other particles, say, between quarks, which carry a so-called colour charge and interact via the strong force described by quantum chromodynamics, QCD? The answer is an emphatic yes - and one can learn a lot from it. The figure shows the spectrum of excited states of the J/Ψ meson, a bound charm quark-antiquark pair. Like the electron-proton pair in the hydrogen atom, the quark-antiquark pair can have only specific energies, it can be excited to a series of states with higher energies, and it can emit and absorb light when transiting between these states. The corresponding photon spectrum - the numbers of photons within a small range of energy counted in a detector - is shown in the plot, with a specific pattern of lines superimposed on a smooth background. The numbers help to identify the lines with the transitions between different states, which are shown schematically in the lower part of the figure. Data have been measured at the Crystal Ball, a spherical detector that completely encloses the quark-antiquark pair.
The photons counted in the spectrum do not correspond to visible light, however, but are short-wavelength gamma rays with an energy in the range between 100 and 500 MeV - that's much more than the 1.9 eV corresponding to the red Hα line in the hydrogen spectrum. This should not come as a surprise: The energy scale of the hydrogen atom is set by the Rydberg constant, R = 13.6 eV, which is proportional to α²m, where α ≈ 1/137 is the fine structure constant - the coupling constant of QED - and m is the mass of the electron. Now, a charm quark has about 3000 times more mass than an electron, and the coupling constant of QCD, the strong interaction, is about 100 times bigger than that of QED. Hence, one could expect spectral lines with energies by a factor 30 million times bigger for the charm-anticharm pair than for the hydrogen atom - as you can see, that's not that bad an estimate.
However, there is an essential difference between the hydrogen atom and charmonium, as the bound charm-anticharm pair is usually called, and it can be spotted in the known spectrum of charmonium states, which is shown in this plot.
[Source: Ted Barnes: The XYZs of charmonium at BES, Int. J. Mod. Phys. A21 (2006) 5583-5591 (arXiv: hep-ph/0608103v1), Fig. 1.]
Here, the known charmonium states are shown as black lines according to their energy, or mass, on the vertical axis, and grouped as per orbital angular momentum of the quark-antiquark pair, labelled by S, P, D, F, along the horizontal axis. In contrast to the hydrogen spectrum, there is no series limit at high energies, which in the hydrogen atom corresponds to ionisation, the separation of the electron and the proton. Instead, energy levels increase rather uniformly, but cross a line, labelled "DD". Above that energy, the charmonium system can decay in a D meson, made up of charm quark and a light antiquark, and the respective antiparticle, the anti-D. This is the manifestation of very characteristic feature of QCD, called colour confinement: No isolated quarks, or other colour charges, can be observed. Instead, if one tries to separate, say, the charm quark and the anticharm quark of the J/Psi; by adding energy, a new quark-antiquark pair will be created, and two mesons will be formed, the D/anti-D pair.
Because of confinement, it is clear that the interaction energy between quarks can not be described by a simple analogy to the Coulomb law for electrical charges. To model confinement, it is stipulated that a Coulomb-type interaction has to be amended by some energy which increases linear with charge separation. In fact, one has tired to reverse-engineer an interaction potential between quarks starting from the charmonium spectrum: Making an ansatz for the interaction energy, one can calculate the corresponding spectrum, and fit the parameters to match the observed spectrum. The most popular ansatz is often called Cornell potential and looks like this:
Understanding confinement of colour charge is an open problem in physics, and the details of the interaction between quarks forming a hadron still contain many riddles. The analysis of the spectrum of quark-antiquark pairs as in charmonium can help to a better understanding of these issues - that's why the spectrum of charmonium is still an active area of research.
The best electrodynamcial analogue to charmonium is not the hydrogen atom, but the bound state of an electron and a positron, called positronium. The nomenclature of charmonia, and the name charmonium itself, derives from positronium physics.
The Cornell potential got his name after the group of physicists at Cornell who had used it within weeks of the discovery of the J/Ψ to analyse the spectrum of its excited states - see E. Eichten et al.: Spectrum of Charmed Quark-Antiquark Bound States, Phys. Rev. Lett. 34 (1975) 369.
Charmonium physics will be one main topic of the PANDA (Proton ANtiproton DArmstadt) experiment at the new "Facility of Antiproton and Ion Research" (FAIR) at GSI, Darmstadt, Germany (see, e.g., Bertram Kopf: Physics with Antiprotons at PANDA, J. Phys.: Conf. Ser. 69 012026).
The Crystal Ball Detector is now in use at the Mainzer Mikrotron (MAMI), Germany.
This post is part of our 2007 advent calendar A Plottl A Day.