Charmonium refers to a class of composite particles formed when a charm quark binds to a charm antiquark. The study of this system offers a unique probe into the force between quarks, known as the strong force and also into quantum chromodynamics.
Any type of quark can bind together with any type of antiquark to make the composite particles known as mesons. However, only the charm (c ) and bottom (b ) quarks form bound states having spectra and energy levels reminiscent of atoms. The charm quark, discovered in 1974, has a mass of approximately 1,500 MeV/c2, or 2.7 10-27 kg.
The hydrogen atom is formed from a proton and an electron bound together by the electric field; charmonium's quarks are bound together by the strong interquark force. The relative motion of the particles gives rise to orbital angular momentum, measured in whole-number multiples of Planck's constant h , which contributes to the total energy of the system. The quarks, like the proton and electron, also possess some intrinsic angular momentum called spin.
Quantization of these angular momenta results in a unique set of allowed energy levels for the system. The spacings between these energy levels are determined by the particle masses and angular momenta and depend on how the force between the bound particles varies with their separation. The energy levels can be inferred by measuring the energies of light emitted when the atomic system relaxes from a higher-energy state En to a lower state Em; the emitted photon has energy En - Em.
Figure 1 shows the spectrum of photon energies observed when one of the excited energy states of charmonium (the so-called ψ´ particle) relaxes to lower-energy levels. The ψ´ charmonium state has a mass of 3,684 MeV/c2. There are higher-mass charmonium states, such as ψ˝ (3770), which prefer to decay into a pair of D (1865) particles (the meson formed from a c quark and a u antiquark) rather than de-excite by photon emission. This type of decay is not possible for ψ´ because its mass is less than 2mD; it must decay into lower-energy states by radiating one or more photons.
The energy levels of charmonium are governed by three quantum numbers. The radial quantum number (integer n ) describes the successive quantum energy steps of a given configuration (e.g., the difference between the n = 2 ψ' and the n = 1 ψ . Next, there is the total spin of the two c quarks. Each quark has an intrinsic angular momentum of ±½h , resulting in a total spin angular momentum s of 0 or 1h . Finally, there is the orbital angular momentum L , in whole-number multiples of h . Spectroscopic notation (from atomic physics) is used to label the charmonium states shown in Figure 1; the nomenclature is 2s + 1LJ, where J is the total angular momentum and L is denoted by the historical notation S for L = 0, P for L = 1h , and so on. In quantum mechanics the various angular momenta add vectorially. For instance, with s = 1 and L = 1, J can take on the values 0, 1, or 2; in the figure this is evident for the s = 1 P states (L = 1h ) that split into three energy levels.
The observation of the charmonium energy levels has verified the spin of the c quark and, more importantly, provided a better idea of the behavior of the strong force. Although the strong force increases linearly with quark separation for distances greater than 1015 meters (and this is why one never sees single quarks!), charmonium tells us that the behavior is like that of the electric force for distances between 10-14 and 10-15 meters.
Bloom, E. D., and Feldman, G. J. "Quarkonium." Scientific American246 (5), 66–77 (1982).
Mark J. Oreglia
"Charmonium." Building Blocks of Matter: A Supplement to the Macmillan Encyclopedia of Physics. . Encyclopedia.com. (November 16, 2018). https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/charmonium
"Charmonium." Building Blocks of Matter: A Supplement to the Macmillan Encyclopedia of Physics. . Retrieved November 16, 2018 from Encyclopedia.com: https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/charmonium
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.