Nuclear physics represents a very sophisticated quantum many-body problem. A nuclei is a dense droplet of very strongly interacting fermions. Furthermore, the interaction between a pair of nucleons is nothing like the simple Coulomb interaction between a pair of electrons in a solid or a molecule. Yet nuclear physics can be taught to undergraduates!
Why? Basically, because (as in most many-body systems) one can describe the low lying quantum states in terms of an effective Hamiltonian which describes weakly interacting quasi-particles (which have the same quantum numbers as protons and neutrons). The dynamics of an individual quasi-particle is determined by the mean field (average potential) of all the other nucleons. This is known as the nuclear shell model, first proposed in 1949 and recognised by the Nobel Prize in 1963.
A nice Physics article by John Schiffer is worth reading (it is just a page) as it puts in context a recent PRL which shows how the tensor component of the average potential can explain experimental data on a wide range of nuclei.
What we do not tell to undergraduate students, though, is that we do not know, still now, how to calculate the mean-field from the bare interaction. A simple Hartree-Fock calculation simply diverges because of the hard repulsive core in the nucleon-nucleon interaction. One could use more elaborated theories, such as the Brueckner-Hartree-Fock theory which produces an effective interaction without hard core (calculated from the bare interaction) acting on an independent particle state. However realistic calculations are so difficult that the theory has been applied only to infinite nuclear matter.
ReplyDeleteDefinitely, nuclear physics is not as easy as we tell students...
Thanks, Cedric for sharing your expertise, as a bona fide practising nuclear theorist. I had not appreciated your point. Even in solid state physics (which starts with the bare Coulomb potential) calculating the mean-field potential is a highly non-trivial exercise (black art!).
ReplyDeleteI look forward to hearing more when you visit UQ next month.