Monday, May 28, 2012

Born-Oppenheimer in nuclear physics

How do single nucleons and associated excitations couple to collective degrees of freedom such as rotations and shape deformations?
Is there a Born-Oppenheimer approximation in nuclear physics?
What is the origin of non-spherical nuclei and the associated symmetry breaking?
Is the notion of a Jahn-Teller effect and conical intersections relevant?

There issues go back to classic ideas in theoretical nuclear physics for which Aage Bohr, Mottelson, and Rainwater were awarded the Nobel Prize in Physics in 1975. This is discussed in an earlier post.
There is also a classic paper by Hill and Wheeler which does include a discussion of conical intersections [I thank Seth Olsen for bringing it to my attention].

The relevant physics is elegantly discussed in a nice review article The Nuclear Collective Motion by Witold Nazarewicz. Here is an extract

He then goes on to discuss how the deformations of nuclei can be understood in terms of the Jahn-Teller effect.

The figure below is a microscopic calculation from a density functional method of the energy as a function of the nuclear deformation of different Nd isotopes. As the mass number A=N+Z increases there is a transition from a spherical nuclei to an axially deformed one.
This figure is taken from a recent RMP Quantum phase transitions in the shape of atomic nuclei

Things I am still looking for discussions are 
1. using diabatic states
2. roles of conical intersections, particularly in dynamics
3. breakdown of Born-Oppenheimer.

1 comment:

  1. I have discovered that, as a quantum chemist, it is very useful to look up nuclear physics literature. I subscribe to the TOC alerts from Phys. Rev. C., and find that about once a month there is a discussion in that journal that also directly applies to molecular theory. Moreover, I find that I can often a clearer insight from the nuclear papers because they are not cluttered by all of the "baggage" that one finds in quantum chemistry. The Hill & Wheeler paper is a good example - the method they describe ("Generator Coordinate Method") is essentially the method known as "multiconfigurational self-consistent field" in the chemistry literature.

    Another good example is the paper that I didn't bring up at the last group meeting. This is a paper by Kvaal on the geometry of effective Hamiltonians*. This paper made several points clear that were not clear after reading many papers from the chemistry literature (almost all of which are cited in the Kvaal paper).

    Kvaal. "Geometry of Effective Hamiltonians" Phys. Rev. C 2008 vol. 78 (4) p.044330.