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.