Atomic clusters are interesting since they do not behave either like simple molecules or like small pieces of matter and thus they provide the missing link between the atoms and bulk materials. Their properties are often puzzling and not yet completely understood. This phenomenon is known in quantum mechanics for more than 60 years. Alpha decay of nuclei occurs in such a manner, a large number of chemical reactions take place because tunneling is possible, in condensed matter physics tunneling is also an ubiquitous phenomenon. When such a particle is interacting with a reservoir the barrier penetration process is modified in a variety of ways, e.g. the tunneling rate is either significantly increased or decreased, depending on circumstances.
Some nuclei can have the shape similar to pear.
What is somewhat surprising however is that such a shape is stable only if the nucleus is at the same time either rotating fast enough or performing some type of shape oscillations. Even though there is compelling experimental evidence showing that some nuclei can have this somewhat unexpected shape, the theoretical understanding is in a somewhat unsatisfactory state. It is conceivable that the stabilization mechanism for this pear-shaped nuclei is linked with the existence of certain types of periodic orbits, whose existence should be proved. An REU student can learn about the solar neutrino problem and the possibility of neutrino oscillations. An REU student interested in numerical physics can work with me in developing codes to calculate many-fermion wave functions.