# Physics Division

## Physics Division Seminars

Physics Division Seminars bring us speakers on a variety of physics
related subjects. Usually these are held in the Building 6008
large Conference Room, at 3:00 pm on the chosen day, but times
and locations may vary. For more information, contact our seminar
chairman,

Alfredo Galindo-Uribarri

Tel (Office): (865) 574-6124 (FAX): (865) 574-1268

#### Fri., October 17, 2003, at 10:30 a.m.

### Some New Perspectives on Pairing in Nuclei

*Stuart Pittel, Bartol Research Institute, University of Delaware, Newark, DE*

Building 6008 Conference Room

Exactly solvable models have a long history of providing useful insight into the properties of many-body quantum systems. In the nuclear regime, this has typically come through the use of models based on group theory. Well known examples are the Elliott SU(3) model and the three dynamical symmetry limits of the U(6) Interacting Boson Model.
Less well known is that the Pairing Model is also exactly solvable, even in the presence of non-degenerate single-particle levels. This model was solved exactly by Richardson in a series of papers in the sixties.^{1}

Over the last couple of years, there has been a revival of work on the Pairing Model, building on its exact solvability. Until very recently, however, most applications focused on issues of relevance to condensed matter systems.
In this talk, I will discuss two recent applications of the Pairing Model to nuclear physics. One involves the study of a generalized pairing model for interacting bosons. As we will see, the exact solvability of this model has enabled us to uncover a new mechanism for reinforcing *sd* dominance in the IBM.^{2} The other involves a mapping of the traditional nuclear Pairing Model onto a classical two-dimensional electrostatic problem. In this case, the outcome is a new pictorial representation of nuclear superconductivity.^{3}

^{1}R.W. Richardson, Phys. Lett. **3**, 277 (1963); R.W. Richardson and N. Sherman, Nucl. Phys. **52**, 221 (1964): R.W. Richardson, J. Math. Phys. **9**, 1327 (1968).

^{2}J. Dukelsky and S. Pittel, Phys. Rev. Lett. **86**, 4791 (2001).

^{3}J. Dukelsky, C. Esebbag and S. Pittel, Phys. Rev. Lett. **88**, (2002).