Nuclear physics: a laboratory for many-particle quantum mechanics

Nuclear structure physics has presented a fruitful testing ground for quantum many-body theory since its beginnings half a century ago. On one hand, the observed phenomena have given rise to models that have been invaluable to interpret the underlying physics. On the other hand, the quest to make a predictive theory has given strong impetus to developing computational tools to solve the many-particle Schroedinger equation. I will review some of these theoretical highlights in nuclear structure, ranging from the modeling and computation of few-body systems to the many-particle finite systems represented by our heavy nuclei. Among the models I discuss are the unitary-limit fermionic Hamiltonian, the Nilsson model of nuclear deformations, and the Richardson-Gaudin model of pairing. Computational strategies that have been very successful in different contexts are the Monte-Carlo methods, the multi-configuration shell model, and the extensions of mean-field theory to restore broken symmetries.