Shortcuts to nuclear structure: lessons in Hartree-Fock, RPA, and the no-core shell model

While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree-Fock (HF) approximation and the random phase approximation (RPA). We review RPA and point out some common misunderstandings, then apply HF+RPA to the no-core shell model. Here the main issue is appropriate treatment of contamination by spurious center-of-mass motion.