Monte Carlo methods for the nuclear shell model and their applications

Shell model quantum Monte Carlo methods are applied to calculate a variety of nuclear properties, in particular for nuclei in the iron region. The methods are based on a decomposition of the many-body propagator as a superposition of one-body propagators of non-interacting nucleons moving in fluctuating auxiliary fields, and can be applied in very large model spaces. Various projection techniques are developed to study the dependence of nuclear properties on good quantum numbers such as parity and spin. The particle-number reprojection method enables us to calculate thermal observables of several nuclei using the Monte Carlo sampling for one nucleus only. Nuclear level densities calculated by this method agree remarkably well with experimental data without any adjustable parameters. Parity-projected Monte Carlo calculations indicate a significant parity dependence of level densities even at the neutron-resonance energies. A simple quasi-particle model is developed to explain this parity dependence. Spin distributions of level densities are studied using the spin projection technique. The Monte Carlo results are compared with the spin-cutoff model and used to extract an energy-dependent moment of inertia. The strong suppression in the moment of inertia of even-even nuclei correlates with pairing effects and is explained by a cranking model. Thermal signatures of the pairing transition are found in the heat capacity of even-even neutron-rich iron isotopes. New commutator techniques are developed to calculate low-order moments of strength functions, and are applied in the study of electromagnetic strength functions in iron-region nuclei.