Many-Body Methods in Nuclear Structure and Related Fields

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The central theme of this proposal is the development of new methods for approximately solving the Schroedingerequation for atomic nuclei and their application to problems ofcontemporary importance in nuclear structure physics. Methods having their parentage in the nuclear shell model and in mean-field theory will be considered, with the goal of developing algorithms that significantly expand their ranges of applicability. A principal focus will be on the development of theDensity Matrix Renormalization Group (DMRG), a method first introduced in the context of quantum spin lattices. Here we will focus on a new DMRG methodology that is tailored to such finite fermi systems as the atomic nucleus. We will also consider its application to an important non-nuclear problem, the two-dimensional Hubbard model, which is of relevance to systems that undergo transitions to superconductivity at high critical temperatures. A second focus will be on the properties ofweakly-bound nuclei far from stability. A method recently proposed for reliably solving the Hartree Fock Bogolyubov mean-field equations for very weakly-bound nuclei will be developed further, so as to make it computationally more viable, and will then be applied systematically to both spherical and axially-deformed nuclei throughout the periodic table. Other methods for solving the Hartree Fock Bogolyubov equations in weakly-bound systems will also be considered, to make sure that the spatial properties of such systems are being reliably treated.