Microscopic theory of nuclear collective states

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A central goal is completion of a two-volume book on the Fundamentals of Nuclear Models with an experimentalist, J.L. Wood. A primary objective of this book is to establish the experimental and mathematical foundations of the models and theories of nuclear structure so that subsequent developments can build upon them. This long-term project, now nearing completion, also ensures that the overall objectives of ours research programs remain in focus. It also serves to identify critical gaps in the data and the theory, that can be filled. Thus, John Wood is a leader of an experimental research team, using ISAC at the Triumf laboratory, for which I am a consulting member. On the theory side, a major part of my program has been to give the macroscopic collective models a microscopic expression in terms of interacting nucleons. Thus, the collective and shell models are seen as complementary and the intuition gained from one is used to guide applications of the other.  For example, a pedagogical development of the collective model in terms of multipole moments instead of the historical shape coordinates, raises the status of the collective model from a liquid-drop model to a solvable submodel of the shell model.  This makes it possible to associate coupling schemes in the shell model with corresponding collective models and relate the symmetry limits of the two models. A challenge, is to handle situations in which incompatible symmetries and coupling schemes are in competition.  Considerable progress was made during the last grant period by focusing on the presently popular quantum phase transitions that occur in systems for which there are competing dynamical symmetries.  We have observed and explained, by introducing the concept of quasi-dynamical symmetry, that one among competing dynamical symmetries tends to dominate.  To take advantage of this observation, we are developing a new approach to quantum many-body theory, without predefined bases, that is designed to handle systems with quasi-symmetries as well as those with symmetries.