Quantum Theories of Fundamental Atomic and Molecular Interactions

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This project is focused on improved theoretical descriptions of the interactions between atoms and/or molecules over a broad range of energy. These elementary interactions are the essential ingredients for the study of quantum many-body systems throughout physics and chemistry, and, increasingly, in biology and the life-sciences as well. In most applications of quantum mechanics to complex many-body systems, the pairwise interactions between atoms and/or molecules are approximated with simple analytical forms dictated by practicality and expedience, but which neglect essential physics. Better representations of these interactions through accurate, first-principle calculations, by contrast, are simply too complicated to incorporate into many-body studies. This project is part of an effort to resolve this conundrum and to develop quantum theories of fundamental atomic interactions that are both sufficiently simple and systematic to be incorporated into quantum many-body theories, and simultaneously accurate enough to capture all the essential physics. The degree to which this can be accomplished may well determine the relevance of theoretical models and simulations of many-body systems to real-world experimental observations. The project builds on the recent success of quantum defect theories for atom-atom and ion-atom interactions. It intends both to apply them to develop better models for many-atom systems, and to extend them to other fundamental atomic interactions such as the electron-atom interaction. Quantum defect theories are general theories of structures and interactions that take advantage of the fact that over most energy ranges of interest, the complexities in atomic interactions, such as their energy and partial wave dependences, are due almost entirely to the long-range interaction, which makes them amenable to systematic and often analytic treatment. The project also intends to take initial steps towards the developments of quantum defect theories for anisotropic interactions, such as the atom-molecule interaction, with the ultimate goal of achieving a unified and an efficient framework for all aspects of atomic and molecular structures and interactions.