Non-relativistic bound states in a finite volume |
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Authors: | Sebastian König Dean Lee H-W Hammer |
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Institution: | 1. Helmholtz-Institut für Strahlen-und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany;2. Department of Physics, North Carolina State University, Raleigh, NC 27695, USA |
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Abstract: | We derive general results for the mass shift of bound states with angular momentum in a periodic cubic box in two and three spatial dimensions. Our results have applications to lattice simulations of hadronic molecules, halo nuclei, and Feshbach molecules. The sign of the mass shift can be related to the symmetry properties of the state under consideration. We verify our analytical results with explicit numerical calculations. Moreover, we comment on the relations connecting the effective range parameter, the binding momentum of a given state and the asymptotic normalization coefficient of the corresponding wave function. We give explicit expressions for this relation in the shallow binding limit. |
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