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##### Exact solutions to a schematic nuclear quark model and colorless superconductivity

**Authors**: H. BOHR and J. DA PROVIDÃŠNCIA

**Ref.**: J. Phys. A - Mathematical and Theoretical **41**, 405202 (2008)

**Abstract**: Exact solutions are found to the equations of a standard nuclear quark model exemplified by the Bonn model which is defined in terms of an effective pairing force. We show, by symmetry arguments, that, in general, the ground state of this model is not color neutral. In particular, color-neutral states have, in general, higher energy than the ground state. A novel BCS-type formalism, which is able to describe exactly color symmetrical BCS states, is used to show that the model admits, but only as excited states, color-neutral superconductivity. Therefore, such a model, with just a pairing force, is unrealistic as a model for the color-neutral confined phase which prevails at normal nuclear densities. Finally, the paper shows that there exists a color-neutral superconducting phase independently of whether the model is based on the pairing force or a more realistic three-body string force.