On the fission mechanism of an ellipsoidal MIT bag

The single-particle spectrum of a light quark moving in the field generated by a heavy quark-antiquark pair placed at the foci of an ellipsoidal bag is calculated in a variational approach. Residual interactions due to gluon exchange are accounted for in the random phase approximation (RPA). It is shown that the Tamm-Dancoff approximation (TDA) corresponding to the traditional semiclassical approach for a spherical cavity is inadequate for αsub(s) = 2.2. In the spherical limit of an empty bag, the mass of the pion is underestimated in the RPA (85 MeV) as compared with an overestimate in the TDA (280 MeV). The RPA becomes unstable at a fixed deformation of the bag, for a constant value of αsub(s). Employing Green function techniques, it is shown that this is an artefact signalling a phase transition from a filled Fermi vacuum to a correlated one. The presence of real quark-antiquark pairs within the ground state is interpreted as a signal that fission may occur. (author)