Virial theorems for the pion cloud in one-radial-mode models

We study virial theorems in models of baryons with interacting quarks and pions restricted to one radial mode. We show in a simplified model, for which an accurate solution can be obtained, that virial theorems are not satisfied in general. This is a consequence of the restriction to one radial mode and not of further approximations. However, we find a class of approximations for which they are automatically satisfied. The fulfillment of virial theorems in one-radial-mode models may therefore be an artifact and not a merit of the approximation. We investigate variational approaches in which the virial theorems are imposed as constraints and demonstrate that such calculations are sensible since they only insignificantly spoil the energy in the unconstrained calculations.