A variational approach to pion scattering on the cloudy bag

Abstract

We present a variational method for calculating the ground state and the scattering states in the model with a pion cloud around a bare nucleon and bare delta. The pion cloud is described by a coherent state, with good angular momentum and isospin ensured by projection techniques. The ground state of the system is determined by minimizing the energy. For the scattering states we use the Kohn variational principle which we adapt for our model. The renormalized coupling constant, the charge radius of proton and neutron and the phase shifts in the P 33, P 31 and P 13 channels are calculated. The form of the interaction is taken from the cloudy bag model. There are three free parameters: the bare coupling constant, the bag radius and the energy of the bare delta. The results for the ground state show that the bare coupling constant almost coincides with its renormalized value and that the radius of the bag is between 1.1 and 1.2 fm. In contrast to some previous calculations, this choice of parameters gives correct phase shifts. The energy of the bare delta is 2.2 pion masses, considerably higher than suggested by some other calculations.