P-wave pion scattering in the Los Alamos soliton model.

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P-wave pion-nucleon scattering at low and intermediate energies has been calculated in the Los Alamos soliton model that describes the nucleon as a self-consistent soliton state of a dynamic QCD bag or core interacting with its pion field. The P-wave phase shifts in the 11 and 33 channels and the inelasticity in the 11 channel are computed within the subspace consisting of at most one physical pion plus one of three soliton states of the dynamic bag or core with its pion field. The soliton states used in the calculation are computed within an approximation that treats only pionic excitations of the self-consistent nontopological soliton ground state corresponding to the nucleon and neglects excited states of the core motion. Within this approximation, the soliton states used are the model's lowest two 11 states and lowest 33 state; these states can be thought of as the nucleon, Roper, and \ensuremath{\Delta} states, where the latter two are in first approximation discrete states in the continuum. The coupling of the excited states to the continuum states gives the states a width in the usual way. The position of the 33 resonance is found to be sensitive to the value of the bag or core radius. The present approximate description of the scattering does not give a resonance in the 11 channel. The implications of these results for future work on the soliton model are discussed.