Pion-nucleus size resonances

The possibility and properties of pion-nucleus optical potential resonances (or size resonances) are investigated. Resonance phenomena in reactions are examined in general, with emphasis on relating the nature of the interaction to the existence of various types of resonances. The pion-nucleus interaction in the form of an optical potential is reviewed from basics. The optical theorem which governs two-body scattering in a many-body environment and its usage for examining the impulse approximation are pointed out. The Kisslinger potential is examined from the continuity equation point of view and two pathologies are uncovered. First, the potential fails to be absorptive everywhere; and second, it becomes singular when the potential exceeds a certain strength. The R-matrix formalism is presented with all necessary modifications for the Kisslinger potential. The controversy on the choice of boundary radium is readdressed to sort out the resonance part of potential scattering properly. π-20spb results show resonances of various partial wave and pion charge can occur in the region of 10 to 40 MeV. The corresponding elastic widths and absorption widths are in the order of 30 to 40 MeV. Lighter nuclei (58Ni) show even larger elastic width. Without further analysis these widths are too large to produce any apparent effect even in the resonant part of the scattering amplitude. However, in a new method of phase shift analyses which consists essentially of extracting the R-function, the broad resonances are shown to be distinct and their parameters can be extracted. This method has widespread possible application for analysing resonances in general