PionNucleus Size Resonances.
Abstract
The possibility and properties of pionnucleus optical potential resonances (or size resonances) are investigated. There are two parts to the thesis. The first is mainly preparatory work. Resonance phenomena in reactions are examined in general, with emphasis on relating the nature of the interaction to the existence of various types of resonancesranging from compound nucleus resonances to size resonances. It is argued that of these only size resonances may exist for the pionnucleus system due to strong pion annihilation. The pionnucleus interaction in the form of an optical potential is reviewed from basics. Many approximations are examined. In particular, the optical theorem which governs twobody scattering in a manybody 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 second pathology, after being remedied, still gives amusing results: for example, an infinite number of bound states, a kink in the wave function, negative elastic width,...etc. Many of these anomalous results can be understood in terms of the pion having a negative effective mass arising from the real part of the optical potential. The second part deals with size resonances specifically. The Rmatrix formalism is presented with all necessary modifications for the Kisslinger potential. The ageold controversy on the choice of boundary radius is readdressed to sort out the resonance part of potential scattering properly. This formalism serves two complementary purposes. It enables one to calculate size resonance parameters from a potential, as well as to judge whether a calculated resonance is narrow enough for observation. (pi)('208)Pb 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 (('58)Ni) 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 Rfunction, 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1980
 Bibcode:
 1980PhDT.......104P
 Keywords:

 Physics: Nuclear