UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Pion-nucleus size resonances Pai, David Mieng


The possibility and properties of pion-nucleus 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 resonances- ranging from compound nucleus resonances to size resonances. It is argued that of these only size resonances may exist for the pion-nucleus system due to strong pion annihilation. The pion-nucleus interaction in the form of an optical potential is reviewed from basics. Many approximations are examined. In particular, 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 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 $-matrix formalism is presented with all necessary modifications for the Kisslinger potential. The age-old controversy on the choice of boundary radius is readdressed to sort out the resonance part of potential scattering properly. This formalism series 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. π⁻²⁰⁸Pb results show resonances of various partial wave and pion charge can occur in the region of 10 to 40 HeV. The corresponding elastic widths and absorption widths are in the order of 30 to 40 HeV. 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.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.