Date of Award
Doctor of Philosophy (PhD)
Professor Y. Nogami
The total and elastic cross sections for pion-nucleus scattering at medium energies are known for several nuclei. There are mainly two theoretical approaches, the optical model potential and the Glauber approximation, which have been used to analyse the pion-nucleus scattering data. These theoretical calculations use some approximations such as the impulse approximation for the πN amplitude, the closure or the fixed scatterer approximation, the neglect of Pauli principle etc. The validity of these approximations cannot be taken for granted. In the 33-resonance energy region where the πN interaction is very strong, the validity of the impulse approximation, especially, is very dubious. In this thesis we examine the accuracy of some of these approximation, in particular that of the impulse approximation.
We evaluate the binding corrections to the impulse approximation by doing a model calculation for pion scattering from a bound nucleon at low and medium energies. We consider a nucleon bound in a shell model potential, which is taken to be a harmonic oscillator. The oscillator parameter is chosen such that the nuclear sizes are fitted. The nucleus under consideration thus contains only one nucleon. A separable πN interaction, which reproduces free πN scattering is assumed. Its parameters are determined such that at low energies it fits the scattering length and effective range of free πN scattering. At medium energies, on the other hand, the separable interaction is fitted to reproduce the 33-resonance. The nucleon recoil is taken into account in fitting the free πN scattering data.
Unlike the free πN scattering, the Schrödinger equation for π-bound nucleon scattering cannot be solved analytically. We obtain the scattering amplitude in this case by means of the Padé approximant. We treat the binding potential exactly. We do not use the closure approximation to sum over the the intermediate nuclear states; instead they are explicitly summed over. At low energies the binding correction is found to be negligible for s-wave πN scattering. At medium energies, however, the binding correction to the impulse approximation is found to be significantly large. There is a downward shift of the resonance energy due to binding. The total cross section at and near the resonance peak increases by about 60-70% compared to that in the impulse approximation. The differential cross section is more strongly forward peaked in comparison to that in the impulse approximation. The effect of the Pauli principle is also considered by excluding appropriate states which are already occupied by other nucleons. It pushes the resonance energy upwards, closer to that in the impulse approximation. Its significance effect is to further change the cross section. The implication of such large binding corrections to the impulse approximation for pion-nucleus scattering are also discussed for a simple model.
We also discuss the Pauli principle effects and the binding corrections to the impulse approximation for kaon-nucleus scattering at low energies. This is done for a model similar to the one used for π-bound nucleon scattering. The binding correction in this case is large compared to that for s-wave πN scattering. This is due to the fact that the s-wave KN interaction is more strong at low energies in comparison to the corresponding πN interaction.
Bajaj, Kamlesh Kumar, "Meson-Nucleus Interaction" (1976). Open Access Dissertations and Theses. Paper 906.