Low energy K-meson-nucleon scattering and elastic scattering and the elastic scattering of pions by alpha-particles

Rashid, A. M. Harun ar (1961) Low energy K-meson-nucleon scattering and elastic scattering and the elastic scattering of pions by alpha-particles. PhD thesis, University of Glasgow.

Abstract

The first part of the Thesis (Parts 1 and 2) describes a theoretical investigation on the S-wave K-nucleon scattering. Although the K-meson-nucleon interaction has received considerable theoretical study, the details of the mechanism remain obscure. In an interaction like this where absorptive processes are known to be quite strong, the requirements of unitarity imply a close relationship between the various channels in the reaction. It is therefore important in any consideration of K-meson-nucleon scattering to take into account virtual processes involving pions and hyperons. This investigation studies the possible importance of one particular virtual process namely scattering via the elementary virtual production of pairs. This is achieved by using a reduced Hamiltonian for which the processes [diagram] are allowed and the only Feynman diagram for K + N elastic scattering is that shown in the figure below [diagram]. The state vector contains terms in the configurations (K + N) , (N + N + ?) and (? + ?) and the problem can be solved exactly to obtain the S-matrix for the reactions [diagram]. Another version of the model in which ? ? B + B (where B is a baryon) is also allowed is investigated but clearly higher configurations can now occur and the model is not exactly soluble. Apart from its application to K + N scattering, the model is of interest in itself as it contains three open channels and an application of Tamm-Dancoff approximation leads to a system of coupled singular integral equations which have to be solved numerically. This was done on the electronic computer of the Glasgow University and both the models were studied for various combinations of coupling constants in the theory. Because a reduced model Hamiltonian has been used, the coupling constants are not directly comparable with those employed in calculations using the full Hamiltonian. However it has been found that for reasonable values of the coupling constants, a substantial fraction of the observed cross-sections can be obtained with this process. The model also correctly predicts the sign of the real part of the scattering amplitude for certain values of the coupling constants. The conclusion from this investigation is therefore that in S-states, pair production by K-mesons and pions must be taken into account in a future relativistic theory. The second part (Part 3) of the thesis describes a calculation on the elastic scattering of pions by alpha-particles. The interaction of pions with alpha particles has not been investigated theoretically so far and in the present study, a variational method which has been found quite successful in the pion-deuteron scattering has been applied to this problem. This method takes into account effects of multiple scattering quite simply and is an improvement over pure impulse approximation. The results of the calculations show that multiple scattering corrections are small and agreement with experimental results without such corrections is reasonably good.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: B H Bransden
• Keywords: High energy physics, Atomic physics
• Date of Award: 1961
• Depositing User: Enlighten Team
• Unique ID: glathesis:1961-73479
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:56
• Last Modified: 14 Jun 2019 08:56
• URI: https://theses.gla.ac.uk/id/eprint/73479