Atomic capture of negative mesons: (II). Fuzzy Fermi-Teller model

Abstract

The Fermi-Teller (FT) model is extended to account for the discrete nature of the energy and angular momentum loss of negative mesons undergoing capture and deexcitation through the excitation of atomic electrons. Statistical fluctuations in the energy loss permit more mesons to be captured at high energy than predicted by the FT model. The variation with atomic number ( Z) of the angular momentum ( l) distribution when the meson is bound with an energy comparable to K-shell electrons is similar to that predicted by the FT model. The fuzzy Fermi-Teller (FFT) model enables us to calculate a number of interesting quantities (e.g. the distribution of angular momentum at various stages of the cascade, the distribution of energy and angular momentum jumps, etc.) which provide insight into the details of the deexcitation process. The effect of an energy gap and polarization potential is investigated. Capture and energy loss cross sections are changed by these parameters, but they have only a small effect on the l-distribution at the K-shell. A parameter is introduced to alter the distribution of energy and angular momentum loss in the outer part of the atom. We find that the angular momentum distribution at the K-shell is sensitive to this aspect of the model and by varying this parameter, we produce changes in the absolute kaonic X-ray yields which approach the magnitude of the periodic variations reported by Wiegand and Godfrey.