Some Theoretical Works on Channelling Effect and Channelling Radiation

The trajectory equations for both relativistic and nonrelativistic channelling particles become very simple under the general channelling conditions. For many potentials, such as Lindhard potential, the expressions of the trajectories can be obtained in closed form. The complete trajectory in the crystal can be traced out easily in both transverse and longitudinal directions. The backscattering probability as a function of the incident angles has been derived in this trajectory picture and is calculated for several cases: 3 Mev proton on Si(110), 1 Mev proton on Au(111), 1.5 Mev electron on Si(110) and 1 Mev electron on Ag(111). The shapes and widths of these theoretical curves fit well with the experimental results. The wave equations for the channelling relativistic electron and positron have been solved by WKB method. In this method potential with any complex functional form can be used and a quantum condition is readily provided to determine the energy levels. Taking a simulated. Moliere potential, the planar channelling radiation spectra of electrons have been calculated for a number of cases. The locations of the peaks obtained agree well with the experiments. A multiplicity of the radiation spectrum for the relativistic positron is predicted and an explanation is given for the single peak observation. More accurate wave functions for the channelling particles have been derived by perturbation theory. Transition matrix, energy level life time and the ratios of the intensities of transitions from different quantum states of electron and positron channelling radiations are estimated.