When relativistic electrons and positrons are channeled along major crystallographic planes of a single crystal, they emit hard X-rays or gamma -radiation due to spontaneous transitions among the discrete energy levels caused by the transverse continuum potential. The authors present results of a calculation for the frequencies of the emitted radiation. The charge density in the solid was calculated self-consistently with the linear muffin tin orbitals method in the atomic spheres approximation (LMTO-ASA) within the local density approximation to the density functional formalism. They then solved the Poisson's equation with this charge density to obtain the potential seen by the external particle. The transverse continuum planar potential was then obtained by numerically averaging this potential along the relevant (110) planes in the solid. The relevant Schrodinger equation was then solved to find the transition energies. When the temperature effects are included, the results for the channeling radiation characteristics from C, Si and Ge are found to be in good agreement with recent experiments. The planar potential calculated above agrees very closely with the empirically derived planar potential from the electron channeling radiation data for Si (110) case. This shows that the channeling radiation data can be reliably used to derive the planar potential seen by the channeled electrons which then can be used to obtain the characteristics of the potential field in the solid.
 

Nuclear Instruments & Methods in Physics Research, Section, 49 39-41, 1988.