Planar Channeling of Electrons and Positrons in Crystals. Local‐Density Calculation of Planar Averaged Potential and Channeling Radiation Spectrum

Abstract

AbstractResults of calculation of channeling potentials in crystals using the local density theory are given. The linear muffin‐tin orbitals method is used in the atomic spheres approximation (LMTO‐ASA) to calculate the planar‐averaged potential seen by MeV electrons and positrons channeled along (110) planes of diamond, Si, and Ge. The calculations thus include the spherical charge relaxation effects (“solid state effects”) in the solid but omits the non‐spherical part. The calculated potentials are in excellent agreement with the empirical potentials derived from channeling radiation experiments, but are significantly different near the atomic planes from the potentials obtained from superposition of the atomic Thomas‐Fermi statistical (Molière) potentials. Agreement of the potentials with the ones obtained from superposition of atomic Doyle‐Turner potentials is reasonably good. Frequencies of emitted radiation from the channeled electrons and positrons are also calculated and compared to experiments. For the crystals considered, it is concluded that the solid state effects on the planar‐averaged potential are moderate to small. It is expected that these effects should be more important for channeling in ionic solids. The deviation of the observed positron channeling radiation from the calculated values for Si and C indicates that the non‐spherical part of the charge relaxation might be relatively important for these solids.