Quantum calculations for the effects of dislocations on channeling and channeling radiation

The channeling process in a crystal bent by dislocations is considered. The Schrödinger equation for the channeled particle motion is separated between longitudinal and transverse parts. The transverse potential and the frequency of channeling radiation in the perfect channel and the two regions of dislocation affected channels are calculated. The corresponding wave functions for the transverse and longitudinal motions are also calculated. In this work, we specifically investigate the effects of longitudinal motion of the particle on the dechanneling parameter and the frequency. The continuity of wave functions and their derivatives is used at the three boundaries and reflection and transmission coefficients are found using these boundary conditions. Finally, we consider the two cases of maximum and minimum dechanneling probabilities.