Theory of many-electron interaction in crystals

P. E. de Brito, E. S. Rodrigues, H. N. Nazareno

Helmut Volz, Hermann Haken

K. Das Gupta

Introduction.-A few new ideas and results in connection with the coherent interaction processes of X-rays in crystals are presented in this talk.This includes the discussion of interaction processes of X-rays and electrons associated with the interference in crystals.The interference is the simplest phenomenon which establishes a correlation between electrons or photons in crystals and thereby introduces coherence in the final output.In the case of X-rays and electrons the most fundamental interference phenomenon is the Bragg scattering in crystals.This is essentially the interaction of electromagnetic waves in case of X-rays and the de Broglie waves in the case of electrons which are to be scattered by the periodic lattice waves involved in the scattering process.In Ewald's [I] dynamical theory of X-ray interference the scattering elements of the crystal act as vibrating dipoles at the lattice sites and the problem is to find in the crystal a balanced or self-consistent state of electromagnetic field and the dipole waves.In Ewald's [I] dynamical theory explaining the Bragg scattering, the scattered waves have the same angular frequency coo of the incident wave.Slater [2] described the interaction between the inci-

Rongguang Zeng, Zejun Ding

Based on Bohmian quantum trajectory theory, an investigation of electron scattering in a thin crystal has been performed. A time-independent interaction potential was employed to describe electron scattering from model crystal. Quantum trajectories were calculated by a numerical solution of the time-dependent Schrödinger equation. The probability density functions and quantum trajectories representing the electron diffraction in real space were obtained from the calculation. The quantum trajectories provide an intuitive dynamics of the interaction process during the electron diffraction.

Assa Auerbach

Stano Pekár