Publication details
Multiple diffraction of particles by a system of point scatterers as an exactly soluble problem using the Ewald concept
| Authors | |
|---|---|
| Year of publication | 1996 |
| Type | Article in Periodical |
| Magazine / Source | J.Phys.: Condens. Matter |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.sci.muni.cz/~mikulik/Publications.html#LMD |
| Field | Theoretical physics |
| Keywords | dynamical theory of diffraction; diffraction; multiple scattering |
| Description | Reflection of a de Broglie plane wave incident on a system if point scatterers (nuclei) forming an ideal semi-infinite crystal is studied using the T-matrix formalism of Ewald's dynamical theory of diffraction. Using from the beginning the two-dimensional translational symmetry of the crystal bordered by a surface, simple exact many-beam analytical formulae for the intensities of the reflected waves are deduced, whereby the Ewald sphere is replaced by "the gamma-diagrams" and the usual three-dimensional dispersion surface by two-dimensional "dispersion plot". The results obtained are valid for arbitrary angles of incidence (including the grazing incidence, Bragg angle near pi/2, near or far from the Bragg reflection position) and for any directions of the reflected waves (including both the coplanar and noncoplanar reflections). The transparent algebraic form of the final formulae allows us to discuss analytically the solutions of the dispersion relation and the intensities of the reflections in two- and many-beam approximations. |