On the theory of nuclear resonant forward scattering of synchrotron radiation

Abstract

The problem of time-dependent nuclear forward scattering of synchrotron radiation is solved using the Heitler's quantum theory of radiation. We have shown a way of derivation of the analytical solution that coincides precisely with the formula, earlier evolved by Kagan et al. [J. Phys. C 12, 615 (1979)] within the approach based on the solution of the Maxwell's equations. The work was stimulated by the result presented by Hoy et al. [Phys. Rev. B 63, 184435 (2001)], where the solution of the problem was obtained in the form of a finite series. This solution was derived after a replacement of the solid crystal by a finite set of the ``effective'' nuclear planes. The mean distance between the planes is much larger than the lattice parameter. Although the solution by Hoy et al. is close numerically to the well known and correct solution for large sample thickness containing many effective planes, it is incorrect for small sample thickness because it artificially limits the number of multiple scattering paths in nuclear target of a particular thickness.