Laue diffraction of divergent beams of Mössbauer and x-ray photons in perfect crystals

Alexey Yaroslav Dzyublik


The dynamical scattering theory is developed for the Laue diffraction of the Mössbauer rays and x-rays spread over the angle comparable with the diffraction angular range, taking into account both the Rayleigh and the resonant nuclear scattering. We consider standard experimental geometry when incident radiation first passes through an entrance slit and afterwards diffracts at the crystal planes within the Borrmann triangle. In calculations of the wave function of -photon, scattered by such strongly absorbing crystals, we apply the saddle-point method. The intensity distribution of the refracted and diffracted beams over the basis of the Borrmann triangle is analyzed.



Mössbauer spectroscopy; Laue diffraction; dynamical scattering theory; photon wave function; x-rays

Full Text:



Zachariasen WH. Theory of X-ray Diffraction in Crystals. New York: J.Wiley, 1945

Batterman BW, Cole H. Dynamical diffraction of X Rays by perfect crystals, Rev. Mod. Phys.1964; 36(3): 681-716

André Authier, Dynamical Theory of X-ray Diffraction. New York: Oxford University Press Inc., 2001

Afanas'ev AM, Kagan Yu. Suppression of inelastic channels in resonant nuclear scattering in crystals, Sov. Phys. JETP, 1965; 21(1): 215-224

Dzyublik AYa. Effect of forced vibrations on scattering of X-Rays and Mössbauer radiation by a crystal , phys. stat. sol. (b), 1984; 123(1): 53-64; 1986; 134(2): 503-513

Kato N. The energy flow of X-rays in an ideally perfect crystal: comparison between theory and experiments, Acta Cryst. 1960; 13(2): 349-356

Dzyublik AYa, Spivak VYu. Laue diffraction of spherical Mössbauer waves, Ukr. J. Phys. 2016; 61(9): 826-834

Dzyublik AYa, Slisenko VI, Mykhaylovskyy VV. Symmetric Laue diffraction of spherical neutron waves in absorbing crystals, Ukr. J. Phys. 2018; 63(2): 174-181

Bialynicki-Birula J. On the wave function of the photon, Acta Phys. Polonica, 1994; 86(1): 97-116

Goldberger ML, Watson KM. Collision Theory, Third Ed. , New York: J. Wiley, 1964

Sitenko AG. Scattering Theory. Berlin Heidelberg: Shpringer, 1999

Belyakov VA. Diffraction of Mössbauer gamma rays in crystals, Soviet Phys. Uspekhi (1975), 18(4): 267-291.

Lavrentiev MA, Shabat BV. Methods of the Theory of Functions of Complex Variable. Moscow: Nauka, 1973

Voitovetskii VK, et al. Diffraction of resonance rays by nuclei and electrons in tin crystals, Soviet Phys. JETP, 1968; 27(5): 729-735

Khrupa VI, Grigoryev DO, Dzyublik AYa. Structure perfection study of crystals containing

micro- and macrodistortions by x-ray acoustic method, Acta Phys. Polonica A, 1994; 86(4): 597-603



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Creative Commons License

This site is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.