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Current issue   Ukr. J. Phys. 2016, Vol. 61, N 9, p.826-834
https://doi.org/10.15407/ujpe61.09.0826    Paper

Dzyublik A.Ya., Spivak V.Yu.

Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
(47, Prosp. Nauky, Kyiv 03680, Ukraine; e-mail: dzyublik@ukr.net)

Laue Diffraction of Spherical Messbauer Waves

Section: Solid Matter
Original Author's Text: English

Abstract: The symmetric Laue diffraction of M¨ossbauer rays is analyzed in the spherical-wave approximation. The saddle-point method is applied to calculate the γ-photon wave function within the Borrmann triangle in a thick crystal with strong nuclear absorption. Both the Rayleigh and resonant nuclear scatterings are taken into account. The interference oscillations of the diffracted beam intensity are shown to appear in the case of the Rayleigh scattering of M¨ossbauer radiation, which may be used for precision measurements of crystal parameters.

Key words: M¨ossbauer effect, Laue diffraction, spherical wave, Borrmann triangle, γ-photon wave function.

References:

  1. B.W. Batterman and H. Cole, Dynamical diffraction of X rays by perfect crystals, Rev. Mod. Phys. 36, 681 (1964) .   https://doi.org/10.1103/RevModPhys.36.681
  2. Andr’e Authier, Dynamical Theory of X-ray Diffraction (Oxford Univ. Press, New York, 2001).
  3. Z.G. Pinsker, Dynamical Scattering of X-rays in Crystals (Springer, Heidelberg, 1978).   https://doi.org/10.1007/978-3-642-81207-1
  4. A.M. Afanas'ev and Yu. Kagan, Suppression of inelastic channels in resonant nuclear scattering in crystals, Sov. Phys. JETP 21 (1), 215 (1965).
  5. Yu. Kagan and A.M. Afanas'ev, Suppression of inelastic channels in resonance scattering of neutrons in regular crystals Sov. Phys. JETP 22, 1032 (1966).
  6. J.P. Hannon and G.T. Trammell, M¨ossbauer diffraction. I. Quantum theory of gamma-ray and X-ray optics, Phys. Rev. 169, 315 (1968).   https://doi.org/10.1103/PhysRev.169.315
  7. J.P. Hannon and G.T. Trammell, M¨ossbauer diffraction. II. Dynamical theory of M¨ossbauer optics, Phys. Rev. 186, 306 (1969).   https://doi.org/10.1103/PhysRev.186.306
  8. N. Kato, The energy flow of X-rays in an ideally perfect crystal: comparison between theory and experiments, Acta Cryst. 13, 349 (1960).   https://doi.org/10.1107/S0365110X60000819
  9. N. Kato, A theoretical study of pendellosung fringes. I. General considerations, Acta Cryst. 14, 526 (1961).   https://doi.org/10.1107/S0365110X61001625
  10. N. Kato, A theoretical study of pendellosung fringes. II. Detailed discussion based upon a spherical wave theory, Acta Cryst. 14, 627 (1961).   https://doi.org/10.1107/S0365110X61001947
  11. N. Kato, J. Phys. Soc. Japan 19, 971 (1964).   https://doi.org/10.1143/JPSJ.19.971
  12. V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, Quantum Electrodynamics (Pergamon, Oxford, 1982).
  13. I. Bialynicki-Birula, On the wave function of the photon, Acta Phys. Pol. 86, 97 (1994).   https://doi.org/10.12693/APhysPolA.86.97
  14. J.E. Sipe, Photon wave functions, Phys. Rev. A 52, 1875 (1995).   https://doi.org/10.1103/PhysRevA.52.1875
  15. I. Bialynicki-Birula, Photon wave functions, Progr. Opt. 36, 245 (1996).   https://doi.org/10.1016/S0079-6638(08)70316-0
  16. R.J. Smith and M.G. Raymer, Photon wave functions, wave-packet quantization of light and coherence theory, New J. Phys. 9, 414 (2007).   https://doi.org/10.1088/1367-2630/9/11/414
  17. P.J. Mohr, Solutions of the Maxwell equations and pho-ton wave functions, Ann. Phys. 325, 607 (2010) .   https://doi.org/10.1016/j.aop.2009.11.007
  18. J. Cugnon, The photon wave function, Open J. Microphys. 1, 41 (2011).   https://doi.org/10.4236/ojm.2011.13008
  19. N. Chandrasekar, Quantum mechanics of photons, Adv. Studies Theor. Phys. 6, 391 (2012).
  20. A.Ya. Dzyublik, NPAE 13, No. 2 (2015).
  21. V.A. Belyakov, Diffraction of M¨ossbauer gamma rays in crystals, Sov. Phys. USP 18, 267 (1975).   https://doi.org/10.1070/PU1975v018n04ABEH004870
  22. M.A. Lavrentiev and B.V. Shabat, Methods of the Theory of Functions of Complex Variable (Nauka, Moscow, 1973) (in Russian).
  23. V.K. Voitovetski˘i et al., Diffraction of resonance gamma-rays by nuclei and electrons in tin single crystals, Sov. Phys. JETP 27, 729 (1968).
  24. V.K. Voitovetskii et al., Experimental evidence of disappearance of the inelastic channel of the nuclear reaction in the interaction of resonant gamma-radiation with nuclei and electrons in a single crystal, Phys. Lett. A 28, 779 (1969).   https://doi.org/10.1016/0375-9601(69)90619-7
  25. V.K. Voitovetskii et al., Observation of the suppression of the inelastic channel of a nuclear reaction in resonant nuclear scattering of gamma-rays in a perfect single crystal, JETP Lett. 11, 91 (1970).
  26. C.G. Shull, Observation of pendellosung fringe structure in neutron diffraction, Phys. Rev. Lett. 21, 1585 (1968).   https://doi.org/10.1103/PhysRevLett.21.1585
  27. C.G. Shull, Perfect crystals and imperfect neutrons, J. Appl. Cryst. 6, 257 (1973).   https://doi.org/10.1107/S0021889873008654