Laue Diffraction of Spherical M¨ossbauer Waves

  • A. Ya. Dzyublik Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
  • V. Yu. Spivak Institute for Nuclear Research, Nat. Acad. of Sci. of Ukraine
Keywords: M¨ossbauer effect, Laue diffraction, spherical wave, Borrmann triangle, y-photon wave function

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 y-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.

References

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

Andr?e Authier, Dynamical Theory of X-ray Diffraction (Oxford Univ. Press, New York, 2001).

Z.G. Pinsker, Dynamical Scattering of X-rays in Crystals (Springer, Heidelberg, 1978).

A.M. Afanas’ev and Yu. Kagan, Suppression of inelastic channels in resonant nuclear scattering in crystals, Sov. Phys. JETP 21 (1), 215 (1965).

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).

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).

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

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

N. Kato, A theoretical study of pendellosung fringes. I. General considerations, Acta Cryst. 14, 526 (1961) https://doi.org/10.1107/S0365110X61001625

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

N. Kato, J. Phys. Soc. Japan 19, 971 (1964).

V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, Quantum Electrodynamics (Pergamon, Oxford, 1982).

I. Bialynicki-Birula, On the wave function of the photon, Acta Phys. Pol. 86, 97 (1994).

J.E. Sipe, Photon wave functions, Phys. Rev. A 52, 1875 (1995).

I. Bialynicki-Birula, Photon wave functions, Progr. Opt. 36, 245 (1996).

R.J. Smith and M.G. Raymer, Photon wave functions, wave-packet quantization of light and coherence the-ory, New J. Phys. 9, 414 (2007) https://doi.org/10.1088/1367-2630/9/11/414

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

J. Cugnon, The photon wave function, Open J. Microphys. 1, 41 (2011) https://doi.org/10.4236/ojm.2011.13008

N. Chandrasekar, Quantum mechanics of photons, Adv. Studies Theor. Phys. 6, 391 (2012).

A.Ya. Dzyublik, NPAE 13, No. 2 (2015).

V.A. Belyakov, Diffraction of M?ossbauer gamma rays in crystals, Sov. Phys. USP 18, 267 (1975).

M.A. Lavrentiev and B.V. Shabat, Methods of the Theory of Functions of Complex Variable (Nauka, Moscow, 1973) (in Russian).

V.K. Voitovetski?i et al., Diffraction of resonance ?-rays by nuclei and electrons in tin single crystals, Sov. Phys. JETP 27, 729 (1968).

V.K. Voitovetskii et al., Experimental evidence of disap-pearance of the inelastic channel of the nuclear reaction in the interaction of resonant ?-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

V.K. Voitovetskii et al., Observation of the suppression of the inelastic channel of a nuclear reaction in resonant nu-clear scattering of gamma-rays in a perfect single crystal, JETP Lett. 11, 91 (1970).

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

C.G. Shull, Perfect crystals and imperfect neu-trons, J. Appl. Cryst. 6, 257 (1973) https://doi.org/10.1107/S0021889873008654

Published
2019-01-05
How to Cite
Dzyublik, A., & Spivak, V. (2019). Laue Diffraction of Spherical M¨ossbauer Waves. Ukrainian Journal of Physics, 61(9), 826. https://doi.org/10.15407/ujpe61.09.0826
Section
Solid matter