Mssbauer Optics of Synchrotron Radiation
at an Isotopic Boundary

V. A. Belaykov^1, * and S. V. Semenov²

¹Landau Institute of Theoretical Physics, Russian Academy of Sciences,
Chernogolovka, Moscow oblast, 142432 Russia
*e-mail: bel@landau.ac.ru

²Russian Research Centre Kurchatov Institute, Moscow, 123182 Russia

Received April 1, 1999

Abstract—The inelastic coherent Mössbauer scattering (ICMS) of synchrotron radiation at an isotopic bound-
ary—a flat interface between two regions of matter which have different concentrations of the Mössbauer iso-
tope—is investigated theoretically. Attention is focused primarily on the ICMS component for which the
absorption of a synchrotron radiation photon by a nucleus occurs with recoil, i.e., with the creation or annihi-
lation of lattice phonons, and the subsequent process of reemission of a photon by the Mössbauer nucleus
occurs without recoil, as a result of which radiation is pumped from the wide synchrotron radiation line into the
narrow Mössbauer line. Formulas similar to the Fresnel formulas, well known in optics, for the transmission
and reflection of light at a dielectric boundary are obtained for ICMS at an isotopic boundary. Specifically, it is
shown that the angle of reflection for ICMS at an isotopic boundary is different from the angle of mirror reflec-
tion of a synchrotron radiation beam, and the direction of the ICMS transmitted through the isotopic boundary
depends on the deviation of its frequency from the exact value of the Mössbauer resonance frequency and in
general is different from the direction of propagation of the synchrotron radiation beam. The suppression of
ICMS at grazing angles of incidence of the synchrotron radiation beam is analyzed. A similar problem is solved
for a plate-shaped sample containing a Mössbauer isotope. It is shown that the specific nature of the ICMS at
an isotopic boundary could be helpful in the problem of Mössbauer filtering of synchrotron radiation. © 2000
MAIK “Nauka/Interperiodica”.

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