Decay of nuclear exciton, excited by synchrotron pulse during Laue diffraction in crystals

 

A. Ya. Dzyublik, V. Yu. Spivak

 

Institute for Nuclear Research of NAS of Ukraine, Kyiv, Ukraine

 

In recent decades scattering of synchrotron radiation (SR) became a popular method for investigating crystals containig Mössbauer isotopes, where the nuclear scattering prevails over the Rayleigh scattering by atomic electrons. During the coherent scattering of γ-quanta the nuclei in a crystal act as a united system, whose excitation is spread over the whole crystal. This excitation is called nuclear exciton. The dynamical scattering theory for diffraction of Mössbauer radiation in crystals, where the incident photons generate nuclear excitons, has been provided in [1]. Its generalization to transmission and diffraction of synchrotron radiation has been given in [2].

However, the authors confined themselves by consideration of the plane waves only. At the same time, in typical diffraction experiments incident γ-quanta are represented by divergent beams, which first pass through a collimating slit. As a consequence, they are described by the wave packets, which are already superposition of plane waves. The Laue diffraction of divergent beams of x-rays was analyzed by Kato [3] in the approximation of spherical waves. We extended Kato’s theory to the case of   Laue diffraction of both Mössbauer radiation [4] and neutrons [5,6] in strongly absorbing crystals.

Using the results of these papers, we report now a quantum-mechanical description of the  Laue diffraction of synchrotron rays in perfect crystals containing Mössbauer isotopes. We take into account that SR pulses are extremely short and respectively widely spread in frequency. The wave function of SR photons are described by double integrals over frequency and angle.

We calculated the decay law p(t) of the nuclear exciton, generated by SR pulses in Laue geometry for  refracted and diffracted beams. This decay curve significantly differ from standard exponential decay law inherent for isolated nuclei. At small times compared to the nuclear lifetime it quickly falls down, that correlates with experimental observations. The deviation of the p(t) from the exponent increases with growing crystal thickness. Besides, p(t) weakly depends on the position of the scanning slit on the basis of the Borrmann triangle.

 

1. A.M.Aфанасьев, Ю.Каган, ЖЭТФ 48, 327, 1965.
2. Yu.Kagan, A.V.Afanas’ev, V.G.Kohn, J. Phys. C: Solid State Phys. 12, 615, 1979.
3. N. Kato, Acta Cryst. 13, 349, 1960.   
4. A. Ya. Dzyublik, V. Yu. Spivak, УФЖ 61, 826, 2016.
5. A. Ya. Dzyublik, V. I. Slisenko,  V.V. Mykhaylovskyy, УФЖ 63, 174, 2018.
6. А.Я.Дзюблик, В.В.Михайловский, В.Ю.Спивак, ЖЭТФ 155, 413, 2019.