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Spin Spontaneous and stimulated parametric (quasi-Cherenkov) X-ray radiation,
chanelling and diffracted chanelling radiation in crystals

PXR geometry


The parametric X-ray radiation (PXR) generated by a particle uniformly moving through a crystal has threshold behavior the same the ordinary Cerenkov radiation and its intensity is proportional to the crystal length or photon absorption length. It is important to stress, that PXR does not should be mixed with so-called resonance radiation. In the contrary of PXR, which frequencies are determined only by a crystal constant, the frequency of resonance radiation depends on a particle energy. PXR was predicted in [1,2].


Due to crystal symmetry the diffraction conditions can be fulfilled for several waves consequently, the multi-wave diffraction can manifest themselves in parametric X-ray radiation (PXR). Indeed, some anomalies in PXR angular distributions were observed in conducting the experiments on PXR generated by relativistic electrons in GaAs [3, 4]. The analysis has shown that 4- and 8-wave Bragg diffraction conditions, correspondingly, were fulfilled in these ex-periments. The specific features observed were supposed to be the manifestation of multi-wave generation of PXR. It gave impetus to theoretical research concerning multi-wave effects in PXR.


For a charged particle channeled along a crystal axis or plane the projectile path is formed by correlated collisions with crystal atoms. The particle moves in a effective potential obtained by smearing the crystal potential along the crystal axis or plane. This motion is accompanied by a special type of radiation, so-called channeling radiation [5]. X-ray radiation from a relativistic oscillator in a crystal is essentially modified under diffraction conditions for emitted photons. A new diffraction radiation is a result of coherent summation of two processes – photon radiation and photon diffraction. It has been called diffraction radiation of oscillator (DRO) [6].

Though predicted back in 1977 [7, 8], DRO has not so far been observed experimentally. Its study is of considerable interest, since DRO may find application in treating different effects in the optics of a relativistic emitter moving in refracting media.

Relativistic oscillator can be formed not only by an unperturbed crystal channel but also by an external ultrasonic or laser field which subjects to the crystal and forms a bent crystal channel, that is the relativistic oscillator can be a channeled particle which moves in some elec-tromagnetic undulator [12].

The high spectral and angular densities of diffraction radiation of oscillator and also narrow spectral and angular widths of radiation reflex give the basis of its application for construction of X-ray coherent radiation source by using relativistic particle beams in crystal. Such system can be considered as a crystal X-ray free electron laser (FEL). The idea of parametric X-ray generator on the basis of channeled electron (positron) beams was firstly expressed in [9]. As it was said above, the radiating oscillator can be formed in different ways. This can be electrons, channeled in averaged crystallographic potential of plane or axes [10] or oscillator formed by an external field or moves in electromagnetic undulator [11].


Experimental observation [12] of x-ray radiation from non-relativistic (50–100 keV) electrons of the electron microscope beam in thin crystal target is reported and described as resulted from interference between parametric x-rays (PXR) and coherent Bremsstrahlung (CB). CB&PXR features are qualitatively described on the base of the pseudo-photon concept. Rigid requirements for thin single crystal membranes are obtained. The experimental set-up, thin silicon crystal target production, measurement procedures, data processing and spectra simula-tion are reported in detail. Each CB&PXR spectral line is attributed to a set of crystallographic planes.

Possibility of tuning of the x-ray frequency by the crystal target rotation is demonstrated for low-energy electrons for the first time. Despite its rather low total quantum yield of CB&PXR for the electrons in the considered energy range, this radiation can be prospective for development of a tabletop tunable x-ray source for structure analysis and crystallography (for example, for spectral-sensitive experiments) due to its brightness in the narrow spectral interval. Production of single crystal membranes is expected to become a high-tech challenge, when developing such a source.


According to the analysis transverse motion of a channeled particle is characterized by a distinct band energy spectrum. Deep in the wells the bands are very narrow, so we can speak about discrete levels in a well.

From the quasiclassical viewpoint, a particle moving in a crystal oscillates back and forth under the action of the electrostatic potential of crystallographic planes and axes. Oscillations of a charged particle result in the production of radiation. From the quantum–mechanical viewpoint, there appear radiative transitions between the energy bands of the transverse motion of particles passing through a crystal [8, 14, 15].

Within the framework of the quantum mechanical correspondence principle, every radiative transition may be described as the radiation of a certain classical oscillator. Since a particle has a longitudinal momentum, we shall deal with a moving one– or two–dimensional “atom”, whose radiation spectrum is considerably influenced by the Doppler effect [16], causing the transformation of relatively low-frequency particle oscillations in a crystal (characteristic frequencies for electrons and positrons are in the optical and soft X-ray spectral ranges) into hard X-ray and gamma-radiation, whose frequency increases with the growth of particle energy. Within the framework of the classical theory, the possibility of generation of gamma-radiation by channeled electrons and positrons and the importance of the Doppler effect in this process were also pointed out by Kumakhov [16].

First experiments on observation of channeling radiation were performed and the radiation spectrum was experimentally revealed in [17-19]. Today, a great number of experimental and theoretical works on this problem are available (see e.g. [20-24]. The major characteristics of the radiation produced by channeled particles may be deduced from the simple reasoning given below [8, 15].


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2. Baryshevsky V. G., Feranchuk I.D. Doklady Akad. Sci. BSSR. 1974. Vol. 18, N 6. P. 499-502.
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4. Afanasenko V. P., Baryshevsky V. G. et al. Letters to Sov. J. Exp. Tech. Phys. 1989. Vol.15. P. 33–35.
5. V.G.Baryshevsky. Chanelling, radiation and reactions in crystals under the high energies . 1982. 256 p.(In Russian)
6. Baryshevsky V. G., Gradovsky O. T., Dubovskaya I. Ya. Izv. Akad. Sci. BSSR. Ser. phys.-math. 1987, N 6. P. 77-81.
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8. Baryshevskii, V. G. and Dubovskaya, I. Ya. (1977). Coherent radiation of the channelling positron (electron), Phys. Status Solidi (b) 82, 1, pp. 403–412.
9. Baryshevsky V. G., Feranchuk I.D. Doklady Akad. Sci. BSSR. 1983. Vol. 27. P. 995.
10. Baryshevsky V. G., Dubovskaya I. Ya. , Zege A. V. Nucl. Instr. Meth. 1990. Vol. 135A. P. 368
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12. V.G.Baryshevsky, I.D. Feranchuk, A.P. Ulyanenkov. Parametric X-Ray Radiation in Crystals: Theory, Experiment and Applications. Series: Springer Tracts in Modern Physics. Springer. 2006
13. V.G. Baryshevsky. High-Energy Nuclear Optics of Polarized Particles. World Press. 2012. 640 p.
14. Baryshevskii, V. G. (1976). Nuclear Optics of Polarized Media (Byelorussian State University Press, Minsk) [in Russian].
15. Baryshevskii, V. G. (1976). Particle spin precession in antiferromagnets, Sov.Phys. Solid State 18 pp. 204–208.
16. Kumakhov, M. A. (1976). On the theory of electromagnetic radiation of charged particles in a crystal, Phys. Lett. A 57, 1, pp. 17–18.
17. Swent, R. L., Pantell, R. H., Alguard, M. J., Berman, B. L. Bloom, S. D. and Datz, S. (1979). Observation of channeling radiation from relativistic electrons Phys. Rev. Lett. 43, 23, pp. 1723–1726.
18. Alguard, M. J., Swent, R. L., Pantell, R. H., Berman, B. L. Bloom, S. D. and Datz, S. (1979). Observation of radiation from channeled positrons, Phys. Rev. Lett. 42, 17, pp. 1148–1151.
19. Cue, N., Bonderup, E., Marsh, B. B., Bakhru, H., Benenson, R. E., Haight, R., Inglis, K., and Williams, G.O. (1980). Transitions between bound states for axially channeled MeV electrons, Phys. Lett. A 80, 1, pp. 26–28.
20. Chevganov, A. B. and Feranchuk, I. D. (1982). A zone spectrum of the ultrarelativistic channelled particles in a crystal, J. Phys. (Paris) 43, 11, pp. 1687–1698.
21. Datz, S., Fearick, R. W., Park, H., Pantell, R. H., Swent, R. L., Kephart, J. O., Klein, R. K. and Berman, B. L. (1983). Electron and positron planar channeling radiation from diamond Phys. Lett. A 96, 6, pp. 314–318.
22. Park, H., Swent, R. L., Kephart, J. O., Pantell, R. H., Berman, B. L., Datz, S. and Fearick, R. W. (1983). Positron and electron channeling radiation from germanium, Phys. Lett. A 96, 1, pp. 45–48.
23. Baryshevsky, V. G. and Feranchuk, I. D. (1985). A comparative analysis of various mechanisms for the generation of X-rays by relativistic particles, Nucl. Instrum. Methods A 228 pp. 490–495.
24. Baryshevsky, V. G., Chevganov, B. A. and Feranchuk, I. D. (1985). Theoretical Interpretation of radiation spectra from channeled positrons, Phys. Lett. A 112,6,7, pp. 346–351.


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