By Vladimir G. Baryshevsky, Ilya D. Feranchuk, Alexander P. Ulyanenkov

ISBN-10: 3540269053

ISBN-13: 9783540269052

This systematic and accomplished monograph is dedicated to parametric X-ray radiation (PXR). This radiation is generated by means of the movement of electrons inside of a crystal, wherein the emitted photons are diffracted via the crystal and the radiation depth severely depends on the parameters of the crystal constitution. these days PXR is the topic of various theoretical and experimental experiences in the course of the international. the 1st a part of the publication is a theoretical therapy of PXR, which incorporates a new method of describe the radiation approach in crystals. the second one half is a survey of PXR experimental effects and the potential purposes of PXR as a device for crystal constitution research and a resource of tunable X-ray radiation.

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Baryshevsky et al: Parametric X-ray Radiation in Crystals STMP 213, 43–56 (2005) c Springer-Verlag Berlin Heidelberg 2005 44 3 Dynamical Theory of PXR ˆ e,c , H ˆ γ,c : plane waves but on the one-particle eigenfunctions of the operators H + − [bν ΨνE (r) + b+ ν ΨνE ] ; Ψˆ (r) = ν + − [aµ A+ µω (r) + aµ Aµω ] . 2) µ + Here bν (b+ ν ) and aµ (aµ ) are the annihilation (creation) operators of electrons and photons, respectively. Both particles are in stationary states, which are de− + + (ΨνE ) or by the vector potential A− scribed by the wavefunction ΨνE µω (Aµω ) for electrons and photons, respectively.

16). 3). e. 3) with the accuracy O(U 2 /E 2 ): − 2 c2 ∆ + m2 c4 − E 2 + 2EU (r) − ic αl ∂ ∂xl U (r) ΨE (r) = 0. 11) where χE is the bispinor for the free electron [1]. e. (pg) ≈ 0. 10) in order to take into account a zone spectrum of the transverse movement [4]. However, the case of channelling is not essential for PXR, and we assume (pg) = 0 and 2(pg) g 2 for relativistic electrons. 2 Wave Functions and Vector Potential in a Crystal (±) ΨE (+) 47 (±) ≈ eipr 1 + ϕE (r) χE ; ˆg eigr {Cg (z)H(z)H(L − z) + Cg (L)H(z − L)} ; B ϕE = g=0 Cg (z) = 1 − ei(p˜g −pz −gz )z ; p˜g = E 2 − m2 − (p⊥ − g ⊥ )2 ; (−) ˆ−g e−igr {C−g (z − L)H(z)H(L − z) + C−g (−L)H(−z)} .

5. 3 PXR in a Mosaic Crystal (m) ω{hkl} = πmc , d{hkl} sin θB ∆θx ≈ ∆θy ≈ 33 ∆ω ≈ γ −1 , ω (m) ωB L ≤ |χ0 |−1 . 47) c The quantitative estimate of the PXR intensity in a thin crystal is possible using a parameter of brightness I, which is now widely accepted for characterization of synchrotron radiation (SR) [24]: I= photons N = I0 . 529 GeV, and angular and spectral divergence ∆θ ≈ 1 mrad, ∆ω/ω ≈ |χ0 |, respectively, the brightness in PXR reﬂection is (m) (m) I{hkl} ≈ α J |χgm (ωB )|2 . 68 . 3 × 1013 J[A] photons .

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