Quantum effects for parametric X-ray radiation during channeling: Theory and first experimental observation

Quantum features of the angular distributions of parametric X-ray radiation of channeled relativistic electrons in a crystal

“…Then, this matrix element was modified in [1,3,4] in order to take into account the band structure of trans verse energy levels of channeled electrons and to avoid the dipole approximation. As in [1,3,4], we use the following formula for the angular distribution of PXRC emitted by the channeled electron captured in the nth quantum state:…”

“…(1) 1 The abbreviation PXRC for parametric X ray radiation at chan neling was introduced for the first time in [2]. …”

“…(1) can be represented in the form [1,3,4] . (3) We emphasize that F nn is a function of the relativis tic factor of the electron γ = E || /mc 2 (where E || is the initial energy of the electron entering the crystal): the wavefunction φ n (y) with the transverse wave vector k y is determined by solving the Schrödinger equation with the relativistic mass γm (see, e.g., [5]).…”

“…The first measurements of the difference between PXRC and PXR [1] at the SAGA LS (γ = E || /mc 2 ≈ 499) showed that this difference is about 6-8%. According to our calculations, it can be much larger if measurements are performed near the "quantum jump," i.e., at such energies of the electron beam at which each new odd level of the subbarrier energy (band) appears.…”

“…Conse quently, this divergence should not affect the experi mental observation of the predicted effect. Indeed, the effect of the beam divergence in the first experiment on the detection of PXRC was uncritical (see [1]). …”