Theory of Low Energy Channeling Radiation: Application to a Germanium Crystal

Abstract

The theory of Channeling Radiation (CR) as applied to a germanium crystal target (spectra and linewidths) is presented here for electron energies less than 12 MeV. For higher electron energies, the channeling radiation spectrum in a germanium crystal is composed of energy lines that are so close to each other that the spectrum results in a broad envelope. The many‐beam formalism and the standard Hartree‐Fock potentials are used to calculate the CR transition energies. The expressions of CR spectral linewidths are derived from the use of the complex optical potential which describes the incoherent scattering from thermally vibrating atoms of the crystal. The population of the different quantum states as a function of the crystal thickness is also obtained. In this study we will present calculations for major axes or planes of a germanium crystal. For other crystals with diamond like structure and other planes or axes, the reader is invited to use the given formulas and parameters.

Simulation of ultra-relativistic electrons and positrons channeling in crystals with MBN Explorer

“…Modeling a crystalline field as a superposition of the atomic fields described by the Molière potentials can lead to intrinsic errors. Though the Molière approximation is a well established and efficient approach, more realistic schemes for the crystalline fields, based, for example, on X-ray scattering factors [69,70], can also be employed for the channeling simulations.…”

Spectral brilliance of channeling radiation at the ASTA photoinjector

“…Figure 7 shows the transition probabilities W mn calculated using Eqs. (11) and (20) for the four bound states at 20 MeV. As mentioned earlier, they obey the approximate selection rule W mn = 0 if |m − n| = odd.…”

“…Experimental estimates show that the scattering angle of channeled particles in a crystal is less than that in an amorphous medium. Estimates of the scaling between the rms multiple scattering angles during channeling and in an amorphous crystal are in the range θ MS,ch ≃ (0.22 − 0.56)θ MS [11,12]. The range of values in the numerical coefficient depends on the crystal thickness, smaller values for larger thickness, but is nearly independent of the beam energy.…”

A general formalism of two-dimensional lattice potential on beam transverse plane for studying channeling radiation

“…The periods of V 2D (x, y) is therefore a x = a y = a/(2 √ 2) in both x and y direction when in Eqs. (20) and (21) has also been obtained previously using the method of strings of ions in the axial channeling model [18], as this is the easiest case for the axial channeling calculation. As shown in Fig.…”

“…Fitting parameters α j and β j for atomic form factor of germanium obtained by Chouffani andÜberall[18], where a = 5.658Å is the lattice constant.…”