Radiation from fast charged particles in crystals: Unified quantal treatment.

Abstract

We present a unified quantal treatment of the various types of radiation emitted by fast, charged, spin-(1/2) or spinless particles which propagate at small angles relative to a set of principal atomic planes or rows in a crystal. [Henceforth, direction(s) parallel or perpendicular to these rows (planes) will be referred to as longitudinal or transverse, respectively.] We analyze the dependence of the emission frequencies and rates on the energy and transverse momentum of the incident particle, distinguishing between two fundamental emission modes. One is the transverse mode (TM), which unifies all radiative transitions that are characterized only by the projected potential (i.e., the periodic transverse variation of the crystal potential), such as channeling, quasichanneling, and TM coherent bremsstrahlung transitions. The other one is the longitudinal mode (LM), which includes all transitions involving longitudinal momentum transfer to the lattice, with or without a simultaneous projected potential transition.Our treatment reduces the input needed for a comprehensive analysis of both TM and LM emission spectra to the set of Bloch eigenfunctions and quasimomenta of the particle which are obtained on considering its interaction with the projected potential only. The resulting expressions for LM emission rates as a function of the frequency and direction of emission give a considerably more complete and quantitatively correct characterization of this emission mode than previous attempts. Contrary to previous works, we analyze explicitly the effects of quantum recoil ${r}_{q}$, which is the ratio of the photon energy to the incident particle energy. The case of ${r}_{q}$\ensuremath{\sim}1 [which is applicable to LM emission from electrons and positrons (\ensuremath{\beta} particles) with energies as low as few tens of MeV and to TM coherent bremsstrahlung from \ensuremath{\beta} particles with energies in the GeV range] is shown to correspond to frequencies, linewidths, and directional distribution of the emission that differ strongly from those obtained in the more familiar limit of ${r}_{q}$\ensuremath{\simeq}0. Quantum-recoil corrections to emission frequencies given by extant theories are shown to be significant even for ${r}_{q}$ considerably smaller than 1.