Angular anisotropy of the RCE X-rays under planar channeling as manifestation of geometric properties of the in-crystal electric field

Planar channeled ion under resonant coherent excitation conditions experiences an action of the oscillating electric field arising in the ion rest frame. We show how the alignment of the angular momentum of coherently excited ions and, hence, the angular anisotropy of their characteristic X-ray radiation are connected with the geometrical and symmetry properties of this field. The consideration is based on two examples of (k,l)=(2,-1) and (1, 3) resonances with 423 MeV/u Fe24+ ions in (22¯0) planar channel of Si crystal, corresponding to different symmetries of the resonant field. In both cases the resonant electric field is elliptically polarized. A choice of an appropriate coordinate frame allows us to show the connection between the geometrical properties of the resonant field and the X-ray angular distributions especially clear. To illustrate, we calculate angular distributions of X-rays for individual ionic trajectories using density matrix formalism and then consider formation of the angular distributions not resolved by ion trajectory. Comparison with recent experimental data is done.