Channeling radiation from relativistic electrons in a thin LiF crystal: When is a classical description valid?

Calculation of channeling radiation from relativistic electrons under (1 1 1) planar channeling conditions in a LiF crystal is performed using both classical and quantum methods. The complicated shape of the periodic (1 1 1) planar potential allows the existence of a different number of discrete energy levels (quantum states) in the potential well formed by planes consisting of only Li atoms and the potential well consisting of only F atoms is large enough to apply the classical method. With increasing electrons energy, the classical method becomes valid to describe CR from under-barrier electrons in a deeper potential well, while one should still apply the quantum method to calculate CR from electrons in neighboring planes. Thus, the quantum feature of a CR spectrum from relativistic electrons maintains its quantum characteristics up to relativistic factors 1000.