Nuclear Instruments and Methods in Physics Research B2 (1984) 67-70 North-Holland, Amsterdam CRYSTAL POTENTIAL PERIODICITY EFFECTS ON THE DYNAMICS OF FAST CHARGED PARTICLES AND THEIR EMISSION OF RADIATION Gershon KURIZKI * and J.K. McIVER Institute for Modern Optics, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131, USA We present an overview of our comprehensive quanta1 theory of the dynamics of fast charged particles in crystals and of the radiation they emit. Unlike previous theoretical investigations in this field, ours takes account of the full three-dimensional periodicity of the crystal potential in all dynamical regimes of the particle motion through the crystal. We show that, contrary to prevailing assumptions, the periodicity of the crystal potential, both along the direction of propagation of the particle and transversely to it, give rise to important observable effects and cannot be ignored even for channeled particles. In particular, we show that channeled particles radiate via momentum transfer to the crystal in terms of reciprocal lattice vectors. Thus the spontaneous radiation spectrum predicted by our theory is much richer than what has been known hitherto. The radiation emitted by relativistic electrons and positrons (j? particles) propagating in crystals has been extensively investigated in recent years, both theoretically and experimentally [1,2]. The theoretical models that have been proposed in this field - primarily Kumakhov’s model of channeling radiation (CR) [3] and Uberall’s model of coherent bremsstrahlung (CB) from quasifree particles [4] - have predicted correctly the main observed features of the radiation spectrum. However, by solving the classical equations of motion of channeled particles, whilst taking account of the periodicity of the crystal potential along the channel, we have shown [5] that these models, which treat CR and CB as unrelated phenomena arising in different regimes of the particle motion through the crystal, yield only part of the full emission spectrum. They cannot account for the significant amount of radiation which, according to our classical calculation, is emitted by channeled particles at combinations of CB and CR frequencies (“sidebands”), due to the perturbing effect of the periodic variation of the potential along their direction of propagation. This classical result has provided the impetus for us to undertake a comprehensive quanta1 study of the effects of crystal potential periodicity in all three dimensions on the emission of radiation in various dynamical regimes of a particle in a crystal. The outcome of this study has been our unified quanta1 theory of radiation from fast charged particles in crystals [6,7]. This theory is based on a general prescription for calculating radiative transitions between Bloch states of the particle. It relies on a dynamical formalism which makes it possible to obtain analytically details of the eigenfunctions and band structure in a variety of dynamical regimes available to a fast charged particle diffracted in the systematic reflections geometry (SRG) in a crystal (i.e. propagating at small angles relative to a set of low-index crystal planes), while retaining the full three-dimensional periodicity of the crystal potential [8]. An extension of this theory incorporates the effects of inelastic scattering of the particle by crystalline degrees of freedom in the general quanta1 formalism for its dynamics and radiative transitions [7], a problem that has not been adequately tackled thus far. Here we wish to present several results of this theory, which will demonstrate the significance of the potential periodicity in all three dimensions in any regime, including the channeling regime, contrary to the prevailing view [l-3]. Using energy and momentum conservation requirements and ignoring inelastic scattering for thin crystals (thus obtaining only the positions of centres of the spectral peaks [7]), we can show that the radiation frequencies in any regime of the particle propagation in the SRG are determined by a * Present address: Department of Chemistry, Tel Aviv University 69978 Tel Aviv, Israel 0168-583X/84/$03.00 Q Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) II. CHANNELING RADIATION