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The problem of excitation of the exciton-impurity complex (EIC) by fast electrons in a non-metallic crystal is considered using a many-electron approach. The operators which describe singlet and triplet state of EIC arc introduced. The expressions for the probability of creation of the EIC are obtained and possible selection rules for corresponding transitions are analysed. A comparison is made with case of generation of free Wannier-Mott exciton. A number of papers [l to 51 was dedicated to the calculation of the excitonimpurity complex (EIC). This made it possible to carry out a theoretical analysis of such interesting physical processes as capture of a large radius exciton by charged point defects 161 and optical cxcitation of the EIC in semiconductors 171. Generation of the EIC by fast electrons which is the subject of our paper, refers to processes of such type. The processes investigated experimentally 18, 91 in connection with the induced luminescence are studied in crystals irradiated by keV electrons. HpHThis many-electron problem may be solved by using the nodal elementary excitation method [lo to 121 for describing the electron subsystem of the crystal.The subsystem of fast electrons is described in terms of an ordinary electron operator. As basis system of one particle function we take a system of Wannier functions without impurity, to which arc added plane waves, which are normalized to the crystal volume. The last function describes moving electrons. In the model considered the valence band is completely filled and the conduction band is empty (simple spin compensated background). The perturbation is caused by Coulomb interaction between the moving electrons and valence electrons of the atoms. We shall consider only terms in the interaction Hamiltonian with unchanged number of particles for each subsystem of electrons (straight scattering).The ground state ofthe crystal was treated with.the nodal elementary excitation method, as described in 110 to 121. The ground state is one which no excitations. That problem has been solved without regard of the influence of impurity atoms in the adopted approximation and it has been treated as in [lo] under the condition

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