On the dipole approximation in the theory of photoionization of the atom

In the nonrelativistic many-electron approximation of the theory of photoionization of the atom in the formalism of secondary quantization and the theory of irreducible tensor operators, analytical structures for the quadrupole transition operator and its matrix element are specified. A new form of the nonrelativistic criterion for the applicability of the dipole approximation is formulated as the ratio of the complete cross sections of one-electron photoionization of an atom via the channels of dipole and quadrupole transitions.