Nonrelativistic quantum theory of non-dipole effects in a multielectron atom: radiation transition operator

In the work of Hopersky A.N. et al., arXiv: 2609.33494v1 [physics. atom-ph] in the Loudon integral representation, the general analytical structure of the complete operator of a multipole radiation transition taking into account non-dipole effects for a multielectron atom is established. In this Letter this structure is converted to the sum only for all multipoles.