A phase-consistent derivation of the electromagnetic multipole operators

The aim of this work is to draw attention to the precise formulation of theelectromagnetic-multipole transition operators and moments, especially the electric ones. Their precise structure fixes their transformations under some operations, as time reversal and hermitian conjugation, and in this way they play an important role as far as properties of their matrix elements are concerned.

Another point of discussion is the consistent use of a well-defined phase convention for the angular-momentum eigenfunctions and their role in the development of the BCS formalism. A numerical example proves the importance of the use of well-defined phase-consistent eigenfunctions, operators, occupation probabilities, etc.