Electromagnetic radiation multipolarity

There exists another more consistent way of obtaining the electron transition operators. We can start with the quantum-electrodynamical description of the interaction of the electromagnetic field with an atom. In this case we find the relativistic operators of electronic transitions with respect to the relativistic wave functions. After that they may be transformed to the well-known non-relativistic ones, accounting for the relativistic effects, if necessary, as corrections to the usual non-relativistic operators. Here we shall consider the latter in more detail. It gives us a closed system of universal expressions for the operators of electronic transitions, suitable to describe practically the radiation in any atom or ion, including very highly ionized atoms as well as the transitions of any multipolarity and any type of radiation (electric or magnetic). 

Alternatively, the Hamiltonian for fhe radiation field in multipolar formalism may be written explicitly in terms of fhe Maxwell field operators. From the second term of Eq. (2), fhe Hamiltonian density for the electromagnetic field is... 

They quanta may carry away different angular momenta (L). IfL= 1,2,3,... the radiations are called dipole, quadrupole, octupole, etc., respectively. Gamma radiation with L = 0 does not exist because the electromagnetic waves have transversal nature (the photons have spin 1). Each multipolarity 2 is characterized by a specific angular distribution. The radiation may be electric or magnetic, depending on the term of the electromagnetic interaction that is responsible for the particular transition. 

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