Photon angular momentum: selection rules and multipolar transition moments

The representation of electromagnetic radiation by means of vector spherical harmonics and Bessel functions is described and used to derive selection rules for atomic electronic transitions which, as expected, show that the angular momentum of the system-atom plus photon-is conserved and, more importantly, provide a very precise description of the angular momentum of the photon involved. Examples of matrix elements for electric dipole, electric quadrupole and magnetic dipole transition moments of the hydrogen atom are calculated and the results compared with those obtained by the usual plane-wave expansion and with more recent results obtained in connection with studies of 'twisted' beams