Interferences between En and Mn (n = 1, 2...) optical transition moments

The operator for interaction between monochromatic electromagnetic field (light) and molecules is usually presented as a two multipolar series % truncated expansions $V^{E1}+V^{E2}+...$ (electro-dipole, electro-quadrupole,...) and $V^{M1}+V^{M2}+...$ (magneto-dipole, magneto-quadrupole, ...). The optical transition probability is proportional to the complex square of the sum of these series, which contains interference terms like $V^{En}V^{En'}$, $V^{Mn}V^{Mn'}$, and $V^{Ep}V^{Mk}$ ($n\ne n'$). In the present study it is shown that all of terms $V^{Ep}V^{Mk}$ may be observed experimentally, if the the molecules are oriented, electrically and magnetically, and the light with appropriate phase shift between electric and magnetic fields. Also, a simple operator for the light-molecule interactions is proposed, as an alternative to Taylor series mentioned above.