Allowed Transitions and Selection Rules

According to Equations (5.14) and (5.15), we see that the probability of a particular transition depends on the electric dipole matrix element /x, given by Equation (5.12). These transitions, which are induced by interactions of the electric dipole element with the electric field of the incident radiation, are called electric dipole transitions. Therefore, electric dipole transitions are allowed when p- 0. 

Provided that a transition is forbidden by an electric dipole process, it is still possible to observe absorption or emission bands induced by a magnetic dipole transition. In this case, the transition proceeds because of the interaction of the center with the magnetic field of the incident radiation. The interaction Hamiltonian is now written as // = Um B, where is the magnetic dipole moment and B is the magnetic field of the radiation. 

EXAMPLE 5.2 Electric dipole versus magnetic dipole transitions. 

In this example, we will roughly estimate the order of magnitude for the intensity ratio of the electric dipole to magnetic dipole transitions. Of conrse, we will assnme that both processes are allowed (which, as shown below, is not possible for a given transition) and that the same excitation intensity is nsed. 

The electric dipole transition probability (expression (5.10)) can be ronghly approximated by 

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