3. Optical transitions between rare-earth levels

3.1 Radiative and non-radiative transitions between 4f levels

Transitions between the levels described above can be either radiative, with photon emission, or non-radiative, with no photon emission but phonon emission, or vibronic, with partial photon and phonon emission. Radiative emissions are either of electric or magnetic dipolar type. Radiative transitions are usually characterized by their "oscillator strength", which are pure numbers less than 1 characterizing the intensity of a transition. The oscillator forces for an unpolarized transition i to j are defined in vacuum by :