In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule.
An atom or a molecule can absorb light and undergo a transition from one quantum state to another.
The oscillator strength of a transition from a lower state to an upper state may be defined by
where is the mass of an electron and is the reduced Planck constant. The quantum states 1,2, are assumed to have several degenerate sub-states, which are labeled by . "Degenerate" means that they all have the same energy . The operator is the sum of the x-coordinates of all electrons in the system, etc.:
The oscillator strength is the same for each sub-state .
Thomas–Reiche–Kuhn sum rule
The sum of the oscillator strength from one sub-state to all other states is equal to the number of electrons :
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