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. For example, if an emissive state has a small oscillator strength, nonradiative decay will outpace radiative decay. Conversely, "bright" transitions will have large oscillator strengths. The oscillator strength can be thought of as the ratio between the quantum mechanical transition rate and the classical absorption/emission rate of a single electron oscillator with the same frequency as the transition.

Theory

An atom or a molecule can absorb light and undergo a transition from one quantum state to another.

may be defined by

is the reduced Planck constant. The quantum states electrons in the system, i.e.

.

The definition can be recast by inserting the Rydberg energy and Bohr radius

are the same, we can get rid of the sum and of the 1/3 factor

Thomas–Reiche–Kuhn sum rule

. In absence of magnetic field results in the relation between matrix elements

1. .

, we arrive at

, the above expression results in a sum rule

. Excluding this term eliminates divergency because of the vanishing denominator.

Sum rule and electron effective mass in crystals

In crystals, the electronic energy spectrum has a band structure is the electron effective mass. It can be shown that it satisfies the equation

band into the same state.

See also

• Atomic spectral line

• Sum rule in quantum mechanics

• Electronic band structure

• Einstein coefficients

References