Oscillator strength
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.[1][2][3]
Theory
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
:
See also
- Atomic spectral line
- Sum rule in quantum mechanics
References
- ↑ W. Demtröder (2003). Laser Spectroscopy: Basic Concepts and Instrumentation. Springer. p. 31. ISBN 978-3-540-65225-0. Retrieved 26 July 2013.
- ↑ James W. Robinson (1996). Atomic Spectroscopy. MARCEL DEKKER Incorporated. pp. 26–. ISBN 978-0-8247-9742-3. Retrieved 26 July 2013.
- ↑ Hilborn, Robert C. (1982). "Einstein coefficients, cross sections, f values, dipole moments, and all that". American Journal of Physics 50 (11): 982. arXiv:physics/0202029. Bibcode:1982AmJPh..50..982H. doi:10.1119/1.12937. ISSN 0002-9505.
- ↑ Edward Uhler Condon; G. H. Shortley (1951). The Theory of Atomic Spectra. Cambridge University Press. p. 108. ISBN 978-0-521-09209-8. Retrieved 26 July 2013.