Oscillator strength

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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]


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

The oscillator strength f_{12} of a transition from a lower state |1\rangle to an upper state |2\rangle may be defined by

  f_{12} = \frac{2 }{3}\frac{m_e}{\hbar^2}(E_2 - E_1) \sum_{\alpha=x,y,z}
 | \langle 1 m_1 | R_\alpha | 2 m_2 \rangle |^2,

where m_e is the mass of an electron and \hbar is the reduced Planck constant. The quantum states |n\rangle, n= 1,2, are assumed to have several degenerate sub-states, which are labeled by m_n. "Degenerate" means that they all have the same energy E_n. The operator R_x is the sum of the x-coordinates r_{i,x} of all N electrons in the system, etc.:

  R_\alpha = \sum_{i=1}^N r_{i,\alpha}.

The oscillator strength is the same for each sub-state |n m_n\rangle.

Thomas–Reiche–Kuhn sum rule[edit]

The sum of the oscillator strength from one sub-state |i m_i\rangle to all other states |j m_j\rangle is equal to the number of electrons N:

  \sum_j f_{ij} = N.

See also[edit]


  1. ^ W. Demtröder (2003). Laser Spectroscopy: Basic Concepts and Instrumentation. Springer. p. 31. ISBN 978-3-540-65225-0. Retrieved 26 July 2013. 
  2. ^ James W. Robinson (1996). Atomic Spectroscopy. MARCEL DEKKER Incorporated. pp. 26–. ISBN 978-0-8247-9742-3. Retrieved 26 July 2013. 
  3. ^ 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. 
  4. ^ 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.