Oscillator strength

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An atom or a molecule can absorb light and undergo a transition from one quantum state to another. The oscillator strength is a dimensionless quantity to express the strength of the transition. The oscillator strength f12 of a transition from a lower state |1 m_1\rangle to an upper state |2 m_2\rangle may be defined by

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

where me is the mass of an electron and \hbar is the reduced Planck constant. The quantum states |n m_n\rangle, n= 1,2,..., are assumed to have several degenerate sub-states, which are labeled by mn. "Degenerate" means that that they all have the same energy En. The operator Rx is the sum of the x-coordinates ri,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 |1 m_1\rangle.

[edit] Sum rule

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:

∑ fij = N.
j

[edit] See also

[edit] References

  • Robert C. Hiborn, Einstein coefficients, cross sections, f values, dipole moments, and all that, Am. J. of Phys. 50, 982 (1982), arXiv:physics/0202029v1
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