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Oscillator strength
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1 reference results for: Oscillator strength
Wikipedia
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 f_{12} of a transition from a lower state |1 m_1rangle to an upper state |2 m_2rangle 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 m_e is the mass of an electron and hbar is the reduced Planck constant. The quantum states |n m_nrangle, n= 1,2,..., are assumed to have several degenerate sub-states, which are labeled by m_n. "Degenerate" means that 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 |1 m_1rangle.

Sum rule

The sum of the oscillator strength from one sub-state |i m_irangle to all other states |j m_jrangle is equal to the number of electrons N:
sum_j f_{ij} = N.

See also

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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