For any possible transition between two states m

For any possible transition between two states m -...

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For any possible transition between two states m,n there exist the Einstein transition coefficients A mn , B mn , B nm . These give the probabilities of transition between these two states. A mn is the spontaneous transition rate per unit time per atom, formally given by in the first-order (electric dipole) expansion. The B values - the stimulated emission coefficient and the absorption coefficient - are related as may be shown by considering thermodynamic equilibrium and detailed balance: Here, for incident radiation intensity at the frequency ν mn equal to U ν , the probability of an induced downward transition, or stimulated emission, is B mn U ν . Transitions with Δ l = ± 1 or Δ s = ± 1 are dipole (permitted) transitions. Other kinds, via electric quadrupole or magnetic dipole moment, are possible but have generally much lower A mn ; hence the term forbidden transitions. The upper levels in these cases are said to be metastable because of their relatively long
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Unformatted text preview: lifetimes. Application of these may be seen in a schematic few-level atom; these are all part of the "ground state" n=0 . Only 4-5 of the possible transitions have high enough probabilities to be observed in a realistic case, satisfying the appropriate selection rules. . An electron may reach an upper level for any of a number of reasons: photoionization from a lower level collisional excitation cascade from a higher level (as in masers) recombination to an excited state two-electron processes Various of these are important for different ions. Having already discussed pure recombination, we still need to deal with collisional excitation of "forbidden" lines. These are important coolants in the energy balance of plasmas at T ~ 10 4 K because only the heavy elements have excited levels at the appropriate energies of a few eV. H and He don't....
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