Four-state system larger systems

The condition for observing induced emission is that the population of the first singlet state Si is larger than that of So, which is far from the case at room temperature because of the Boltzmann distribution (see above). An inversion of population (i.e. NSi > Nso) is thus required. For a four-level system inversion can be achieved using optical pumping by an intense light source (flash lamps or lasers) dye lasers work in this way. Alternatively, electrical discharge in a gas (gas lasers, copper vapor lasers) can be used. 

For all the examples discussed, excluding excited states, we have taken as a prototype the beryllium atom. The reason for this choice stems from the fact that in this four-electron system one finds already a great deal of the complexities present in larger systems. For excited states, we have considered a simpler example involving the helium atom. 

In band theory, two-electron excitation across the gap gives an A state at 2 ia with transition moment fioia from IB, and this cancels the 5 == 1 term in Eq. (42). In correlated systems, the nA state derived from two-electron excitation [96,97] of G shifts below 2E b and the transition dipole fx A B becomes larger than yu iB, as follows analytically for dimers. The sum rule compensates for decreasing E a - E b with increasing fx A)B-The NLO fits in Section IV are based on Table 6.6 and place nA, slightly lower than in PPP oligomers. The indicated fXnA B/f a B 1.3 must be increased to 2 to satisfy Eq. (43) within these four states. 

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