Excited transition, energy density required

For molecules, the energy density required to saturate the excited transition can be as much as three orders of magnitude higher than for atoms. This may be seen from Equation 23 in terms of a saturation spectral energy density with a result similar to but more complicated than that of Equation 20. 

Given expressions for A(1) and B(1), Eqs. (58M63) provide the means to evaluate the required perturbed excitation energies and transition densities. The derivation of Aa) and B(1) is fairly involved and it will only be very briefly outlined here. For further details see (47). 

Therefore, a timing value less than 1.00 is faster than a Direct calculation and values greater than 1.00 are slower. The timing data includes the time required to perform the TDDFT calculation that is also required to produce the unperturbed transition densities and excitation energies as well as the time required to calculate the MCD parameters. 

This density of states is probably a minimum at the bottom of the conduction band and increases to a maximum in the center of the band. When x in Na WO is small, optical excitation would be to the bottom of the conduction band, where the energy level density is small. Any finite number of transitions would necessitate use of several adjacent levels, which would be significantly spread out on an energy scale. When x in Na WOs approaches unity, the band is well populated and the Fermi energy is in a region where there are many states of almost identical energy. Any finite number of transitions would require a smaller spread between the adjacent levels, and hence the optical absorption curve would be narrower. 

Recently, however, emission from the (2,1) and (3,2) levels has been observed (Zuckerman et al., 1971). These levels radiatively decay in a very short time to the lower levels (see energy diagram). Thus collisional excitation of these levels would require molecular densities of probably 107 of 108 cm-3, so that these transitions should be ideal for investigating the dense cores of black clouds. 

Up to now/ the dimer laser system has been described alone in terms of population inversion between suitable energy levels/ and for this description the condition S2 > A 2 is indeed the only necessary condition for cw laser oscillation/ as long as the thermal population density in the lower laser level remains negligibly low. However/ as this optically pumped laser system is a coherently excited three level system/ the coherent emission can also be described as stimulated Raman scattering/ which is resonantly enhanced by the common level 3 of the pump and laser transitions. This coupled two photon or Raman process does not require a population inversion between levels 3 and 2 and introduces qualitatively new aspects which appreciably influence and change the normal laser behaviour. For a detailed and deeper description of the coherently excited three level dimer... 

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