Dipole emission profile

This expression is a useful starting point for a computation of spectral moments and profiles. Equation 2.68 allows the computation of the dipole emission profile if / (t) falls off to zero sufficiently fast for t —> +oo. Equation 2.69, on the other hand, has less stringent conditions on the dipole function itself and is more broadly applicable (dense fluids) when combined with Eq. 2.66. 

In addition to the collinearity assumption (the ground and excited-state dipole moments are taken as coUinear), specific solute-solvent interactions are not considered and solvent effects on absorption and emission profiles are neglected. Incomplete relaxation prior to emission is always possible. Also, the use of some solvatochromic equations can lead to negative values and imaginary values for some compounds. Finally, it is important to remember that, even if the ground- and excited-state dipole moments are con dered to be collinear or at least approximately collinear, parallel and antiparallel orientations of the ground- and excited-state dipole moments should be considered... 

Because of the low collision rate in the high vacuum environment of a Fourier transform mass spectrometer (FTMS), vibrationally excited molecular ions cool predominantly by IR fluorescence. For typical IR transition dipole moments and frequencies in the mid-IR, spontaneous emission is expected to occur at a rate in the range of 1-100 s To energize an ion efficiently using IR multiple-photon excitation (MPE), the rate of photon absorption - the product of absorption cross section and photon flux - should exceed the emission rate. From such a back-of-an-envelope estimate, one finds that radiation sources producing several Watts/cm are required to induce efficient dissociation [141], Note that the demands on laser power may further increase because of the limited residence time of the ions in the laser field, collisional deactivation in traps at higher pressures, limited spectral overlap between molecular absorption and laser emission profiles, etc. 

Steady-state emission spectra of the Eu(III) coordination polymers in the solid state are shown in Fig. 2.8 (right). Emission bands were observed at around 578, 591, 613, 650, and 698 nm, and are attributed to the f-f transitions of Dq- F/with 7 = 0, 1, 2, 3, and 4, respectively. The emission band at 613 nm ( Do- Fa) is due to electric dipole transitions, which is strongly dependent on the coordination geometry. Their time-resolved emission profiles revealed single-exponential decays with millisecond scale lifetimes. The observed emission lifetimes from Dq excited level (xobs) were determined from the slopes of logarithmic decay profiles. The emission lifetimes of [Eu(hfa)3(dpb)] , [Eu(hfa)3(dpbp)] , and [Eu(hfa)3 (dppcz)] were determined to be 0.93, 0.85, and 0.93 ms, respectively (Fig. 2.9). 

The natural linewidth of a molecular spectral line in the MMW region is related inversely to the spontaneous emission coefficient of the upper state (Equation 1.5) and consequently imparts a Lorenteian shape to the line profile (Equation 1.32). As the upper state can radiate to more than one lower state, the actual natural linewidth is related to the sum of the squared dipole moment matrix elements of the states involved. In any case its contribution to the overall linewidth is negligible in comparison with the other broadening contributions at 100 GHz it would be 10 Hz. 

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