Time dependence relative resonance frequency

The LICS, produced by an idealized Continuous-Wave (CW) laser (steady amplitude and single-frequency laser), can differ substantially from the structure produced by a pulsed laser, since the AC Stark shifts produce time-dependent detunings relative to one- and two-photon resonance. The time-dependent pulse and frequency effects in population trapping in LICS have received attention in theoretical works [93]. Using numerical approaches, as well as approximate analytical solution, it was shown that the trapped population in realistic atomic systems can be sufficiently decreased, to the point when no population remains in the system, by the increase in laser energies. Furthermore, the use of properly chirped laser pulses not only helps to increase the trapped population but also makes the system more stable against increases in the pulse energy. 

In the case of Gd(III) ion T e is large and is replaced by a function of the correlation time, rc and the resonance frequency, where l/rc = /T c+ l/rr. Still the r-6 dependence holds good in the Gd3+ complexes for the relative relaxation rates for different ligand nuclei. 

The r dependence of the relative resonance Raman intensities of two modes is much more sensitive to their difference in frequency than to their difference in displacement. The reason for this dependence is found in the short time dynamics of the wavepackets which is much more sensitive to the frequency at a given displacement than to the displacement for a given frequency. This simple physical picture provides an explanation for why very low frequency metal-ligand modes in a big molecule often do not appear in the resonance Raman spectrum even though the modes have appreciable displacements. 

If one denotes by vj, pj and rj, respectively, the resonance frequency, the relative concentration and the mean residence time of a nucleus at an adsorption site , then the shape of the NMR spectrum for a system with two different sorts of adsorption sites j = a, b with pa + pb = 1 strongly depends on the quantity ... 

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