Impulsive limit

One expects the timescale of the nonadiabatic transition to broaden for a stationary initial state, where the nuclear wavepacket will be less localized. To mimic the case of a stationary initial state, we have averaged the results of 25 nonstationary initial conditions and the resulting ground-state population is shown as the dashed line in Fig. 8. The expected broadening is seen, but the nonadiabatic events are still close to the impulsive limit. Additional averaging of the results would further smooth the dashed line. 

In Ref. 38 expressions for t T) are given without making a high-temperature approximation. In the following, however, we assume that 2kBT > hoi. When the inhomogeneous width is very small, t (T) becomes (in the high-temperature and impulsive limits)... 

Then, within the impulsive limit, carrying out the double integration involved in the calculation of p 4 (r, t) and using Equation (4), we find the amplitude of the direct fifth-order off-resonant scattering polarization ... 

Dhar L, Rogers JA, Nelson KA. Time-resolved vibrational spectroscopy in the impulsive limit. Chem Rev 1994 94 157-193. 

The isolated atom friction is frequency independent and modeled by kinetic theory. This is the impulsive limit. 

The reduced frequency (5 of the bromine oscillator is 1.39, while the reduced atom-bath vibrational frequency is <3 = 0.41. In this case B(<3) is given by Eq. (3.20). In Table III the values of BBM(nd)(8o)) and are listed. These show that the fi = 1 term dominates primarily because of the adiabatic nature of the collision. The value of / B(nc5) is 0.106, compared to the impulsive limit... 

The quantity in square brackets in (3.5) resembles the overlap kernel in the time-dependent theory of the continuous-wave absorption spectrum [34], but here involves the nonstationary ground state wave packet vibrational wave function. The interference signal in the impulsive limit directly measures the overlap between pseudo-rotating wave packets propagated in the ground and excited states for a time... 

In order to obtain the overall rate constants for dissociation at high pressures, equation (1.37) must be solved. This requires a complete set of collisional transition rates in phase space, i.e. k(q,p This set of course is extremely difficult to obtain. However, for the high velocity limit of collisions, the impulsive limit , k(q,p q, p ) can be deter-mined. With these values equation (1.37) can be simplified by expansion of the collision integrals, analogous to the conversion of the master equation (1.34) into a diffusion equation (1.58), at least for... 

The difference between (3.27,28) is that in obtaining (3.28) we have allowed the trajectory of the incident particle to "readjust" its motion during the collision event. This suggests that we can to some extent correct the results derived from (3.20) and (3.15) to remove the effects of the frozen-lattice assumption by a simple renormalization. That is, we could modify (3.26) [and (3.23)] by requiring that the results match the known impulsive limits. Equation (3.26) thus becomes... 

Figure 4(a) also demonstrates that laser pulses of finite duration tend to smooth out the details of molecular time-dependent observables. To give a representative example of the dependence of the pump-probe signals on the pulse duration. Fig. 4 compares pump-probe signals obtained for pulse durations (a) ti = T2 = 20 fs, (b) t =0, T2 = 20 fs, and (c) ti = T2 = 40 fs. It is interesting to note that impulsive preparation of the molecular system with a (5-function pulse (b) results only in minor changes of the pump-probe signal. This indicates that in the present case the impulsive limit is virtually achieved by resonant 20 fs pulses, as the pulse duration is shorter than the characteristic (e.g. vibrational) time scales of the molecular system. The... 

To examine the effect of coherence on fluorescence anisotropy, consider a system with a ground state (state 1) and two electronically excited states (2 and 3), and assume as before that the interaction matrix elements 7/i2, T/is and H23 are zero in the absence of radiation. Suppose that an ensemble of systems in the ground state is excited with a weak pulse of light that is much shorter than the lifetime of the excited state (Ti). In the impulsive limit, the populatimi of excited state 2 generated by the pulse is... 

Fig. 11.10 Dependence of three-pulse photon-echo signals on delay time (3, as calculated in the impulsive limit with Eq. (11.43) for /] = T (the delay between pulses 1 and 2) = 5 (A) and with Eq. (11.44) for ti = T =—5 (B). The delay between pulses 2 and 3 (/2 = T) was 0, 10 or 100, as indicated. The units of time are arbitrary. All calculations used the Kubo relaxation function (Eq. 10.69) with tc = 40 time units and

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