Rotation period

The quantity riV/RT is equal to six times the rotational period. The rotational relaxation time, p, should he shorter than the fluorescence lifetime, t, for these equations to apply. It is possible to perform calculations for nonspherical molecules such as prolate and oblate ellipsoids of revolution, but in such cases, there are different rotational rates about the different principal axes. 

In principle, pulsed excitation measurements can provide direct observation of time-resolved polarization decays and permit the single-exponential or multiexponential nature of the decay curves to be measured. In practice, however, accurate quantification of a multiexponential curve often requires that the emission decay be measured down to low intensity values, where obtaining a satisfactory signal -to-noise ratio can be a time-consuming process. In addition, the accuracy of rotational rate measurements close to a nanosecond or less are severely limited by tbe pulse width of the flash lamps. As a result, pulsed-excitation polarization measurements are not commonly used for short rotational periods or for careful measurements of rotational anisotropy. 

The value of tan A depends upon the modulation frequency, the excited state lifetime, and the rate of rotation. The value decreases to zero when the rotation period is either longer or shorter than the excited state lifetime and is a maximum when the two times are comparable in magnitude. Tan A also increases as the modulation frequency increases. For spherical rotators, the measured value of tan A for a given modulation frequency and excited state lifetime allows the rotational rate to be calculated from... 

Crossed beam studies involving both neutrals and ions will provided detailed information relating to the potential energy surfaces and reaction mechanisms for organometallic reactions (19). These studies are especially revealing when the reactions are direct and involve intermediates whose lifetime does not exceed a rotational period. 

Diameter of nucleus, estimated (km) Rotation period (hours)... 

It is also interesting to note that the long-term power variations of the disk noise (part [b] of figure 4.19) seem to be related to the disk rotation period (0.77s for a 78 rpm record). This result indicates that the noise present on this particular analog disk is certainly not stationary, but that it could be cyclostationary [Gardner, 1994], More elaborate tests would be needed to determine if this noise is indeed cyclostationary, and what type of cyclostationarity is actually involved (the simplest model would be an amplitude modulated stationary process) [Gerr and Allen, 1994],... 

One important class of exceptions to the preceding discussion is provided by prereactive or postreactive van der Waals (vdW) complexes. The lifetimes for such resonances can be much longer than that for conventional transition state resonance trapped near the saddle point. In the discussion of the F+HCl reaction below, we shall see that resonances of this sort can have lifetimes much longer than the rotational period of the complex and thus may show INR signatures. 

Within the rotational sudden approximation we assume that the interaction time is much smaller than the rotational period of the fragment molecule so that the diatom BC does not appreciably rotate from its original position while the two fragments separate. In terms of energies, this requires the rotational energy, Erot, to be much smaller than the total available energy. If that is true, the operator for the rotational motion of BC, hrot, can be neglected in (3.16). The partial differential equation thus becomes an ordinary differential equation,... 

Let us for simplicity discuss a triatomic molecule, for example H2O, with fi perpendicular to the plane defined by the three atoms. In that case, the photon will mainly excite molecules that are perpendicularly aligned to the Eo vector, i.e., that lie in a plane perpendicular to Eo- If the dissociation time is small compared to the rotational period of the parent molecule, the rotational vector of OH will be preferentially directed parallel to the laboratory 2-axis because the recoil of H and OH proceeds in-plane. This would lead to a distribution in the projection quantum number mj which is strongly peaked near mj j. For a parallel transition, on the other hand, we would expect the opposite situation, i.e, j would be aligned perpendicularly to the 2-axis and P(mj) would peak near mj - 0. 

The experiments described above used nanosecond laser pulses, which are much longer than the rotational period of the molecules. At the termination of the pulse, the pendular state that is formed relaxes adiabatically to a free-rotor eigenstate. If instead picosecond laser pulses are used, a rotational wave packet is formed by successive absorption and re-emission of photons during the laser pulse. Such wave packets are expected to display periodic recurrences of the alignment after the end of the pulse. 

In analogy with the one-dimensional analysis, the Jj are defined over complete periods of the orbit in the (qj,Pj) plane, Jj = ptdq j. If one of the separation coordinates is cyclic, its conjugate momentum is constant. The corresponding orbit in the (qj,Pj) plane of phase space is a horizontal straight line, which may be considered as the limiting case of rotational periodicity, for which the cyclic qj always has a natural period of 2-k, and Jj = 2irpj for all cyclic variables. 

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