Collisional bandwidth

The impact of bath molecules on the atoms of the molecule of interest cannot be treated as impulsive because the strong binding forces of chemical bonds places a significant fraction of the vibrational sjjectrum of the molecule above the collisional bandwidth, broadly defined as the reciprocal of the duration of a collision. Thus collisional vibrational relaxation and excitation are inefficient relative to rotational relaxation. Binary collision theory is well develojjed at the microcanonical level because of the its importance in chemical reactions. The relationship to the friction is of interest, " primarily because stochastic treatments have the potential of bridging the gas-phase limit of resolved binary collisions and the liquid phase where collective phenomena of the solvent can preclude interpretation in terms of binary collisions. 

It is of interest to compare the half-widths at half-intensity of the spectral functions of the three systems shown in Fig. 3.2. These amount to roughly 140, 80 and 50 cm-1 for He-Ar, Ne-Ar and Ar-Kr, respectively, which are enormous widths if compared to the widths of common Doppler profiles, etc. The observed widths reflect the short lifetimes of collisional complexes. From the theory of Fourier transforms we know that the product of lifetime, At, and bandwidth, A/, is of the order of unity, Eq. 1.5. The duration of the fly-by interaction is given roughly by the range of the induced dipole function, Eq. 4.30 (1/a = 0.73 a.u. for He-Ar), divided by the mean relative speed, Eq. 2.12. We obtain readily ... 

The discussion presented above applies only for impulsive collisions for which Pc 1. that is, m. This is not a realistic formulation, except near the threshold for dissociation. In most cases of interest the vibrational frequencies are too high relative to the collision bandwidth cuq defined in Section III C. For a single degree of freedom (n = 1) it is essential to include the frequency dejjendence of the collisional friction discussed in that section. In this case the energy diffusion coefficient D(E) is modeled by Eq. (4.9) which, in the limit of constant friction, is in accord with Eq. (5.1), deduced from the density of states. At low bath pressures, where the collisions are resolved, D(E) is the second moment of P(E, ), ... 

The observed bands are more than twenty times broader than the bandwidth of the laser radiation (-5-15 cm i). The increased width could be caused by vibrational hot-bands, but these should be largely eliminated in the spectra because the ions are collisionally cooled prior to interaction with the laser pulse. However, the zero-point motion of the central proton on the extremely flat PES likely extends over an unusually large area, leading to the exploration of a much larger part of... 

In this contribution we present two laser spectroscopic methods that use coherent resonance Raman scattering to detect rf-or laser -induced Hertzian coherence phenomena in the gas phase these novel coherent double resonance techniques for optical heterodyne detection of sublevel coherence clearly extend the above mentioned previous methods using incoherent light sources. In the case of Doppler broadened optical transitions new signal features appear as a result of velocity-selective optical excitation caused by the narrow-bandwidth laser. We especially analyze the potential and the limitations of the new detection schemes for the study of collision effects in double resonance spectroscopy. In particular, the effect of collisional velocity changes on the Hertzian resonances will be investigated. 

Our studies of the effect of velocity-changing collisions in an rf-laser double resonance experiment contribute to a new vista into the role of collisictis in laser spectroscopy of sub-level structures the limitation of the observation time of the active atoms due to narrow-bandwidth optical excitation and simultaneous velocity diffusion can be of importance for a variety of spectroscopic techniques that use a velocity-selective excitation and detection of either sublevel populations or sublevel coherence. On the other hand, the collisional velocity diffusion of sublevel coherence within an optical Doppler distribution can also give rise to new and surprising phenomena as will discussed in the next section. 

A CO2 laser operates on the emission bands between vibrational combination states generating emission on discrete rovibrational transitions in the i>i and 2 2 3 bands, centred around 10.6 and 9.6 pm, respectively. Population inversion is achieved by collisional energy transfer from plasma-excited N2 to CO2, usually in a mixture with He. A particular rovibrational emission line can be selected using a rotatable diffraction grating incorporated in the laser cavity. CO2 lasers can achieve very high continuous-wave (cw) power levels of up to 100 W from commercially available systems. In addition, CO2 lasers are robust, narrow-bandwidth and low-cost systems well able to induce IRMPD, but a disadvantage is clearly its limited tunability. It should be noted that fixed-frequency CO2 lasers are used routinely in commercial MS platforms to induce dissociation as an alternative to CID. 

Consider next the more reasonable case in which the atoms of the particles form a bonded molecule. The collisional friction acting on the atoms of the molecule is reduced by screening in proportion to the "surface area" exposed to the bath molecules by the atom embedded in the particle[l7]. This is typically about 0.5 or less. The atom frictions can be transformed into mode frictions 3(5 E(5)) using the transformation to appropriate mode coordinates, where E( ) is the energy in mode 5. Hydrodynamic contributions are not additive and the friction associated with the R coordinate for most systems is modelled from the zero-frequency frictions of each particle. In most cases the barrier frequency a)m of the transition state of V(R) defined in the next section, is sufficiently small relative to the atom-atom collision bandwidths or the inverse of the structural relaxation time of the... 

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