Collision-induced line broadening

Lamb peaks (inverse Lamb dips) at the line centers of the absorbing transitions (Sect. 2.3). The line profiles of these peaks are determined by the pressure in the absorption cell, by saturation broadening, and by transit-time broadening (Vol. 1, Sect. 3.4). Center frequency coq, linewidth Aco, and line profile Pl(co) are measured as a function of the pressure p (Fig. 8.2). The slope of the straight line Aco p) yields the line-broadening coefficient [977], while the measurement of coo p) gives the collision-induced line shift. 

The single-mode laser naturally gives less output power than a multimode laser with the same active volume since its induced emission is concentrated into a smaller frequency range. This loss in intensity, however, is much less than one would expect from the ratio of linewidths or from the reduction in oscillating mode number 3i. 32,41) jbis is due to the fact, that not only atoms with the exact transition frequency can contribute to the induced emission, but also those inside the homogeneous linewidth which is determined by collision processes in the case of gas lasers or by crystal line broadening in solid lasers... 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

Induced spectra actually consist of contributions arising from free-to-free, free-to-bound, bound-to-bound, and bound-to-free transitions. At temperatures much greater than the well depth of the intermolecular potential, kT e, the observed induced absorption is nearly fully due to free-to-free transitions as Welsh and associates suggest, but individual dimer lines or bands may still be quite prominent unless pressure broadening and perhaps other processes (like ternary interactions) have obliterated such structures. However, at lower temperatures, kT collision-induced is a poor choice. 

These line shapes are generally not very useful for collision-induced absorption work, because pressure broadening, Doppler effect and instrumental resolution are here of no great concern. In Chapters 5 and 6 we will consider a number of other ad hoc model functions that have acquired a certain significance in collision-induced absorption. 

Spectroscopists have always known certain phenomena that are caused by collisions. A well-known example of such a process is the pressure broadening of allowed spectral lines. Pressure broadened lines are, however, not normally considered to be collision-induced, certainly not to that extent to which a specific line intensity may be understood in terms of an individual atomic or molecular dipole transition moment. The definition of collisional induction as we use it here implies a dipole component that arises from the interaction of two or more atoms or molecules, leading at high enough gas density to discernible spectral line intensities in excess of the sum of the absorption of the atoms/molecules of the complex. In other... 

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

Fig. 5. Zero pressure extrapolated cross sections for the competitive collision-induced dissociation processes of (H20)Na+(NH3) with xenon in the threshold region as a function of kinetic energy in the center-of-mass frame (lower axis) and laboratory frame (upper axis). Solid lines show the best fits to the data using the model of Eq. (7) convoluted over the neutral and ion kinetic energies and the internal energies of the reactants, using common scaling factors. Dashed lines show the model cross sections in the absence of experimental energy broadening for reactants with an internal energy of 0 K. Adapted from [45]...

The two main sources of information about atomic and molecular structure and interatomic interactions are provided by spectroscopic measurements and by the investigation of elastic, inelastic, or reactive collision processes. For a long time these two branches of experimental research developed along separate lines without a strong mutual interaction. The main contributions of classical spectroscopy to the study of collision processes have been the investigations of collision-induced spectral line broadening and line shifts (Vol. 1, Sect. 3.3). 

The collision-induced additional line broadening ap% is therefore often called pressure broadening. 

The broadening Fj is proportional to the probability of the excited state k) decaying into any of the other states, and it is related to the lifetime of the excited state as r. = l/Fj . For Fjt = 0, the lifetime is infinite and O Eq. 5.14 is recovered from O Eq. 5.20. Unfortunately, it is not possible to account for the finite lifetime of each individual excited state in approximate theories based on the response equations (O Eq. 5.4). We would be forced to use a sum-over-states expression, which is computationally intractable. Moreover, the lifetimes caimot be adequately determined within a semiclassical radiation theory as employed here and a fully quantized description of the electromagnetic field is required. In addition, aU decay mechanisms would have to be taken into account, for example, radiative decay, thermal excitations, and collision-induced transitions. Damped response theory for approximate electronic wave functions is therefore based on two simplifying assumptions (1) all broadening parameters are assumed to be identical, Fi = F2 = = r, and (2) the value of F is treated as an empirical parameter. With a single empirical broadening parameter, the response equations take the same form as in O Eq. 5.4 with the substitution to to+iTjl, and the damped linear response function can be calculated from first-order wave function parameters, which are now inherently complex. For absorption spectra, this leads to a Lorentzian line-shape function which is identical for all transitions. 

There are three methods which have been used to study collisions of Rydberg atoms with neutrals. They are direct measurement of collisionally induced population changes, line shift and broadening measurements, and photon echo measurements.23 In this chapter we describe the first of these. The last two are described in the chapter immediately following. 

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