Collision induced rotational relaxation

An extremely brief survey is given here of some of the experimental techniques and strategies of small molecule, gas phase, frequency domain, electronic spectroscopy. More complete discussions axe found in Demtroder (1996). 

There are many reasons that one might want to record, assign, and interpret the electronic spectrum of a diatomic molecule. These include qualitative (which molecular species are present) and quantitative (what is the number density of a known quantum state of a known molecule) analysis, detection of trace constituents (wanted, as in analysis of ore samples for a precious metal, or unwanted, as in process diagnostics where specific impurities are known to corrupt an industrial process), detection of atmospheric pollutants, monitoring of transient species to optimize a combustion process by enhancing efficiency or minimizing unwanted byproducts, laboratory determinations of transition frequencies and linestrengths of interstellar molecules, and last but certainly not least, fundamental studies of molecular structure and dynamics. 

Foremost is record a spectrum To accomplish this one needs a light source, a means of monochromatizing the light either before or after it interacts with the target molecules, a scheme for wavenumber calibration which is of absolute accuracy superior to the resolution of the experiment, a molecule source, and a signal detector. Often, a single device fulfills several of these requirements, such 

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Tusa J., Sulkes M., Rice S. A. Very low energy cross sections for collision-induced rotational relaxation of I2 seeded in a supersonic free jet, Proc. Natl. Acad. Sci. USA 77, 2367-9 (1980). 

Figure 1.3 A bandhead occurs in the ft-branch of red-degraded (B < B") BaO AlE+ — Xl + bands that appear in the Ba + N2O chemiluminescence spectrum. The low-J lines in the ft branch are arranged toward higher frequency as J increases, pile up near the bandhead, and then move toward lower-frequency as J increases beyond Jh = (3B — B")/]2(B" — B ). The returning ft-branch crosses the band origin and overlays the P-branch. The top spectrum is recorded at 0.2 Torr and the (t/ = 1, v" — 2) band contains two spikes, which are ft(44) and P(46) lines that originate from an a3II(u = 0) A1 +(u = 1) J = 45 doorway state (see Section 6.5.5). In the bottom spectrum, recorded at 24 Torr, the spikes are absent due to collision induced rotational relaxation (from Field, 1976).

SOj and CO . —Collision-induced rotational relaxation within the A A2 excited-state manifold of SOj has been studied/ Excitation of single rovibronic levels... 

Collision-induced rotational relaxation is very much more efficient when resonant transfer of electronic energy is possible than when it is not possible. The cross-sections reported for rotational energy transfer in collisions of Bjy and benzene molecules, and in collisions of... 

The collision-induced electronic relaxation is, in general, slow as compared to the rotational relaxation within a single vibronic state. This... 

State, which exhibits significant anisotropy in the lab frame. It is the manipulation of the rotational wavefunction by the helium interaction that governs collision-induced Zeeman relaxation of molecules. 

Collision-Induced Rotational, Spin, and A-Doublet Relaxation... 

Fig. 12.13. Experimental arrangement and level scheme for measuring collision-induced rotational and vibrational relaxation processes in molecular ground states...

Because non-adiabatic collisions induce transitions between rotational levels, these levels do not participate in the relaxation process independently as in (1.11), but are correlated with each other. The degree of correlation is determined by the kernel of Eq. (1.3). A one-parameter model for such a kernel adopted in Eq. (1.6) meets the requirement formulated in (1.2). Mathematically it is suitable to solve integral equation (1.2) in a general way. The form of the kernel in Eq. (1.6) was first proposed by Keilson and Storer to describe the relaxation of the translational velocity [10]. Later it was employed in a number of other problems [24, 25], including the one under discussion [26, 27]. 

Here p is the radius of the effective cross-section, (v) is the average velocity of colliding particles, and p is their reduced mass. When rotational relaxation of heavy molecules in a solution of light particles is considered, the above criterion is well satisfied. In the opposite case the situation is quite different. Even if the relaxation is induced by collisions of similar particles (as in a one-component system), the fraction of molecules which remain adiabatically isolated from the heat reservoir is fairly large. For such molecules energy relaxation is much slower than that of angular momentum, i.e. xe/xj > 1. 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

Early optically detected microwave transition linewidth studies (Pratt and Broida, 1969) suggested that CN A2II(u = 10) —> B2E+(u = 0) collision-induced transitions through perturbed levels occur at gas-kinetic collision rates, faster than pure rotational relaxation. The pressure dependence of chemiluminescence in the Ba + N2O system also implied BaO b3II(u = 10) —> A1E+(u = 1) collisional transfer through spectroscopic doorways (Field, et al., 1974). 

Studied both experimentally and theoretically. The nature and rates of these processes have a strong influence on the characteristics of many laser chemistry processes. The rapidity of collision-induced intersystem crossing and of vibrational and rotational relaxation rates of highly excited molecules vitiates some claims of colhsion-free experiments, but it introduces additional interesting collision-dependent aspects of laser chemistry to be explored. 

In most cases, the rotation-level spacing is small as compared to kT. Therefore, rotational relaxation may be considered as a reversible process leading to a rapid establishment of the Boltzmann equilibrium between populations of rotational levels within a given vibronic state. The equilibrium (Boltzmann) density matrix is diagonal, i.e., all phase information is lost during the rotational (collision-induced) relaxation. The effect may be described by the supplementary terms to (2)... 

As alluded to earlier, the spin-rotation interaction couples different spin states and induces spin relaxation in collisions of ground-state molecules with He atoms. Figure 4.17 shows that by increasing the electric field, it is possible to adiabatically transfer the initial pure spin state into a mixture of different spin states, thereby... 

Generally, collision-induced quenching is far more efficient for rotation than vibration. Rotational quenching is driven by the angular anisotropy of the helium interaction with the molecule, and the timescale for a small impact parameter cold collision is similar to a rotational period. Vibrational relaxation, on the other hand, is driven by the dependence of the interaction potential on the internuclear separation in the... 

This spin-spin driven helium induced Zeeman relaxation is likely to be the dominant relaxation mechanism for molecules for which the spin-spin coefficient (kss) is larger than the spin-rotation coefficient (ysr). It is not clear from this qualitative model whether the additional 1 (jlb of magnetic moment gained in moving from E molecules to E states is worth the trouble. If the spin-spin driven Zeeman relaxation of E molecules is too strong, the trap lifetime will be substantially limited by inelastic collisions and not the trap depth. In 2003, a quantitative calculation was performed by Krems and colleagues that predicted a favorable Zeeman relaxation rate coefficient for imidogen (NH) with helium [35,36]. Furthermore, experiments... 

Other relaxation mechanisms come into play when dipole-dipole relaxation is less efficient. The spin-rotation (SR) interaction is important for spin-5 nuclei in smaller molecules, particularly in the gas phase. The nucleus experiences magnetic fields due to the differential rotation of charge with the molecular frame, and fluctuations of these fields, as with collisions, induce relaxation. This mechanism is distinguished by increase in the rate with increase in temperature and with decrease in viscosity, in contrast to the mechanisms depending on molecular tumbling. This is because the mechanism is more effective with increased population of the higher rotational states. The rate depends on the spin-rotation coupling tensor (C) and its anisotropy (as the square) and appropriate moments of inertia (/), values of which may be available from rotational spectroscopy. 

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