Excited state angular momenta distribution

In the preceding chapter we ascertained the mutual orientation of the dipole moment d and of the angular momentum J of the molecule. The next step is to consider the probability of a molecule with arbitrary spar tial orientation of the angular momentum J absorbing light of a given polarization (in laboratory coordinates). 

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Let us analyze how to find the excited state multipole moments bPq-As explained in the previous paragraph, at excitation by weak light the probability density pb(0, state angular momentum distribution is proportional to the absorption probability G(0,multipole moments, Pq of an excited level b can be found as... 

Fig. 2.2. Isometric projections of probability density pb(0,

If, however, such a sample is excited with a directional laser beam, and particularly a polarised laser beam, the vectorial nature of the interaction between the molecule and the light will usually give rise to an anisotropic excited state distribution. Subsequent fluorescence will then result in polarised emission. Greene and Zare (1982,1983) have shown how this polarisation can be related to the moments of the angular momentum distribution, with the dominant contribution given by the second moment/ 2) (the alignment) when using linearly polarised one-photon excitation, where for each Ji... 

As the Auger transitions do not change the shape of the angular momentum distribution, the particle quickly reaches the (/= — ) orbits (Hartmann 1989) and from those - owing to the Al = 1 rule - can make circular, (n, 1 = n — 1) —> (n — 1, Z = n — 2) transitions only (O Fig. 28.3). Typical exotic-atoms X-ray spectra are presented in O Fig. 28.4 note that the spectra are dominated by circular transitions from highly excited states. 

Many experiments employing LIF to extract the population and or the anisotropy of the nascent angular momentum distribution are carried out with pulsed lasers exhibiting rather limited coherence properties. Under these conditions coherence between the lower and excited state may be neglected and the more simple rate equational approach to model the laser-molecule interaction is appropriate. 

This book presents a detailed exposition of angular momentum theory in quantum mechanics, with numerous applications and problems in chemical physics. Of particular relevance to the present section is an elegant and clear discussion of molecular wavefiinctions and the detennination of populations and moments of the rotational state distributions from polarized laser fluorescence excitation experiments. 

Reaction 58 has been observed, and the rotational distribution measured is thermal, in marked contrast to similar measurements in H2O. Theoretical calculations suggest that this is because there is an exit valley that lies close to the bent geometry of the H2S molecule. Thus, the excited state can dissociate without producing a large amount of angular momentum in the SH fragment. 

Fig. 7.15. Angular correlation spectra (left) and corresponding derived positronium momentum distributions F(p) (see the text for details) for silica aerogel under the following conditions (a) vacuum (b) 1 atmosphere of N2 gas (c) 0.1 atmospheres of O2 gas (d) 0.2 atmospheres of 02 gas (e) 0.4 atmospheres of O2 gas (f) 0.8 atmospheres of O2 gas. The arrows on the right-hand diagrams indicate the momenta corresponding to the excitation energies of the a1Ag and the b1Eg states of O2. A discussion of the components marked I and II can be found in the text.

In this chapter we discuss only the scalar aspect of rotational excitation, i.e., the forces which promote rotational excitation and how they show up in the final state distributions. The simple model of a triatomic molecule with total angular momentum J = 0, outlined in Section 3.2, is adequate for this purpose without concealing the main dynamical effects with too many indices and angular momentum coupling elements. The vector properties and some more involved topics will be discussed in Chapter 11. 

Rotational excitation as a consequence of overall rotation of the parent molecule before the photon is absorbed does not reveal much dynamical information about the fragmentation process. It generally increases with the magnitude of the total angular momentum J and thus increases with the temperature of the molecular sample. In order to minimize the thermal effect and to isolate the dynamical aspects of photodissociation, experiments are preferably performed in a supersonic molecular beam whose rotational temperature is less than 50 K or so. Broadening of final rotational state distributions as a result of initial rotation of the parent molecule will be discussed at the end of this chapter. 

Fig. 10.5. Measured rotational state distributions of OH following the dissociation of the three lowest bending states of H2O (open circles). In addition to the bending quanta H20(X) also contains 4 respectively 3 quanta of OH stretching excitation. The local mode nomenclature nm k) is explained in Section 13.2. The total angular momentum is zero in all cases. The filled circles represent the harmonic oscillator approximation defined in the text. Reproduced from Schinke, Vander Wal, Scott, and Crim (1991).

Let the distribution Pb(0, excited state (see Fig. 4.1(6)) arise under the action of light in the form of a short pulse (6-pulse). The magnetic field B creates precession around B not only of the angular momentum of a separate molecule, but also of the distribution over the ensemble. Since, however, all momenta J are in precession with one and the same angular velocity ujj (4.2), their mutual positions with respect to each other remain the same. Hence, the whole rose of vectors J is in precession as a single entity, which means that the... 

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