Gerade states

It should be pointed out, however, that the details of the vibronic structure of the Lb band are significantly different in some of the spectra which have appeared in the literature and which have been mentioned above. For example, while Jones et al. [44] and Dick et al. [46] have reported only one relatively strong peak in the range 600-625 nm, Mikami et al. [45] observed two peaks. There are also differences in the relative intensities of the Lb transition and the transition to the gerade state around 450 nm. In [44,45], the spectra were obtained in the same solvent (cyclohexane) and for similar concentrations (0.05 M in one case, 0.1 M in the other), while in [46] the solvent used was ethanol. In all three cases the experiments utilized linearly polarized light and detected the 2P-induced fluorescence. The observed differences are probably ascribable to some other experimental condition or a source of error that was not accounted for. This is another example of the repro-... 

Figure 13.3 depicts the lowest four eigenfunctions of the ungerade symmetry (multiplied with the X — A transition dipole function). They are anti-symmetric with respect to the interchange of i i and R2 and therefore they have a node on the symmetry line i i = R2. Some examples for gerade states will be shown in Figure 14.4. The assignment Imn ) reflects the leading term in expansion (13.7). For example, 21 ) means that the function dominates the expansion while the coefficients for the other basis functions are considerably smaller. The corresponding wavefunction is approximately given by...

Fig. 14.4. Vibrational eigenfunctions, multiplied by the X —> A transition dipole function, for the gerade states of H20(X). All wavefunctions are symmetric with...

For example, in a doubly-excited N=3 linear chain with a center of inversion (D,) symmetry), (10) yields zero for ungerade states and y for gerade states. 

The trimer states, which in most cases can be called Efimov trimers, are interesting objects. Their existence can be seen from the Born-Oppenheimer picture for two heavy atoms and one light atom in the gerade state. Within the Born-Oppenheimer approach the three-body problem reduces to the calculation of the relative motion of the heavy atoms in the effective potential created by the light atom. For the light atom in the gerade state, this potential is + (/ ), found in the previous subsection. The Schrodinger equation for the wavefunction of the relative motion of the heavy atoms, Xv(R), reads... 

The symmetry of the spin-orbit operator was derived in section 10.3. The spatial part of this operator transforms as the vector of rotations R = (Rx, Ry, Rz)- This means that the spin-orbit operator will connect states of different spatial symmetry. In C2v, for example, states of all spatial symmetries are connected by the spin-orbit operator. In D2h, the gerade states are all connected by the spin-orbit operator, and likewise the ungerade states, but there is no connection between gerade and ungerade states because the spin-orbit operator commutes with the inversion operator (it is an even operator). The spin operator transforms as a spherical tensor of rank 1 it is essentially a triplet operator. Therefore, it can connect states whose S and Ms values differ by 0 or 1. 

Coriolis interaction parameters (cm" ), first between the 4 ungerade states, and second between the 3 gerade states (all values in cm ). 

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