Rotational spectra spin-rotation interaction

As we shall see, each of these two terms, one for each nucleus, describes a second-rank scalar interaction between the electric field gradient at each nucleus and the nuclear quadrupole moment. De Santis, Lurio, Miller and Freund [44] included two other terms which involve the nuclear spins. One is the direct dipolar coupling of the 14N nuclear magnetic moments, an interaction which we discussed earlier in connection with the magnetic resonance spectrum of D2 its matrix elements were given in equation (8.33). The other is the nuclear spin-rotation interaction, also discussed in connection with H2 and its deuterium isotopes. It is represented by the term... 

This might appear to be a satisfactory conclusion, so far as the analysis of the observed spectrum is concerned. However, Carrington and Gammie [111] have reexamined the analysis and concluded that there does not appear to be any obvious reason why the nuclear spin-nuclear spin dipolar interaction should be neglected, since it is likely to be similar in magnitude to the nuclear spin-rotation interaction. This interaction was discussed for 112 in chapter 8, where it was represented, in spherical tensor form, by the term... 

In several papers a more detailed consideration of the rotational structure of the energy levels for symmetric-top molecules with a ground E term is given. In particular, in the work of Child (1963) the /-type doubling resulting from JTE is revealed, while in the paper of Brown (1971) the spin-orbital interaction for the 2E term (beside the JTE) is taken into account. However, since the pure rotational spectrum is not considered in these works, they are not discussed here. 

The first point to be made concerns the accuracy with which the model of Eq. (1) can be used to fit the microwave spectrum. The typical measurement accuracy of most microwave spectroscopists ranges from 0.01 to 0.2 MHz. It has been found that the model can reproduce the observed microwave spectrum with an accuracy on the order of 10 kHz, except in situations where molecular vibrations are large such as in the bending vibration of H20 and H2S6,7 or the nearly free internal rotation in CH3OH.8 Effects such as spin-rotation interactions and spin-spin interactions contribute splittings on the order of 10 kHz and are observed only under exceptionally high resolution. The effects of... 

Fig. 4. Radio frequency spectrum of H2 in the vicinity of the proton resonance frequency [4] in first clearly observed multiple line spectra with coherent radiation. The resonance frequencies are primarily determined by the interaction of the proton magnetic moment with the external magnetic field, but the states of different mj and mj are displaced relative to each other by the different values of the nuclear spin-spin and spin rotational interaction energies [4].

When we studied the radio-frequency spectrum of D2 we hit another surprise [5]. The separation of the spectral lines in D2 were greater than in H2 even though the nuclear spin-spin interaction and the nuclear spin molecular rotation interaction should be much less. We found a similar anomaly for HD. We finally interpreted this as due the deuterium nucleus having a quadrupole moment (being ellipsoidal in shape) which gave rise to a spin dependent electrical interaction. The existence of the quadrupole moment, in turn, implied the existence of a new elementary particle force called a tensor force. In this way, magnetic resonance made a fundamental contribution to particle physics. 

The PH2D microwave spectrum for two rotational transitions showed a hyperfine structure due to 31P spin-rotation interaction with (Caa + Cbb)/2 = (Caa+Ccc)/2 = -98 3 kHz (a, b, c=principal inertial axes) [13]. 

Varberg, T.D., Roberts, J.C. The isotopic dependence of the spin-rotation interaction The rotational spectrum of cadmium hydride in its state, J. Mol. Spectrosc. 223 (2004) 1-8. 

Figure 6.1 Effect of spin-rotation interaction on the i = 2<— 1 rotational transition of a diatomic molecule with one nuclear spin (Ig = j, with C < 0). The spectrum at the bottom is the one without spin-rotation interaction, while the one at the top illustrates the splittings due to spin-rotation interaction.

As the spin-rotation interaction splits lines in the rotational spectrum, the unit of the spin-rotation constant is kHz. 

This is, first of all, due to the manifold of rotational and vibrational levels within each electronic state and furthermore to a larger variety of angular momentum coupling, such as spin-rotation interaction, A-type doubling, fine and hyperfine structure. In addition different kinds of perturbations may further increase the line density and the complexity of the spectrum. Even for small molecules, such as diatomic or triatomic molecules, the spacings between rotational lines of an electronic transition may become much smaller than the Doppler-width. This implies that single rotational lines often cannot be resolved with "classical" Doppler-limited techniques. 

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

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