Spin-rotation coupling

QUANTUM MONODROMY AND MOLECULAR SPECTROSCOPY A. Spin-Rotation Coupling... 

The simplest example of angular momentum coupling is provided by the scaled spin-rotation coupling Hamiltonian... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

Cs quadrupole coupling 19F nuclear spin-rotation coupling... 

In the second scheme to be considered, labelled case (b/ ,v), S and / are coupled to form an intermediate G, which is then coupled with N to form F. This scheme is appropriate when the hyperfine interaction between S and / is strong compared with spin-rotation coupling, and we will meet it elsewhere, most notably in the H ion. The basis kets are written in the form tj, A S, I, G G, N, F) and the hyperfine matrix elements is this basis are calculated in later chapters. The most natural extension of Hund s case (b), known as case (bpj), is that in which /, the resultant of/Vand.S coupling, is coupled with/to form/. The corresponding basis kets are rj, A N, S, J J, I, F) and we will often meet matrix elements calculated in this basis. 

Figure 8.31. Nuclear hyperfine splitting of the J = 1 rotational level of CsF in its X 1 + state. The major splitting is due to the 133Cs quadrupole interaction, and the smaller doublet splitting arises from the 19F nuclear spin-rotation coupling. The diagram is drawn for zero apphed electric field, and the strongest electric dipole transitions are indicated.

These, then, are the reasons why magnetic resonance methods, microwave or far-infrared laser, have had limited success with 2A diatomic radicals. Similar considerations apply to nonlinear polyatomic radicals in doublet states success in far-infrared laser magnetic resonance depends upon the magnitude of the spin-rotation coupling, and the size of the energy mismatch between the transition frequency and the laser frequency, since the mismatch has to be magnetically tuned. This becomes less of a limitation as more laser frequencies become available, except that one then needs to know in advance which laser frequency to choose. It becomes part of the search problem ... 

This is because the hyperfine (Fermi contact) interaction is larger than the spin-rotation coupling. The lowest rotational transition, N = 1 0, was found to be split by a combi-... 

The CN radical in its 21 ground state shows fine and hyperfine structure of the rotational levels which is more conventional than that of CO+, in that the largest interaction is the electron spin rotation coupling../ is once more a good quantum number, and the effective Hamiltonian is that given in equation (10.45), with the addition of the nuclear electric quadrupole term given in chapter 9. The matrix elements in the conventional hyperfine-coupled case (b) basis set were derived in detail in chapter 9,... 

We have chosen to use the hyperfine-coupled representation, where for 12CH, F is equal to J 1 /2. An appropriate basis set is therefore t], A N, A S, J, /, F), with MF also important when discussing Zeeman effects. As usual the effective zero-field Hamiltonian will be, at the least, a sum of terms representing the spin-orbit coupling, rigid body rotation, electron spin-rotation coupling and nuclear hyperfine interactions, i.e. 

A fast-mixing nozzle in an FT microwave spectrometer was used to measure rotational constants, centrifugal distortion constants, Cl-nuclear quadrupole- and spin-rotational coupling constants for the isotopomers (CH2)2S- C1F and (CH2)2S- C1F <1996CPL119>. The complex, with symmetry, has an arrangement of the S-CIF nuclei that is about 3.5° off collinearity. The Cl-F axis makes an angle of 95° with thiirane s C-2 axis. 

Where, C is the spin-rotation coupling constant (SRCC) and J is the rotational angular moment. This interaction becomes a relaxation mechanism if (i) the rotational angular momentum is modulated due to intermolecular interactions (torques) or (ii) the spin-rotational coupling becomes modulated when the orientation of the molecule is modulated due to collisions with other molecules. 

Another effect is the modulation of the rotational angular momentum of the ion and the interaction of this momentum with the spin angular momentum by means of its spin-rotational coupling. This mechanism (43) may be used to explain the absence of hyperfine splitting from vanadyl prophyrin in solution, whereas it is observed in the glassy state where spin-rotational relaxation will not be present. 

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