Hamiltonian, nuclear quadrupole rotational

The most important terms in the effective hyperftne Hamiltonian are those which describe the nuclear quadrupole and nuclear spin-rotation interactions ... 

The predominant isotope of cesium is 133Cs which has a nuclear spin I of 7/2 its quadrupole moment and g-factor will be denoted by Q and gi. The 19F nucleus has spin /2 of 1 /2 (and therefore no quadrupole moment) and a nuclear g-factor denoted g2. The nuclear hyperfine Hamiltonian used by English and Zorn [51] was the sum of five terms representing the 133Cs quadrupole interaction, the 133Cs nuclear spin-rotation interaction, the 19F nuclear spin-rotation interaction, the dipolar (tensorial) interaction between the 133Cs and 19F nuclear spins, and the scalar interaction between the two nuclear spins. Consistent with the conventions in use at the time, this Hamiltonian was written in the following form ... 

The effective Hamiltonian contained terms for both nuclei describing the orbital hy-perfine interaction, the electric quadrupole interaction and the nuclear spin-rotation interaction ... 

In microwave spectroscopy, pure rotational transitions are studied. If one or more nuclei in the molecule has a nuclear quadrupole moment, the quadrupole Hamiltonian [Eq. (6)] has to be included in the quantum mechanical treatment because the field gradient q [Eq. (5)] is dependent on the rotational wave function. The nuclear quadrupole interaction, which causes the rotational transitions to split into hyperfine structure, can usually be treated as a perturbation to the rotational Hamiltonian. 

The resolution of the molecular beam experiments is high enough to observe even rather small nuclear hyperfine interactions such as the spin-spin and spin-rotation interactions as well as the larger quadrupole coupling interactions. The largest terms in the Hamiltonian for the hyperfine splittings are given below 66) ... 

We are now in a position to write down the Hamiltonian operator for all nuclear spin and quadrupole terms for a diatomic molecule we allow for the possibility that both nuclei are involved and therefore sum over the nuclear index a. The terms are expressed in a molecule-fixed rotating coordinate system with origin at the nuclear centre of mass, except that we retain Ia as being quantised in a space-fixed axis system. We number the terms sequentially and then describe their physical significance. 

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,... 

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