Effective Zeeman Hamiltonian

Collecting all these various contributions together, Watson showed that a more accurate description of the isotopic mass dependence is given by 

The Ukt are isotopically invariant parameters. Our discussion of the RKR potential in section 6.13.3 showed that the potential Vn(R) can be determined from a knowledge of Gv and Bv. Since the parameters Uu with l 2 can be calculated from Vn(R), it follows that they are exactly determined by the values of Uu with t = 0 and 1. The simplest case of Uq2 is a familiar one. The relationship in question, 

The effect of a magnetic field on a diatomic molecule has been described in detail in section 3.7. An extra term is added to the magnetic vector potential of each electron i of the form 

There are also some smaller terms which are quadratic in B and have the general form 

The scalar conttibution, with k = 0, is constant for all levels of a molecule and so cannot be measured in practice. The anisotropic k = 2 contribution, on the other hand, is readily determinable. 

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Here, co represents the Euler angles (orbital Zeeman interaction, we see that it has off-diagonal matrix elements which link electronic states with A A = 0, 1, as well as purely diagonal elements. It is clearly desirable to remove the effect of these matrix elements by a suitable perturbative transformation to achieve an effective Zeeman Hamiltonian which acts only within the spin-rotational levels of a given electronic state rj, A, v), in the same way as the zero-field effective Hamiltonian in equation (7.183). 

The cross term between X and Xr<)t can be treated in exactly the same way The result is a second-order contribution to the effective Zeeman Hamiltonian of the form... 

A recent paper [32] has suggested that the primary g-factors, gs and g L, should be defined as negative quantities so that they reveal the alignment of the magnetic dipole moment relative to the angular momentum. If this convention is adopted, the signs of the two contributions to the effective Zeeman Hamiltonian, given above, must be reversed. 

The first level to be studied in detail by Tichten [35] was the N = 2 level of both para-Hi and ortho-H2. He measured a series of fixed-frequency magnetic resonance transitions, determining effective g- values and proving the identification of the c3nu state in the process. An effective Zeeman Hamiltonian may be written, in the space-fixed axis system,... 

The second-order contribution of the orbital Zeeman term with itself produces a term in the effective Hamiltonian which is quadratic in 5. It therefore has the same form as the diamagnetic susceptibility contribution to the energy it provides the paramagnetic or high-frequency contribution to the susceptibility of the molecular system. The resultant term in the effective Zeeman Hamiltonian is... 

The effective Zeeman Hamiltonian for an asymmetric top molecule in an open-shell state has been given by several authors in the literature, for example Pryce [50Pry] or Bowater, Brown, and Carrington [73 Bow], The operator can be written in Cartesian tensor notation as [80Eve] ... 

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