Magnetic resonance Zeeman resonances

Figure 7-3. (a) Zeeman splming of triplet exeiton sublevels as a Imietion ol the applied magnetic Held, (b) Change in PL intensity at magnetic resonance. 

Interactions with an applied magnetic field are particularly important for open shell free radicals, many with 2 n ground states having been studied by magnetic resonance methods. The Zeeman Hamiltonian may be written as the sum of four terms ... 

We calculate the effects of the Hamiltonian (8.105) on these zeroth-order states using perturbation theory. This is exactly the same procedure as that which we used to construct the effective Hamiltonian in chapter 7. Our objective here is to formulate the terms in the effective Hamiltonian which describe the nuclear spin-rotation interaction and the susceptibility and chemical shift terms in the Zeeman Hamiltonian. We deal with them in much more detail at this point so that we can interpret the measurements on closed shell molecules by molecular beam magnetic resonance. The first-order corrections of the perturbation Hamiltonian are readily calculated to be... 

The rotational and Zeeman perturbation Hamiltonian (X) to the electronic eigenstates was given in equation (8.105). It did not, however, contain terms which describe the interaction effects arising from nuclear spin. These are of primary importance in molecular beam magnetic resonance studies, so we must now extend our treatment and, in particular, demonstrate the origin of the terms in the effective Hamiltonian already employed to analyse the spectra. Again the treatment will apply to any molecule, but we shall subsequently restrict attention to diatomic systems. 

Many other diatomic molecules with1X ground states have been studied by molecular beam magnetic resonance. Where magnetic nuclei are present, magnetic focusing is based upon the nuclear Zeeman effects. This is the case with 15N2 for which the... 

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,... 

We are now in a position to examine the details of the Zeeman effect in the para-H2, TV = 2 level, and thereby to understand Lichten s magnetic resonance studies. For each Mj component we may set up an energy matrix, using equations (8.180) and (8.181) which describe the Zeeman interactions, and equations (8.201), (8.206) and (8.214) which give the zero-field energies. Since Mj = 3 components exist only for J = 3, diagonalisation in this case is not required. For Mj = 2 the J = 2 and 3 states are involved. For Mj = 0 and I, however, the matrices involve all three fine-structure states and take the form shown below in table 8.7. Note that /. is equal to a0 + 3 63-2/4 and the spin-rotation terms have been omitted. The diagonal Zeeman matrix elements are... 

The Zeeman Hamiltonian given in equation (8.322) is sufficient to provide a semi-quantitative description of the magnetic effects but, as was described in our discussion of the magnetic resonance spectrum of H2, it is an approximate form. The local magnetic field experienced by the H and F nuclei is not quite the same as the applied laboratory field because of shielding effects due to the surrounding electrons. In addition the rotational Zeeman interaction should be described not by the single constant... 

Figure 9.12. Microwave magnetic resonance spectra of NO in the J = 3/2 level of the 2n3/2 component, recorded by Brown and Radford [37]. Part (a) shows the 15N160 spectrum, with a very small A-doublet splitting, a larger second-order Zeeman splitting of the three AM/ = 1 components, and a doublet splitting from the 15N nucleus, which has I = 1/2. Part (b) shows the 14N160 spectrum, which is similar to that shown in (a), except that there is now a triplet splitting from the 14N nucleus, which has 7 = 1. The microwave frequency was 2879.9 MHz.

Figure 9.14. Upper Zeeman behaviour of the yl-doublet and proton hyperfme levels of OH in the J = 3/2 F (2113/2) rotational level, and the electric dipole transitions. Lower stick diagram of the magnetic resonance spectrum obtained by Radford at a frequency of 9263 MHz [7],...

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