Quadrupole interactions spin hamiltonian describing

The theory of the magnetic hyperfine interactions in NCI is essentially the same as that already described for the PF radical in the previous section, except that the nuclear spins / are 1 for 14N and 3/2 for 35C1. The form of the effective Hamiltonian for the quadrupole interaction and its matrix elements for two different quadrupolar nuclei was described in some detail in chapter 8 when we discussed the electric resonance spectra of CsF and LiBr. We now use the same case (b) hyperfine-coupled basis set as was used for PF. The quadrupole Hamiltonian for the two nuclei can be written as the sum of two independent terms as follows ... 

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

The last three terms of the spin Hamiltonian shape the Mossbauer spectrum because they describe the interaction of the nucleus with the atom, the solid and the external magnetic field. The term I - A - S describes the magnetic interaction between the nucleus and the atom. This acts through components of the atomic spin which are determined by the Boltzmann population of the spin Hamiltonian states shown in Figure 4.2. Thus the first three terms of the spin Hamiltonian act to determine values for the components of S that are used in the magnetic interaction that shapes the Mossbauer spectrum. The mechanisms involved in this nucleus-atom interaction I A S will be discussed in detail in the next section. The quadrupole interaction term represents the interaction of the nuclear quadrupole moment with the EFG produced by the atom and the lattice. The principal component of the EFG is V — d Vldz (V is the electric potential at the nucleus) and the asymmetry parameter =... 

The simulated spectra in Figure 18 represent a series of replicate ESEEM experiments performed on a system containing a single Cu- N interaction with a Fermi contact interaction energy of 26 MHz and quadrupole coupling (e Qqzz) of 3.5 MHz. It is immediately evident from these simulations that the behavior observed at the X-band is reproduced at the W-band provided that the spin-Hamiltonian model that is used to describe experiments at the X-band is not affected in the extremely high magnetic fields of the W-band i.e., no introduction of nonlinear effects). The W-band ESEEM spectra of the Type I copper center of azu-... 

Simulations reported in this and other reviews (Singel, 1989) demonstrate that, based on the spin-Hamiltonian model, effective zero-field nuclear quadrupole interaction parameters can be obtained by invoking a condition known as exact cancellation. On the basis of observations made concerning what experimental conditions yield optimal performance in ENDOR and ESEEM experiments, it has been suggested in this review that level crossing and the associated cross-relaxation is responsible for the deep modulation and corresponding narrow lines in the ESEEM spectrum. If level crossing and the resultant cross-relaxation processes are, in fact, the requisite condition for deep ESEEM, then the techniques described here are... 

The energy levels of the lanthanide ionic moment are perturbed somewhat by interaction with the magnetic dipole and electric quadrupole moments of its nucleus and to a lesser extent the nuclei of ligand ions. The magnetic hyperfine interaction has been described from the nuclear standpoint in section 1.2.1 where the hyperfine constant A was introduced in the hamiltonian 5(fhf = AI J of (18.8). In any subset of levels resulting from the CEF interaction (18.109) which are characterized by an effective spin S, the magnetic hyperfine interaction can be written in the form... 

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen-... 

The information obtained from the spin Hamiltonian, the 3x3 matrices g, D, A, and P, is very sensitive to the geometric and electronic structure of the paramagnetic center. The electron Zeeman interaction reveals information about the electronic states the zero-field splitting describes the coupling between electrons for systems where S > Vi the hyperfine interactions contain information about the spin density distribution [8] and can be used to evaluate the distance and orientation between the unpaired electron and the nucleus the nuclear Zeeman interaction identifies the nucleus the nuclear quadrupole interaction is sensitive to the electric field gradient at the site of the nucleus and thus provides information on the local electron density. 

The most important examples of 2S states to be described in this book are CO+, where there is no nuclear hyperfine coupling in the main isotopomer, CN, which has 14N hyperfine interaction, and the Hj ion. A number of different 3E states are described, with and without hyperfine coupling. A particularly important and interesting example is N2 in its A 3ZU excited state, studied by De Santis, Lurio, Miller and Freund [19] using molecular beam magnetic resonance. The details are described in chapter 8 the only aspect to be mentioned here is that in a homonuclear molecule like N2, the individual nuclear spins (1 = 1 for 14N) are coupled to form a total spin, It, which in this case takes the values 2, 1 and 0. The hyperfine Hamiltonian terms are then written in terms of the appropriate value of h As we have already mentioned, the presence of one or more quadrupolar nuclei will give rise to electric quadrupole hyperfine interaction the theory is essentially the same as that already presented for1 + states. 

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

In accordance with the works we assume that for analysing the effect of RF pulses on the quadrupolar spin system, it is sufficient to consider only three t)q)es of interactions quadrupolar interaction, homonuclear dipole-dipole interaction and the nuclear-spin interaction with the magnetic component of the RF field. Before the initiation of the multi-pulse sequence the quadrupolar system is described by two Hamiltonians quadrupolar Hq and the part of the homonuclear dipole-dipole Hamiltonian Hj secular in relation to the quadrupole Hamiltonian, the sum of which can be regarded as the effective Hamiltonian of the spin system independent of the time factor. 

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