Nuclear line broadening interaction

A further characteristic line broadening interaction occurs for nuclei with nuclear spinsf>l/2 in addition to the interactions discussed above [seeEq.(l)]. These nuclei exhibit an electric quadrupole moment that interacts with the electric field gradient at the site of the nucleus. The NMR spectriun of quadrupole nuclei with half-integer nuclear spins (7=3/2,5/2,...) consists of the -hl/2 -1/2 central transition and the so-called satellite transitions ( l/2 3/2, 3/2 quadrupole interaction it is practically impossible to excite the whole spectriun non-selectively, i.e., the central transition is often selectively observed. 

Fig. 3. Line shape function of the central transition of a quadrupole nucleus with a half-integer nuclear spin, calculated for /Jq=0 in the limiting case of rapid magic angle spinning assuming that the electric quadrupole interaction is the dominating line broadening interaction...

As the TieS lengthen and l/Tie (s ) approaches the size of the electron—nuclear interaction, considerable NMR line broadening can occur, and it may not be possible to acquire high-resolution NMR spectra under these conditions. The effect of Tie on the nuclear relaxation times is discussed in more detail in ref 22. Large hyperfine constants are observed (of many MHz) when the nuclear and electronic spins are on the same atom. For example, a hyperfine constant A/h of —324 MHz was measured by electron... 

The broad lines obtained for solid-state NMR spectra without applying any line-narrowing improvements are due to the different behaviour of nuclear spin interactions in solids compared to liquids. These interactions are averaged to zero or reduced to the isotropic values in liquids by the fast molecular motions, whereas the fixed (and different) orientations (with respect to the external magnetic field Bq) of the local environments of NMR active isotops in the rigid lattice of a solid cause line broadenings. The recorded broad NMR line patterns are superpositions of resonances from randomly oriented individual nuclei due to a random distribution of different orientations, since zeolitic materials usually are microcrystalline powders. Table 1 summarizes the nuclear spin interactions and their behaviour in liquids versus solids (17). 

In order to demonstrate the physical significance of asymjjtotic nonadiabatic transitions and especially the aiialj-tical theory developed an application is made to the resonant collisional excitation transfer between atoms. This presents a basic physical problem in the optical line broadening [25]. The theoretical considerations were mad( b( for< [25, 27, 28, 29, 25. 30] and their basic id( a has bec n verified experimentally [31]. These theoretical treatments assumed the impact parameter method and dealt with the time-dependent coupled differenticil equations imder the common nuclear trajectory approximation. At that time the authors could not find any analytical solutions and solved the coupled differential equations numerically. The results of calculations for the various cross sections agree well with each other and also with experiments, confirming the physical significance of the asymptotic type of transitions by the dipole-dipole interaction. 

The quadrupolar moments of nuclei with I > 1/2 may interact with electric field gradients in their environments. Depending on the symmetry of the nuclear environment, these interactions can lead to considerable line broadening due to both first- and second-order terms (for a detailed discussion see ref. 17). While both first-and second-order terms each contain angular (relative to the direction of B0) terms only the former contains 3 cos2 0 - 1, like the dipolar interaction term. 

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