Polarisation double-spin

Double spin polarisation (DSP) covers the doubly excited configurations of two types ... 

The dipolar coupling is also central to many schemes for magnetisation transfer between nuclei using double resonance techniques such as cross-polarisation. The data become more difficult to unravel when a nucleus experiences numerous different dipolar interactions at the same time. Even an increase to just three spins causes the lineshape... 

Many multiple resonance methods such as cross-polarisation (CP), Rotational Echo Double Resonance (REDOR), and Transferred Echo Double Resonance (TEDOR) are available. Their application can be differentiated between systems involving exclusively spin- /2 nuclei and those containing quadrupolar nuclei. The presence of quadrupolar nuclei may prohibit straightforward application of these experiments and can affect the interpretation of the results. There are, however, benefits arising from the presence of quadrupolar nuclei, as illustrated by the Transfer of Populations by Double Resonance (TRAPDOR) experiment which will only work for quadrupolar nuclei. 

The experiment described above is termed selective population transfer (SPT), or more precisely in this case with proton spin inversion, selective population inversion, (SPI). It is important to note, however, that the complete inversion of spin populations is not a requirement for the SPT effect to manifest itself. Any unequal perturbation of the lines within a multiplet will suffice, so, for example, saturation of one proton line would also have altered the intensities of the carbon resonance. In heteronuclear polarisation (population) transfer experiments, it is the heterospin-coupled satellites of the parent proton resonance that must be subject to the perturbation to induce SPT. The effect is not restricted to heteronuclear systems and can appear in proton spectra when homonuclear-coupled multiplets are subject to unsymmetrical saturation. Fig. 4.20 illustrates the effect of selectively but unevenly saturating a double doublet and shows the resulting intensity distortions in the multiplet structure of its coupled partner, which are most apparent in a difference spectrum. Despite these distortions, the integrated intensity of the proton multiplet is unaffected by the presence of the SPT because of the equal positive and negative contributions (see Fig. 4.19d). Distortions of this sort have particular relevance to the NOE difference experiment described in Chapter 8. 

To summarise, the pure valence correlation (double excitations) tends to lower the spin-orbit splitting while the valence spinors relaxation (single excitations) tends to increase the splitting. Concerning the role of the core orbitals, the whole core polarisation, core-core and core-valence correlations taken into account via a semi-empirical CPP tend to enhance this splitting. ... 

The differences in the population and depopulation rate constants and the phosphorescence probabilities of the three components of the triplet states form the basis of all the methods for Optical Detection of Magnetic Resonance in triplet states of jr-electron systems. These methods were developed after the discovery of optical spin polarisation and extended to inorganic solids. The essential physical difference from the optical double resonance in atoms developed by Alfred Kastler is to be found in the selection mechanism in optical double resonance, the polarisation of the resonant UV light, i.e. the symmetry of an applied field, is responsible for the selection. In optical spin polarisation, the selection is due to the spin-orbit coupling, and thus to an internal field. 

The Overhauser shift is very small the contribution to Avesr/ esr of the protons is of order 10" and that of less abundant nuclear spins, e.g. is of order 10" [34]. Their measurement is accomplished by a double resonance technique. The shift A Bov of the resonance field for ESR is measured at a constant ESR-microwave frequency vesr (e.g. 9.4 GHz), while at the same time a strong radio-frequency field with the variable frequency Vjfis applied. When Vjf= v mr the nuclear-spin resonance, e.g. the nuclear-spin resonance of the protons at Vrf=Vp, will be saturated. This produces equal populations of the two nuclear-spin Zeeman levels, causing the nuclear-spin polarisation P to vanish. This leads according to Eq. (9.27) to a shift of the ESR resonance field by an amount... 

It seems that a better suited approach should make use of a series of actual measurements on an evolving material quantum system. In fact, two-level atoms, equivalent to spin systems, show a formal analogy with light polarisation. Whereas the configuration space of polarisation transforms according to symmetry group SO(3), the symmetry of spin transformation is SU(2), which is a double covering of SO(3), and locally isomorphic with the latter one [17]. Thus, similar visualisations of the dynamics of both systems apply. 

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