Nuclear coherence

Figure 5 Diagram showing contours that arise from broad hyperfine lines detected hy nuclear coherence transfer echoes under conditions of (a) weak and (h) strong hyperfine coupling...

The first two terms are the nuclear coherent (3.15) and incoherent scattering (3.9) and the last term is the purely magnetic scattering (3.26). The third term is an interference term between nuclear and magnetic scattering and is zero if ij x, if the scattering is purely nuclear or purely magnetic, and if P = 0. P describes the polarization of the incident beam (0 < P < 1). 

From (3.39) we see that nuclear coherent scattering is always non spin-flip (-(- -(-,--), as is nuclear incoherent scattering which is due to the random iso-... 

These enable intense homo- and hetero-nuclear coherence and polarisation transfers to take place, not to mention cross-relaxation (polarisation transfer under the influence of dipolar coupling) (Figure 5.19). Usually, the following sequence of operations is carried out. 

Laser-Induced Electronic and Nuclear Coherent Motions in Chiral Aromatic Molecules... 

Laser-Induced Electronic and Nuclear Coherent Motions. 

Laser-Induced Electronic tind Nuclear Coherent Motions... 

Interactions with nucleus or Nuclear photoelectric effects Nuclear coherent Nuclear Compton ... 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

The pulse EPR methods discussed here for measuring nuclear transition frequencies can be classified into two categories. The first involves using electron nuclear double resonance (ENDOR) techniques where flie signal arises from the excitation of EPR and NMR transitions by microwave (m.w.) and radiofrequency (r.f) irradiation, respectively. In the second class of experiments, based on flic electron spin echo envelope modulation (ESEEM) effect, flic nuclear transition frequencies are indirectly measured by the creation and detection of electron or nuclear coherences using only m.w. pulses. No r.f irradiation is required. ENDOR and ESEEM spectra often give complementary information. ENDOR experiments are especially suited for measuring nuclear frequencies above approximately 5 MHz, and are often most sensitive when the hyperfine interaction in not very anisotropic. Conversely, anisotropic interactions are required for an ESEEM effect, and the technique can easily measure low nuclear frequencies. 

The disadvantage of the fast echo decay in two-pulse ESEEM can be circumvented with the three-pulse ESEEM experiment shown in Figure 5b. In this pulse sequence the first two nil pulses create nuclear coherence that develops during the evolution time T and decays with the transverse nuclear relaxation time 72n which is usually much longer than the corresponding relaxation time 7m of the electrons. The third nJl pulse transfers the nuclear coherence back to observable electron coherence. The modulation of the stimulated echo is given by... 

It is worth reiterating that nuclear coherence, comprising nuclear frequencies of the spin system, is created by the first two m.w. pulses. During evolution time T the nuclear coherence accumulates phase, and the transfer of this nuclear coherence back to electron coherence with the third m.w. pulse causes the stimulated echo intensity to be modulated by the nuclear frequencies, enabling their measurement. 

Three different ID ESEEM schemes using the pulse sequence in Figure 5c and die nuclear CTE have been proposed deadtime-free ESEEM by nuclear coherence transfer echoes (DEFENCE) [24], the combination peak (CP) experiment, and the... 

Three different kinds of peaks appear in flie HYSCORE spectrum after the FT of the time-domain signal along both dimensions, as depicted in Figure 7. The first terms of Eq. (21) wifli coefficients C and Cp originate from the transfer of nuclear coherence to polarization (and vice versa) and lead to the axial peaks (OjCOn), (0,(034) and (to 12,0), ((034,0) (open circles). These peaks are usually not of interest and are typically removed by a baseline correcrtion. 

Figure 9. HYSCORE spectra of MCRbps (see schematic for structure), (a) X-band (9.7 GHz) spectrum at 20 K, with signals assigned to Hy and Hri. (b) Q-band (35.3 GHz) spectrum at 20 K. The position of the principal values, determined from the full set of HYSCORE and ENDOR spectra, are indicated. The intense signal on the diagonal around (-5,5) MHz is due to an incomplete transfer of nuclear coherences between the two electron spin manifolds by the non-ideal n pulse. Modified with permission from [38]. Copyright 2006, Wiley-VCH.

The remote-echo detector is shown in Figure 11. In this method the electron spin echo at the end of the pulse sequence, which uses Vi < rnuclear coherence generator, is not recorded. Instead, at the time of echo formation an additional nil pulse transfers the electron coherence to longitudinal magnetization. The echo amplitude information can thus be stored for a time interval up to the order of T. After a fixed time delay h < T l, the z-magnetization is read out using a two-pulse echo sequence with a fixed time interval X2 > r. Remote echo detection can be applied to many experiments, including three-pulse ESEEM and HYSCORE, and thus can eliminate blind spots with an appropriate choice of small ri. Note, however, that it may suffer from reduced sensitivity due to the increased sequence time. 

In the HYSCORE experiment only nuclear frequencies in different manifolds belonging to the same paramagnetic center are eorrelated with each other. For multinuclear spin systems the assignment of nuelear frequencies is often not straightforward, since some of the correlation peaks may not be observed in the HYSCORE speetrum due to the small intensity of the nuelear transitions in one of the two Ws manifolds. Additional information can be gained if correlations of nuclear frequencies within the same manifold can be obtained. Cross-peaks that represent such correlations can be created by replacing the nonselective transfer n pulse in the HYSCORE sequence by the double nuclear-coherence transfer (DONUT) mixer % - t - n [58]. This DONUT-HYSCORE experiment with the pulse sequence ji/2 -ti nil - echo results in crosspeaks and (twp i, copj). The presence of these cross-peaks in the DONUT-... 

The residual hyperfine spliding can be eliminated with the pulse sequence shown in Figure 13b. In contrast to the previous pulse sequence, the nuclear coherence during die decoupling pulses evolves now in bodi electron spin manifolds. It... 

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