Spin echo decay rate

In general the Cooper pairs in conventional superconductors induced by phonons have. -symmetry where the gap opens uniformly on the Fermi surface and the temperature dependence of physical quantities below Tc is exponential. On the other hand, when the attractive force originates from spin or electron charge fluctuations, the Cooper pair has p- or d-wavc symmetry where the gap disappears on lines or points on the Fermi surface and the physical quantities have power-law temperature dependences. The quantities that are measured by NMR and nuclear quadrupole resonance (NQR) are the nuclear spin-lattice relaxation rate, 1 / T, the Knight shift, K, the spin echo decay rate, 1/T2 and the NQR frequency, vq. The most important quantities, K and 1/77 for the determination of the symmetry of the Cooper pairs are reviewed in the following sections. 

Bulut and Scalapino58 calculated the Gaussian spin echo decay rate, 1 / Tjq which is proportional to Xq the, v and d-wave model and proposed the measurement of 1 /Tig to distinguish between the d- or. v-wave. The experiment by Itoh et al,59 coincided well with the calculation on the d-wave model. 

The Gaussian spin echo decay rate 1/72G through the spin fluctuations is expressed as... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

Fig. 8. Spin-echo amplitude A(8G)/A(0) vs. x (see Eq. 2) in a poly-isobutylene-benzene solution containing 59 vol. % benzene. Initial decay rate is due to solvent diffusion, slower decay describes polymer diffusion figure shows only the lowest 1/4 of the abscissa domain used in fitting the double exponential (after Ref. 29>, with permission).

Diffusion-ordered spectroscopy (DOSY)45 is a NMR spectroscopic technique that separates the NMR signals of different compounds according to their diffusion coefficient (D, their rate of diffusion in a particular medium). A series of spin echo spectra is measured with different pulsed field gradient strengths, and the signal decays are fitted to give diffusion coefficients for each compound present. In 2D DOSY this... 

Kinetics of electron transfer have been measured for the electron return from all the reduced acceptors to oxidized P-700. The rates of the forward steps, however, are poorly known in the absence of convincing kinetic absorption data. Electron spin echo provides a submicrosecond time resolution. A decay phase of 170 ns has been attributed to the electron transfer from Fx to or F [67], but it could also be attributed to the reoxidation of A, . 

The development has been slower in ESR as faster relaxation rates (three orders of magnitude) and wider spectral ranges (three-four orders of magnitude) have provided technical obstacles. The free induction decay (FID) can be employed to obtain spectra of paramagnetic species in liquids, analogous to the procedure in NMR. For solid samples the FID is usually too fast to obtain a spectrum. The electron spin echo modulation (ESEEM) method is the common technique to obtain spectra of paramagnetic species in solids. 

The two-pulse echo decay is sometimes too fast to obtain a satisfactory frequency spectrum after Fourier transformation. In this case the three-pulse sequence shown in Fig. 2.21(a) is an alternative. It gives rise to a stimulated echo at time r after the third k/2 pulse. The decay rate is limited by the electron spin-lattice relaxation time Ti, which is usually longer than the phase memory relaxation time Tm for the two-pulse decay. 

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