Nuclear spin, precession

In a spin system, each nuclear spin precesses around its individual effective static field Beff = B0 + Be(ms), (Sect. 3.3). Since the resonance frequency of a nuclear transition is proportional to B=ff, ENDOR lines for different types of nuclei may be observed in the same frequency range. 

An alternating magnetic field Bl with frequency irradiating an ensemble of nuclear spins precessing in the static field B0 may overcome the energy difference AE if it meets two conditions The vector of the alternating field B1 must rotate in the plane of precession with the Larmor frequency v0 of the nuclei to be observed (Fig. 1.4(a)). 

In a magnetic field of strength B, the resonating nuclear spins precess with the Larmor frequency... 

This contains an TCP of the TpaL tensor, which is derived from the electron spin and dipole-dipole interaction tensor(See equation (11)). Hence, the first question we confront is whether those tensors are correlated or not. In case they are not the total TCP can be decomposed into a product of auto correlations for the the electron spin and dipole-dipole interaction tensor, respectively. In case they are, however, it is necessary to consider the whole TCP and the electron spin has to be correlated with the dipole-dipole interaction tensor. The time dependence in the electron spin tensor can be obtained by integrating the time dependent Schrbdinger equation for the electron spin under the electron spin Hamiltonian. The electron spin is just like the nuclear spin precessing around the external magnetic field and influenced by molecular dynamics. 

Rates that are fast on the NMR linC Shape time scale (peaks fail to decoalesce at high temperatures) sometimes may be measured by observation at a different resonance frequency. Normally, nuclear spins precess around the field at their Larmor frequency. Application of the usual 90 pulse in the x direction places the spins in the xy plane, along they axis. (See Figure 1-15a). Continuous irradiation along the y axis (not a pulse) forces... 

To describe Fourier transform (FT) NMR spectroscopy and pulse techniques, it is best to picture the nuclear spins aligned with and against the field as in Figure A. 1.2(a). The nuclear spin precesses about the --axis with the frequency, v, given in equation (A. 1.5). 

In NMR spectroscopy, nuclear spins precess about the static magnetic field, Bq, at the Larmor frequency, [Pg.548]

NMR usually assumes that the nuclear spins precess at the same frequency neglecting chemical shift differences arising from different chemical types of... 

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Free induction decay A decay time-domain beat pattern obtained when the nuclear spin system is subjected to a radiofrequency pulse and then allowed to precess in the absence of Rf fields. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Hyperfine structure arises through the interaction of the electron spin with a nuclear spin. Consider first the interaction of the electron spin with a single magnetic nucleus of spin , In an applied magnetic field the nuclear spin angular momentum vector, of magnitude (/ / -f l)]l/2, precesses around the direction of the field in an exactly analogous way to that of the electron spin. The orientations that the nuclear spin can take up are those for which the spin in the z-direction, M, has components of ... 

Another surprise was that nuclear spins also become polarized by the magnetic layer after several minutes. This polarization acts like a magnetic field causing electron spin to precess at a frequency and in a direction controlled by the magnetic layer. 

If all nuclear spins in the sample were in exactly the same field, this signal would not decay, as the name implies, but would persist "forever." In any real sample, though, local fields cause different nuclei to be in slightly different total fields, and their moments ft precess at slightly different frequencies. Thus, following a 90° pulse, the moments y initially precess coherently but eventually get out of phase with each other, causing M to "decay" to zero. 

The inversion of Bcff for the low-frequency line takes place at a = 2 vn = 2 Ng B0. As a consequence the nuclear spin states belonging to ms = 1/2 change their precession direction from l.h. (ais0 < a J) to r.h. (aiso > aj J). For ms = -1/2, ENDOR transitions are only observed with a l.h. rotating field. 

PAC atomic probes (e.g., mIn or mHf) possess a nuclear quadrupole moment and a magnetic dipole. Even if no field acts on the PAC nucleus, the successive emission of the y-photons through an intermediate state exhibits an appreciable angular anisotropy between the emission directions. If the (isolated) nucleus is then brought into a perturbing field (e.g., on a specific lattice site which is next to a vacancy), the angular anisotropy becomes time-dependent due to the precession of the nuclear spin. For example, if the PAC nucleus in the crystal is exposed to a (static) electric... 

Precession of the nuclear spins about B0 is energetically favored (Fig. 1.3 (b)) since the component of the nuclear magnetic moment vector fi in the direction of B0 reinforces the magnetic field (Fig. 1.3 (a)). 

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