Spin motion

Therefore, in NMR, one observes collective nuclear spin motions at the Lannor frequency. Thus the frequency of NMR detection is proportional to Nuclear magnetic moments are connnonly measured either... 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

M continually decreases under the influence of spin-spin relaxation which destroys the initial phase coherence of the spin motion within they z-plane. In solid-state TREPR, where large inliomogeneous EPR linewidths due to anisotropic magnetic interactions persist, the long-time behaviour of the spectrometer output, S(t), is given by... 

The K quantum number ean not ehange beeause the dipole moment lies along the moleeule s C3 axis and the light s eleetrie field thus ean exert no torque that twists the moleeule about this axis. As a result, the light ean not induee transitions that exeite the moleeule s spinning motion about this axis. 

Each electron in an atom has two possible kinds of angular momenta, one due to its orbital motion and the other to its spin motion. The magnitude of the orbital angular momentum vector for a single electron is given, as in Equation (1.44), by... 

Vector spaces which occur in physical applications are often direct products of smaller vector spaces that correspond to different degrees of freedom of the physical system (e.g. translations and rotations of a rigid body, or orbital and spin motion of a particle such as an electron). The characterization of such a situation depends on the relationship between the representations of a symmetry group realized on the product space and those defined on the component spaces. 

Spin-orbit coupling problems are of a genuine quantum nature since a priori spin is a quantity that only occurs in quantum mechanics. However, already Thomas (Thomas, 1927) had introduced a classical model for spin precession. Later, Rubinow and Keller (Rubinow and Keller, 1963) derived the Thomas precession from a WKB-like approach to the Dirac equation. They found that although the spin motion only occurs in the first semiclassical correction to the relativistic classical electron motion, it can be expressed in merely classical terms. 

The classical spin motion that follows from the above considerations can be viewed as a dynamics on the sphere S2 driven by the Hamiltonian dynamics in phase space. To see this one first transforms the (redundant) fourdimensional representation of the matrix degrees of freedom, corresponding... 

One should note that the phase shift becomes time-independent and maximal for a = 1, i.e., at the resonance condition v = vG. The frequency spectrum 4>(a) bears a sine shape with a bandwidth inversely proportional to the number of oscillations of the gradient field (Fig. 4). Such a behaviour was also predicted in Ref. 15. Recording in a systematic way the phase shift as a function of vG without space encoding would be a very fast and efficient method to scan in a whole object the possible frequencies of spin motions. 

Fig. 2.1 Spin history leading to the formation of the spin-echo. Longitudinally polarized neutrons enter from the left. Upper part spin motion. Lower part NSE setup, Ti/2-flipper between belonging current rings, primary main precession solenoid l symmetry scan...

Magnetic properties are due to the orbital and spin motions of electrons in atoms. The relation between the magnetic dipole moment p and the angular momentum J of an electron of charge e and mass m can be expressed as... 

The rotational energies represent the spinning motions of a molecule, when the entire molecule rotates around one of its inertial axes. This should not be confused with internal rotation which is the rotational motion of one part of a molecule with respect to some other part of the same molecule. 

Figure 2.5 The orbital and spin motions of an electron around a nucleus are equivalent to circular electric currents I and i these produce magnetic fields shown by their force lines (broken curves)...

Any one orbital can therefore contain two electrons at most, and these must have opposite spin motions (Figure 2.8). 

The dynamic state is defined by the values of certain observables associated with orbilal and spin motions of the electrons and with vibration and rotation of [lie nuclei, and also by symmetry properties of the corresponding stationary-state wave functions. Except when heavy nuclei ate present, the total electron spin angular momentum of a molecule is separately conserved with magnitude Sh. and molecular slates are classified as singlet, doublet, triplet., . according to the value of the multiplicity (25 + I). This is shown by a prefix superscript lo the term symbol, as in atoms. 

Note the plus mi and s plus ms make two equivalent pairs of angular momentum quantum numbers. The former pair is for the orbital motion, and the latter for the spin motion. 

Both the orbital and the effective spinning motions of the electron have associated angular moments quantized in units of ii = 1.055 x 10-34 Js. It is an elementary exercise in physics to show that the relationship between the magnetic dipole moment /< and the angular momentum L for a moving particle of mass m and charge Q is... 

Expanding the wave function in a linear combination of pure spin functions could yield the correct secular equations and thus correct eigenvalues. However, such spin-only wave functions could not be considered complete since complete wave functions must describe both the spatial and spin motions of electrons and must be antisymmetric under exchange of any two electrons. It would be better to rewrite the VB model (18) in the second quantization form as given in Eq. (20), in which its eigenstates can be taken as a linear combination of Slater determinants or neutral VB structures. Then... 

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