Spin magnetism

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

As mentioned in Section Wl, an electron has magnetism associated with a property called spin. Magnetism is directional, so the spin of an electron is directional, too. Like orbital orientation, spin orientation is quantized Electron spin has only two possible orientations, up or down. The spin orientation quantum number )... 

Following the hypothesis of electron spin by Uhlenbeck and Goudsmit, P. A. M. Dirac (1928) developed a quantum mechanics based on the theory of relativity rather than on Newtonian mechanics and applied it to the electron. He found that the spin angular momentum and the spin magnetic moment of the electron are obtained automatically from the solution of his relativistic wave equation without any further postulates. Thus, spin angular momentum is an intrinsic property of an electron (and of other elementary particles as well) just as are the charge and rest mass. 

The spin magnetic moment Mg of an electron is proportional to the spin angular momentum S,... 

The spin magnetic moment Ms of an electron interacts with its orbital magnetic moment to produce an additional term in the Hamiltonian operator and, therefore, in the energy. In this section, we derive the mathematical expression for this spin-orbit interaction and apply it to the hydrogen atom. 

We attempt to describe NMR Imaging in a simplified manner using only three essential equations that explain why we see a signal and what it looks like. The first equation describes the nuclear spin magnetization, thus the strength of the NMR signal (and indeed much more) ... 

The essence of the DDIF method is to first establish a spin magnetization modulation that follows the spatial variation of the internal magnetic field within the individual pore. Such modulation is created by allowing spins to precess in the internal magnetic field. Then the diffusion-driven time-evolution (often decay) of such a modulation is monitored through a series of signal measurements at various evolution times tD. The time constant of this decay corresponds to the diffusion time of a molecule (or spin) across the pore and thus is a direct measure of the pore size. 

This method has been used for the reconstruction of charge densities from X-ray data [1-3], for maps of nuclear densities from unpolarized neutron data [4-6] as well as for distributions of spin (magnetization) density [7-9].The density... 

When a magnetic field is applied to an electron or nuclear spin, the spin quantization axis is defined by the field direction. Spin magnetic moments... 

Hamiltonian with the energy from appropriate terms in the true Hamiltonian. The latter terms include the interaction between the external field and the magnetic moment produced by the orbiting electron, the interaction between the external field and the magnetic moment due to electron spin, and the interaction between the orbital magnetic moment and the spin magnetic moment. These interactions may be expressed as a perturbation to the total Hamiltonian for the system where... 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

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