Vectors magnetic moment

Compound Propogation vector Magnetic moment Distortion ... 

If the angular momentum of a free electron is represented by a spin vector S=(S, S, S ), the magnetic moment... 

Vector representation of momenta and vector coupling approximations 7.1.2.1 Angular momenta and magnetic moments... 

Figure 7.2 Vectors I and s and magnetic moments and associated with orbital and spin angular momenta when the motions are (a) in the same direction and (b) in opposite directions...

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...

An intuitive model of the process can be given. Consider the proton, with / = i then there are two states, characterized by m = +5 and m = —5. In the absence of an applied field, these states are equally populated. The states may be pictured as corresponding to opposite orientations of a tiny bar magnet, which is a crude way of visualizing the magnetic moment vector. Clearly in the absence of an applied field, the orientation of the moment should not affect the energy of the nucleus. 

Figure 4-4. (A) Magnetic moment vector i. precessing about applied field vector Hq. (B) Addition...

Here Iais the magnetic moment of nucleus A and Ra is the position (the nucleus is the natural Gauge origin). Adding this to the external vector potential in eq. (10.62) and expanding as in (10.63) gives... 

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

This simplified treatment does not account for the fine-structure of the hydrogen spectrum. It has been shown by Dirac (22) that the assumption that the system conform to the principles of the quantum mechanics and of the theory of relativity leads to results which are to a first approximation equivalent to attributing to each electron a spin that is, a mechanical moment and a magnetic moment, and to assuming that the spin vector can take either one of two possible orientations in space. The existence of this spin of the electron had been previously deduced by Uhlenbeck and Goudsmit (23) from the empirical study of line spectra. This result is of particular importance for the problems of chemistry. 

Hund37 in 1926 and of oxygen and nitric oxide by Van Vleck38 in 1928 were triumphs of the theory of spectra. The magnetic moment of an atom or monatomic ion with Russell-Saunders coupling of the quantum vectors is... 

Figure 1.1 Representation of the precession of the magnetic moment about the axis of the applied magnetic field, Bo- The magnitude /r, of the vector corresponds to the Boltzmann excess in the lower energy (a) state.

Magnetization vector (M) The resultant of individual magnetic moment vectors for an ensemble of nuclei in a magnetic field. 

Three basic equations (3.10-3.12) are needed to describe the technique. In the equations, p is the magnetic moment of the electron, sometimes also written as pe, g is called the g factor or spectroscopic splitting factor, S is defined as the total spin associated with the electron (in bold type because it is considered as a vector), B is the imposed external magnetic field (also defined as a vector quantity), and... 

The angular momentum and magnetic moment of nuclei act as parallel or antiparallel vectors, and the ratio between these is known as the magnetogyric ratio, y. The magnetogyric ratio is given in terms of equation 3.23 ... 

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