If the angular momentum of a free electron is represented by a spin vector S=(S, S, S ), the magnetic moment... [Pg.1548]

Vector representation of momenta and vector coupling approximations 7.1.2.1 Angular momenta and magnetic moments... [Pg.201]

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

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. [Pg.139]

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. [Pg.32]

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... [Pg.90]

Magnetization vector (M) The resultant of individual magnetic moment vectors for an ensemble of nuclei in a magnetic field. [Pg.416]

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... [Pg.85]

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 ... [Pg.94]

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