Angular momentum in atoms

There are two extreme approaches to the description of vibroiiic states in crystals. The crystal states may be regarded as products of molecular vibronic states, or as linear combinations of vibronic site states. In the former case the electrons and nuclei in the unit cell couple independently, while for the latter description the intramolecular vibronic interactions are assumed to dominate. These two approaches are somewhat analogous to y and LS coupling of spin and orbital angular momentum in atoms and are called strong and weak coupling, respectively. The approach to the classification of states is different for each case. 

E. XT. Condon and G. H. Shortley, Theory of Atomic Spectra, Cambridge University Press, 1935 M. E. Bose, Elementary Theory of Angular Momentum, John Wiley and Sons, Inc., New York, 1957 A. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, 1957. 

If we replace the z-component of the classical angular momentum in equation (6.87) by its quantum-mechanical operator, then the Hamiltonian operator Hb for the hydrogen-like atom in a magnetic field B becomes... 

In the present calculation the SIC potential is introduced for each angular momentum in a way similar to the SIC one for atoms [9]. The effects of the SIC are examined on the CPs of three materials, diamond, Si and Cu compared with high resolution CP experiments except diamond [10, 11]. In order to examine the quasi-particle nature of the electron system, the occupation number densities of Li and Na are evaluated from the GWA calculation and the CPs are computed by using them [12, 13]. 

In these equations, (24)-(26), orthonormal orbits are denoted by indices Vs. Equation (26) means that the orbiting electron interacting with itself, that is self-interaction, exists. This is unphysical. In order to remove this unphysical term, the SIC is taken into account by the following procedure. The SIC for the LDA in the density functional method has been treated for free atoms and insulators [16], and found an important role in determining the energy levels of electrons. However, no established formula is known to take into account the SIC for semiconductors and metals. As a way of trial, in the present calculation, the atomic SIC potential is introduced for each angular momentum in a way similar to the SIC potential for atoms [17] as follows ... 

Thus, PBCs function to preserve mass, particle number, and, it can be shown, total energy in the simulation cell. In an MD simulation, PBCs also conserve linear momentum since linear momentum is not conserved in real contained systems, where container walls disrupt the property, this is equivalent to reducing the number of degrees of freedom by 3. However, this effect on system properties is typically negligible for systems of over 100 atoms. Obviously, PBCs do not conserve angular momentum in the simulation cell of an MD simulation, but over time the movement of atoms in and out of each wall of the cell will be such that... 

The unpaired d electrons in an isolated transition metal ion or atom possess orbital angular momentum in addition to the spin momentum, and these couple together to give a total angular momentum J. The Zeeman interaction for these ions can be expressed by Eqs. (1) and (2) if S is replaced by J and g by the Lande g factor ... 

An interesting approach has been attempted in the works of Vasyutin-skii and coworkers [252, 254, 380] who showed, for the case of Csl, TIBr and Rbl, that conservation of angular momentum in the photodissociation process caused by circularly polarized light produces orientation of the atoms formed, the latter enabling measurement by means of magnetic resonance of the atomic products created. This is so if the lifetime of the... 

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