Coulomb and spin-orbit interaction

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin-orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius Rs which is embedded into an infinite medium with dielectric constant e. This leads to a reduction AFk of the Slater parameters (Newman, 1973) ... 

The first approximation to paramterize equation (1) is to assume that all electrons move in a central potential. If we then limit the analysis to a single configuration, we need discuss only the Coulomb and spin-orbit interaction between the equivalent f-electrons. With the aid of tensor operators the Coulomb interaction can be expressed as... 

In 1962, Sugano showed that the Seitz model (115) could be interpreted as a molecular orbital model (123), an interpretation that clarifies analysis of these systems. In this interpretation, the absorption bands observed in the TI(I) doped alkali halide system come from the electronic transition aigf a g) hu), but the excited states are still calculated assuming an ionic interaction between the metal and the hgand. Since the thallium-chlorine bond is actually largely covalent, Bramanti et al. (118) modified the approach and used a semiempirical molecular orbital (MO) calculation to describe the energy levels of T1(I) doped KCl. Molecular orbitals were constructed by the linear combination of atomic orbitals (LCAO) method from the 6s and 6p metal orbitals and the 3p chlorine orbitals. Initial calculations were conducted with the one-electron approximation the method was then expanded to include Coulomb and spin-orbit interactions. The results of Bramanti et al. were consistent with experimental... 

Coulomb and spin-orbit interactions In the lowest approximation (Slater, 1929), the potential seen by an electron on a lanthanide ion is treated as spherically symmetric ( central field approximation ) in this approximation, the Hamiltonian is... 

Configuration interaction and spin-dependent interactions Section 3.1.1 provides a basic framework for computing free-ion energies and eigenfunctions. When the simple Coulomb and spin-orbit interactions are used, however, discrepancies of the order of a few hundred wave numbers remain between calculated and experimental energy levels. A more complete free-ion Hamiltonian includes the following additional interactions ... 

It appears then from experimental data that not only do local atomic correlations persist in the metallic environment, but they dominate perturbations due to the crystalline lattice. Deviations from the atomic model are therefore going to be difficult to detect. Hund s rules are a consequence of the Coulomb and spin-orbit interactions within the 4f shell but, whilst their success confirms the importance of... 

For higher values of n (in f ) the number of J levels increases markedly. Table 1 shows the number of levels that can be obtained for various f configurations considering only the Coulombic and spin-orbit interactions [5]. 

The Coulombic and spin-orbit interactions represent the major... 

For Rydberg states of pure msnd configuration, the Hamiltonian Hq, which takes Coulomb and spin-orbit interactions of the valence electrons into account, can be written as... 

Hua and Vohra (1997) did not give an explanation why the levels in YAIO3 behave completely different to what is usually observed. In principle, the observed blue shift of these levels point to increasing Coulomb and spin-orbit coupling interactions, which should be connected with an increasing local volume (see also sect. 4.3). Whether such a behavior is reasonable or not could be answered only by further investigations as for example using... 

In conventional collision experiments the strong Coulomb interaction generally masks the much weaker relativistic spin-dependent interactions. The role of the spin-dependent interactions, such as the exchange and spin—orbit interactions, has also been clarified by sophisticated measurements with spin-polarised electrons and/or spin-polarised targets, sometimes employing spin analysis after the collision process (Kessler, 1985, 1991 Hanne, 1983). 

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

Interaction of the momenta is contained in a non-spherical part of the Coulomb interaction and in the spin-orbit interaction. The value of the energy of the interaction of two momenta depends on the angle between them, therefore, in such a case the definite inter-orientation of all one-electronic momenta is settled. Differently oriented states have different energy, i.e. the zero-order level splits into sublevels and its degeneracy disappears. 

The LSJ-coupling scheme introduced above is called the Russell-Saunders coupling scheme [RSa25], It is based on the validity of equ. (1.9). The other extreme coupling case follows if the spin-orbit interaction dominates the Coulomb interaction between the electrons. This is called the jjJ-coupling scheme and requires that... 

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