Parameters spin-orbit, definition

The first term is characterized by a scalar, 7, and it is the dominant term. Be aware of a convention disagreement in the definition of this term instead of -27, some authors write -7, or 7, or 27, and a mistake in sign definition will turn the whole scheme of spin levels upside down (see below). The second and third term are induced by anisotropic spin-orbit coupling, and their weight is predicted to be of order Ag/ge and (Ag/ge)2, respectively (Moriya 1960), when Ag is the (anisotropic) deviation from the free electron -value. The D in the second term has nothing to do with the familiar axial zero-field splitting parameter D, but it is a vector parameter, and the x means take the cross product (or vector product) an alternative way of writing is the determinant form... 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

Even if the corresponding parameters of the ss and soo interactions are forced to remain equal to each other in a least-square calculation (as justified by their definitions), twenty new independent parameters have been added to the already existing ten electrostatic and two spin-orbit parameters. But since the 4f5d configuration comprises 20 levels, at most eight new SDl parameters could be... 

Recently the usefulness of the parameters e and A have been discussed by Bartschat and Blum. They have found that whereas a comparison between experimental and numerical results only allows the theoretical model to be tested as a whole, including all approximations made in describing the scattering process and on the atomic wavefunctions, a comparison of e and A may allow individual dynamical assumptions to be tested. For instance a P state excitation process can be considered as a two step process where initially an elastic scattering occurs, in the presence of spin-orbit interactions, followed by an excitation in which spin-dependent forces may be neglected. In this instance the states = 1 and ] = -1 are coherently excited and a definite phase relation exists between a and This results in cos e = 1... 

Here, S is the total spin of the cluster, J is the parameter of the HDVV exchange interaction, t is the parameter of double exchange, Sa and 5 are the spins of the cluster ions, and is the minimal of these spins. For the sake of definiteness the orbitals are assumed to be spherical, and the symmetry labels of D4h point group are employed. The presence of these levels in the electronic spectrum of MV dimers and their mixing by the out-of-phase mode q (q = (Qa - Qb)lV2 Qa and Qb are the full symmetric vibrational modes of the cluster fragments (Fig. 29a))... 

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