The tensor-operator and group-theoretical methods of Racah are used to examine the following contributions to the Hamiltonian of a rare-earth ion: ( a ) the Coulomb interaction between the electrons, ( b ) the spin-orbit coupling of the electrons, and ( c ) the term arising from the influence of an external electrostatic field such as occurs when the rare-earth ion is situated in a crystal lattice. With regard to ( a ), the positions of all the terms of the configurations f 2 , f 3 and f 4 , as well as all the terms of other configurations f n whose multiplicities are the highest or the highest but one, are tabulated on the basis of a hydrogenic 4 f wave function. The theory of ( b ) is developed, and the parameter λ defining the spin-orbit splitting of a term is given for all terms whose energies have been found, ( c ) is treated by similar techniques and the theory is related to the one at present in use. All the general methods are illustrated by examples.
A b initio calculations are performed on the electronic states of UF6, UF6+, and UF−6 using a relativistic effective core potential (ECP) for uranium and a nonrelativistic ECP f...
The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a loca...
Effective core potentials for the Ar, Kr, and Xe atoms derived from numerical Hartree–Fock and Dirac–Hartree–Fock wave functions are applied in SCF and CI calculations of homonu...
A b initio effective spin-orbit operators, based on relativistic effective core potentials, are used to determine the spin-orbit coupling constants for CH(X 2Πr), OH(X 2Πi), SiH...
Inelastic collisions of O(1D) with Ar, Kr, and Xe have been treated in the multistate Landau–Zener and the close-coupling approximations. The coupling mechanism is spin–orbit mi...
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