Ground configuration splitting in UCl5

1977 ◽  
Vol 55 (10) ◽  
pp. 937-942 ◽  
Author(s):  
A. F. Leung ◽  
Ying-Ming Poon
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Point Charge Model ◽  
X Ray Crystallography ◽  
Charge Model ◽  
Crystal Field Parameters

The absorption spectra of UCl5 single crystal were observed in the region between 0.6 and 2.4 μm at room, 77, and 4.2 K temperatures. Five pure electronic transitions were assigned at 11 665, 9772, 8950, 6643, and 4300 cm−1. The energy levels associated with these transitions were identified as the splittings of the 5f1 ground configuration under the influence of the spin–orbit coupling and a crystal field of C2v symmetry. The number of crystal field parameters was reduced by assuming the point-charge model where the positions of the ions were determined by X-ray crystallography. Then, the crystal field parameters and the spin–orbit coupling constant were calculated to be [Formula: see text],[Formula: see text], [Formula: see text], and ξ = 1760 cm−1. The vibronic analysis showed that the 90, 200, and 320 cm−1 modes were similar to the T2u(v6), T1u(v4), and T1u(v3) of an UCl6− octahedron, respectively.

The spectrum of Tm III in CaF 2

1964 ◽  
Vol 277 (1370) ◽  
pp. 289-296 ◽  
Keyword(s):  
Crystal Field ◽  
Coupling Parameter ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Paramagnetic Resonance ◽  
Hyperfine Constant ◽  
Charge Model ◽  
Resonance Data ◽  
Atomic Beams

The crystal field of CaF 2 is evaluated on a point-charge model, and from comparison with the crystal field constants derived from the optical spectrum (Kiss 1962) of Tm III in CaF 2 , empirical values of < r 4 >= 4.3 a.u., < r 6 > = 36 a.u. are found. These are considerably larger than the estimates of Freeman & Watson (1962). The crystal field data reveal a small discrepancy with the paramagnetic resonance data of Hayes & Twidell (1961), which can be resolved by the introduction of an orbital k -factor which is slightly less than unity (1 — k — 0009 ± 0-001). Comparison with the spectrum of Tm I measured by atomic beams (Ritter 1962) shows that the magnetic hyperfine constant for a free Tm III ion is (2.2 ± 0.5 )% greater, while the spin-orbit coupling is 1.2% greater, assuming a core polarization correction of the same magnitude as that measured for Eu III in CaF 2 . Similar effects are shown to occur for Ho III in CaF 2 . The results suggest that the values of < r -3 > and the spin-orbit coupling parameter ζ are only about 1 to 2 % greater for the free divalent 4 f ions than for the atoms.

Magnetic Susceptibilities of 2T2 Ions. Part 1

1972 ◽  
Vol 50 (10) ◽  
pp. 1468-1471 ◽  
Author(s):  
Alan D. Westland
Keyword(s):  
Magnetic Susceptibility ◽  
Excited State ◽  
Reduction Factor ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Magnetic Susceptibilities

An expression for the magnetic susceptibility of octahedral d1 complexes is derived exactly in terms of an orbital reduction factor k taking into account the presence of the formal 2E excited state. Sample calculations show that the improved expression gives results for susceptibility which are lower at times by several percent from those given by previous expressions. The results given by Figgis using Kotani's method are adequately precise when the spin–orbit coupling constant is no larger than ~0.1 Dq.

Determination of the spin orbit coupling and crystal field splitting in wurtzite InP by polarization resolved photoluminescence

2018 ◽  
Vol 112 (7) ◽  
pp. 071903 ◽  
Author(s):  
Nicolas Chauvin ◽  
Amaury Mavel ◽  
Ali Jaffal ◽  
Gilles Patriarche ◽  
Michel Gendry
Keyword(s):  
Crystal Field ◽  
Orbit Coupling ◽  
Crystal Field Splitting ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Field Splitting

Space-group operations and time-reversal for a Dirac electron in a crystal field

1958 ◽  
Vol 243 (1235) ◽  
pp. 546-554 ◽  
Keyword(s):  
Dirac Equation ◽  
Crystal Field ◽  
Time Reversal ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Band Theory ◽  
Space Group ◽  
Basic Formalism ◽  
Dirac Electron

It is shown in the first part how the basic formalism of the theory of spin-orbit coupling in the band theory of crystals can be deduced at once from the Dirac equation without the usual ambiguities over improper rotations associated with the formalism based on the Pauli-Schrödinger equation. In the second part it is shown that the original proofs of the time-reversal theorems given by Wigner are unnecessarily complicated.

ELECTRONIC PROPERTIES OF A HYDROGENIC IMPURITY IN A QUANTUM WIRE WITH V-SHAPED CROSS-SECTION: SPIN-ORBIT COUPLING, RELATIVISTIC CORRECTION AND CONDUCTANCE

2013 ◽  
Vol 24 (07) ◽  
pp. 1350041 ◽  
Author(s):  
R. KHORDAD ◽  
H. BAHRAMIYAN
Keyword(s):  
Cross Section ◽  
Quantum Wire ◽  
Energy Levels ◽  
Relativistic Correction ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Hydrogenic Impurity ◽  
Mass Approximation ◽  
Shaped Cross Section

The effects of spin-orbit coupling (SOC) and relativistic correction (RC) on the energy levels of a hydrogenic impurity in a GaAs/Ga 1-x Al x As quantum wire are studied. The quantum wire has a V-shaped cross-section and the impurity located in its center. Our numerical calculations have done using a variational procedure within the effective mass approximation. Our results show that (i) the splitting due to the SOC decreases with increasing the wire width, (ii) the SOC and RC increase when the concentration increases, (iii) the SOC is zero for l = 0 (l is angular momentum) and nonzero for l ≠ 0, (iv) for a given wire width, the RC is different for l = 0 and l = 1 due to expectation values of [Formula: see text] and [Formula: see text] (r is distance between the electron and impurity). We also computed the conductance of the quantum wire with and without impurity.

Study on the Absorption Spectra of Ga2Se3:Co2+ Single Crystals

2009 ◽  
Vol 64 (12) ◽  
pp. 834-836
Author(s):  
Chao Ni ◽  
Yi Huang ◽  
Maolu Du
Keyword(s):  
Experimental Data ◽  
Fine Structure ◽  
Bond Length ◽  
Single Crystals ◽  
Crystal Field ◽  
Energy Levels ◽  
Crystal Field Parameter ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Cubic Crystal

Introducing the average covalent factor N and considering the interaction of the cubic crystal field, the spin-orbit coupling and Tree’s correction effects, the crystal field parameter Dq was calculated. Also the varying tendency of Dq with the bond length R was investigated. Using the complete diagonalizing method the energy levels of the fine structure of Ga2Se3:Co2+ single crystal were calculated and assigned. The calculated and assigned results are consistent with the experimental data

Theory of spin-orbit coupling in atoms, II. Comparison of theory with experiment

1963 ◽  
Vol 271 (1347) ◽  
pp. 565-578 ◽  
Keyword(s):  
Wave Functions ◽  
Coupling Constants ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Outer Electron ◽  
Coupling Constant ◽  
Radial Wave ◽  
Order Of Magnitude ◽  
Experimental Values

Results of calculations of the spin-orbit coupling constant for 2 p , 3 p , 4 p , and 3 d shell ions and atoms are presented. The calculations are based on a theory developed in a previous paper. Excellent agreement of this theory with experiment is obtained for the 2 p and 3 d shell ions, while calculations using the familiar < ∂ V / r ∂ r > expression for the coupling constant lie 10 to 20 % too high. The exchange terms discussed in the earlier paper make a contribution to the coupling constant of the same sign and order of magnitude as the ordinary shielding terms. For the 3 p and 4 p shell atoms, the calculated coupling constants based on the exact theory and on the < ∂ V / r ∂ r > expression both tend to lie below the experimental values. An explanation for this disagreement is suggested, based on the noded nature of the outer-electron radial wave functions for these atoms. The importance of the residual-spin-other-orbit interaction is discussed, and it is shown that ignoring the form of this interaction may lead to a large variation in the coupling constant within a configuration.

Theory of spin-orbit coupling in atoms I. Derivation of the spin-orbit coupling constant

1962 ◽  
Vol 270 (1340) ◽  
pp. 127-143 ◽  
Keyword(s):  
Exact Expression ◽  
Orbit Coupling ◽  
Tensor Operator ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Coupling Constant ◽  
Hartree Fock ◽  
Operator Form ◽  
Hartree Potential

An exact expression for the spin-orbit coupling constant is derived within the Hartree-Fock description of the atom by considering the two body mutual spin-orbit interaction between electrons. The interaction is rewritten in tensor operator form and the contribution of outer electron-core interactions to the coupling constant is calculated. We find that the usual expression < 3F/r8r > where V is the Hartree potential is only approximate, and that certain exchange type terms, which arise because we are dealing with a two-body interaction and determinantal wave function, must also be included. These exchange terms are not simply related to the ordinary electrostatic exchange. The resulting expression for the spin-orbit coupling constant is given in terms of radial integrals which can be calculated using Hartree or Hartree—Fock wave functions. We also discuss the effective magnetic Hamiltonian to be used for the calculation of matrix elements within an atomic configuration.

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