Fine Structure Intervals in Transition Elements

1975 ◽  
Vol 53 (21) ◽  
pp. 2421-2427 ◽  
Author(s):  
Jacek Karwowski ◽  
K. M. S. Saxena ◽  
Serafin Fraga
Keyword(s):  
Fine Structure ◽  
Ground State ◽  
Orbit Interaction ◽  
Matrix Elements ◽  
Transition Elements ◽  
Hartree Fock ◽  
Positive Ions ◽  
Transition Series ◽  
The Matrix ◽  
New Formulation

A new formulation for the evaluation of the matrix elements of the spin-own orbit interaction in many-electron atoms has been applied to the evaluation of the interaction matrices for pN, dN, and fN configurations, using functions that are simultaneous eigenfunctions of the operators J2, L2,S2, and.Jz; the complete results are available as indicated in the text. Using this formulation, the fine structure intervals for the ground states of the neutral atoms and the first three positive ions of the elements of the three transition series have been calculated within the framework of the monoconfigurational approximation, including the electrostatic and spin-own orbit interaction between the states arising from the configuration under consideration. In each case, the spin–orbit parameter and the set of Slater–Condon integrals, obtained from the numerical Hartree–Fock function for the ground state, were used.

Orbit–orbit interaction inn fN electron configurations

1969 ◽  
Vol 47 (17) ◽  
pp. 1885-1888 ◽  
Author(s):  
K. M. S. Saxena ◽  
G. Malli
Keyword(s):  
Orbit Interaction ◽  
Matrix Elements ◽  
Atomic Systems ◽  
Hartree Fock ◽  
The Matrix

The expressions of the matrix elements of the orbit–orbit interaction for various fN electron configurations are computed and tabulated for general usage. These expressions are used to evaluate the Hartree–Fock values of the orbit–orbit interaction in all the states for a large number of fN electron atomic systems.

Electronic Structure of the Transition Elements

1973 ◽  
Vol 51 (6) ◽  
pp. 644-647
Author(s):  
K. M. S. Saxena ◽  
S. Fraga
Keyword(s):  
Electronic Structure ◽  
Excited States ◽  
Ground State ◽  
Ground States ◽  
Negative Ions ◽  
State Function ◽  
Transition Elements ◽  
Hartree Fock ◽  
Positive Ions ◽  
Single Set

Numerical Hartree–Fock functions have been determined for the ground states and first excited states of the configurations 3dN4s0 and 3dN4s2 for the negative ions, neutral atoms, and first four positive ions of all the transition elements. The validity of the approximation, embodied in the use of a single set of parameters determined from the ground state function of a configuration for the prediction of the spectroscopic levels arising from it, has been examined in detail in the case of Fe I, 3d64s2, where independent calculations have been carried out for all the excited states.

Orbit–orbit interaction in positive ions of transition elements

1968 ◽  
Vol 46 (12) ◽  
pp. 1469-1471 ◽  
Author(s):  
Jon Thorhallsson ◽  
Serafin Fraga
Keyword(s):  
Orbit Interaction ◽  
Spin Orbit ◽  
Transition Elements ◽  
Spin Orbit Interaction ◽  
Hartree Fock ◽  
Positive Ions ◽  
Parent State ◽  
Order Of Magnitude

The orbit–orbit interaction in a number of positive ions of transition elements has been evaluated from analytical Hartree–Fock functions. This interaction is the same for the various states arising from a given configuration and with the same parent state and, in many cases, of an order of magnitude comparable to the spin–orbit interaction.

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

An Investigation on the Fine Structure Levels in the Ground State Configuration for the Antimony Anion

2014 ◽  
Vol 69 (8-9) ◽  
pp. 397-402
Author(s):  
Leyla Özdemir ◽  
Sadiye Tuna
Keyword(s):  
Fine Structure ◽  
Ground State ◽  
Transition Probabilities ◽  
Relativistic Effects ◽  
Electric Quadrupole ◽  
Radiative Transition ◽  
Ground State Configuration ◽  
Hartree Fock ◽  
First Time ◽  
State Configuration

We have investigated the correlation, relativistic, and isotope shift effects on the fine structure levels in the ground state configuration for the antimony anion ( Sb-). Energies and radiative transition probabilities (for magnetic dipole, M1, and electric quadrupole, E2) have been obtained using the multiconfiguration Hartree-Fock method within the framework of the Breit-Pauli Hamiltonian. Therefore, the most important configuration interaction and relativistic effects have been included. Comparisons with other available works are presented. For some M1 and E2 lines the considered transition probabilities are reported for the first time

scholarly journals Triaxiality in the odd-A nuclei 109−117I studied through a microscopic rotationparticle coupling

2018 ◽  
Vol 178 ◽  
pp. 02030
Author(s):  
Swati Modi
Keyword(s):  
Systematic Study ◽  
Coming Out ◽  
Ground State ◽  
Rotor System ◽  
Matrix Elements ◽  
Triaxial Deformation ◽  
The Matrix

A systematic study of ground state spectrum with the triaxial deformation γ for odd-A Iodine isotopes 109−117I is carried out with the nonadiabatic quasiparticle approach. The rotation-particle coupling is accomplished microscopically such that the matrix elements of a particle-plus-rotor system are written in terms of the rotor energies. The 5/2+ state is confirmed as ground state for odd-A 111−117I and also coming out as lowest in energy for 109I.

Coherent X-ray Scattering Factors for Various Configurations of Lanthanides and Their Positive Ions

1975 ◽  
Vol 53 (1) ◽  
pp. 93-96 ◽  
Author(s):  
Robert Benesch ◽  
K. M. S. Saxena
Keyword(s):  
Ground State ◽  
Wave Functions ◽  
X Ray ◽  
Hartree Fock ◽  
Positive Ions ◽  
X Ray Scattering ◽  
Scattering Factor ◽  
Ray Scattering

Coherent X-ray scattering factors have been computed from numerical Hartree–Fock wave functions for the neutral lanthanides and for their single-, double-, and triple-positive ions having the most commonly occurring 6sm4fn ground state configurations. For small scattering angles, the scattering factors for the ions vary among the various configurations. At large scattering angles all configurations for a given ion yield similar values for the scattering factor.

scholarly journals DIAGONAL AND NONDIAGONAL MATRIX ELEMENTS OF THE EFFECTIVE HAMILTONIAN OF ELECTRONS IN A SEMICONDUCTOR (TAKING INTO ACCOUNT SPIN-ORBIT INTERACTION)

2020 ◽  
pp. 120-127
Author(s):  
Voxob Rustamovich Rasulov ◽  
Rustam Yavkachovich Rasulov ◽  
Akhmedov Bahodir Bahromovich ◽  
Ravshan Rustamovich Sultanov
Keyword(s):  
Wave Function ◽  
Matrix Element ◽  
Valence Band ◽  
Heavy Hole ◽  
Orbit Interaction ◽  
Effective Hamiltonian ◽  
Spin Orbit ◽  
Matrix Elements ◽  
The Matrix ◽  
Split Band

The matrix elements of the effective Hamiltonian of current carriers are calculated as in the Kane approximation, where the conduction band, the valence band consisting of light and heavy hole subbands, and the spin-split band, as well as in the Luttinger-Kohn model, are considered. KEYWORDS: matrix element, effective Hamiltonian, current carriers, wave function.

Absorption Spectrum of Mn2+ Ions Doped in Zinc Thallium Sulphate Hexahydrate

1989 ◽  
Vol 44 (1) ◽  
pp. 19-22
Author(s):  
J. Lakshmana Rao ◽  
M. Ramachandra Reddy ◽  
S. V. J. Lakshman
Keyword(s):  
Absorption Spectrum ◽  
Fine Structure ◽  
Optical Absorption ◽  
Liquid Nitrogen ◽  
Ground State ◽  
Optical Absorption Spectrum ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Octahedral Symmetry ◽  
Spin Orbit Interaction

Abstract The optical absorption spectrum of Mn2+ ions doped in zinc thallium sulphate hexahydrate has been studied at room and liquid nitrogen temperatures. The observed bands are assigned as transitions from the 6A1g(S) ground state to various excited quartet levels of Mn2+ ion in octahedral symmetry. The fine structure observed in the 4T2g(D) band is explained as due to spin-orbit interaction. All the observed band positions have been fitted with the parameters B, C, Dq and α .

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