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.

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.

Spin–orbit and spin–other–orbit interactions for f4 electron configuration

1969 ◽  
Vol 47 (17) ◽  
pp. 1829-1862 ◽  
Author(s):  
K. M. S. Saxena ◽  
Gulzari Malli
Keyword(s):  
Electron Configuration ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Atomic Systems ◽  
Hartree Fock ◽  
The Matrix

General expressions for the reduced matrix elements of spin–orbit and spin–other–orbit interactions are evaluated for all the states arising from f4 electron configuration. These are used to calculate the Hartree–Fock values of the matrix elements of the above-mentioned interactions for Nd(4f4), Dy(4f10), and Ho3+ (4f10) atomic systems.

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.

Electron Spin–Spin Contact Interaction in Atoms with fn Configurations

1971 ◽  
Vol 49 (15) ◽  
pp. 2031-2032 ◽  
Author(s):  
K. M. S. Saxena ◽  
B. W. N. Lo ◽  
S. Fraga
Keyword(s):  
Contact Interaction ◽  
Electron Spin ◽  
Numerical Calculations ◽  
Matrix Elements ◽  
Hartree Fock ◽  
The Matrix ◽  
Lanthanide Atoms

The expressions of the matrix elements of the electron spin–spin contact interaction have been tabulated for all the states arising from fn configurations. Numerical calculations have been carried out for a large number of lanthanide atoms and ions using accurate numerical Hartree–Fock functions.

ON THE SPIN–ORBIT INTERACTION IN DIATOMIC MOLECULES. I

1958 ◽  
Vol 36 (3) ◽  
pp. 309-328 ◽  
Author(s):  
I. Kovács
Keyword(s):  
Diatomic Molecules ◽  
Electron System ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Molecular Constants ◽  
Spin Orbit Interaction ◽  
The Matrix

The purpose of the present paper is to give further details of an investigation of the spin–orbit interaction in diatomic molecules. The first part of the paper deals with perturbations between states of odd multiplicity in a two-electron system. With the aid of the matrix elements which have been obtained, a comparison of the perturbations in the various components of a given state and in some cases a comparison of perturbations in two different states is possible. Also for certain cases it has been possible to establish relationships between the matrix elements which give the magnitude of the perturbations and experimentally measurable molecular constants of the perturbed states.

scholarly journals Theoretical Stark Broadening Parameters for UV–Blue Spectral Lines of Neutral Vanadium in the Solar and Metal-Poor Star HD 84937 Spectra

Atoms ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 64
Author(s):  
Cristóbal Colón ◽  
María Isabel de Andrés-García ◽  
Lucía Isidoro-García ◽  
Andrés Moya
Keyword(s):  
Spectral Lines ◽  
Matrix Elements ◽  
Stark Broadening ◽  
Laboratory Plasma ◽  
Hartree Fock ◽  
The Matrix ◽  
Line Widths ◽  
And Shifts ◽  
Semi Empirical ◽  
Metal Poor Star

Using Griem’s semi-empirical approach, we have calculated the Stark broadening parameters (line widths and shifts) of 35 UV–Blue spectral lines of neutral vanadium (V I). These lines have been detected in the Sun, the metal-poor star HD 84937, and Arcturus, among others. In addition, these parameters are also relevant in industrial and laboratory plasma. The matrix elements required were obtained using the relativistic Hartree–Fock (HFR) method implemented in Cowan’s code.

Approximate solutions to the one-particle Dirac equation: numerical results

1986 ◽  
Vol 64 (3) ◽  
pp. 297-302 ◽  
Author(s):  
R. A. Moore ◽  
T. C. Scott
Keyword(s):  
Dirac Equation ◽  
Numerical Solutions ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Fine Structure Constant ◽  
Matrix Elements ◽  
Atomic Systems ◽  
The Matrix ◽  
The One ◽  
Significant Figures

The zero-, first-, and second-order differential equations in a previously defined hierarchy of equations giving approximate solutions to the one-particle Dirac equation and the corresponding eigenvalue contributions are each written as power series in α, the fine structure constant, for an arbitrary, spherically symmetric potential. These equations are solved numerically for the hydrogen-atom potential to obtain wave functions to order α2 and eigenvalues to order α4 for all states with n = 1–4, inclusive. The numerical solutions are then used to evaluate a number of matrix elements to order α2. A comparison with the exact expressions shows that the numerical values for the coefficients of the different powers of α have at least six significant figures in the eigenfunctions and eigenvalues and five in the matrix elements. Thus, the procedure is validated and can be applied with confidence to other atomic systems.

ON THE SPIN–ORBIT INTERACTION IN DIATOMIC MOLECULES. II

1958 ◽  
Vol 36 (3) ◽  
pp. 329-351 ◽  
Author(s):  
I. Kovács
Keyword(s):  
Diatomic Molecules ◽  
Electron System ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Molecular Constants ◽  
Spin Orbit Interaction ◽  
The Matrix

This paper deals with perturbations between states of even multiplicity in a three-electron system. With the aid of the matrix elements which have been obtained, a comparison of the perturbations in the various components of a given state and in some cases a comparison of perturbations in two different states is possible. Also for certain cases it has been possible to establish relationships between the matrix elements which give the magnitude of the perturbations and experimentally measurable molecular constants of the perturbed states.

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