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.

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.

Complete Electron Spin–Spin Contact Interaction in Atoms with fn Configurations

1972 ◽  
Vol 50 (9) ◽  
pp. 870-872 ◽  
Author(s):  
K. M. S. Saxena ◽  
B. W. N. Lo ◽  
S. Fraga
Keyword(s):  
Contact Interaction ◽  
Electron Spin ◽  
Ground States ◽  
Neutral Atoms ◽  
Total Electron ◽  
Hartree Fock ◽  
Positive Ions

The total electron spin–spin contact interaction, including both the inter and intrashell contributions, has been evaluated from existing numerical Hartree–Fock functions, for the ground states of the neutral atoms and doubly and triply charged positive ions from La to Yb.

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.

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.

The Feasibility of Numerical Calculations of Vias Using the Matrix-Penciled Moment Method

PIERS Online ◽  
2010 ◽  
Vol 6 (1) ◽  
pp. 36-40 ◽  
Author(s):  
Hailiang Li ◽  
Yu Tian ◽  
Tong Ling
Keyword(s):  
Moment Method ◽  
Numerical Calculations ◽  
The Matrix

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Sternheimer Antishielding Functions ß(r) and γ(r) for Rare Earth Atoms

1986 ◽  
Vol 41 (1-2) ◽  
pp. 37-46 ◽  
Author(s):  
K. D. Sen ◽  
P. C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Rare Earth ◽  
Valence State ◽  
Wave Functions ◽  
Electric Field Gradients ◽  
Hartree Fock ◽  
Field Gradients ◽  
Lanthanide Atoms ◽  
Hf Wave ◽  
Self Consistency ◽  
Consistency Effects

The Sternheimer shielding-antishielding functions ß(r) and γ(r) are reported for all the fourteen lanthanide atoms at the uncoupled Hartree-Fock level of theory. Each atom is considered in two valence state configurations, 4fn 5d0 and 4 fn-1 5d1, and the nonrelativistic HF wave functions have been used. The 5d1 configuration leads to a smaller net antishielding than the 4fn configuration by ~ 6-12% in the series. The electron-electron self consistency effects are found to be less than 5% in the series. The importance of the calculated antishielding functions in the antishielding theory of electric field gradients in noncubic metals is discussed.

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