Theoretical oscillator strengths III. Transitions in Au I, Hg II, Pb IV, and Bi V spectra

1976 ◽  
Vol 54 (22) ◽  
pp. 2272-2278 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Theoretical Data ◽  
Relativistic Effects ◽  
Wave Functions ◽  
The Other ◽  
Oscillator Strengths ◽  
Semiempirical Approach ◽  
Calculated Line ◽  
Exchange Effects ◽  
Active Electron ◽  
Relativistic Oscillator

In the course of this investigation the relativistic oscillator strengths were calculated for some transitions in the principal, sharp, and diffuse series of the Au I, Hg II, Pb IV, and Bi V spectra. The radial integrals were computed employing the wave functions for the active electron obtained by a semiempirical approach which allowed for exchange effects. A comparison between the calculated line and multiplet f values and the other available experimental and theoretical data is presented. The influence of the relativistic effects on the oscillator strengths values for the transitions under consideration is discussed.

Relativistic oscillator strengths for np2 → np(n + 1)s transition array of SnI and PbI spectra in jj and intermediate coupling

1979 ◽  
Vol 57 (2) ◽  
pp. 147-151 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Transition Probabilities ◽  
Theoretical Data ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Intermediate Coupling ◽  
Hartree Fock ◽  
Semiempirical Approach ◽  
Exchange Effects ◽  
Relativistic Oscillator ◽  
Transition Array

The relativistic oscillator strengths for the np2 → np(n + 1)s transition array as well as the lifetimes of levels of the np(n + 1)s configuration in SnI and PbI spectra were calculated in jj and intermediate coupling. The relativistic radial integrals were computed employing the wave functions obtained by a semiempirical approach which allowed for exchange effects. The results obtained are compared with existing experimental and theoretical data. The significance of intermediate coupling for oscillator strengths computations is discussed. The agreement with experiment is for the present semiempirical results generally better (particularly for the PbI spectrum) than for oscillator strength deduced from 'Optimized Hartree–Fock–Slater' transition probabilities, which were published previously.

Theoretical oscillator strengths II. Transitions in principal, sharp, and diffuse spectral series of Al III, Ga III, In III, and Tl III spectra

1976 ◽  
Vol 54 (2) ◽  
pp. 130-136 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Theoretical Data ◽  
Relativistic Effects ◽  
Oscillator Strengths ◽  
Spectral Series ◽  
Semiempirical Approach ◽  
Exchange Effects ◽  
Optical Electron ◽  
Semiempirical Formula ◽  
Relativistic Oscillator ◽  
Good Agreement

A calculation is reported of nonrelativistic and relativistic oscillator strengths for the principal, sharp, and diffuse series, as well as some lifetimes, in the spectra of doubly ionized aluminum, gallium, indium and thallium. The wave functions that were used were obtained by employing a semiempirical approach which included exchange effects (the semiempirical [Formula: see text] method). Fairly good agreement was obtained with the available experimental and other theoretical data. A comparison of the nonrelativistic and relativistic oscillator strengths indicates that the influence of spin–orbit interaction of the optical electron, as well as other relativistic effects, is important in the case of even moderately heavy ions or atoms. Some systematic trends in the calculated oscillator strengths were found along the spectral series as well as along the sequence of homologous ions.

Theoretical relativistic oscillator strengths I. Transitions in principal, sharp, and diffuse series of Al I, Ga I, In I, and Tl I spectra

1976 ◽  
Vol 54 (2) ◽  
pp. 118-129 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Experimental Data ◽  
Excited States ◽  
Principal Series ◽  
Semiempirical Method ◽  
Oscillator Strengths ◽  
Relative Line ◽  
Exchange Effects ◽  
The One ◽  
Relativistic Oscillator ◽  
Good Agreement

The oscillator strengths for the sharp, principal, and diffuse series in the spectra of Al I, Ga I, In I, and Tl I are calculated as well as the lifetimes of their lowest excited states. The wave functions that were used were calculated by employing a relativistic semiempirical method which included exchange effects. Very good agreement with the most reliable experimental data was obtained for the fik values in the sharp series as well as for the calculated lifetimes. The discrepancies in the diffuse series are ascribed to the failure of the one-electron approach in the case of strongly perturbed series. The observed deviations in the relative line strengths from the values predicted neglecting the spin–orbit interaction were also investigated. Some systematic trends in the calculated oscillator strengths that were found for the sharp and principal series appear to be corroborated by experimental data for the sharp series in the spectra of Al I, Ga 1, In I.andTl 1.

RELATIVISTIC EFFECTS IN THE CALCULATION OF OSCILLATOR STRENGTHS : "AB INITIO" METHODS

1979 ◽  
Vol 40 (C1) ◽  
pp. C1-109-C1-114
Author(s):  
J. P. Desclaux
Keyword(s):  
Ab Initio ◽  
Relativistic Effects ◽  
Oscillator Strengths ◽  
Ab Initio Methods

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

Relativistic oscillator strengths for transitions in the principal spectral series of the silver isoelectronic sequence

1995 ◽  
Vol 35 (4) ◽  
pp. 239-246 ◽  
Author(s):  
I. Martín ◽  
M. A. Almaraz ◽  
C. Lavin
Keyword(s):  
Oscillator Strengths ◽  
Spectral Series ◽  
Isoelectronic Sequence ◽  
Relativistic Oscillator

Theoretical ionization energies and oscillator strengths for the sodium isoelectronic sequence

1969 ◽  
Vol 47 (8) ◽  
pp. 835-838 ◽  
Author(s):  
R. P. McEachran ◽  
C. E. Tull ◽  
M. Cohen
Keyword(s):  
Matrix Element ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Ionization Energies ◽  
Core Approximation

Orbital wave functions for a number of 2S, 2P0, 2D, and 2F0 states of Na, Mg+, and Al2+ have been calculated by means of the frozen core approximation. The oscillator strengths of all allowed dipole transitions have been determined using both length and velocity formulations for the transition matrix element; these results agree with each other to within a few percent.

Energies, wavelengths, lifetimes, E1, M1, E2, and M2 transitions rates for the sulfur isoelectronic sequence Fe XI, Nb XXVI–In XXXIV

2017 ◽  
Vol 95 (4) ◽  
pp. 393-401 ◽  
Author(s):  
K. Wang ◽  
S. Li ◽  
R. Si ◽  
C.Y. Chen ◽  
J. Yan ◽  
...  
Keyword(s):  
Quantum Electrodynamics ◽  
Energy Levels ◽  
Theoretical Data ◽  
Electric Quadrupole ◽  
Oscillator Strengths ◽  
Transition Rates ◽  
Isoelectronic Sequence ◽  
Fusion Plasma ◽  
Magnetic Quadrupole ◽  
Theoretical Results

Energies, wavelengths, lifetimes, oscillator strengths, electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transition rates among the 42 fine structure levels belonging to the 3s23p4, 3s23p33d, and 3s3p5 configurations for S-like Fe and S-like ions with 41 ≤ Z ≤ 49 are calculated using the fully relativistic multiconfiguration Dirac–Fock (MCDF) method. In the calculations, contributions from correlations within the n = 6 complex, Breit interaction, and quantum electrodynamics effects are included. Detailed comparisons are made between the present results and the available experimental and other theoretical data. We found that our calculated energy levels generally agree within ≤0.5% with the experimentally compiled results, and the transition rates agree within ≤12% with other theoretical results for a majority of the transitions. These accurate theoretical data should be beneficial in fusion plasma research and astrophysical applications.

Experimental and Theoretical Studies of 2- (naphthalen-1-yl (piperidin-1-yl) methyl)phenol Compound

2020 ◽  
Vol 42 (6) ◽  
pp. 818-818
Author(s):  
Yeliz Ula Yeliz Ula
Keyword(s):  
Molecular Orbital ◽  
Theoretical Data ◽  
Biologically Active ◽  
Oscillator Strengths ◽  
Excitation Energies ◽  
Petasis Reaction ◽  
Vis Spectroscopy ◽  
Phenol Compound ◽  
Lowest Unoccupied Molecular Orbital ◽  
Experimental Values

The 2- (naphthalen-1-yl (piperidin-1-yl) methyl) phenol compound is an alkylaminophenol compound and has been experimentally synthesized by the Petasis reaction. In this study Structural analysis was carried out by FT-IR, NMR, UV-Vis spectroscopy. The high antioxidant value of the compound showed that it could be a potential biologically active drug. Theoretical data support all experimental analysis of the new compound. Comparisons were made by double method. For this purpose, DFT (B3LYP) and HF methods have been used with 6-311G ++ (d, p) set. Also, the compoundand#39;s electronic and structural properties (bond lengths, bond angles and dihedral angles), the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies, electrostatic potential (MEP), vibrational frequencies, Mulliken atomic charges, excitation energies, and oscillator strengths were calculated. As a result; the theoretical and experimental values were found to be compatible.

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