An expansion of Hartree-Fock and correlation energies, relativistic corrections and the dipole matrix element in the powers of of 1/Z

1977 ◽  
Vol 27 (1) ◽  
pp. 7-16
Author(s):  
U. I. Safronova ◽  
A. B. Bolotin
Keyword(s):  
Matrix Element ◽  
Dipole Matrix Element ◽  
Hartree Fock ◽  
Relativistic Corrections

Electric-dipole matrix-element formulas in hyperspherical coordinates with applications toH−and He

1986 ◽  
Vol 33 (2) ◽  
pp. 1000-1007 ◽  
Author(s):  
Chang-Hwan Park ◽  
Anthony F. Starace ◽  
Jiang Tan ◽  
Chii-Dong Lin
Keyword(s):  
Matrix Element ◽  
Electric Dipole ◽  
Dipole Matrix Element ◽  
Hyperspherical Coordinates

Relativistic Corrections to the Fermi Matrix Element

1958 ◽  
Vol 1 (12) ◽  
pp. 456-457 ◽  
Author(s):  
A. Altman ◽  
W. M. MacDonald
Keyword(s):  
Matrix Element ◽  
Relativistic Corrections

An analytical approach for the energy spectrum and optical properties of gated bilayer graphene

RSC Advances ◽  
2014 ◽  
Vol 4 (61) ◽  
pp. 32117-32126 ◽  
Author(s):  
Cheng-Peng Chang
Keyword(s):  
Optical Properties ◽  
Energy Spectrum ◽  
Matrix Element ◽  
Absorption Spectra ◽  
Analytical Approach ◽  
Bilayer Graphene ◽  
Wave Functions ◽  
Dipole Matrix Element ◽  
Exact Energy

An analytical approach is developed to access the exact energy spectrum, wave functions, dipole matrix element (Mfi) and absorption spectra (A(ω)) of gated Bernal bilayer graphene.

An expansion method for calculating atomic properties IV. Transition probabilities

1964 ◽  
Vol 280 (1381) ◽  
pp. 258-270 ◽  
Keyword(s):  
Wave Function ◽  
Matrix Element ◽  
Transition Probabilities ◽  
Expansion Method ◽  
The State ◽  
Diagonal Matrix Element ◽  
Expectation Value ◽  
First Order ◽  
Hartree Fock ◽  
Atomic Properties

An earlier expression for the expectation value of a single-electron operator which isstationary with respect to first-order variations of the state wave function has been generalized to the case of an off-diagonal matrix element connecting two different states. Explicit calculations are carried out of the probabilities of dipole transitions between configurations 1 s a 2 s b 2 p c and 1 s a 2 s b–1 2 p c+1 for all members of the isoelectronic sequences from helium to neon and the importance of taking into account the mixing of degenerate configurations is demonstrated. The accuracy is at least comparable to that of the Hartree-Fock approximation and in cases where degeneracy is important it is much superior.

Constant-dipole-matrix-element model for Faraday rotation in amorphous semiconductors

1987 ◽  
Vol 35 (17) ◽  
pp. 9298-9300 ◽  
Author(s):  
B. Vanhuyse ◽  
W. Grevendonk ◽  
G. J. Adriaenssens ◽  
J. Dauwen
Keyword(s):  
Matrix Element ◽  
Faraday Rotation ◽  
Element Model ◽  
Amorphous Semiconductors ◽  
Dipole Matrix Element

scholarly journals Expectation Values of the Neutral Chromium Radius

Atoms ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 51
Author(s):  
Nafeesah Abdul Rahim Yaqub ◽  
Rabia Qindeel ◽  
Norah Alonizan ◽  
Nabil Ben Nessib
Keyword(s):  
Atomic Data ◽  
Expectation Values ◽  
Laboratory Plasma ◽  
Thomas Fermi ◽  
Hartree Fock ◽  
Relativistic Approximation ◽  
Relativistic Corrections ◽  
Plasma Applications

Neutral Chromium (Cr I) is an important element in many laboratory plasma applications. In this work, expectation values of the radius for Cr I are calculated. These atomic data are calculated with three different atomic codes: Cowan code using the Hartree–Fock Relativistic approximation, SUPERSTRUCTURE and AUTOSTRUCTURE codes using scaled Thomas–Fermi–Dirac–Amaldi potential. Relativistic corrections are introduced according to the Breit–Pauli approach. The 3 d 5 4 s , 3 d 4 4 s 2 , 3 d 5 4 d , 3 d 5 4 p and 3 d 4 4 s 4 p configurations are included to obtain the expectation values of radius of Cr I and compared with available data. The novelty of our work is to obtain new values of < 1 r > , < r > , and < r 2 > for the configuration of 4 p and 4 d and the values of < r 3 > for all orbitals configurations considered in this work.

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: IV. OSCILLATOR STRENGTHS IN THE HELIUM ISOELECTRONIC SEQUENCE

1967 ◽  
Vol 45 (6) ◽  
pp. 2079-2090 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Matrix Element ◽  
Excited States ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Good Agreement

Orbital wave functions for a number of singlet and triplet S, P, and D states of the helium sequence through C+4 have been calculated using an approximation described earlier. The wave functions have been employed to calculate the oscillator strengths for all allowed dipole transitions between these states, using both the length and velocity forms of the transition matrix element. Our results are in good agreement with the most accurate values available.

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