Atomic fine-structure inversions explained as first-order relativistic corrections to the Hartree-Fock energy

1981 ◽  
Vol 14 (23) ◽  
pp. 4469-4487 ◽  
Author(s):  
N C Pyper ◽  
P Marketos
Keyword(s):  
Fine Structure ◽  
First Order ◽  
Hartree Fock ◽  
Relativistic Corrections

scholarly journals Energy, fine structure, hyperfine structure, and transitions for the high-lying multi-excited 4Pe,o states of B-like ions

2016 ◽  
Vol 94 (5) ◽  
pp. 448-457
Author(s):  
Chun Mei Zhang ◽  
Yan Sun ◽  
Chao Chen ◽  
Feng Wang ◽  
Bin Shao ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Fine Structure ◽  
Hyperfine Structure ◽  
Excited States ◽  
Quantum Electrodynamic ◽  
Higher Order ◽  
Variation Method ◽  
First Order ◽  
Relativistic Corrections ◽  
First Order Perturbation

The energies of the high-lying multi-excited states 1s22s2pnl and 1s22p2nl 4Pe,o (n ≥ 2) for B-like C+, N2+, F4+, and Mg7+ ions are calculated using Rayleigh–Ritz variation method with multiconfiguration interaction, and the inclusion of mass polarization and relativistic corrections. The fine structure and hyperfine structure for these systems are investigated using first-order perturbation theory. The configuration structure of the high-lying multi-excited series is identified not only by energy, but also by its contribution to normalization of the angular spin components, and it is further tested by the addition of relativistic corrections and fine structure splittings. Transition wavelengths including the quantum electrodynamic effects and higher-order relativistic corrections are determined.

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

The Myocardial Signature: Absolute Backscatter, Cyclical Variation, Frequency Variation, and Statistics

1986 ◽  
Vol 8 (2) ◽  
pp. 107-120 ◽  
Author(s):  
T. L. Rhyne ◽  
K. B. Sagar ◽  
S. L. Wann ◽  
G. Haasler
Keyword(s):  
Fine Structure ◽  
Cross Section ◽  
Rayleigh Scattering ◽  
Cardiac Cycle ◽  
Frequency Variation ◽  
Myocardial Ultrastructure ◽  
Order Model ◽  
Integrated Backscatter ◽  
Cyclical Variation ◽  
First Order

This paper studies the absolute myocardial backscatter as a function of the frequency and phase of the cardiac cycle. This was achieved by calibration of the ultrasonic instrumentation and the random diffraction process. We have discovered a first-order model in which the scattering from the myocardium is Rayleigh scattering with a cardiac cycle variation in the scattering cross section. Furthermore, the statistics are approximately those of a radio frequency waveform with two independent Gaussian components (Rayleigh envelope). Deviations from the first-order model suggest measurable fine structure related to myocardial ultrastructure. This model has profound effects on the choice of optimal radiation patterns and signal processing schemes for preparing diagnostic parameters (e.g., integrated backscatter).

Perturbation theory of short-range atomic interactions

1970 ◽  
Vol 317 (1531) ◽  
pp. 545-574 ◽  
Keyword(s):  
Perturbation Theory ◽  
Short Range ◽  
Similarity Transformation ◽  
Order Theory ◽  
First Order ◽  
Hartree Fock ◽  
First Order Theory ◽  
Atomic Interactions ◽  
Cusp Conditions ◽  
Molecular Calculations

A new united atom perturbation theory of the interaction of two atoms at small separations is described. The key feature is a similarity transformation of the Schrödinger equation which enables the cusp conditions to be satisfied at both nuclei and preserves the correct molecular symmetry. The first-order theory is examined in detail and compared with other united atom theories. Numerical calculations are presented for the ground states of the systems H + 2 , HeH 2+ HeH, He 2 and Li + He, based mainly on Hartree-Fock wavefunctions for the united atoms, and are compared with accurate molecular calculations. The agreement is remarkably good for separations up to 1 bohr.

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