Excited states, perturbation theory, and the stability problem in the restricted hartree-fock method for open shells

1984 ◽  
Vol 20 (3) ◽  
pp. 243-251
Author(s):  
M. M. Mestechkin ◽  
G. E. Vaiman ◽  
G. T. Klimko
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Stability Problem ◽  
Hartree Fock ◽  
Open Shells ◽  
The Stability

scholarly journals THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

2021 ◽  
pp. 118-125
Author(s):  
V. Ternovsky ◽  
A. Svinarenko ◽  
Yu. Dubrovskaya
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Theoretical Data ◽  
Zeroth Approximation ◽  
Relativistic Energy ◽  
Many Body ◽  
Hartree Fock ◽  
Ytterbium Atom ◽  
Many Body Perturbation Theory ◽  
Experimental Values

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach.  The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation  theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

scholarly journals And Yet It Stands

2018 ◽  
Vol 48 (2) ◽  
pp. 123-179
Author(s):  
Massimiliano Badino
Keyword(s):  
Perturbation Theory ◽  
Solar System ◽  
Stability Problem ◽  
Analytical Techniques ◽  
The Moon ◽  
The Stability

The proof of the stability of the solar system has been customarily presented as the solution of a great riddle originated by Newton and completed by Laplace. In this paper, I suggest a different narrative. I argue that Newton considered the stability of the solar system more a theological problem than a physical one and that he never raised the question whether the system is stable or unstable. After the introduction of analytical techniques, astronomers and mathematicians, concerned especially with practical problems such as the behavior of the Moon and with the improvement of perturbation theory, also largely neglected the issue of stability. It was only in 1781, when the cultural and scientific conditions were ripe, that Lagrange, not Laplace, finally set and solved, according to the standard of the time, the stability problem.

scholarly journals Calculation of Polarizabilities for Atoms with Open Shells

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1950
Author(s):  
Vladimir Dzuba
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Configuration Interaction ◽  
New Physics ◽  
Atomic Clocks ◽  
Interaction Method ◽  
Configuration Interaction Method ◽  
Open Shells ◽  
New Generation ◽  
Dynamic Polarizabilities

A version of the configuration interaction method for atoms with open shells (the Configuration Interaction with Perturbation Theory—CIPT method, PRA 95, 012503 (2017)) is extended for calculation of static and dynamic polarizabilities. Its use is demonstrated by calculation of the polarizabilities for the ground and excited states of Er, Tm and Yb. It is proved to be an useful tool in designing a new generation of optical atomic clocks sensitive to new physics.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

scholarly journals Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

2020 ◽  
Vol 153 (20) ◽  
pp. 201103
Author(s):  
Yoshifumi Noguchi ◽  
Miyabi Hiyama ◽  
Motoyuki Shiga ◽  
Hidefumi Akiyama ◽  
Osamu Sugino
Keyword(s):  
Excited States ◽  
State Of The Art ◽  
Critical Role ◽  
Quantum Mechanical ◽  
The Stability
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