Perturbation theory with a model zeroth approximation for molecules: A new form of polarization potential

1989 ◽  
Vol 30 (1) ◽  
pp. 141-144
Author(s):  
A. V. Glushkov ◽  
N. N. Dudnik
Keyword(s):  
Perturbation Theory ◽  
Polarization Potential ◽  
Zeroth Approximation ◽  
New Form

CONVERGENT WEAK COUPLING EXPANSIONS FOR LATTICE FIELD THEORIES THAT LOOK LIKE PERTURBATION SERIES

1989 ◽  
Vol 01 (01) ◽  
pp. 47-87 ◽  
Author(s):  
GERHARD MACK ◽  
ANDREAS PORDT
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Weak Coupling ◽  
Free Field ◽  
Perturbation Series ◽  
Field Theories ◽  
Lattice Field Theory ◽  
Lattice Field ◽  
Local Coupling ◽  
New Form

We propose a new form of convergent weak coupling expansion for the lattice field theory. It has the advantage that it is very similar to standard (Feynman) perturbation theory. Convergence is proven for sufficiently weak local coupling, i.e. when the theory is close to a free field theory. In the proof, use of analyticity in field variables, as pioneered by Kupiainen and Gawedzki, is supplemented with techniques for handling derivatives with respect to free propagators.

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 A Precise Determination of Some Critical Terms in the Solar System

1979 ◽  
Vol 81 ◽  
pp. 91-93
Author(s):  
Jean Chapront ◽  
Rudolf Dvorak
Keyword(s):  
Perturbation Theory ◽  
Solar System ◽  
High Precision ◽  
Precise Determination ◽  
Small Divisors ◽  
The Mean ◽  
New Form ◽  
Very High

A new form to determine the contribution of some special small divisors in perturbation theory is presented in this paper. We can avoid to calculate all the kλ+k′λ as it has to be done normally (λ and λ′ designate the mean longitudes of the two regarded planets). For a chosen k and k′ we calculate with a very high precision the contribution to the perturbation of the elements with the aid of the Hansen's coefficients.

scholarly journals Global Colour Model of QCD and Its Relationship to the NJL Model, Chiral Perturbation Theory and Other Models

1997 ◽  
Vol 50 (1) ◽  
pp. 103 ◽  
Author(s):  
Reginald T. Cahill ◽  
Susan M. Gunner
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Mass Formula ◽  
Gluon Propagator ◽  
Chiral Perturbation ◽  
Successful Model ◽  
Njl Model ◽  
New Form ◽  
The Difference ◽  
Bag Constant

The Global Colour Model (GCM) of QCD is a very successful model. Not only is it formally derivable from QCD but under various conditions it reduces to the NJL model and also to Chiral Perturbation Theory, and to other models. Results presented include the effective gluon propagator, the difference between constituent and exact quark propagators, various meson and nucleon observables, a new form for the mass formula for the Nambu–Goldstone mesons of QCD, and the change in the MIT bag constant in nuclei.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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