Méthode du moment angulaire inversé. Partie II : Application aux problèmes hyperfins diatomiques

1975 ◽  
Vol 53 (5) ◽  
pp. 542-552 ◽  
Author(s):  
J-L. Féménias ◽  
C. Athénour
Keyword(s):  
Angular Momentum ◽  
Experimental Verification ◽  
Experimental Results ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Method Of Calculation ◽  
Straightforward Method ◽  
Mi Theory

We present a straightforward method of calculation in rotational molecular problems based on the theory of reversed angular momentum (MI theory) previously discussed. After some general remarks and calculations, we test this method by calculating some well known hyperfine matrix elements in diatomic problems, showing thus its easy handling. The first experimental verification relative to intensity factors in hyperfine diatomic transitions that the method enabled us to calculate, is presented with a brief survey of the recent experimental results obtained from the analysis of the [Formula: see text] system of NbN.

Méthode du moment angulaire inversé. Partie I : La théorie MI

1975 ◽  
Vol 53 (5) ◽  
pp. 533-541 ◽  
Author(s):  
J-L. Féménias ◽  
C. Athénour
Keyword(s):  
Angular Momentum ◽  
Wave Functions ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Normal Theory ◽  
Commutation Relations ◽  
Minus Sign ◽  
Mi Theory ◽  
Optimal Set ◽  
General Method

In order to present a general method of calculating wave functions, matrix elements, and intensity factors in molecular rotational problems, we deal here with a theory of reversed angular momentum (MI theory), i.e. momentum whose components obey commutation relations with an anomalous minus sign. This theory is built following the principal corresponding steps of the normal theory and a simple correspondence is established between both of them allowing us to perform calculations in the former and to give the results using the formalism of the latter.In particular we dwell here on the consistency of conventions and notations and on a rigorous presentation of spherical tensor operators in MI theory together with the choice of the optimal set of them leading to simplest calculations.

Tensorial calculations in molecular spectroscopy

1979 ◽  
Vol 57 (11) ◽  
pp. 2030-2044
Author(s):  
Jean-Louis Féménias
Keyword(s):  
Angular Momentum ◽  
Molecular Spectroscopy ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Molecular Physics ◽  
Mechanical Formulation ◽  
The Matrix ◽  
Tensor Operators

A strict quantum mechanical formulation of Van Vleck's concept of Reversed Angular Momentum is given. This generalization leads to a method suitable for the calculation of the matrix elements of all kinds of tensor operators in molecular physics. Applications and examples are described for the diatomic case. Various interactions—in the non-rotating or in the rotating molecule—are studied, and some intensity factors are derived in an original way. In all cases, the simplicity, generality, rapidity, and consistency of the method are tested and, where relevant, compared with other techniques.

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

Stresses in compact end closures for cylindrical pressure vessels

1969 ◽  
Vol 4 (1) ◽  
pp. 57-64
Author(s):  
R W T Preater
Keyword(s):  
Cylindrical Shell ◽  
Rigid Body ◽  
Optimum Design ◽  
Cross Section ◽  
Experimental Verification ◽  
Pressure Vessels ◽  
Rigid Body Motion ◽  
Experimental Results ◽  
Body Motion ◽  
Annular Ring

Three different assumptions are made for the behaviour of the junction between the cylindrical shell and the end closure. Comparisons of analytical and experimental results show that the inclusion of a ‘rigid’ annular ring beam at the junction of the cylider and the closure best represents the shell behaviour for a ratio of cylinder mean radius to thickness of 3–7, and enables a prediction of an optimum vessel configuration to be made. Experimental verification of this optimum design confirms the predictions. (The special use of the term ‘rigid’ is taken in this context to refer to a ring beam for which deformations of the cross-section are ignored but rigid body motion is permitted.)

EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

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