Développement complet de la polarisabilité des molécules tétraédriques XY4

1991 ◽  
Vol 69 (1) ◽  
pp. 26-35 ◽  
Author(s):  
A. Boutahar ◽  
M. Loete
Keyword(s):  
General Expression ◽  
Coupling Scheme ◽  
Order Of Approximation ◽  
Raman Intensity ◽  
Matrix Elements ◽  
New Model ◽  
Vibration Rotation ◽  
Tetrahedral Molecules ◽  
Group Polarizability

A new model of polarizability is presented consistent with the Hamiltonian of tetrahedral molecules XY4. Using a coupling scheme in the Td group, polarizability operators are obtained up to any order of approximation for all vibration–rotation bands of any symmetry. This model leads to an unique formula for matrix elements of these operators. We also give the general expression for the Raman intensity of a transition.

Développement complet de l'hamiltonien de vibration–rotation adapté à l'étude des interactions dans les molécules toupies sphériques. Application aux bandes ν2 et ν4 de 12CH4

1977 ◽  
Vol 55 (20) ◽  
pp. 1802-1828 ◽  
Author(s):  
Jean-Paul Champion
Keyword(s):  
Ground State ◽  
Coupling Scheme ◽  
Order Of Approximation ◽  
Matrix Elements ◽  
Coupling Coefficients ◽  
Linear Combinations ◽  
Coriolis Interaction ◽  
Raman Transitions ◽  
The Matrix ◽  
Vibration Rotation

Using an unsymmetrized coupling scheme in the group Td, we determine all the vibration–rotation operators of the Hamiltonian of XY4 molecules, including all possible interactions, up to any order of approximation. We define a basis of Hamiltonian matrices of which the matrix elements are functions of coupling coefficients of the group chain [Formula: see text] only. Thus, we develop a general formalism available for any vibrational sublevels of whatever symmetry. The parameters relative to the different vibrational sublevels are known linear combinations of the coefficients of the Hamiltonian expansion. From these, we deduce simple relations between the parameters associated with the ground state, the fundamentals, and the harmonic and combination bands.We apply this formalism to the study of the Coriolis interaction between ν2 and ν4 of CH4. With only 21 parameters for the two bands, we obtain a standard deviation of 34 mK for 251 Raman transitions of ν2 and 20 mK for 243 ir transitions of ν4.

Développement complet du moment dipolaire des molécules tétraédriques. Application aux bandes triplement dégénérées et à la diade ν2 et ν4

1983 ◽  
Vol 61 (8) ◽  
pp. 1242-1259 ◽  
Author(s):  
M. Loete
Keyword(s):  
Dipole Moment ◽  
Simultaneous Analysis ◽  
Coupling Scheme ◽  
Contact Transformation ◽  
Order Of Approximation ◽  
Matrix Elements ◽  
Transformation Technique ◽  
The Matrix ◽  
Formal Expansion ◽  
Vibration Rotation

Using a coupling scheme in the Td group, we determine all the vibration–rotation operators of the dipole moment of XY4 molecules up to any order of approximation. We give the matrix elements for these operators and general formulas for the calculation of the infrared transition intensities. This general formalism is available for any transition between vibrational sublevels of any symmetry. It can be used for the analysis of isolated bands and for the simultaneous analysis of interacting bands as well. We show that this method can be applied to the calculation of Raman intensities and to XY6 molecules.In some cases, it is possible to carry out a tensorial extension from the Td group to the O(3) group. We have constructed the operators of the dipole moment adapted to this process using a coupling scheme in O(3). In particular, we give the matrix elements for a triply degenerate band.We use the contact transformation technique to explain the parameters introduced in the formal expansion of the dipole moment. We define the contact transformation operators in a tensorial form. We apply this method in the case of the two interacting bands ν2 and ν4.

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

Matrix elements of the proton–neutron symplectic model

2018 ◽  
Vol 27 (03) ◽  
pp. 1850021 ◽  
Author(s):  
H. G. Ganev
Keyword(s):  
Shell Model ◽  
Long Range ◽  
Coupling Scheme ◽  
Model Coupling ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Physical Operator ◽  
Major Shell ◽  
The Matrix ◽  
Transition Operators

The tensor properties of the [Formula: see text] algebra generators are determined in respect to the reduction chain [Formula: see text], which defines a shell-model coupling scheme of the proton–neutron symplectic model (PNSM). They are further used to calculate the matrix elements of the basic [Formula: see text] operators of the PNSM in the space of fully symmetric representations in the [Formula: see text]-coupled basis using a generalized Wigner–Eckart theorem. The obtained results allow further the matrix elements of any physical operator of interest, such as the relevant transition operators or the collective potential, to be calculated. As an illustration, the matrix elements of the basic irreducible tensor terms which appear in the [Formula: see text] decomposition of the long-range full major-shell mixing proton–neutron quadrupole–quadrupole interaction are presented.

Quasi-particles in atomic shell theory

1970 ◽  
Vol 315 (1520) ◽  
pp. 27-37 ◽  
Keyword(s):  
Shell Theory ◽  
Particle Creation ◽  
Rotation Group ◽  
Coupling Scheme ◽  
Matrix Elements ◽  
Spin Orientation ◽  
Quasi Particle ◽  
Quantum Numbers ◽  
Fractional Parentage ◽  
Electronic Configurations

A new scheme is described for defining and classifying the states of the electronic configurations l N . The spaces for which the spin orientation is either up or down are both factored into two parts. Each of these parts (distinguished by a symbol Ɵ) corresponds to the irreducible representatio n (½ ½ ... ½ ) of the rotation group R Ɵ (2 l +1). The generators for this group are constructed from quasi-particle creation and annihilation operators. The angular momentum quantum numbers l Ɵ arising from the decomposition of (½ ½ ... ½) into representations of R Ɵ (3) can be used to couple the four parts together. No ambiguities arise when l < 9, thereby giving a very satisfactory coupling scheme. No coefficients of fractional parentage (c. f. p.) are required in the calculation of matrix elements. Simple explanations are given for some null c. f. p. and for some repeated eigenvalues of an operator that had previously been used to classify the state s of g N .

The Dipole Moment Function of H79Br Molecule

1972 ◽  
Vol 27 (11) ◽  
pp. 1563-1565 ◽  
Author(s):  
D. N. Urquhart ◽  
T. D. Clark ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for H79Br molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r-re)n . These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M1 and M2 .

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