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.

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.

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.

scholarly journals Терагерцовая спектроскопия магнитоэлектрика HoAl-=SUB=-3-=/SUB=-(BO-=SUB=-3-=/SUB=-)-=SUB=-4-=/SUB=-

2022 ◽  
Vol 130 (1) ◽  
pp. 59
Author(s):  
А.М. Кузьменко ◽  
В.Ю. Иванов ◽  
А.Ю. Тихановский ◽  
А.Г. Пименов ◽  
А.М. Шуваев ◽  
...  
Keyword(s):  
Crystal Field ◽  
Excited States ◽  
Ground State ◽  
Theoretical Study ◽  
Low Frequency ◽  
Local Symmetry ◽  
Matrix Elements ◽  
The Matrix ◽  
Excitation Conditions ◽  
Ground Multiplet

Experimental and theoretical study of submillimeter (terahertz) spectroscopic and magnetic properties of the rare-earth aluminum borate HoAl3(BO3)4 were performed at temperatures 3–300 K. In the transmittance spectra a number of resonance lines were detected at frequencies 2–35 cm–1 for different radiation polarizations. These modes were identified as transitions between the lower levels of the ground multiplet of the Ho3+ ion split by the crystal field, including both transitions from the ground state to the excited ones and transitions between the excited states. The established excitation conditions of the observed modes and the simulation of the spectra made it possible to separate the magnetic and electric dipole transitions and to determine the energies of the corresponding states, their symmetry, and the matrix elements of the transitions. Low-frequency lines that do not fit into the established picture of the electron states of Ho3+ were also found; these lines, apparently, correspond to the ions with the distorted by defects local symmetry of the crystal field.

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.

scholarly journals Triaxiality in the odd-A nuclei 109−117I studied through a microscopic rotationparticle coupling

2018 ◽  
Vol 178 ◽  
pp. 02030
Author(s):  
Swati Modi
Keyword(s):  
Systematic Study ◽  
Coming Out ◽  
Ground State ◽  
Rotor System ◽  
Matrix Elements ◽  
Triaxial Deformation ◽  
The Matrix

A systematic study of ground state spectrum with the triaxial deformation γ for odd-A Iodine isotopes 109−117I is carried out with the nonadiabatic quasiparticle approach. The rotation-particle coupling is accomplished microscopically such that the matrix elements of a particle-plus-rotor system are written in terms of the rotor energies. The 5/2+ state is confirmed as ground state for odd-A 111−117I and also coming out as lowest in energy for 109I.

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 .

DOMINANCE OF LONG DISTANCE EFFECTS IN THE KL-KS MASS DIFFERENCE

1990 ◽  
Vol 05 (19) ◽  
pp. 1477-1483 ◽  
Author(s):  
K. TERASAKI ◽  
S. ONEDA
Keyword(s):  
Asymptotic Behavior ◽  
Vector Meson ◽  
Ground State ◽  
Mass Shell ◽  
Mass Difference ◽  
Matrix Elements ◽  
Long Distance ◽  
Distance Effects ◽  
Intermediate States ◽  
The Matrix

It is argued that the asymptotic behavior of the matrix elements of Hw involving on-mass-shell ground-state mesons with infinite momenta, which were instrumental in explaining the |ΔI|=1/2 rule in the K→ππ decays, actually implies [Formula: see text]. The long distance effects (contributions of PS and vector meson poles and ππ intermediate states) may reproduce the observed KL−Ks mass difference, consistent with the |ΔI|=1/2 rule. Its estimate is however sensitive to the η-η′-… mixing.

High-resolution Fourier transform study of the ν11 and ν7 fundamentals of cyclopropane

1984 ◽  
Vol 62 (12) ◽  
pp. 1369-1373 ◽  
Author(s):  
Josef Pliva ◽  
J. W. C. Johns
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Spectroscopic Constants ◽  
Hamiltonian Matrix ◽  
Matrix Elements ◽  
Vibrational States ◽  
Coriolis Interaction ◽  
Band Origin ◽  
The Matrix ◽  
Parallel Band

The absorption spectrum of cyclopropane, C3H6, was measured in the region between 790 and 950 cm−1 on a high-resolution Fourier transform spectrometer. The section containing the Q-branches of the perpendicular band of the ν11 vibration of species E′ was deconvolved to an effective line width of 0.0020–0.0025 cm−1. The structure of the ν11 band is strongly affected by l-type resonance. A total of 88 sub-bands with KΔK = −42 to 45 have been assigned in this band. The K = 4–3 and 2–3 sub-bands both exhibit K doubling of the lines with high J resulting from a combined effect of the off-diagonal matrix elements [Formula: see text], [Formula: see text], and [Formula: see text] with the l doubling in the K = 1, l = 1 state. Otherwise, the ν11 band is found to be free of perturbations by other vibrational states, in spite of the fact that a Jx,y Coriolis interaction is allowed by selection rules with the ν7 band (species [Formula: see text]) whose band origin is only 14.38 cm−1 below that of ν11. This shows that the value of [Formula: see text] is essentially zero. Also, the allowed Jz Coriolis interaction with the ν10 state, which lies 160.01 cm−1 above ν11, does not noticeably affect the two bands. A Hamiltonian matrix, including the matrix elements responsible for the K doubling and l-type resonance, was used for the treatment of the ν11 band. A set of accurate ground state constants and spectroscopic constants for the upper state ν11 is reported that reproduces 3240 observed lines of this band with a standard deviation of 0.0009 cm−1. Lines of the parallel band ν7 are just barely seen between the ν11 lines, which are perhaps 30–50 times stronger. Spectroscopic constants for the ν7 band have been obtained from 135 individual lines assigned to the Q- and R-branches of sub-bands with K = 6–21.

Fine Structure Intervals in Transition Elements

1975 ◽  
Vol 53 (21) ◽  
pp. 2421-2427 ◽  
Author(s):  
Jacek Karwowski ◽  
K. M. S. Saxena ◽  
Serafin Fraga
Keyword(s):  
Fine Structure ◽  
Ground State ◽  
Orbit Interaction ◽  
Matrix Elements ◽  
Transition Elements ◽  
Hartree Fock ◽  
Positive Ions ◽  
Transition Series ◽  
The Matrix ◽  
New Formulation

A new formulation for the evaluation of the matrix elements of the spin-own orbit interaction in many-electron atoms has been applied to the evaluation of the interaction matrices for pN, dN, and fN configurations, using functions that are simultaneous eigenfunctions of the operators J2, L2,S2, and.Jz; the complete results are available as indicated in the text. Using this formulation, the fine structure intervals for the ground states of the neutral atoms and the first three positive ions of the elements of the three transition series have been calculated within the framework of the monoconfigurational approximation, including the electrostatic and spin-own orbit interaction between the states arising from the configuration under consideration. In each case, the spin–orbit parameter and the set of Slater–Condon integrals, obtained from the numerical Hartree–Fock function for the ground state, were used.

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