Theoretical Calculations of Relative Intensities in Hyperfine Diatomic Transitions

1974 ◽  
Vol 52 (4) ◽  
pp. 361-368 ◽  
Author(s):  
J. L. Féménias ◽  
C. Athénour ◽  
R. Stringat
Keyword(s):  
Dipole Moment ◽  
Intensity Distribution ◽  
Ground State ◽  
Hyperfine Coupling ◽  
Theoretical Calculations ◽  
Electronic States ◽  
Wave Functions ◽  
Optical Transitions ◽  
Matrix Elements ◽  
Coupling Case

A method of calculating molecular wave functions in complex 'hyperfine' coupling cases is presented. It enables us to express (bβJ) and (bβS) wave functions in terms of more simple (aβ) functions, and to connect their parities and symmetry characters to those of 'classical' (b) wave functions. With the help of these expansions of (bβJ) and (bβS) wave functions, we have carried out the calculation of the reduced matrix elements of electric dipole moment M in order to study the intensity distribution in optical transitions between excited diatomic electronic states belonging to the (aβ), (intermediate aβ–bβJ), and (bβJ) coupling case, and a ground state belonging to the (bβS) coupling case. First comparisons with experimental results in the ScO molecule are made, and these enable us to give theoretical confirmation to some previous assumptions.

Avoided-crossing molecular-beam spectroscopy of symmetric tops. I. Phosphoryl fluoride (OPF3)

1981 ◽  
Vol 59 (1) ◽  
pp. 150-171 ◽  
Author(s):  
Irving Ozier ◽  
W. Leo Meert
Keyword(s):  
Dipole Moment ◽  
Molecular Beam ◽  
Wave Functions ◽  
Matrix Elements ◽  
Centrifugal Distortion ◽  
Electric Resonance ◽  
Avoided Crossing ◽  
Mixing Matrix ◽  
The Individual

A new avoided-crossing technique using a conventional molecular beam electric resonance spectrometer has been developed for studying symmetric rotors. By means of an external electric field, two levels with different values of K are made nearly degenerate and normally forbidden electric-dipole transitions between the interacting levels are observed. Mixing matrix elements ηST with ΔK = ± 3 arise from the centrifugal distortion dipole moment μD and mixing terms ηHYP, with ΔK = ± 1, ± 2 arise from the nuclear hyperfine Hamiltonian. Explicit expressions for ηHYP are given in an Appendix. Many of these terms break the symmetry of both the rotational and nuclear spin parts of the wave functions. The avoided-crossing method is discussed in detail, with emphasis on its application to the measurement of (A0–B0). It is shown how the technique can be used to determine the perpendicular moment μD, as well as μJ, and μK, the constants which characterize the dependence of the parallel dipole moment μ on J and K, respectively. Other applications include the experimental investigation of the selection rules for the individual terms in ηHYP and the determination of the sign of the rotational g-factors [Formula: see text] and [Formula: see text].∙The method has been applied to phosphoryl fluoride (OPF3). It has been determined that (A0–B0) = 217.4987(44) MHz, μD = 5.856(20) × 10−6 D, μJ = −3.38(10) × 10−6 D, and both [Formula: see text] and [Formula: see text] are negative.

scholarly journals Electronic structure with dipole moment and ionicity calculations of the low-lying electronic states of the ZnF molecule

2017 ◽  
Vol 95 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Soumaya Elmoussaoui ◽  
Nayla El-Kork ◽  
Mahmoud Korek
Keyword(s):  
Dipole Moment ◽  
Ground State ◽  
Bound States ◽  
Radiative Lifetime ◽  
Electronic States ◽  
Rotational Constant ◽  
Transition Dipole Moment ◽  
Transition Dipole ◽  
Complete Active Space ◽  
Self Consistent Field

Adiabatic potential energy curves of the 28 low-lying doublet and quartet electronic states in the representation 2s+1Λ(±) of the zinc monofluoride molecule are investigated using the complete active space self-consistent field (CASSCF) with multi-reference configuration interaction (MRCI) method including single and double excitations with the Davidson correction (+Q). The internuclear distance Re, the harmonic frequency ωe, the static and transition dipole moment μ, the rotational constant Be, and the electronic transition energy with respect to the ground state Te are calculated for the bound states. The transition dipole moment between some doublet states is used to determine the Einstein spontaneous A21 and induced emission [Formula: see text] coefficients, as well as the spontaneous radiative lifetime τspon, emission wavelength λ21, and oscillator strength f21. The ground state ionicity qionicity and equilibrium dissociation energy DE,e are also computed. The comparison between the values of the present work and those available in the literature for several electronic states shows very good agreement. Twenty-three new electronic states have been studied in the present work for the first time.

The β+ Decay of 234Np and Other Isospin-Forbidden 0+→ 0+ Fermi Transitions

1984 ◽  
Vol 39 (12) ◽  
pp. 1168-1171
Author(s):  
C. T. Yap ◽  
E. L. Saw
Keyword(s):  
Nuclear Matrix ◽  
Coulomb Potential ◽  
Deformation Parameter ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Matrix Elements ◽  
Β Decay ◽  
A Value ◽  
Experimental Values ◽  
Good Agreement

Although experimental values of the Fermi nuclear matrix elements vary widely from about 1 × 10-3 to 40 × 10-3 for isospin-forbidden 0+→0+ β transitions, theoretical calculations using the Coulomb potential and Nilsson wave functions yielded values of MF in reasonably good agreement, except that of 234Np. However, our calculation of MF for this decay as a function of the deformation parameter β yielded a value of MF in good agreement with experiment for values of β between 0.1 and 0.2.

scholarly journals Влияние электрон-дырочной асимметрии на электронную структуру спиральных краевых состояний в квантовой яме HgTe/HgCdTe

2020 ◽  
Vol 62 (3) ◽  
pp. 447
Author(s):  
М.В. Дурнев
Keyword(s):  
Electronic Structure ◽  
Energy Spectrum ◽  
Quantum Wells ◽  
Wave Functions ◽  
Optical Transitions ◽  
Edge States ◽  
Matrix Elements ◽  
Electron Hole ◽  
G Factor ◽  
Analytical Expressions

We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band kp-model, which takes into account the absence of a spacial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective g-factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions - electron-hole asymmetry and the absence of an inversion centre - are simultaneously satisfied, the spectrum of edge electrons deviates from the linear one, and we obtain the corresponding corrections.

Theoretical calculation of the low-lying quartet states of the CrF molecule

2011 ◽  
Vol 89 (10) ◽  
pp. 1304-1311 ◽  
Author(s):  
A. Hamdan ◽  
M. Korek
Keyword(s):  
Dipole Moment ◽  
Potential Energy ◽  
Ground State ◽  
Electronic States ◽  
Rotational Constant ◽  
Electronic Energy ◽  
Harmonic Frequency ◽  
First Time ◽  
Theoretical Results ◽  
Good Agreement

The potential energy curves have been investigated for the 11 lowest quartet electronic states in the 2s+1Λ± representation below 28 000 cm–1 of the molecule CrF via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Eight electronic states have been studied theoretically for the first time. The harmonic frequency ωe, the internuclear distance re, the rotational constant Be, the electronic energy with respect to the ground state Te, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues Ev, the rotational constant Bv, and the abscissas of the turning points rmin and rmax have been calculated for electronic states up to the vibrational level v = 38. The comparison of these values to the theoretical results available in the literature shows a very good agreement.

Ab initio calculations of the XI molecules (X = Li, Na, K, Rb) with the ionicity and laser cooling analysis

2020 ◽  
Vol 98 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Israa Zeid ◽  
Rania Al Abdallah ◽  
Nayla El-Kork ◽  
Mahmoud Korek
Keyword(s):  
Dipole Moment ◽  
Ab Initio ◽  
Laser Cooling ◽  
Ground State ◽  
Bound States ◽  
Electronic States ◽  
Spectroscopic Constants ◽  
Ionic Character ◽  
Canonical Function ◽  
Dissociation Energies

For the alkali iodide molecules LiI, NaI, KI, and RbI, ab initio CASSCF/(MRCI+Q) calculations have been employed to investigate the adiabatic potential energy curves and the static dipole moment curves of the low-lying singlet and triplet electronic states in the representation 2S+1Λ(+/−). The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment μe, and the dissociation energies De have been computed for the bound states. Additionally, the percentage ionic character fionic around the equilibrium position of the ground state and the (2)1Σ+ state has been estimated. Using the canonical function approach, these calculations have been followed by a rovibrational calculation from which the rovibrational constants Ev, Bv, Dv, and the abscissas of the turning points Rmin and Rmax for the investigated bound states are calculated.

Note on the wave functions used for point-ion-lattice calculations of F-centres

1966 ◽  
Vol 19 (12) ◽  
pp. 2193
Author(s):  
CK Coogan ◽  
HG Hecht
Keyword(s):  
Ground State ◽  
Hyperfine Coupling ◽  
Spherical Wave ◽  
Alkali Halides ◽  
Higher Order ◽  
Wave Functions ◽  
Crystal Symmetry ◽  
Basis Set ◽  
Slater Type ◽  
Ground State Energies

Slater type ns wave functions, differing from the spherically symmetrical wave functions used by Gourary and Adrian, have been tried as a basis set for calculating wave functions of electrons in F-centres in alkali halides. Combinations of 1s, 2s, and 3s Slater functions still yielded ground state energies slightly higher than that calculated by Gourary and Adrian. It is concluded both that the GA wave functions were very well chosen and that more significant changes, particularly in the calculated hyperfine coupling, would come from adding terms of higher-order harmonics, compatible with the crystal symmetry, to the spherical wave functions.

scholarly journals Dipole Moment Functions of HF and HI Molecules Using an Anharmonic Potential

1983 ◽  
Vol 38 (1) ◽  
pp. 16-19 ◽  
Author(s):  
Manfred H. Kluckner ◽  
B. Sesh Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Electric Dipole ◽  
Wave Functions ◽  
Matrix Elements ◽  
Least Squares Fit ◽  
Anharmonic Potential ◽  
The Matrix ◽  
Moment Functions ◽  
Vibration Rotation

Abstract Vibration-rotation wave functions for HF and HI are computed by solving the radial Schroedinger wave equation numerically using an anharmonic potential function with seven adjustable parameters. With these wave functions the matrix elements of [(r - re)/re]n are computed. These are then applied in a least squares fit to experimentally measured values of the electric dipole matrix elements to yield the dipole moment coefficients M0, M1,..., M5 .

Radial matrix elements and dipole moment function for the ground state of CO

1977 ◽  
Vol 65 (2) ◽  
pp. 306-312 ◽  
Author(s):  
Sidney M. Kirschner ◽  
Robert J. Le Roy ◽  
John F. Ogilvie ◽  
Richard H. Tipping
Keyword(s):  
Dipole Moment ◽  
Ground State ◽  
Moment Function ◽  
Matrix Elements
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