scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

scholarly journals Extended theoretical transition data in C i–iv

2021 ◽  
Vol 502 (3) ◽  
pp. 3780-3799
Author(s):  
W Li ◽  
A M Amarsi ◽  
A Papoulia ◽  
J Ekman ◽  
P Jönsson
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Internal Validation ◽  
Hartree Fock ◽  
Relativistic Configuration ◽  
The Difference ◽  
The One ◽  
Relative Differences

ABSTRACT Accurate atomic data are essential for opacity calculations and for abundance analyses of the Sun and other stars. The aim of this work is to provide accurate and extensive results of energy levels and transition data for C i–iv. The Multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used in this work. To improve the quality of the wavefunctions and reduce the relative differences between length and velocity forms for transition data involving high Rydberg states, alternative computational strategies were employed by imposing restrictions on the electron substitutions when constructing the orbital basis for each atom and ion. Transition data, for example, weighted oscillator strengths and transition probabilities, are given for radiative electric dipole (E1) transitions involving levels up to 1s22s22p6s for C i, up to 1s22s27f for C ii, up to 1s22s7f for C iii, and up to 1s28g for C iv. Using the difference between the transition rates in length and velocity gauges as an internal validation, the average uncertainties of all presented E1 transitions are estimated to be 8.05 per cent, 7.20 per cent, 1.77 per cent, and 0.28 per cent, respectively, for C i–iv. Extensive comparisons with available experimental and theoretical results are performed and good agreement is observed for most of the transitions. In addition, the C i data were employed in a re-analysis of the solar carbon abundance. The new transition data give a line-by-line dispersion similar to the one obtained when using transition data that are typically used in stellar spectroscopic applications today.

Semi-empirical Molecular Orbital Energy Levels of the Hexammine and Chloroammine Complexes of Co(IV)

1967 ◽  
Vol 22 (2) ◽  
pp. 170-175 ◽  
Author(s):  
Walter A. Yeranos ◽  
David A. Hasman
Keyword(s):  
Molecular Orbital ◽  
Energy Levels ◽  
Empirical Evaluation ◽  
Wave Functions ◽  
Electronic Transitions ◽  
Orbital Energy ◽  
Molecular Orbital Energy ◽  
The One ◽  
Semi Empirical

Using the recently proposed reciprocal mean for the semi-empirical evaluation of resonance integrals, as well as approximate SCF wave functions for Co3+, the one-electron molecular energy levels of Co (NH3) 3+, Co (NH3) 5Cl2+, and Co (NH3) 4Cl21+ have been redetermined within the WOLFSBERG–HELMHOLZ approximation. The outcome of the study fits remarkably well with the observed electronic transitions in the u.v. spectra of these complexes and prompts different band assignments than previously suggested.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

scholarly journals Electronic states and persistent currents in nanowire quantum ring

2018 ◽  
Vol 52 (4) ◽  
pp. 486
Author(s):  
I.A. Kokurin
Keyword(s):  
Magnetic Field ◽  
Energy Levels ◽  
Persistent Current ◽  
Orbit Coupling ◽  
Quantum Ring ◽  
Pure Spin ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Persistent Currents ◽  
The One

AbstractA new model of a quantum ring defined inside a nanowire is proposed. The one-particle Hamiltonian for electron in [111]-oriented nanowire quantum ring is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling. The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of spin-orbit coupling and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gates can lead to pure spin persistent current with the charge current being zero.

Study of Electromagnetic Multipole Transition Half-Lives of One-Hole 15O–15N and One-Particle 17O–17F Mirror Nuclei

2013 ◽  
Vol 68 (10-11) ◽  
pp. 709-714 ◽  
Author(s):  
Mohammadreza Pahlavani ◽  
Behnam Firoozi
Keyword(s):  
Experimental Data ◽  
Wave Functions ◽  
The Other ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Matrix Elements ◽  
Saxon Potential ◽  
N Isotopes ◽  
The One ◽  
Theoretical Results

Energy spectrum and wave functions are obtained numerically with a potential consisting of Woods-Saxon, Coulomb, and spin-orbit coupling parts for the nuclei 15O, 15N, 17O, and 17F. The radial parts of the wave functions are used to calculate some matrix elements of electromagnetic transitions. These results are applied to calculate half-lives of low-lying exited states in the one-particle 17O and 17F as well as in the one-hole 15O and 15N isotopes. The calculated half-lives are compared with available experimental and theoretical results based on harmonic oscillator wave functions and Weisskopf units. In comparison with the results calculated from the other methods, our results based on the Woods-Saxon potential indicate a satisfactory agreement with accessible experimental data.

Energy levels and radiative transitions of the K-shell excited sextet states in boron-like sulfur ion

2016 ◽  
Vol 94 (10) ◽  
pp. 1054-1060 ◽  
Author(s):  
Yan Sun ◽  
CuiCui Sang ◽  
KaiKai Li ◽  
XinYu Qian ◽  
Feng Hu ◽  
...  
Keyword(s):  
Fine Structure ◽  
Relativistic Effect ◽  
Transition Probabilities ◽  
Theoretical Calculations ◽  
Energy Levels ◽  
Oscillator Strengths ◽  
Variation Method ◽  
First Order ◽  
Radiative Transitions ◽  
First Order Perturbation

Theoretical calculations are reported for energy levels and transition probabilities of the K-shell excited sextet series 6Se,o(m) and 6Po,e(m) (m = 1–7) for the astrophysically important element sulfur. Energy levels, fine structure splittings, and transition parameters of the high-lying sextet series 6Se,o(m) and 6Po,e(m) (m = 1–7) in boron-like sulfur ion are calculated with the multi-configuration Rayleigh–Ritz variation method. To obtain the accurate energy level, the relativistic corrections and mass polarization effect are included by using the first-order perturbation theory. Configuration structures of these sextet series are assigned according to the energies, percentage contributions of basis states to the eigenvector, relativistic effect corrections, and verification of fine structure splittings. The oscillator strengths, transition probabilities, and wavelengths of electric-dipole transitions between 6So,e(m) and 6Pe,o(m) (m = 1–7) states are also systematically calculated and discussed.

Investigation of isospin excited and mixed-symmetry states in even–even N = Z nuclei

2018 ◽  
Vol 27 (08) ◽  
pp. 1850065 ◽  
Author(s):  
Falih H. Al-Khudair
Keyword(s):  
Excited States ◽  
Degrees Of Freedom ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Systematic Investigation ◽  
Wave Functions ◽  
Mixed Symmetry ◽  
Mixed Symmetry States ◽  
Boson Model

Mixed-symmetry and isospin excited states are typical of the interacting boson model with isospin (IBM-3). With a view to look for such states, levels scheme of the IBM-3 dynamical symmetry is discussed. A systematic investigation in the proton and neutron degrees of freedom of the energy levels has been carried out. A sequence of isospin excitation bands has been identified. We have analyzed the wave functions and given the symmetrical labeling of the states. The transition probabilities between the isospin excitation states of model limits are analyzed in terms of isoscalar and isovector decompositions. The present calculations suggest that a combination of isospin excitation and mixed-symmetry states can provide substantial information on the structure of nuclear states. Calculations for [Formula: see text] and [Formula: see text] nuclei are presented and compared with the results of the shell model and available experimental data.

Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry

2011 ◽  
Vol 66 (6-7) ◽  
pp. 457-460
Author(s):  
Said Laachir ◽  
Mohamed Moussetad ◽  
Rahma Adhiri
Keyword(s):  
Crystal Field ◽  
Ground State ◽  
Energy Levels ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Field Energy ◽  
Energy Matrix ◽  
Cubic Symmetry ◽  
Diagonalization Method ◽  
Erbium Ion

This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively

scholarly journals Hyperfine Structure and Relaxation Times of 4-Oxo-TEMPO/Methyl Alcohol Solutions in Weak and Strong Fields

1991 ◽  
Vol 46 (11) ◽  
pp. 976-982 ◽  
Author(s):  
M. Sünnetçioğlu ◽  
G. Bingöl ◽  
R. Sungur
Keyword(s):  
Free Radical ◽  
Hyperfine Structure ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Double Resonance ◽  
Relaxation Times ◽  
Electronic Relaxation ◽  
First Order ◽  
Saturation Method ◽  
First Order Perturbation

AbstractThe hyperfine structure of the 4-Oxo-TEMPO (2,2,6,6-tetramethyl-4-oxopiperidin-oxyl-l) free radical was investigated. Theoretical investigation includes four methyl groups protons close to the unpaired electron. Energy levels and transition probabilities were found by using second order and first order perturbation theory, respectively, and from these data theoretical spectra of the free radical were obtained. Diluted solutions in CH3-OH were prepared and the spectra were recorded with a double resonance spectrometer (1.53 mT) and Varian E-9X-band ESR spectrometer (~0.3 T). In order to understand the influence of time dependent phenomena on the linewidths, electronic relaxation times of 4-Oxo-TEMPO and its perdeuterated form (PDT) were measured at two different fields by using cw saturation method.

The valence-bond theory of molecular structure - III. Cyclo butadiene and benzene

1955 ◽  
Vol 227 (1170) ◽  
pp. 288-312 ◽  
Keyword(s):  
Intrinsic Value ◽  
Energy Levels ◽  
Valence Bond ◽  
Wave Functions ◽  
Empirical Theory ◽  
Different Types ◽  
Rigorous Framework ◽  
Bond Theory ◽  
Complete Sets ◽  
The One

The revised valence-bond (VB) theory of previous papers is applied in non-empirical calculation of the lower π -electron levels of cyclo butadiene and benzene. For the first of these molecules, complete sets of all non-polar and polar, singlet and triplet structures are employed; for the second, 89 singlet and 69 triplet structures were selected from the complete sets of 175 singlet and 189 triplet structures. The calculations, which follow unfamiliar lines but which proved not too heavy, are outlined in some detail. The results for cyclo butadiene agree with those of Craig, who employed a complete MO basis; but previous calculations on benzene are surpassed in accuracy, except in the case of the ground state which is apparently well represented by a few MO configurations. The primary aim of the present work was, however, simply to exploit the valence-bond approach as a practicable alternative to the MO method, with exactly similar ‘non-empirical’ potentialities. Energy levels, wave functions and bond orders were calculated in a variety of approximations, numerical results converging slowly to their final values as configurations were added, so that the function of different types of structure should be revealed: and ‘higher’ structures—those, for instance, which are doubly -polar—were found to have an unexpected importance. This supports the view that calculations making any pretence of being non-empirical cannot easily be extended to systems which explicitly involve more than a few electrons. The orthodox VB approach is re-examined, within this rigorous framework, and is found to have less intrinsic value than might have been hoped; the shortcomings of the conventional empirical theory are further revealed. Semi-empirica! developments are briefly investigated. The revised VB theory contains only a few numerically large parameters: these are, in the first place, ‘resonance’ integrals (of the one-electron type encountered in MO theory) and, secondly, the energies of the various polar configurations relative to the non-polar; by adjusting the latter quantities empirically it is possible partly to overcome one of the principal defects of the non-empirical theory—namely, its use of the Hückel approximation in which changes in the σ-bonded framework, accompanying π -electron ‘polarizations’, are ignored. It seems likely that considerable progress can be made along these lines.

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