scholarly journals Analytical approximation for oscillator strengths of H-like ions

1990 ◽  
Vol 8 (4) ◽  
pp. 709-714 ◽  
Author(s):  
E. Minguez
Keyword(s):  
Oscillator Strength ◽  
Analytical Approximation ◽  
Oscillator Strengths ◽  
Analytical Formulas ◽  
Analytical Expressions

The main objective of this work is to find analytical formulas for the oscillator strength f of hydrogen-like ions. It is well known that f is proportional to the energy of the transitions between eigenstates (ΔE), and to the square of the R matrix. Therefore, the problem of calculating f can be reduced to finding analytical expressions for both parameters, ΔE and R. Hence these expressions would be in accordance with quantum results based on more sophisticated calculations.

Oscillator Strength Measurements in the Vacuum-Ultraviolet by the Emission Method

1988 ◽  
Vol 102 ◽  
pp. 353-356
Author(s):  
C. Goldbach ◽  
G. Nollez
Keyword(s):  
Oscillator Strength ◽  
Vacuum Ultraviolet ◽  
Oscillator Strengths ◽  
Emission Method ◽  
Absolute Scale ◽  
Good Agreement

AbstractThe principles and the realization of an experiment devoted to oscillator strength measurements in the vacuum-ultraviolet by the emission method are briefly presented. The results obtained for the strong multiplets of neutral nitrogen and carbon in the 1200-2000 Å range yield an absolute scale of oscillator strengths in good agreement with the most recent calculations.

Dipole oscillator strength distributions and properties for SO2, CS2, and OCS

1985 ◽  
Vol 63 (3) ◽  
pp. 417-427 ◽  
Author(s):  
Ashok Kumar ◽  
William J. Meath
Keyword(s):  
Oscillator Strength ◽  
Cross Sections ◽  
Ground State ◽  
Strength Properties ◽  
Oscillator Strengths ◽  
Sum Rule ◽  
Strength Data ◽  
Dilute Gases ◽  
Dipole Oscillator ◽  
Strength Distributions

Dipole oscillator strength distributions have been constructed and used to evaluate integrated oscillator strengths, and a variety of dipole oscillator strength properties, for ground state SO2, CS2, and OCS. Each distribution has been constructed by using experimental and theoretical photoabsorption cross sections and by subjecting the resulting dipole oscillator strength data to constraints provided by the Thomas–Reiche–Kuhn sum rule and molar refractivity data for the relevant dilute gases. The discussion includes graphical presentations of how various spectral regions of the dipole oscillator strength distributions contribute to the more important dipole properties.

scholarly journals MUTUAL COUPLING COEFFICIENTS OF ROTATING RECTANGULAR DIELECTRIC RESONATORS IN CUT-OFF RECTANGULAR WAVEGUIDE

2021 ◽  
pp. 48-54
Author(s):  
Alexander Trubin
Keyword(s):  
Transmission Lines ◽  
Rectangular Waveguide ◽  
Information Transfer ◽  
Dielectric Resonators ◽  
Coupling Coefficients ◽  
Metal Waveguide ◽  
Communication Devices ◽  
Dielectric Filter ◽  
Analytical Formulas ◽  
Analytical Expressions

Background. A further increase in the speed of information transfer is determined by more stringent requirements for the elements of communication devices. One of the most important components of such devices is various filters, which are often made on the basis of dielectric resonators. Calculation of the parameters of multi-section filters is impossible without further development of the theory of their design. The development of filter theory is based on electrodynamic modelling, which involves calculating the coupling coefficients of dielectric resonators in various transmission lines. Objective. The aim of the research is to calculate and study the coupling coefficients of rectangular dielectric resonators with a rectangular metal waveguide when their axes rotate. Investigation of new effects to improve the performance of filters and other devices based on them. Methods. Methods of technical electrodynamics are used to calculate and analyse the coupling coefficients. The end result is to obtain new analytical formulas for new structures with rectangular dielectric resonators, which make it possible to analyse and calculate their coupling coefficients. Results. New analytical expressions are found for the coupling coefficients of dielectric resonators with the rotation of their axes in a rectangular waveguide. Conclusions. The theory of designing filters based on new structures of dielectric resonators with rotation of their axes in metal waveguides has been expanded. New analytical relationships and new patterns of change in the coupling coefficients are found. Keywords: dielectric filter; rectangular dielectric resonator; rotation; coupling coefficients.

scholarly journals Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

2014 ◽  
Author(s):  
Mohammad I. Younis
Keyword(s):  
Analytical Solutions ◽  
Galerkin Approximation ◽  
Single Mode ◽  
Beam Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Analytical Formulas ◽  
Euler Bernoulli Beam ◽  
Analytical Expressions ◽  
Multi Mode

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

scholarly journals Two approaches for automating analysis of electromagnetic processes in non-linear circuits with valves

2019 ◽  
Vol 139 ◽  
pp. 01085 ◽  
Author(s):  
Khushnud Sapaev ◽  
Shukhrat Umarov
Keyword(s):  
Numerical Integration ◽  
Linear Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Equivalent Circuits ◽  
Electric Circuits ◽  
Electromagnetic Processes ◽  
Integration Formulas ◽  
Analytical Formulas ◽  
Analytical Expressions

This article analyses and compares two approaches related to automating modeling of valve electric circuits with piecewise linear approximation of valve characteristics. The first approach is based on operator equivalent circuits’ analytical formulas and on analytical expressions programming which describe equivalent circuits on each conduction interval of valve elements. The second approach provides implementation of a system for modeling valve converters based on implicit numerical integration formulas.

scholarly journals An analytical approximation of the transient response of a voltage dependent supercapacitor model

2019 ◽  
Vol 39 (3) ◽  
pp. 310-319
Author(s):  
Tomislav Barić ◽  
Hrvoje Glavaš ◽  
Ružica Kljajić
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Nonlinear Differential Equation ◽  
Exact Analytical Solution ◽  
Initial Response ◽  
Analytical Approximation ◽  
Weight Functions ◽  
Transient Phenomenon ◽  
Voltage Dependent ◽  
Analytical Expressions

Supercapacitors are well known for their voltage dependent capacity. Due to this, it is not possible to obtain the exact analytical solution of the nonlinear differential equation which describes the transient charging and discharging. For this reason, approximations of differential equations must be carried out in order to obtain an approximate analytical solution. The focus of this paper is on a different approach. Instead of approximating the differential equation and obtaining analytical expressions for such approximations, an intuitive approach is chosen. This approach is based on the separation of the initial response from the rest of the transient phenomenon. Both parts of the transient phenomenon are described with adequate functions. Using appropriate weight functions, both functions are combined into a single function that describes the whole transient phenomenon. As shown in the paper, such an approach gives an excellent description of the whole transient. Also, it provides simpler expressions compared to those obtained by approximation of the nonlinear differential equation. With respect to their accuracy, these expressions do not lag behind the aforementioned approach. The validity of the presented analytical expressions was confirmed by comparing their results with those obtained by numerically solving the nonlinear differential equation.

Dipole oscillator strength distributions and related properties for ethylene, propene and 1-butene

1983 ◽  
Vol 61 (7) ◽  
pp. 1027-1034 ◽  
Author(s):  
B. L. Jhanwar ◽  
William J. Meath ◽  
J. C. F. MacDonald
Keyword(s):  
Oscillator Strength ◽  
Cross Sections ◽  
Ground State ◽  
Oscillator Strengths ◽  
Detailed Model ◽  
Sum Rule ◽  
Strength Data ◽  
Dilute Gases ◽  
Dipole Oscillator ◽  
Strength Distributions

Dipole oscillator strength distributions (DOSDs) have been constructed for ground state ethylene, propene, and 1-butene. Each DOSD is constructed by using available experimental and theoretical photoabsorption cross sections and by constraining the resulting dipole oscillator strength data to satisfy the Thomas – Reiche–Kuhn sum rule and molar refractivity constraints. The latter were obtained from experimental refractive index measurements of relevant dilute gases. The recommended DOSDs, and the values of integrated "band" oscillator strengths, and the dipole oscillator strength sums Sk and Lk (for a variety of k values) obtained from them, are reported. The discussion includes an analysis of the reliability of the results using 1-butene as a detailed model.

f-f spectral studies of holmium(III) complexes

1983 ◽  
Vol 36 (4) ◽  
pp. 695 ◽  
Author(s):  
K Iftikhar ◽  
N Ahmad
Keyword(s):  
Coordination Number ◽  
Oscillator Strength ◽  
Magnetic Moment ◽  
Visible Region ◽  
Mixed Ligand ◽  
Oscillator Strengths ◽  
Mixed Ligand Complexes ◽  
Spectral Studies ◽  
Nitrogen Donors ◽  
Covalency Parameters

Holmium(III) mixed-ligand complexes containing ligands having oxygen and nitrogen donors have been spectrophotometrically investigated. The observed spectra in the visible region have been analysed to calculate covalency parameters (β, b� and δ), oscillator strengths and Judd-Ofelt parameters. The degree of covalency in the complexes increases with increase in coordination number. The hypersensitivity is correlated with the degree of covalency and number of coordinated ligands. The higher values of covalency parameters, oscillator strength and magnetic moment in the ten-coordinate HoIII is taken as evidence of participation of f-orbitals in bonding.

Analytical formulas for the Stark effect on intensity of hydrogen radiation lines

2003 ◽  
Vol 81 (5) ◽  
pp. 755-769 ◽  
Author(s):  
A A Kamenski ◽  
V D Ovsiannikov
Keyword(s):  
Perturbation Theory ◽  
Green Function ◽  
Field Strength ◽  
Stark Effect ◽  
Selection Rule ◽  
Magnetic Quantum Number ◽  
Matrix Elements ◽  
Analytical Formulas ◽  
Degenerate States ◽  
Analytical Expressions

A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced Coulomb–Green function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.–n, 32.70.Fw

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