Reactance Matrices Research Articles

New version of program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

New version of program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Rovibrational cross sections from reactance matrices calculated in adiabatic nuclei approximation

Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this Method of solution issue) Transformation for vibrational excitation is obtained by integrating the real and imaginary parts of the body-frame tComputer: CDC 6400; Installation: Computing Centre, The matrices over internuclear separation. Vibrational wave funcUniversity of Western Ontario, London, Ontario tions are assumed to be given. The rotational transformation Operating system: SCOPE involves an eight-fold sum over angular momenta [1]. The

Resonance and intermediate-coupling effects in electron scattering with highly charged ions. II. Autoionization and dielectronic recombination

The role of resonances in electron-impact excitation of highly charged ions is examined and some methods are described in order to take account of autoionization and dielectronic recombination. The intermediate-coupling calculations of paper I are extended to include these processes and effective collision strengths are obtained. Results are presented to illustrate particular features in a number of transitions in ${\mathrm{Fe}}^{24+}$ and ${\mathrm{Mo}}^{40+}$. Resonance analysis is carried out employing numerical interpolation techniques and multichannel quantum-defect theory, employing reactance matrices in nine-state close-coupling and distorted-wave approximations. It is shown that all three effects considered in the present study, departure from $\mathrm{LS}$ coupling, resonance enhancement due to autoionization, and reduction in autoionization enhancement due to dielectronic recombination, can be of considerable importance in the cross sections of highly ionized systems. In the high-$Z$ ions of the helium isoelectronic sequence the contribution of autoionizing resonances remains large even after all probable radiative channels are included, although the net autoionization effect decreases with $Z$.

Collision strengths for the fine-structure transitions within the 1s22s22p23P ground state of Ne V

Electron collision strengths for the fine-structure transitions within the 1s22s22p23P ground state of Ne V have been calculated using the R-matrix program. Configuration interaction wavefunctions have been employed in the calculations and computations have been made in a large energy region below 40 Ryd. All partial waves with L<or=9 have been included and the reactance matrices obtained in the LS coupling scheme from the R-matrix program have been transformed to pair coupling using the program JAJOM. The collision strengths obtained show a complex pattern of resonances in the entire threshold energy region and are given graphically for electron energies below 0.8 Ryd. The entire collision strength spectrum has been averaged over a Maxwellian distribution of electron velocities and the results so obtained for the effective collision strengths are tabulated for electron temperatures below 1*106K.

Calculation of the rate coefficients for the electron impact excitation of the n=2 terms of O IV

The collision strengths for the excitation of the n=2 terms in O IV from the ground and metastable terms have been calculated for energies from the first excitation threshold to 5.6 Ryd in a close-coupling approximation. The resonance structure obtained in the reactance matrices has been fitted and the resulting analytic fits used to generate the collision strengths at a fine energy mesh. These collision strengths were then integrated to obtain rate coefficients for temperatures between 104 and 2*105K.

Some new results in the theory of normal distributed networks

The aim of this paper is to prove a partial converse of a representation theorem for normal distributed lossless two-port networks. The representation theorem states that the scattering matrix of a normal distributed lossless two-port network has a compact representation in terms of simple algebraic functions. In this paper it is shown that any 2 \times 2 matrix satisfying the conditions of the representation theorem is quasi-bounded-real (QBR). This result implies that the impedance and admittance matrices computed from the scattering matrix are reactance matrices in the rational case and quasi-reactance matrices in the nonrational case. These results have important applications in the synthesis of microwave filters and impedance transformers.

Cross sections and excitation rates for electron collisions with heliumlike ions

We describe the techniques and the approximations used in extensive calculations for cross sections and reaction-rate parameters for electron-impact excitation of a number of heliumlike ions. All transitions involving the ground state and the $n=2$ states are considered. Calculations are made in the distorted-wave approximation using configuration-interaction wave functions to represent the target states. Autoionizing resonances in the scattering cross sections are included through bound-channel correlation-type functions and through quantum-defect-theory analysis of the reactance matrices. The resonances are shown to make considerable contributions to the cross sections and thereby, in many cases, to enhance the excitation-rate coefficients by a significant factor. This should have important consequences for practical applications in the analysis of laboratory and astrophysical plasmas. The accuracy of our approximations is also discussed.

Residue matrices and related properties in two-variable reactance functions

In this paper, the characterization of a two-variable reactance polynomial φ(λ,μ) is given in terms of the residue matrices of a single variable reactance matrix, Y(λ). Specificially, if Y(λ) is expressed in terms of its partial fraction as Y(λ)=λH ∞+Σ H i+jβ i λ+jω i +G where the residue matrices in general are p.s.d. Hermitian, then the ranks of these residue matrices are fixed in relation to the construction of φ(λ,μ) as the determinant of the two-variable reactance matrix μ1+Y(λ). Three theorems concerning these ranks—one each corresponding to the finite poles, poles at ∞ and the behaviour at λ=0 of Y(λ) are stated and proved. Several properties following from these theorems are studied. Also, implications of these theorems from a network theoretic point of view, like the minimum number of gyrators required to synthesize Y(λ) to yield the specific type of φ(λ,μ) etc., are studied. In the sequel, the concept of “generalized compact pole conditions” is introduced. Finally, these results are applied for the generation of two-variable reactance functions and matrices.

On the ranks of certain matrices

A few basic results regarding the ranks of certain types of matrices are presented. Also, some bounds on the ranks of the real and imaginary parts of a positive semi-definite Hermitian matrix are worked out. Applications of particular cases of these results in the areas like passive network synthesis, generation of two-variable reactance matrices, etc., are pointed out.

New version of program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

New version of program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Fine structure cross sections from reactance matrices — a more versatile development of the program jajom

We present in this work new quantum Stark broadening data 8 neon-like ions from Mg III to Cl VIII and separately Fe XVII and Br XXVI: twenty spectral lines for each of the mentioned 8 ions have been considered. To the best of our knowledge, among the 160 Stark widths provided for these ions, only three lines of Mg III and six of Si V were calculated in precedent works, the rest Stark widths are new, and no results have been found to compare with. The only comparisons have been performed with the available data. We present some of the collision data (collision strengths, cross sections, ...) used in our broadening calculations, and we compare them to other results. The comparison shows an acceptable agreement which can help us to decide about the accuracy of our Stark broadening calculations. We use also our quantum calculations to provide systematic trends of Stark widths with the effective charge Z of all the Ne-like ions from Mg III to Br XXVI. We find that for most of these lines, there is a regularity with the charge Z in this iso-electronic sequence. We hope that our calculations can fill the lack of line broadening data used in stellar spectroscopy and plasma diagnostics, and we hope also that the provided relation between Stark broadening and the charge Z can be useful for the deduction of Stark widths of all the neon-like ions between Mg III and Br XXVI without labour calculations.

Low-energy scattering of electrons by atomic oxygen

The method of polarized pseudostates has been used to calculate cross sections for the elastic scattering of electrons by atomic oxygen. These pseudostates are added to the close-coupling expansion to give a polarization potential in agreement with experimental values of polarizability. The resulting elastic cross sections are in good agreement with other theoretical calculations as well as with experiment for energies up to 10 eV. The reactance matrices obtained in this calculation have been used to calculate collision strengths for fine-structure transitions in the ground-state $^{3}P$ term for electron temperatures above 5000\ifmmode^\circ\else\textdegree\fi{} K.

Rovibrational cross sections from reactance matrices calculated in adiabatic nuclei approximation

Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this Method of solution issue) Transformation for vibrational excitation is obtained by integrating the real and imaginary parts of the body-frame tComputer: CDC 6400; Installation: Computing Centre, The matrices over internuclear separation. Vibrational wave funcUniversity of Western Ontario, London, Ontario tions are assumed to be given. The rotational transformation Operating system: SCOPE involves an eight-fold sum over angular momenta [1]. The

Use of consistent phase conventions in calculating angular distributions of scattering cross sections and application to electron-hydrogen-atom inelastic scattering

The practical problem of consistent use of a phase convention in calculating differential cross sections from scattering or reactance matrices is discussed, and in two instances (electron-hydrogen-atom and positron-hydrogen-atom scattering) where an inconsistency has been found, we correct some previously published differential-cross-section formulas. We present the first correct calculations of close-coupling-approximation differential cross sections for the $1s\ensuremath{-}2p$ electron-hydrogen-atom scattering process. We compare the differential cross sections from the 3-state and the 6-state close-coupling-approximation scattering matrices of Burke and co-workers.

Electron scattering from the excited states of neutral sodium

Cross sections are calculated for elastic and superelastic (including spin-flip) collisions with the first excited state of sodium, for transitions between the first three excited states, and for transitions between the fine-structure states of the 3p and 3d doublets, from reactance matrices calculated in a four state (3s-3p-3d-4s) close coupling approximation.

New methods for calculating scattering cross sections for rearrangement collisions

A new method for calculating quantum-mechanical reactance matrices (and hence cross sections) for rearrangement collisions is discussed and tested. This method avoids the integral kernels which usually appear in the coupled differential equations describing the wave function for rearrangement scattering. The method is applied to an example rearrangement scattering problem (elastic and inelastic electron-hydrogen-atom scattering) with good results.

Program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Program for calculating differential and integral cross sections for quantum mechanical scattering problems from reactance or transition matrices

Fine structure cross sections from reactance matrices

To calculate fine-structure electron–atom collision cross-section, a set including 3 codes was developed at University College London, presented in Computer Physics Communications: SUPERSTRUCTURE (1974), UCL Distorted wave (1998), JAJOM (1972, 1978). Due to improvements in computers, more ambitious calculations of atomic data were performed. Unfortunately, unexpected problems have appeared which required an update version of these codes, presented here.

The calculation of energy levels for atoms in configurations ls22s22pqnl

Reactance matrices for electron collisions with ions in configurations ls22s22p9(q= 1 to 5), calculated by Saraph, Seaton &amp; Shemming (1969), have been fitted to analytic functions of the energy and extrapolated to energies which give bound states with configurations ls22s22pq(SiLi)nlSL. The positions of the bound states are calculated using methods of many-channel quantum defect theory. Allowance can be made for the fine-structure energy of the ion core, by using a representation (SiLiJi) or a pair-coupling representation (SiLi)nlj,J. The calculated level positions are compared with positions determined experimentally. The most detailed results are for the np levels, but some results are given for nsand ndlevels. Some semi-empirical adjustments are made in the calculated matrices, so as to obtain improved agreement between observed and calculated levels. In many cases the most serious source of error in the calculations is the neglect of interactions between configurations 2s22pqnland 2s2pq+1n'l'. For the more highly ionized systems these interactions give rise to perturbed series. A discussion of results for valence-electron states in the neutral atoms, CI, NI, OI, FIand NeIis followed by a discussion of the various iso-electronic sequences. The results enable us: (i) To assess the accuracy of the calculated reactance matrices. (ii) To make identifications. In most cases, but not all cases, the assignments obtained for parentage, and for pair-coupling quantum numbers, agree with assignments which have been suggested previously. In some cases it is found that large admixtures of states occur and that no meaningful assignments of parentage or pair-coupling quantum numbers can be made. (iii) To make predictions. Calculated positions of energy levels, and error estimates, are given for some levels which have not been observed.