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Journal ArticleDOI

Stieltjes imaging of atomic and molecular photoabsorption profiles

15 Sep 1973-Chemical Physics Letters (North-Holland)-Vol. 22, Iss: 1, pp 60-64
TL;DR: In this article, the effective transition frequencies and oscillator strenghts obtained from principal representations of spectral moments, or from variational procedures using appropriate square-integrable basis functions, are employed in the Stieltjes imaging of atomic and molecular photoabsorption profiles.
About: This article is published in Chemical Physics Letters.The article was published on 1973-09-15. It has received 100 citations till now.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a number of theoretical approaches for electron-atom scattering in the intermediate energy regime have been proposed, including extensions of low-energy methods, the use of optical potentials and extensions of the Born approximation by the inclusion of higher-order terms.
Abstract: Over the last few years there has been much interest, both theoretically and experimentally, in electron-atom scattering at intermediate energies. The theoretical work has been driven mainly by the many applications in astronomy, laser physics and plasma physics which require accurate data for their interpretation and by experimental advances which provide an important stimulus to theory. The increasing availabililty of more powerful computers has enabled the development of more sophisticated theoretical methods to study electron scattering in the intermediate energy regime, which faces particular difficulties owing to the infinite number of open channels which occur in this energy region. In order to obtain accurate results in the intermediate energy region, the theoretical approaches used must be able, in some way, to allow for loss of flux into these highly excited states and continuum states of the target atom or ion. Recent theoretical approaches which have been proposed include extensions of low-energy methods, the use of optical potentials and extensions of the Born approximation by the inclusion of higher-order terms.

108 citations

Journal ArticleDOI
TL;DR: In this article, the Stieltjes imaging procedure is used for the construction of accurate approximations to photoabsorption and dispersion profiles in atoms and molecules in simple atomic systems.
Abstract: Variational and moment‐theory techniques for the construction of accurate approximations to photoabsorption and dispersion profiles in atoms and molecules are described and applied to simple atomic systems. It is shown that appropriately defined principal pseudostates, when employed in ab initio variational calculations, furnish the discrete transition frequencies and oscillator strengths that provide so‐called principal representations of spectral moments. The Tchebycheff‐Stieltjes‐Markoff moment theory ensures that the principal frequencies and strengths furnish the information necessary for constructing convergent images of both the discrete and continuum portions of photoabsorption profiles. Evaluation of the appropriate principal value integrals results in convergent Stieltjes images of the associated photodispersion profiles. Detailed applications in the cases of the negative hydrogen ion and atomic hydrogen show that the Stieltjes imaging procedure is rapidly convergent for both the discrete and continuum portions of absorption and dispersion profiles in simple systems. Additional illustrative applications in the cases of atomic helium and lithium show that photoabsorption profiles with simple structures can be accurately imaged even when the pseudostates employed are not necessarily principal ones. The present development extends previously described variational and moment‐theory techniques for approximating frequency‐dependent dipole polarizabilities in their analytic regions to the real frequency axis within photoabsorption intervals. Moreover, the Stieltjes theory shows that conventional configuration interaction methods with square‐integrable basis functions can be employed in the calculation of principal pseudostates and associated photoabsorption and dispersion profiles, thereby avoiding the explicit construction of accurate approximations to the complete set of discrete and continuum eigenstates required in more customary approaches.

108 citations

Journal ArticleDOI
TL;DR: The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described and the connection to related energy transfer and ionization processes is drawn.
Abstract: Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

102 citations

Journal ArticleDOI
TL;DR: A review of the process of extraction of continuum information from operators discretized in finite sets of square integrable (L 2 ) basis functions is given, with emphasis on the close relationships between the Stieltjes method and Gaussian integration as mentioned in this paper.

82 citations

Journal ArticleDOI
TL;DR: In this paper, a simple projection procedure was devised that retains the computational simplicity of the frozen-core approximation and gives cross sections in good accord with measured values, which is similar to the one presented in this paper.

66 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the spectrum of oscillator strength for neutral atoms in their ground states is surveyed with particular regard to recent progress in the far uv-soft x-ray range and to the theoretical interpretation of data from experiments and from numerical calculations.
Abstract: Information on the spectrum of oscillator strength for neutral atoms in their ground states is surveyed with particular regard to recent progress in the far uv-soft x-ray range and to the theoretical interpretation of data from experiments and from numerical calculations. The analysis brings out numerous aspects of atomic mechanics and problems that remain unsolved. An effort is made to interconnect different theoretical approaches within the framework of the theory of atomic spectra.

1,332 citations

Journal ArticleDOI
TL;DR: In this article, the Bethe theory has been updated with a number of new developments which need to be included in that body of material, such as the ${z}^{3}$ effect and the stopping power for particles at extreme relativistic energies.
Abstract: Since the appearance of the title paper, a number of new developments have occurred which need to be included in that body of material. We present additional remarks and clarifications which supplement and update numerous aspects of the Bethe theory discussed in the earlier paper. We also bring the bibliography up to date. Plasma stopping power, the ${z}^{3}$ effect, and stopping power for particles at extreme relativistic energies are among the new topics included. We make several comments on Fano's earlier review article, Ann. Rev. Nucl. Sci. 13, 1 (1963).

1,233 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that for the simpler systems (i.e., systems with a single electron outside closed shells) the method gives remarkably accurate results; indeed, it appears superior to the normal rather laborious procedure involving the computation of the necessary wave functions, in each individual case, by solution of the appropriate Hartree or Fock differential equation.
Abstract: It is shown that in calculating transition integrals it is permissible to neglect the departure of the potential of an atom or ion from its asymptotic Coulomb form. This enables a general analytical expression for the transition integral to be derived. Tables are compiled from which the absolute strengths of large numbers of spectral lines can at once be obtained if the term values of the upper and lower levels are known. s-p , p-d and d-f transitions are all treated. Comparison with experimental data shows that for the simpler systems (i. e. systems with a single electron outside closed shells) the method gives remarkably accurate results; indeed, it appears superior to the normal rather laborious procedure involving the computation of the necessary wave functions, in each individual case, by solution of the appropriate Hartree or Fock differential equation. The method (in its most elementary form) may not be so satisfactory for complex systems (i. e. systems with unclosed shells) owing to difficulties associated with the identification of certain energy parameters. However, the rather scanty comparison data available suggest that even for such systems it yields useful (and in some cases precise) information on the line strengths. Incidentally, in the course of the work the accuracy of a few wave functions based on the self consistent field approximation (including exchange) was tested by using them to evaluate line strengths from both the dipole moment and the dipole velocity formulae. Appreciable defects were revealed.

942 citations

01 Jan 1972
TL;DR: In this paper, the Bethe theory has been updated with a number of new developments which need to be included in that body of material, such as the ${z}^{3}$ effect and the stopping power for particles at extreme relativistic energies.
Abstract: Since the appearance of the title paper, a number of new developments have occurred which need to be included in that body of material. We present additional remarks and clarifications which supplement and update numerous aspects of the Bethe theory discussed in the earlier paper. We also bring the bibliography up to date. Plasma stopping power, the ${z}^{3}$ effect, and stopping power for particles at extreme relativistic energies are among the new topics included. We make several comments on Fano's earlier review article, Ann. Rev. Nucl. Sci. 13, 1 (1963).

832 citations

Book
01 Jan 1970
TL;DR: In this paper, an on-line book provided in this website is described, which is an online approximant in theoretical physics, and when you read more every page, what you will obtain is something great.
Abstract: Read more and get great! That's what the book enPDFd pade approximant in theoretical physics will give for every reader to read this book. This is an on-line book provided in this website. Even this book becomes a choice of someone to read, many in the world also loves it so much. As what we talk, when you read more every page of this pade approximant in theoretical physics, what you will obtain is something great.

276 citations