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# Schwinger variational principle

About: Schwinger variational principle is a research topic. Over the lifetime, 120 publications have been published within this topic receiving 2139 citations.

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TL;DR: In this paper, a new vairational principle for scattering theory was proposed, which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering, and demonstrated the rapid convergence of the phase shift with respect to the number of basis functions for both the open and closed-channel orbitals.

Abstract: We propose a new vairational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below k^2=0.64 demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open- and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostates) is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our 1s-2s―-2p― calculation are comparable to those of 1s-2s-2p-3p―-3d― calculation of Matese and Oberoi [Phys. Rev. A 4, 569 (1971)], which are very close to the exact values. Several aspects of the convergence characteristics are also discussed.

240 citations

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TL;DR: In this article, a detailed overview of variational functions and their applications in photoionization and electron-molecule collisions is presented, as well as a detailed discussion of the numerical and computational procedures used in applications.

186 citations

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TL;DR: In this paper, an eikonal-Born-series approach is compared with the usual Glauber approximation, which is shown to be seriously deficient, and applications are made to the elastic scattering of electrons by atomic hydrogen and helium.

Abstract: We analyze elastic electron-atom scattering at intermediate and high energies by combining the Born series and eikonal series to get a consistent picture of the scattering amplitude through order ki-2. Our eikonal-Born-series approach is compared with the usual Glauber approximation, which is shown to be seriously deficient. We also discuss the Schwinger variational principle, exchange effects, and forward dispersion relations. Applications are made to the elastic scattering of electrons by atomic hydrogen and helium. The agreement between our results and the experimental data is very good. © 1973 The American Physical Society.

114 citations

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TL;DR: The Schwinger multichannel method as discussed by the authors was designed to account for exchange, polarization and electronically multi-channel coupling effects in the low-energy region of electron scattering from molecules with arbitrary geometry.

Abstract: The Schwinger multichannel method [K. Takatsuka and V. McKoy, Phys. Rev. A 30, 1734 (1984)], which is based on the Schwinger variational principle for the scattering amplitude [J. Schwinger, Phys. Rev. 72, 742 (1947)], was designed to account for exchange, polarization and electronically multichannel coupling effects in the low-energy region of electron scattering from molecules with arbitrary geometry. The applications of the method became more ambitious with the availability of computer power combined with parallel processing, use of norm-conserving pseudopotentials and improvement of the description of target excited states (minimal orbital basis for single configuration interaction). The most recent applications involving 33 and 45 electronically open channels for phenol and ethylene molecules, represent good examples of the present status of the method. In this colloquium, we review the strategy and point out new directions to apply the method in its full extension.

98 citations

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01 Oct 1976TL;DR: In this article, a new approach to the scattering of electromagnetic radiation by dielectric scatterers and application of it to the case of scattering by homogeneous spheroidal and ellipsoidal raindrops is presented.

Abstract: A new approach to the scattering of electromagnetic radiation by dielectric scatterers and application of it to the case of scattering by homogeneous spheroidal and ellipsoidal raindrops is presented. We transform the (singular) integral equation for the scattering into an integral equation for the Fourier transform of the internal field, which has a nonsingular kernel. This equation is solved by reducing it by quadrature into a set of algebraic equations. The scattering amplitude so obtained is shown to satisfy the Schwinger variational principle, and the method is thus both numerically stable and known to be convergent. We present sample calculations for spheres, for spheroids, and for ellipsoids.

89 citations