Frame-transformation approximation for low-energy e−–1Σ+systems using the non-iterative integral equation method

1977 ◽  
Vol 55 (5) ◽  
pp. 442-451 ◽  
Author(s):  
Charles A. Weatherford ◽  
Ronald J. W. Henry
Keyword(s):  
Integral Equation ◽  
Cross Sections ◽  
Vibrational Excitation ◽  
Integral Equation Method ◽  
Laboratory Frame ◽  
The Body ◽  
Low Energy ◽  
Body Frame ◽  
Close Coupling ◽  
Frame Transformation

A discussion of the frame-transformation approximation appropriate for prediction of rotational and vibrational excitation cross sections for low-energy e−–1Σ+ systems is described. Explicit quantum number parameterizations of the time-independent Hamiltonian for both the body frame and the laboratory frame are given. A dynamical frame-transformation technique is described within the computational framework of the non-iterative, integral equation solution to the close-coupling scattering equations.

An integral-equation method for determining the fluid motion due to a cylinder heaving on water of finite depth

1980 ◽  
Vol 372 (1748) ◽  
pp. 93-110 ◽  
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Integral Equations ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Finite Depth ◽  
The Body ◽  
Wave Source ◽  
Method Of Integral Equations ◽  
Infinite Set

The method of integral equations is used here to calculate the virtual mass of a half-immersed cylinder heaving periodically on water of finite constant depth. For general sections this method is more appropriate than the method of multipoles; particular sections that are considered are the circle and the ellipse. Green’s theorem is applied to the potential and to a fundamental solution (wave source) satisfying the conditions at the free surface, at the bottom and at infinity, but not necessarily on the body. An integral equation for the potential on the body only is thus obtained. For the simplest choice of fundamental solution the method breaks down at a discrete infinite set of frequencies, as is well known. When the fundamental solution was modified, however, a different integral equation could be obtained for the same unknown function and this was found not to break down for the circle and ellipse. The present numerical results are in good agreement with those obtained by the method of multipoles which for the circle is more efficient than the method of integral equations but which is not readily applicable to other sections. Much effort now goes into such calculations.

scholarly journals Resonant excitation of molecules by low-energy electrons

2008 ◽  
Vol 6 (1) ◽  
pp. 41-55 ◽  
Author(s):  
Goran Poparic
Keyword(s):  
Cross Sections ◽  
Valence State ◽  
Vibrational Excitation ◽  
Rydberg States ◽  
Low Energy ◽  
Resonant Excitation ◽  
Excitation Spectra ◽  
Energy Excitation ◽  
The Cross ◽  
Near Threshold

Low-energy electron impact vibrational and electronic excitation cross sections of the CO, N2 and CO2 molecules are measured by use of a high resolution crossed-beams double trochoidal electron spectrometer. The spectrometer is designed to work in standard and time-of-flight regimes. The energy dependences of the resonant vibrational excitation of the first several vibrational levels of the N2, CO, and CO2 molecules, have been measured. Characteristic substructures in energy excitation spectra in the cases of N2 and CO have been obtained and discussed for some vibrational channels for the first time. The ratio of forward-to-backward scattered electrons from the 2? resonance in CO is found to be equal to 1, and thus the angular distribution of scattered electrons to be symmetric relative to 90?. This conclusion supports the fact that the contribution of the p? partial wave is dominant in the energy region of the 2? resonance in CO. The energy dependences of the near threshold resonant excitation of the valence and Rydberg states of the N2 and CO molecules have been measured. The cross sections of the near threshold resonant excitation of the C 3?u valence state, and the E 3?+ g and a'' 1?+ g Rydberg states of the N2 molecule have been measured. In the case of the CO molecule, the cross sections of the near threshold resonant excitation of the a 3? valence state, and the b 3?+ and B 1?+ Rydberg states have been measured. Resonant structures in excitation functions of all measured electronic states are observed and their locations are compared with resonances obtained in different decay channels.

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