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A Variational Calculation of the Elastic: Scattering of Electrons, by Hydrogen Atoms (Classic Reprint) - Tapa blanda
Sinopsis
Explore a practical approach to electron-hydrogen collisions using a variational lens that clarifies cross-section calculations. This work applies Schwinger’s variational expression to elastic scattering, showing how Born trial fields can make complex integrals tractable and improve results over the ordinary Born approximation at low energies.
This edition discusses how a static Hartree field, as well as the full Green’s function, affect scattering amplitudes. It reveals how higher atomic states and the continuum contribute to polarization phenomena during collisions, and it compares variational results with exact calculations to demonstrate accuracy and limits. The text also outlines the mathematical foundation, the treatment of exchange and polarization, and the practical steps to evaluate multi-dimensional integrals involved in the method.
- Foundations of the Schwinger variational method for scattering problems.
- How Born trial fields simplify the calculation of cross-sections at low energies.
- The roles of excited states and the continuum in elastic scattering.
- A comparison of variational results with exact and Born approximations.
Ideal for readers of advanced atomic physics and researchers exploring collision theory and cross-section calculations.
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Excerpt from A Variational Calculation of the Elastic: Scattering of Electrons, by Hydrogen Atoms
One of the important problems of upper atmospheric and astrophysical research is the determination of the frequencies of collisions between electrons and atomic systems. Informa tion on this subject can be obtained from a knowledge of the total cross-section, Q, and to some extent from the differential cross-section, (hg), of the collision.
The temperatures at which these collisions occur are of such a magnitude that the electron energies are of the order of a fraction of an electron volt, and at these low energies the problems associated with experimental determinations of the cross-sections become complex. Consequently there is a deficiency of experimental data. It is therefore essential to have theoretical methods for calculating the cross-sections.
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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from A Variational Calculation of the Elastic: Scattering of Electrons, by Hydrogen Atoms
A Variational Calculation of the Elastic: Scattering of Electrons, By Hydrogen Atoms was written by Howard Boyet and Sidney Borowitz. This is a 68 page book, containing 9256 words and 11 pictures. Search Inside is enabled for this title.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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A Variational Calculation of the Elastic: Scattering of Electrons
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: New. Print on Demand. This book contributes to the study of elastic scattering of electrons by hydrogen atoms (a topic of great importance to astrophysics and upper atmospheric research) offering a variational method for calculating cross sections using Schwinger's variational expression for the direct elastic scattered amplitude. In particular, it applies the method to hydrogen atoms in the energy range 0-10 volts, which is a range currently lacking in experimental data. The methods employed in this book resolve the issue of evaluating the integrals inherent in Schwinger's variational method (which had previously made such calculations difficult) by using Born trial fields. The results of the calculations provide valuable insights into the contributions of the excited states and the continuum to the elastic scattering, and reveal the vital roles played by these factors in the polarization of the charge distribution. This book demonstrates the importance of properly accounting for the elastic effects of the atom's excited states and continuum, particularly in the absence of experimental data in this energy range. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332208982_0
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A Variational Calculation of the Elastic Scattering of Electrons, by Hydrogen Atoms Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332208982
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A Variational Calculation of the Elastic Scattering of Electrons, by Hydrogen Atoms Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781332208982
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