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X-ray interactions with matter

David M. Paganin

in Coherent X-Ray Optics

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198567288
eISBN:
9780191717963
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567288.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter considers the interactions of X-rays with matter. It opens by developing X-ray wave equations in the presence of scatterers, taking the Maxwell equations as a starting point. The ... More


LATTICE DYNAMICS

A.M. Stoneham

in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507802
eISBN:
9780191709920
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507802.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the key approximations in crystal lattice dynamics in a way that is particularly helpful for defect studies. It discusses the Born-Oppenheimer approximation, the adiabatic ... More


The theory of Compton scattering

W. Schülke

in X-Ray Compton Scattering

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198501688
eISBN:
9780191718045
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198501688.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter deals with the theory of the double differential photon scattering cross-section in both non-relativistic and relativistic treatments. It shows how the Impulse Approximation leads to a ... More


Particle collisions

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0013
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter looks at problems that deal with the Born approximation; scattering theory (partial-wave analysis); low-energy scattering (resonant scattering); scattering of fast particles (Eikonal ... More


Superconducting Alloys

Nikolai B. Kopnin

in Theory of Nonequilibrium Superconductivity

Published in print:
2001
Published Online:
January 2010
ISBN:
9780198507888
eISBN:
9780191709722
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507888.003.04
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains how to incorporate scattering by random impurity atoms into the general Green function formalism of the theory of superconductivity. The cross-diagram technique based on the ... More


The MUSIC algorithm and scattering by an inhomogeneous medium

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter examines the case of a penetrable scatterer with an index of refraction that can be space-dependent and is assumed to be different from the constant background index. The inverse ... More


Transport equations for the one-body density

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0021
Subject:
Physics, Nuclear and Plasma Physics

This chapter begins by calculating the Wigner transform for the von Neumann equation for the one-body density operator. It shows how the Liouville equation follows in leading order in an expansion to ... More


Lewis’ “cubical atom” model. Molecular orbital calculations on the one-electron molecule H 2 + and the two-electron molecule H2

Arne Haaland

in Molecules and Models: The molecular structures of main group element compounds

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199235353
eISBN:
9780191715594
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235353.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter reviews G. N. Lewis' seminal paper of 1916 that introduced the concept of the electron-pair bond. The potential energy curves for the two lowest electronic states of the hydrogen ... More


Multiple Impurity Scattering

Klaus Morawetz

in Interacting Systems far from Equilibrium: Quantum Kinetic Theory

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198797241
eISBN:
9780191838743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797241.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

Furnished with basic ideas about the scattering on a single impurity, the motion of a particle scattered by many randomly distributed impurities is approached. In spite of having a single particle ... More


π-electron theories of conjugated polymers

William Barford

in Electronic and Optical Properties of Conjugated Polymers

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199677467
eISBN:
9780191757402
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199677467.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

Semi-empirical π‐electron theories of conjugated polymers are introduced, starting from the fundamentals of the Born-Oppenheimer approximation and sp-hybridization. The models described include the ... More


Introduction

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized ... More


Hamiltonians and solution techniques

Sandip Tiwari

in Semiconductor Physics: Principles, Theory and Nanoscale

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198759867
eISBN:
9780191820830
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198759867.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

Chapter 1 introduces several of the common principles, techniques and approximations that will be employed throughout the text. Classically, the Hamiltonian is the sum of kinetic energy and potential ... More


Adiabatic approximation

Jeffrey A. Cina

in Getting Started on Time-Resolved Molecular Spectroscopy

Published in print:
2022
Published Online:
April 2022
ISBN:
9780199590315
eISBN:
9780191747601
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199590315.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter spells out the description of molecular structure and dynamics in terms of the adiabatic or Born-Oppenheimer approximation. Adiabatic electronic eigenstates are defined using a unitary ... More


Scattering in three dimensions

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses scattering in three spatial dimensions. It introduces the concepts of the scattering amplitude and cross-section. The chapter discusses the Born approximation and how to ... More


Molecules

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0027
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses some elementary molecular physics. Its goal is to understand the reason why neutral atoms form aggregates, that is, molecules, solids, and the matter which we see around us. ... More


The Schrödinger Equation in the Presence of Fields

Stephan P. A. Sauer

in Molecular Electromagnetism: A Computational Chemistry Approach

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199575398
eISBN:
9780191775109
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575398.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamiltonian for the electronic Schrödinger equation of a molecule in the presence of external and internal static electric or magnetic fields. It starts off with the ... More


Nuclear motion

Carsten A. Ullrich

in Time-Dependent Density-Functional Theory: Concepts and Applications

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199563029
eISBN:
9780191775130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199563029.003.0017
Subject:
Physics, Condensed Matter Physics / Materials

This chapter focuses on the coupling of electron dynamics and nuclear motion. In principle, electronic and nuclear degrees of freedom both have to be treated quantum mechanically and on an equal ... More


Density-Functional Theory

Jürgen Kübler

in Theory of Itinerant Electron Magnetism, 2nd Edition

Published in print:
2021
Published Online:
October 2021
ISBN:
9780192895639
eISBN:
9780191915833
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895639.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The atomic and electronic degrees of freedom for a crystalline solid are separated using the Born–Oppenheimer approximation. The Hartree–Fock approximation is then applied to the electronic problem, ... More


Scattering in Classical and Quantum Physics

J. Iliopoulos and T.N. Tomaras

in Elementary Particle Physics: The Standard Theory

Published in print:
2021
Published Online:
December 2021
ISBN:
9780192844200
eISBN:
9780191926983
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192844200.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Scattering experiments provide the main source of information on the properties of elementary particles. Here we present the theory of scattering in both classical and non-relativistic quantum ... More


Scattering of Electromagnetic Radiation in Materials

Richard Freeman, James King, and Gregory Lafyatis

in Electromagnetic Radiation

Published in print:
2019
Published Online:
February 2019
ISBN:
9780198726500
eISBN:
9780191793325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198726500.003.0011
Subject:
Physics, Atomic, Laser, and Optical Physics

The formulation of generalize electromagnetic scattering is given. Previously derived multipole expansions using the language of scattering are presented and applied to resonant and plasmon ... More


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