Quantum Theory of High-Energy Ion-Atom Collisions: 1st Edition (Hardback) book cover

Quantum Theory of High-Energy Ion-Atom Collisions

1st Edition

By Dzevad Belkic

CRC Press

432 pages | 71 B/W Illus.

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pub: 2008-11-13
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Suitable for graduate students, experienced researchers, and experts, this book provides a state-of-the-art review of the non-relativistic theory of high-energy ion-atom collisions. Special attention is paid to four-body interactive dynamics through the most important theoretical methods available to date by critically analyzing their foundation and practical usefulness relative to virtually all the relevant experimental data.

Fast ion-atom collisions are of paramount importance in many high-priority branches of science and technology, including accelerator-based physics, the search for new sources of energy, controlled thermonuclear fusion, plasma research, the earth’s environment, space research, particle transport physics, therapy of cancer patients by heavy ions, and more.

These interdisciplinary fields are in need of knowledge about many cross sections and collisional rates for the analyzed fast ion-atom collisions, such as single ionization, excitation, charge exchange, and various combinations thereof. These include two-electron transitions, such as double ionization, excitation, or capture, as well as simultaneous electron transfer and ionization or excitation and the like—all of which are analyzed in depth in this book.

Quantum Theory of High-Energy Ion-Atom Collisions focuses on multifaceted mechanisms of collisional phenomena with heavy ions and atoms at non-relativistic high energies.

Table of Contents

Basic Notions and Main Observables in Scattering Problems

Observables and elementary processes

Energy as the most important physical property

Classification of collisions

The role of wave packets

Adiabatic switching of interaction potentials

Collimation of beams of projectiles

General waves and quantum mechanical waves

Probability character of quantum collisions

Requirements of the Theory for the Experiment

Elementary events versus multiple scatterings

Average probabilities

Total cross sections

Differential cross sections

Total probabilities

Transmission phenomena

Quantum mechanical currents and cross sections

Continuous Spectrum and Eigen-Problems of Resolvents

Completeness and separability of Hilbert spaces

The key realizations of abstract vector spaces

Isomorphism of vector spaces

Eigen-problems for continuous spectra

Normal and Hermitean operators

Strong and weak topology

Compact operators for mapping of weak to strong limits

Strong differentiability and strong analyticity

Linear and Bilinear Functionals

Linear functionals for mapping between vector spaces and scalar fields

The Ries–Freshe theorem

Bilinear functionals

Definition of a Quantum Scattering Event

Hamiltonian operators and boundedness

Evolution operators and Møller wave operators

The Cauchy strong limit in non-stationary scattering theory

Three criteria for a quantum collisional system

The Adiabatic Theorem and the Abel Strong Limit

Adiabatic theorem for scattering states

Adiabatic theorem and existence of wave operators

The Abel strong limit in stationary scattering theory

Exponential screening of potentials and adiabatic theorem

Adiabatic theorem and Green operators

Adiabatic theorem and Lippmann–Schwinger equations

Non-Stationary and Stationary Scattering via Strong Limits

The Abel limit and Lippmann–Schwinger equations

The Abel limit and Fourier integrals

Scattering Matrix and Transition Matrix

Abel limit and scattering operators

Matrix elements of scattering operators

Transition operators

Spectral Analysis of Operators

The Abel limit with no recourse to the Cauchy limit

The spectral theorem

Unitary operators and strong topology

The Abel limit for Møller wave operators

The link between Møller operators and Green resolvents

The Existence and Completeness of Møller Wave Operators

Linearity and isometry of wave operators

Boundedness of wave operators in the whole Hilbert space

The Schur lemma on invariant subspaces for evolution operators

Intertwining relations for evolution and wave operators

The role of spectral projection operators

Completeness of Møller wave operators

Scattering operator derived from intertwining wave operators

Four-Body Theories for Fast Ion-Atom Collisions

Main features of interactive four-body dynamics

Notation and basic formulae

The entrance channel

The exit channels

Perturbation Series with the Correct Boundary Conditions

Lippmann–Schwinger equations

Born expansions with the correct boundary conditions for four-body collisions

The Dodd–Greider Series for Four-Body Collisions

Derivation of the distorted waves for the initial states

Double Electron Capture

The CDW-4B method

The SE-4B method

The CDW-EIS-4B method

The CDW-EFS-4B method

The BDW-4B method

The BCIS-4B method

The CB1-4B method

Comparison between theories and experiments

Simultaneous Transfer and Ionization

The CDW-4B method

Comparison between theories and experiments

Single Electron Detachment

The MCB-4B method

Comparison between theories and experiments

Single Electron Capture

The CDW-4B method

The CDW-BFS (prior BDW-4B) and CDW-BIS (post BDW-4B method)

Simultaneous Transfer and Excitation

The CDW-4B method for the TE process

The TEX mode for radiative decays of asymmetric systems

The CDW-4B method for TEX modes

The CDW-4B method for the TE process in asymmetric collisions

Target charge ZT and the interference between RTEX and NTEX modes

The TEA mode for nearly symmetrical systems: the Auger decay

The CDW-4B method for TEA modes

Description of the final state

Cross sections for TEA modes

The CDW-4B method in the Feshbach resonance formalism

Comparison between theories and experiments for electron spectra near Auger peaks

Concluding Remarks and Outlooks

List of acronyms in the main text and bibliography



Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mathematical Physics
SCIENCE / Quantum Theory
SCIENCE / Molecular Physics