Belkic Quantum Theory of High-Energy Ion-Atom Collisions

1. Auflage 2010
ISBN: 978-1-58488-729-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 432 Seiten

One of the Top Selling Physics Books according to YBP Library Services
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.

Zielgruppe

Researchers and graduate students in chemistry and atomic and computational physics.

Autoren/Hrsg.

Belkic, Dzevad

Fachgebiete

• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

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

References

Index