Quantum Theory of High-Energy Ion-Atom Collisions (Hardcover)

Basic Notions and Main Observables in Scattering ProblemsObservables and elementary processesEnergy as the most important physical propertyClassification of collisionsThe role of wave packetsAdiabatic switching of interaction potentialsCollimation of beams of projectilesGeneral waves and quantum mechanical wavesProbability character of quantum collisions Requirements of the Theory for the ExperimentElementary events versus multiple scatteringsAverage probabilitiesTotal cross sectionsDifferential cross sectionsTotal probabilitiesTransmission phenomenaQuantum mechanical currents and cross sectionsContinuous Spectrum and Eigen-Problems of ResolventsCompleteness and separability of Hilbert spacesThe key realizations of abstract vector spacesIsomorphism of vector spacesEigen-problems for continuous spectraNormal and Hermitean operatorsStrong and weak topologyCompact operators for mapping of weak to strong limitsStrong differentiability and strong analyticityLinear and Bilinear FunctionalsLinear functionals for mapping between vector spaces and scalar fieldsThe Ries?Freshe theoremBilinear functionalsDefinition of a Quantum Scattering EventHamiltonian operators and boundednessEvolution operators and Møller wave operatorsThe Cauchy strong limit in non-stationary scattering theoryThree criteria for a quantum collisional systemThe Adiabatic Theorem and the Abel Strong LimitAdiabatic theorem for scattering statesAdiabatic theorem and existence of wave operatorsThe Abel strong limit in stationary scattering theoryExponential screening of potentials andadiabatic theoremAdiabatic theorem and Green operatorsAdiabatic theorem and Lippmann?Schwinger equationsNon-Stationary andStationary Scattering via Strong LimitsThe Abel limit and Lippmann?Schwinger equationsThe Abel limit and Fourier integralsScattering Matrix and Transition MatrixAbel limit and scattering operatorsMatrix elements ofscattering operatorsTransition operatorsSpectral Analysis of OperatorsThe Abel limit with no recourse to the Cauchy limitThe spectral theoremUnitary operators and strong topologyThe Abel limit for Møller wave operatorsThe link between Møller operators and Green resolventsThe Existence and Completeness of Møller Wave OperatorsLinearity and isometry of wave operatorsBoundedness of wave operators in the whole Hilbert spaceThe Schur lemma on invariant subspaces for evolution operatorsIntertwining relations for evolution and wave operatorsThe role of spectral projection operatorsCompleteness of Møller wave operatorsScattering operator derived from intertwining wave operatorsFour-Body Theories for Fast Ion-Atom Collisions Main features of interactive four-body dynamics Notation and basic formulae The entrance channel The exit channelsPerturbation Series with theCorrect Boundary Conditions Lippmann?Schwinger equations Born expansions with the correct boundary conditions for four-body collisionsThe Dodd?Greider Series for Four-Body CollisionsDerivation of the distorted waves for the initial statesDouble Electron CaptureThe 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 experimentsSimultaneous Transfer and IonizationThe CDW-4B method Comparison between theories and experiments Single Electron Detachment The MCB-4B method Comparison between theories and experiments Single Electron CaptureThe CDW-4B methodThe CDW-BFS (prior BDW-4B) and CDW-BIS (post BDW-4B method) Simultaneous Transfer and ExcitationThe 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 collisionsTarget 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