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Preface
Introduction
Scope and Results
Prerequisites and Organization of the Book
Many-Body Schrödinger Operators, Conditions and Notation
Regular upper NN-Body Schrödinger Operators
Principal Example, Dynamical Nuclei
upper NN-Body Schrödinger Operators with Infinite Mass Nuclei
Principal Example, Fixed Nuclei
Generalized upper NN-Body Schrödinger Operators
Spaces, PsDOs and Notation
Reduction to a One-Body Problem
An Abstract Reduction Scheme
Non-multiple Two-Cluster Threshold Case
Multiple Two-Cluster Threshold, script upper F 1 intersection script upper F 2 equals StartSet 0 EndSetmathcalF1capmathcalF2={0}
script upper F 1 intersection script upper F 2 equals StartSet 0 EndSetmathcalF1capmathcalF2={0} the Case lamda 0 equals normal upper Sigma 2λ0=Σ2 and lamda 0 not an element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0-.25ex-.25ex-.25ex-.25exσpp(H')
The Case lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H')
lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H') Non-multiple Case
lamda 0 element of sigma Subscript p p Baseline left parenthesis upper H prime right parenthesisλ0inσpp(H') Multiple Case
Multiple Two-Cluster Case, script upper F 1 intersection script upper F 2 not equals StartSet 0 EndSetmathcalF1capmathcalF2neq{0}
script upper F 1 intersection script upper F 2 not equals StartSet 0 EndSetmathcalF1capmathcalF2neq{0} a General Approach
Spectral Analysis of upper H primeH' Near lamda 0λ0
Mourre Estimate
Proof of Proposition 4.3
Multiple Commutators and Calculus
Computing a Commutator
Positive Commutator Estimates
A Rellich-Type Theorem
LAP Bound
Microlocal Bounds and LAP
Rellich-Type Theorems
The Case lamda 0 equals normal upper Sigma 2λ0=Σ2
Extended Eigentransform for lamda 0 equals normal upper Sigma 2λ0=Σ2
Attractive Slowly Decaying Effective Potentials
Repulsive Slowly Decaying Effective Potentials
Homogeneous Degree negative 2-2 Effective Potentials
The Case lamda 0 greater than normal upper Sigma 2λ0&gtΣ2
Extended Eigentransform for lamda 0 greater than normal upper Sigma 2λ0&gtΣ2
Attractive Slowly Decaying Effective Potentials
Repulsive Slowly Decaying Effective Potentials
Homogeneous Degree negative 2-2 Effective Potentials
Physical Models
Resolvent Asymptotics Near a Two-Cluster Threshold
Very Short-Range Effective Potentials
Two-Cluster Threshold Resonances
Resolvent Asymptotics Near the Lowest Threshold
Resolvent Asymptotics Near Higher Two-Cluster Thresholds
Repulsive Slowly Decaying Effective Potentials
Resolvent Asymptotics for Physical Models Near Two-Cluster Thresholds
Elastic Scattering at a Threshold
Sommerfeld's Theorem, Attractive Slowly Decaying Effective Potentials
Elastic Scattering at lamda 0λ0, Attractive Slowly Decaying Effective Potentials
Scattering for the One-Body Problem at Zero Energy
Elastic Scattering for the upper NN-Body Problem at lamda 0λ0
Elastic Scattering at lamda 0λ0, a `Geometric' Approach
Elastic Scattering at normal upper Sigma 2Σ2
Scattering for Physical Models at a Two-Cluster Threshold, Case script upper A overTilde equals script upper A 1widetildemathcalA=mathcalA1
Effective script upper O left parenthesis r Superscript negative 2 Baseline right parenthesismathcalO(r-2) Potentials, Atom–Ion Case
Non-transmission at a Threshold for Physical Models
Criteria for Non-transmission
Proof of (8.3), Case (I)
Proof of (8.3), Case (II)
Proof of (8.3), Case (III)
An Example of Transmission
Threshold Behaviour of Cross-Sections in Atom–Ion Scattering
Finiteness of Total Cross-Sections in Atom–Ion Scattering
Total Cross-Sections at normal upper Sigma 2Σ2, Non-multiple Two-Cluster Case
Total Cross-Sections at normal upper Sigma 2Σ2, Multiple Two-Cluster Case
Appendix Bibliography
Index