Vladimir S. Lebedev

Physics of highly excited atoms and ions

1. Introduction.- 1.1 Physical Properties and Features of Rydberg Atoms and Ions.- 1.2 Scope of the Book.- 2. Classical and Quantum Description of Rydberg Atom.- 2.1 Classical Motion in a Coulomb Field.- 2.1.1 Orbital Electron Motion.- 2.1.2 Action Variables.- 2.2 Wave Functions: Coordinate Representation.- 2.2.1 Quantum Wave Function of Hydrogen-like States.- 2.2.2 JWKB Approximation.- 2.2.3 Semiclassical Approach in Action Variables.- 2.3 Wave Functions: Momentum Representation.- 2.3.1 Hydrogenlike Wave Functions.- 2.3.2 Momentum Wave Functions with Quantum Defect.- 2.4 Density Matrix and Distribution Function.- 2.4.1 Classical Distribution Functions.- 2.4.2 Coulomb Greens Function.- 2.4.3 Density Matrix.- 2.4.4 Wigner Function.- 3. Radiative Transitions and Form Factors.- 3.1 Probabilities of Radiative Transitions.- 3.1.1 General Formulas.- 3.1.2 Semiclassical and Asymptotic Approaches.- 3.1.3 Summed over Angular Quantum Numbers Line Strength. Kramers Approximation.- 3.2 Photoionization and Photorecombination.- 3.2.1 General Formulas.- 3.2.2 Asymptotic Approach.- 3.2.3 Kramers Formulas and Gaunt Factor.- 3.3 Transition Form Factors.- 3.3.1 General Formulas.- 3.3.2 n-n? Transitions: Quantum Expressions.- 3.3.3 n-n? Transitions: Asymptotic Expressions.- 3.3.4 nl - nl? Transitions: Semiclassical Expressions.- 3.3.5 Classical Approach.- 3.3.6 Angular Factors for Complex Atoms.- 4. Basic Approaches to Collisions Involving Highly Excited Atoms and Ions.- 4.1 Formulation of Problem.- 4.1.1 Features of Collisions with Neutral and Charged Particles.- 4.1.2 Stationary Problem of Scattering.- 4.2 Born Approximation: Momentum Representation.- 4.3 Time-Dependent Approach: Impact-Parameter Representation.- 4.3.1 Close Coupled Equations for Transition Amplitudes.- 4.3.2 Normalized Perturbation Theory.- 4.3.3 Connection with Momentum Transfer Representation.- 4.4 Semiclassical Approach in Action Variables.- 4.4.1 Classical Perturbation Theory.- 4.4.2 Relation between Classical and Quantum Values.- 4.4.3 Model of Equidistant Levels and Correspondence Principle for S-Matrix.- 4.5 Impulse Approximation Approach.- 4.5.1 Quantum Impulse Approximation.- 4.5.2 Binary Encounter Approach.- 5. Collisions of Rydberg Atom with Neutral Particles: Weak-Coupling Models.- 5.1 Quasi-free Electron Model.- 5.2 Scattering of Ultra-Slow Electrons by Atoms and Molecules.- 5.2.1 Electron-Atom Scattering.- 5.2.2 Electron-Molecule Scattering.- 5.3 Semiclassical Theory: Impact-Parameter Approach with Fermi Pseudopotential.- 5.3.1 Historical Sketch.- 5.3.2 Probabilities of the nl J ? n?l? J? and nl ? n?l? Transitions.- 5.3.3 Binary-Encounter Theory: nl ? n? and n ? n? Transitions.- 5.4 Impulse Approximation for Rydberg Atom-Neutral Collisions.- 5.4.1 Introductory Remarks.- 5.4.2 Fast and Slow Collisions.- 5.4.3 Cross Sections of Slow Collisions: General Expressions.- 5.4.4 Expressions Through the Form Factors and Scattering Length Approximation.- 5.4.5 Total Scattering Cross Section.- 5.4.6 Resonance on Quasi-discrete Level.- 5.4.7 Validity Criteria of Quasi-free Electron Model and Impulse Approximation.- 6. Elementary Processes Involving Rydberg Atoms and Neutral Particles: Effects of Electron-Projectile Interaction.- 6.1 Classification of Processes and Theoretical Treatments.- 6.2 Transitions between the Fine-Structure Components and Elastic Scattering.- 6.2.1 Weak Coupling Limit.- 6.2.2 Extension to Strong-Coupling Region.- 6.3 Orbital Angular Momentum and Energy Transfer: l-Mixing and n, l-Changing Processes.- 6.3.1 Semiclassical Unitarized Approach to Inelastic nl ? n? Transitions.- 6.3.2 Quasi-elastic Limit: l-Mixing Process.- 6.3.3 Effective Scattering Length.- 6.3.4 Scaling Laws.- 6.4 Ionization of Rydberg Atom by Atomic Projectile.- 6.5 Quenching of Rydberg States: Thermal Collisions with Atoms.- 6.5.1 Collisions with Rare Gas Atoms.- 6.5.2 Collisions with Alkali-Metal Atoms.- 6.6 Quenching and Ionization of Rydberg States: Thermal Collisions with Molecules.- 6.6.1 Quasi-resonant Energy Exchange of Rydberg Electron with Rotational Motion of Molecule.- 6.6.2 Ion-Pair Formation and Charge Transfer: Collision of Rydberg Atom with Electron-Attaching Molecule.- 7. Effects of Ion Core in Rydberg Atom-Neutral Collisions.- 7.1 Mechanisms of Perturber-Core Scattering.- 7.2 Separated-Atoms Approach: Shake-Up Model.- 7.2.1 General Treatment.- 7.2.2 Dipole Approximation.- 7.3 Quasi-molecular Approach: Basic Assumptions.- 7.4 Exchange of Rydberg Electron Energy with Translational Motion of Atoms.- 7.4.1 Matrix Elements of Transitions within One Electronic Term of Quasi-molecular Ion.- 7.4.2 Cross Sections of De-excitation and Ionization.- 7.4.3 Collisions of Highly Excited Hydrogen with Helium.- 7.5 Resonant Excitation and Ionization.- 7.5.1 Exchange of Electron Energy in Quasi-molecule.- 7.5.2 Dipole Transitions Between Symmetrical and Antisymmetrical Terms.- 7.5.3 Quadrupole Transitions in Nonsymmetrical Collisions of Rare Gas Atoms.- 8. Inelastic Transitions Induced by Collisions of Rydberg Atom (Ion) with Charged Particles.- 8.1 Basic Problems.- 8.2 n-Changing Transitions.- 8.2.1 Classical Approach.- 8.2.2 Born Approximation.- 8.2.3 Semiclassical Approach.- 8.2.4 Coulomb-Born Approximation.- 8.3 l-Changing Transitions.- 8.3.1 Born Approximation.- 8.3.2 Close Coupling Method.- 8.3.3 Method of Effective Magnetic Field.- 8.3.4 Fitting Formulas.- 8.3.5 Comparison with Experiment.- 9. Spectral-Line Broadening and Shift.- 9.1 Classical and Quantum Treatments of Impact Broadening.- 9.1.1 Impact-Parameter Method.- 9.1.2 Quantum Formulas.- 9.2 Theory of Width and Shift of Rydberg Levels in Gas.- 9.2.1 Mechanism of Core-Perturber Scattering.- 9.2.2 Mechanism of Electron-Perturber Scattering.- 9.3 Comparison of Theory with Experiment.- 9.3.1 Broadening and Shift in Rare Gases.- 9.3.2 Broadening and Shift in Alkali-Metal Vapors.- 9.4 Broadening of n - n? Lines in a Plasma.- List of Symbols.- References.

Separating codes and a new combinatorial search model

We propose a new group testing model, which is related to separating codes and cover-free codes.

Photodissociative absorption by H 2 + in the solar photosphere

Photoabsorption by systems of hydrogen atoms and protons in the solar photosphere is studied. Analytical formulas for the partial cross sections for photodissociation of the H2+ molecular ion are derived for the cases of fixed vibrational-rotational energy levels and averaging over a Boltzmann distribution for a given temperature. The photoabsorption coefficients for bound-free and free-free transitions of H-H+ in the solar photosphere are calculated. These are compared with the absorption coefficients for photo-ejection of an electron from a negative hydrogen ion H− and free-free transitions of an electron in the field of a hydrogen atom H. Results can be applied to the Sun and hotter stars.

Bounds for threshold and majority group testing

We consider two generalizations of group testing: threshold group testing (introduced by Damaschke [8]) and majority group testing (a further generalization, including threshold group testing and a model introduced by Lebedev [15]).

The phylogeny and systematics of the endemic Ethiopian Lophuromys flavopunctatus species complex based upon random amplified polymorphic DNA (RAPD) analysis

Abstract Random amplified polymorphic DNA (RAPD) analysis was performed to clarify systematics and phylogenetic relationships within the Ethiopian endemic representatives of Lophuromys flavopunctatus species complex. Data were analysed by both phenetic (UPGMA) and phylogenetic (neighbor-joining (NJ) and maximum parsimony) procedures. NJ and maximum parsimony analyses yielded identical phylogenetic trees that demonstrate the basal position of L. melanonyx with L. brevicaudus splitting next and sister-group relationship for L. brunneus–L. chrysopus. This phylogenetic pattern is congruent with inferences from allozymes for the considered species suggesting early divergence of Afroalpine species and recent origin of forest taxa. Thus, the results demonstrate that RAPD-PCR might be a useful technique for phylogenetic analysis at the species levels in vertebrates. Controversial taxonomy of L. brevicaudus, L. brunneus and L. chrysopus is clarified, with their specific ranks confirmed on the basis of tree topology and genetic distances.

Finding one of D defective elements in some group testing models

In contrast to the classical goal of group testing, we consider the problem of finding m defective elements out of D (m ≤ D). We analyze two different test functions. We give adaptive strategies and present lower bounds for the number of tests and show that our strategy is optimal for m = 1.

Group testing problem with two defectives

AbstractWe consider the classical (2,N) group testing problem, i.e., the problem of finding two defectives among N elements. We propose a new adaptive algorithm such that for

A Combinatorial Model of Two-Sided Search

N = \left\lfloor {2\tfrac{{t + 1}} {2} - t \cdot 2\tfrac{t} {4}} \right\rfloor

Shadows under the word-subword relation

the problem can be solved in t tests.

Majority group testing with density tests

We study a new model of combinatorial group testing in a network. An object the target occupies an unknown node in the network. At each time instant, we can test or query a subset of the nodes to learn whether the target occupies any of such nodes. Unlike the case of conventional group testing problems on graphs, the target in our model can move immediately after each test to any node adjacent to each present location. The search finishes when we are able to locate the object with some predefined accuracy s a parameter fixed beforehand, i.e., to indicate a set of s nodes that include the location of the object. In this paper we study two types of problems related to the above model: i what is the minimum value of the accuracy parameter for which a search strategy in the above sense exists; ii given the accuracy, what is the minimum number of tests that allow to locate the target. We study these questions on paths, cycles, and trees as underlying graphs and provide tight answer for the above questions. We also considered a restricted variant of the problem, where the number of moves of the target is bounded.