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Abstract
Recent years have seen tremendous progress in research on cold and controlled molecular collisions, both in theory and in experiment. The advent of techniques to prepare cold and ultracold molecules and ions, to store them in optical lattices or in charged quasicristalline structures, and to use them in crossed or merged beam experiments have opened many new possibilities to study the most fundamental aspects of molecular interactions. At the same time, theoretical work has made progress in tackling these problems and accurately describing quantum effects in complex systems, and in proposing viable options to control chemical reactions at ultralow energies. Through tutorials on both the theoretical and experimental aspects of research in cold and ultracold molecular collisions, this book provides advanced undergraduate students, graduate students and researchers with the foundations needed to understand this exciting field.
Andreas Osterwalder is a Senior Scientist at Ecole Polytechnique Fédérale de Lausanne, Switzerland, where he leads a team working on developing a merged beam technique to study neutral chemical reactions below 1K.
Olivier Dulieu is Research Director at Laboratoire Aimé Cotton, CNRS, France. His research interests include the theory of structure and dynamics of cold and ultracold neutral and ionic molecules, quantum chemistry, molecular spectroscopy and field-assisted dynamics.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero | i | ||
| Foreword | v | ||
| Preface | ix | ||
| Contents | xiii | ||
| Chapter 1 Low-temperature Chemistry in Uniform Supersonic Flows | 1 | ||
| 1.1 Introduction | 1 | ||
| 1.2 The CRESU Technique | 6 | ||
| 1.2.1 Uniform Supersonic Flows | 6 | ||
| 1.2.2 Kinetics Techniques in Combination with Uniform Supersonic Flows | 12 | ||
| 1.2.3 Limitations of the CRESU Technique | 15 | ||
| 1.3 Case Studies | 16 | ||
| 1.3.1 Radical–Radical Reactions: O + OH O2 + H | 17 | ||
| 1.3.2 Radical–Molecule Reactions—O(3P) + Alkenes | 18 | ||
| 1.3.3 Reactions with Barriers and the Roleof Tunnelling—The F + H2 Reaction | 22 | ||
| 1.3.4 Thermodynamics—The HO3 Radical | 25 | ||
| 1.3.5 Kinetics of Cluster Formation: Water Clusters (H2O)n | 28 | ||
| 1.3.6 Product Branching Studies at Low Temperatures—C2H + Butenes | 34 | ||
| 1.3.7 Product Branching Studies at Low Temperatures—The CPUF Technique | 36 | ||
| 1.4 Conclusion and Perspectives | 39 | ||
| References | 41 | ||
| Chapter 2 Cold Molecular Collisions: Quantum Scattering Calculations and Their Relevance in Astrophysical Applications | 46 | ||
| 2.1 Introduction | 46 | ||
| 2.2 Quantum Scattering Calculations | 48 | ||
| 2.2.1 Elastic and Inelastic Processes | 48 | ||
| 2.2.2 Born–Oppenheimer Approximation | 49 | ||
| 2.2.3 Center-of-mass Frame of Coordinates | 51 | ||
| 2.2.3.1 Classical Mechanics Framework | 51 | ||
| 2.2.3.2 Quantum Mechanics Framework | 52 | ||
| 2.2.4 Structure of the Hamiltonian, Scattering Equation, and Boundary Conditions | 53 | ||
| 2.2.5 Spectrum of the Monomer Hamiltonian | 55 | ||
| 2.2.6 Partial Wave Expansion and Scattering Matrix | 56 | ||
| 2.2.7 Solving Scattering Equations | 59 | ||
| 2.2.8 Decoupling Approximations | 62 | ||
| 2.2.9 Collisional Excitation of Non-linear and Open-shell Molecules | 63 | ||
| 2.2.9.1 Collisions of Rare-gas Atoms with 2 Electronic State Molecule | 64 | ||
| 2.2.9.2 Hund's Case (a) Wavefunction and Potential Matrix Elements for an Atom–2 Molecule Complex | 67 | ||
| 2.3 Astrophysical Applications | 69 | ||
| 2.3.1 Context | 69 | ||
| 2.3.2 Collisional Rate Coefficients and Their Use in Radiative Transfer Calculations | 71 | ||
| 2.3.3 Available Data | 73 | ||
| 2.3.4 The Importance of Accurate Rate Coefficients | 74 | ||
| 2.4 Examples | 75 | ||
| 2.4.1 CO(X1 + ) | 75 | ||
| 2.4.2 OH(2) | 79 | ||
| 2.5 Conclusion | 85 | ||
| References | 88 | ||
| Chapter 3 Low-energy Scattering in Crossed Molecular Beams | 92 | ||
| 3.1 Introduction | 92 | ||
| 3.2 Basic Notions on Molecular Collisions | 93 | ||
| 3.2.1 System Description | 93 | ||
| 3.2.1.1 Laboratory Frame Versus Centre-of-mass Frames | 93 | ||
| 3.2.1.2 Centrifugal Barrier | 96 | ||
| 3.2.2 Collision Cross-section | 97 | ||
| 3.2.2.1 Opacity Function | 97 | ||
| 3.2.2.2 Integral and Differential Cross-section | 98 | ||
| 3.2.2.3 Influence of Collision Energy: Classical ExcitationFunctions for Endo/Exoergic Processes | 100 | ||
| 3.2.2.4 Microreversibility and Yield Function | 101 | ||
| 3.2.2.5 Microcanonic to Canonic Transform: From Cross-section to Rate Coefficient | 103 | ||
| 3.3 Molecular Beams and Detection Techniques | 104 | ||
| 3.3.1 Crossed Supersonic Beams | 105 | ||
| 3.3.1.1 Molecular Supersonic Beam | 106 | ||
| 3.3.1.2 Crossed Molecular Beams | 113 | ||
| 3.3.1.2.1 Principle. | 113 | ||
| 3.3.1.2.2 Beam Velocity Control. | 114 | ||
| 3.3.1.2.3 Experimental Setup. | 115 | ||
| 3.3.1.2.4 Relative Translational Energy: Energy Spread. | 116 | ||
| 3.3.1.2.5 Merged Beams. | 118 | ||
| 3.3.2 Detection Techniques | 121 | ||
| 3.3.2.1 ``Universal'' Detection (MS + TOF) and TOF MS Detection | 121 | ||
| 3.3.2.2 Spectroscopic Methods and Doppler Profiles | 123 | ||
| 3.3.2.3 Velocity-map Imaging (VMI) | 123 | ||
| 3.3.3 Signal Acquisition and Treatment | 125 | ||
| 3.3.3.1 Noise Reduction | 125 | ||
| 3.3.3.2 Uncertainty Propagation | 126 | ||
| 3.4 Relation Between Measured Data and Observable Quantities | 126 | ||
| 3.4.1 Production Flux and Cross-section | 126 | ||
| 3.4.2 Interaction Time | 131 | ||
| 3.4.3 Flux-to-density Conversion | 134 | ||
| 3.5 Selected Examples | 137 | ||
| 3.5.1 Reactive Collisions | 137 | ||
| 3.5.1.1 C+ CxHy Reactions | 137 | ||
| 3.5.1.2 S + HD Reaction Dynamics | 140 | ||
| 3.5.2 Inelastic Collisions: O2 +H2 | 143 | ||
| 3.6 Conclusion | 146 | ||
| References | 146 | ||
| Chapter 4 Long-range Interactions Between Ultracold Atoms and Molecules | 150 | ||
| 4.1 Introduction | 150 | ||
| 4.2 Multipolar Expansion of the Potential Energy Between Two Distant Charge Distributions | 157 | ||
| 4.2.1 The Interaction Energy in Cartesian Coordinates | 158 | ||
| 4.2.1.1 Electrostatic Potential Created by the Distribution A at a Distant Point | 158 | ||
| 4.2.1.2 Interaction Energy Between Distribution B and an External Weakly Varying Electrostatic Potential | 161 | ||
| 4.2.1.3 Interaction Energy Between the Distributions A and B | 162 | ||
| 4.2.2 Calculation in Spherical Coordinates | 164 | ||
| 4.2.2.1 Calculation in the Body-fixed Frame | 165 | ||
| 4.2.2.2 Calculation in the Space-fixed Frame | 166 | ||
| 4.3 Perturbative Calculation of Long-range Interactions | 168 | ||
| 4.3.1 Matrix Elements of Multipole-moment Operators | 169 | ||
| 4.3.2 Potential Energy in an External Electric Field | 171 | ||
| 4.3.3 First-order Energy Correction from Long-range Interactions | 174 | ||
| 4.3.4 Second-order Energy Correction from Long-range Interactions | 175 | ||
| 4.3.4.1 Induction Energy | 176 | ||
| 4.3.4.2 Dispersion Energy | 177 | ||
| 4.3.4.3 Second-order Energy Correction and Irreducible Tensors | 178 | ||
| 4.3.5 Example: Long-range Interaction Between Two Alkali-metal Atoms | 182 | ||
| 4.3.5.1 Interaction Between Two Ground-state Atoms | 182 | ||
| 4.3.5.2 Interaction Between One Ground-state Atom and One Atom of a Different Species in the First Excited State | 184 | ||
| 4.3.5.3 Interaction Between One Ground-state Atom and One Atom of the Same Species in the First Excited State | 185 | ||
| 4.4 Long-range Interactions Between Two Heteronuclear Alkali-metal Diatomic Molecules in an External Electric Field | 186 | ||
| 4.4.1 Calculation in the Body-fixed Frame Without an External Field | 187 | ||
| 4.4.1.1 Calculation for Each Individual Rotational Level | 187 | ||
| 4.4.1.2 Calculation for Coupled Rotational Levels | 190 | ||
| 4.4.2 Calculation in the Space-fixed Frame | 192 | ||
| 4.4.2.1 Choice of Basis for the Unperturbed Space | 193 | ||
| 4.4.2.2 Dipole–Dipole Interaction Without Electric Field | 195 | ||
| 4.4.2.3 Application of an External Electric Field | 196 | ||
| 4.5 Conclusion | 197 | ||
| References | 198 | ||
| Chapter 5 Interactions of Atoms and Molecules in Cold Chemistry | 203 | ||
| 5.1 Introduction | 203 | ||
| 5.1.1 Preface | 203 | ||
| 5.1.2 Relevance | 205 | ||
| 5.1.3 State of the Art | 206 | ||
| 5.2 Atomic and Molecular Interactions—A GeneralTheory | 207 | ||
| 5.2.1 The Born–Oppenheimer Approximation | 207 | ||
| 5.2.2 Definition of the Interaction Energy | 210 | ||
| 5.2.3 Components of the Interaction Energy | 211 | ||
| 5.2.4 Electrostatic Energy | 213 | ||
| 5.2.5 Induction Energy | 215 | ||
| 5.2.6 Dispersion Energy | 216 | ||
| 5.2.7 Exchange Energy | 217 | ||
| 5.2.8 Many-electron SAPT | 218 | ||
| 5.2.9 Problem of Charge Transfer | 219 | ||
| 5.3 State-of-the-art Quantum Chemistry Methodsfor Calculations of Potential Energy Surfaces | 219 | ||
| 5.3.1 Hartree–Fock Approximation and Electron Correlation | 220 | ||
| 5.3.2 Hartree–Fock Interaction Energy | 222 | ||
| 5.3.3 Correlated Methods: Interaction Energies in MBPTand CC frameworks | 223 | ||
| 5.3.4 Open-shell Systems | 226 | ||
| 5.3.5 Multireference Methods | 227 | ||
| 5.3.6 DFT Methods | 230 | ||
| 5.3.7 Basis Set Issues and Explicitly Correlated Wavefunctions | 232 | ||
| 5.4 Example Systems | 236 | ||
| 5.4.1 He–NH and N–NH Systems | 236 | ||
| 5.4.2 He–OH(2) | 241 | ||
| 5.4.3 NH–NH and O2–O2 | 244 | ||
| 5.4.4 Alkali-metal and Alkaline-earth Atoms Interacting with Molecules | 248 | ||
| 5.4.5 Interactions Involving He(3S) and Ne(3P) Atoms | 253 | ||
| 5.5 Remarks on Accuracy in Calculations forCold Systems | 255 | ||
| 5.5.1 Scattering Length Dependence on theInteraction Potential | 255 | ||
| 5.5.2 Highly Accurate Long-range Potential | 260 | ||
| 5.6 Summary and Outlook for the Future | 262 | ||
| References | 263 | ||
| Chapter 6 Effects of External Magnetic Fields on Cold Molecular Collisions | 276 | ||
| 6.1 Introduction | 276 | ||
| 6.2 Molecular Collisions | 278 | ||
| 6.3 Molecular Energy Levels in External Fields | 280 | ||
| 6.3.1 1+ Molecules: KRb and RbCs | 280 | ||
| 6.3.2 2+ Molecules: YbF, CaF, SrF | 284 | ||
| 6.3.3 3 Molecules: NH | 287 | ||
| 6.3.4 2 Molecules: OH | 289 | ||
| 6.4 Coupled-channel Equations for Molecules in External Fields | 292 | ||
| 6.4.1 Fully Uncoupled Basis | 293 | ||
| 6.4.2 Total Angular Momentum Basis | 294 | ||
| 6.5 Elastic Collisions: Controlling the Scattering Length | 297 | ||
| 6.6 Inelastic Collisions: Controlling Molecular Spin Relaxation | 301 | ||
| 6.6.1 2+ Molecules | 302 | ||
| 6.6.2 3 Molecules | 304 | ||
| 6.7 Summary and Outlook | 308 | ||
| References | 309 | ||
| Chapter 7 Role of Resonances at Ultracold Temperatures | 313 | ||
| 7.1 Introduction | 313 | ||
| 7.2 Scattering Theory: An Overview | 314 | ||
| 7.2.1 General Results | 315 | ||
| 7.2.1.1 Channels | 315 | ||
| 7.2.1.2 Single-channel Case | 316 | ||
| 7.2.1.3 Multichannel Case | 321 | ||
| 7.2.1.4 The Close-coupling Method | 324 | ||
| 7.2.2 Jost Function | 328 | ||
| 7.2.2.1 Single-channel Case | 328 | ||
| 7.2.2.2 Multichannel Case | 329 | ||
| 7.3 Resonances | 331 | ||
| 7.3.1 Resonances in the Single-channel Case | 331 | ||
| 7.3.1.1 Breit–Wigner Formula | 332 | ||
| 7.3.1.2 Time Delay | 334 | ||
| 7.3.1.3 Effect of Background Scattering | 335 | ||
| 7.3.2 Multichannel Case | 336 | ||
| 7.3.3 Feshbach Resonances | 339 | ||
| 7.3.3.1 General Results | 340 | ||
| 7.3.3.2 A Simple Example | 345 | ||
| 7.4 Simple Reactions: Photoassisted Reactions | 350 | ||
| 7.4.1 Photoassociation and Dissociation: Theory | 350 | ||
| 7.4.2 Photoassociation and Dissociation: Examples | 354 | ||
| 7.4.3 Feshbach Optimized Photo-Association (FOPA) | 357 | ||
| 7.5 Simple Chemical Reactions | 363 | ||
| 7.5.1 General Theory | 363 | ||
| 7.5.2 Systems with Reaction Barrier | 365 | ||
| 7.5.3 Higher Partial Waves and Spin Symmetry Effects | 374 | ||
| 7.5.4 Tuning Resonances | 381 | ||
| 7.6 Conclusions | 384 | ||
| References | 385 | ||
| Chapter 8 Experiments with Large Superfluid Helium Nanodroplets | 389 | ||
| 8.1 Introduction | 389 | ||
| 8.2 The State of Large Helium Droplets | 391 | ||
| 8.2.1 Excitations in a Helium Droplet | 391 | ||
| 8.2.2 Evaporative Cooling of Helium Droplets | 398 | ||
| 8.3 Production of Large Droplets | 401 | ||
| 8.4 Characterisation of the Helium Droplet Beam | 409 | ||
| 8.4.1 Determining the Sizes of Large Helium Droplets and Embedded Clusters | 409 | ||
| 8.4.2 Size Distribution of Helium Droplets | 412 | ||
| 8.4.3 Determination of Droplet Velocity | 415 | ||
| 8.4.4 Imaging Droplets by Microscopy | 416 | ||
| 8.5 Formation Kinetics of Large Clustersin He Droplets | 418 | ||
| 8.6 Spectroscopy in Helium Droplets | 421 | ||
| 8.6.1 Optical and Infrared Spectroscopy | 421 | ||
| 8.6.2 Chemical Reactions in Helium Droplets | 425 | ||
| 8.7 Deposition Experiments | 426 | ||
| 8.8 X-ray Coherent Diffractive Imaging Experiments | 429 | ||
| 8.9 Conclusions | 435 | ||
| References | 435 | ||
| Chapter 9 Molecular Impurities Interacting with a Many-particle Environment: From Ultracold Gases to Helium Nanodroplets | 444 | ||
| 9.1 Introduction | 444 | ||
| 9.2 Superfluidity and Bose–Einstein Condensation | 448 | ||
| 9.3 Molecular Impurities Trapped Inside Superfluids | 451 | ||
| 9.4 Theoretical Description of the Molecular Impurity Problem | 456 | ||
| 9.4.1 Molecular Hamiltonian | 456 | ||
| 9.4.1.1 Angular Momentum Operators in the Molecular and Laboratory Frames | 457 | ||
| 9.4.1.2 Linear Molecules | 459 | ||
| 9.4.1.3 Symmetric-top Molecules | 459 | ||
| 9.4.1.4 Asymmetric-top Molecules | 461 | ||
| 9.4.2 Boson Hamiltonian | 461 | ||
| 9.4.2.1 Introduction to Second Quantization | 461 | ||
| 9.4.2.2 A System of Interacting Bosons | 462 | ||
| 9.4.2.3 Bogoliubov Approximation and Transformation | 463 | ||
| 9.4.2.4 Angular-momentum Representation of the Boson Operators | 466 | ||
| 9.4.3 Molecule–Boson Interaction | 467 | ||
| 9.5 The Angulon Quasiparticle | 471 | ||
| 9.5.1 Second-order Perturbation Theory | 471 | ||
| 9.5.2 Non-perturbative Analysis in the Weak Coupling Regime | 473 | ||
| 9.5.3 The Canonical Transformation | 481 | ||
| 9.5.4 The Limit of a Slowly Rotating Impurity | 484 | ||
| 9.6 Conclusions and Outlook | 486 | ||
| References | 489 | ||
| Chapter 10 Cold Ion Chemistry | 496 | ||
| 10.1 Introduction | 496 | ||
| 10.2 Theory of Ion–molecule Collisions and Reactions | 497 | ||
| 10.2.1 Elastic Collisions | 497 | ||
| 10.2.2 Inelastic Collisions | 499 | ||
| 10.2.3 Capture Models | 501 | ||
| 10.2.4 Radiative Processes | 506 | ||
| 10.3 Experimental Methods | 507 | ||
| 10.3.1 Ions in Flows and Beams | 507 | ||
| 10.3.2 Ion Trapping | 510 | ||
| 10.3.3 Buffer-gas Cooling | 512 | ||
| 10.3.4 Laser and Sympathetic Cooling | 514 | ||
| 10.3.5 State-preparation of Neutral Molecules and Ions | 517 | ||
| 10.4 Review of Selected Results | 520 | ||
| 10.4.1 Temperature Dependence of Reaction Rates | 520 | ||
| 10.4.2 Combined Cold-molecules–Cold-ions Experiments | 522 | ||
| 10.4.3 Ion–Atom Hybrid Traps | 524 | ||
| 10.5 Conclusions and Outlook | 527 | ||
| References | 528 | ||
| Chapter 11 Controlling a Quantum Gas of Polar Molecules in an Optical Lattice | 537 | ||
| 11.1 Introduction | 537 | ||
| 11.2 Creation of Ultracold Molecules | 538 | ||
| 11.2.1 Magneto-association | 540 | ||
| 11.2.2 Coherent Optical Transfer | 542 | ||
| 11.3 Quantum-state Controlled Chemical Reactions and Dipolar Collisions | 545 | ||
| 11.3.1 Quantum State Control of the Molecule | 545 | ||
| 11.3.2 Inducing the Dipole Moment in a Laboratory Frame with DC and AC Electric Fields | 546 | ||
| 11.3.3 Role of Quantum Statistics in Collisions | 548 | ||
| 11.3.4 Reduced Dimensions: Quantum Stereodynamics of Chemical Reactions in a Two-dimensional gas | 550 | ||
| 11.3.5 Sticky Collisions: Three-molecule Collision Channels | 554 | ||
| 11.4 Suppression of Chemical Reactions in a Three-dimensional Lattice | 555 | ||
| 11.4.1 The Continuous Quantum Zeno Mechanism: Stability from Strong Dissipation | 555 | ||
| 11.4.2 Long-lived Molecules in a Three-dimensional Optical Lattice | 557 | ||
| 11.4.3 Quantum Magnetism with Polar Molecules in a Three-dimensional Optical Lattice | 559 | ||
| 11.4.4 A Low-entropy Quantum Gas of Polar Molecules in a Three-dimensional Optical Lattice | 563 | ||
| 11.5 Outlook: New Directions | 568 | ||
| 11.5.1 Evaporative Cooling of Reactive Dipolar Molecules in Quasi-Two-dimensional Geometry | 568 | ||
| 11.5.2 Putting Molecules Under the Microscope: High Resolution Imaging | 569 | ||
| 11.5.3 Large, Stable Electric Fields Provided with In vacuo Electrodes | 569 | ||
| 11.5.4 Detection of Cold Chemical Reaction Products | 572 | ||
| 11.5.5 Molecules with both Electric and Magnetic Dipoles | 572 | ||
| References | 573 | ||
| Chapter 12 Ultracold Collisions of Molecules | 579 | ||
| 12.1 Introduction | 579 | ||
| 12.2 The Schrödinger Equation | 581 | ||
| 12.2.1 The Schrödinger Equation for One Particle | 581 | ||
| 12.2.2 The Schrödinger Equation for Two Colliding Particles | 582 | ||
| 12.2.2.1 Coordinate Systems | 582 | ||
| 12.2.2.2 Types of Collisions | 585 | ||
| 12.3 In the Region Far from Collision | 587 | ||
| 12.3.1 Asymptotic Form of the Wavefunction | 587 | ||
| 12.3.2 Observables | 588 | ||
| 12.4 In the Region of Collision | 590 | ||
| 12.4.1 Partial Wave Expansion | 590 | ||
| 12.4.2 Coupled Equations | 594 | ||
| 12.4.3 Long-range Interactions Described by an Electrostatic Multipole–Multipole Expansion | 596 | ||
| 12.4.4 Propagation: Log-derivative Z Matrix | 597 | ||
| 12.4.5 Symmetry Considerations | 598 | ||
| 12.4.5.1 Inversion Symmetry | 598 | ||
| 12.4.5.2 Permutation Symmetry | 599 | ||
| 12.4.5.3 Collisions in External Fields | 600 | ||
| 12.5 Matching the Two Regions | 601 | ||
| 12.5.1 Reactance Matrix K: Relation with Z | 601 | ||
| 12.5.2 Scattering Matrix S: Relation with K | 602 | ||
| 12.5.3 Transition Matrix T: Relation with Observables | 604 | ||
| 12.5.4 Link to Scattering of Structureless Particles: The Central Potential Problem | 605 | ||
| 12.6 Behaviour at Ultralow Energy: Scattering Length and Threshold Laws | 607 | ||
| 12.7 Application to Ultracold Collisions of Dipolar Molecules in Electric Fields | 609 | ||
| 12.7.1 A Simplified Problem | 610 | ||
| 12.7.1.1 Long-range Interaction | 610 | ||
| 12.7.1.2 A Short-range Tunable Condition | 611 | ||
| 12.7.2 Molecules in an Electric Field | 613 | ||
| 12.7.3 Collisions of Molecules in an Electric Field | 614 | ||
| 12.7.3.1 Molecules in the Ground Rotational State: Enhancement of the Loss Rates | 617 | ||
| 12.7.3.2 A Quantum Threshold Model | 619 | ||
| 12.7.3.3 Molecules in the First Rotational Excited State:Suppression of the Loss Rates | 621 | ||
| 12.8 Conclusion and Perspectives | 624 | ||
| References | 627 | ||
| Chapter 13 Coherent Control of Cold Collisions | 633 | ||
| 13.1 Introduction | 633 | ||
| 13.2 The Concept of Coherent Control | 634 | ||
| 13.3 The Difficulty of Coherently Controlling Collisions | 639 | ||
| 13.4 Coherent Control of Photoassociation | 642 | ||
| 13.4.1 Pump–Dump Photoassociation with Short Pulses: Optimizing the Photoassociation Efficiency | 643 | ||
| 13.4.2 Enhancing the Initial Pair Density for Photoassociation | 646 | ||
| 13.4.3 Pump–Dump Photoassociation with Short Pulses: Optimizing the Dump Step | 649 | ||
| 13.4.4 Short-pulse Photoassociation Experiments | 652 | ||
| 13.5 Further Prospects for the Coherent Control of Cold Collisions | 654 | ||
| 13.6 Summary | 657 | ||
| References | 658 | ||
| Subject Index | 663 |