Download or read book Approximate Potential Calculations in Molecular Scattering Theory written by Timothy Glen Mattson and published by . This book was released on 1985 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattering Theory of Molecules Atoms and Nuclei written by Luiz Felipe Canto and published by World Scientific. This book was released on 2013 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a coherent and comprehensive account of quantum scattering theory with applications to atomic, molecular and nuclear systems. The motivation for this is to supply the necessary theoretical tools to calculate scattering observables of these many-body systems. Concepts, which are seemingly different for the atomic/molecular scattering from those for nuclear systems, are shown to be the same once the physical units such as energy, length are diligently clarified. Many-body resonances excited in nuclear systems are the same as those in atomic systems and come under the name of Feshbach resonances. We clarify this. We also lean heavily on semi-classical methods to explain the physics of quantum scattering and especially the interference seen in the angle dependence of the cross section. Having in mind a wider readership, the book includes sections on scattering in two dimensions, which is of use in surface physics. Several problems are also included at the end of each of the chapters.
Download or read book Potential Scattering in Atomic Physics written by P. G. Burke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph was written while the author was a visitor at the Center for Theoretical Studies at the University of Miami, Coral Gables, Florida. The author wishes to thank Professor Behram Kursunoglu for the warm hospitality extended to him at the Center and to acknowledge the many interesting and fruitful discussions which he had with other visitors and with members of staff at the Center. Philip G. Burke v Contents 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Scattering by a Short-Range Potential. . . . . . . . . . . . . . . 5 3. Scattering by a Coulomb Potential. . . . . . . . . . . . . . . . . . 11 4. Scattering by a Spin-Orbit Potential . . . . . . . . . . . . . . " 17 5. Scattering by One-Electron Atoms. . . . . . . . . . . . . . . . . . 23 6. Low-Energy Effective-Range Theory. . . . . . . . . . . . . . . . 39 7. Bound States and Resonances. . . . . . . . . . . . . . . . . . . . . . 55 8. Variational Methods and Bound Principles. . . . . . . . . . 75 9. Integral Equation Methods and the Born Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 10. Semiclassical and Eikonal Methods . . . . . . . . . . . . . . . . . 117 Appendix. The Coupling of Angular Momenta . . . . . . . . . . . 127 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 vii 1 Introduction In this monograph we study the scattering of a particle by a potential field with particular reference to elastic electron scat tering by a neutral atom or by an ion. This subject is clearly of interest in its own right as a branch of quantum mechanical scattering theory. However, it also serves as an introduction to many of the basic theoretical concepts which are used in inelastic electron scattering and ionization. Consequently this mono graph can be viewed as an introduction to texts where these subjects are treated.
Download or read book Algorithms and Computer Codes for Atomic and Molecular Quantum Scattering Theory written by and published by . This book was released on 1979 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Transfer of Molecular Energies by Collision Recent Quantum Treatments written by F. A. Gianturco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: I I These Lecture Notes are intended as an introduction to the theoretical formulation and computational aspects of the molecular energy transfer processes which take place in an increasingly sophisticated range of molecular scattering experiments. They are directed to chemistry graduate students and emphasize the quantum mechanical approach, with little or no attention to classical and semi classical treatments or to formal presentations. Several Sections of the first Chapters are based on lectures given at the Graduate School of Physics of the University of Genoa a few years ago and I thank the students for their sense of duty in following to the end all those no tation-filled blackboards and transparencies. The kind patience of my wife Carolyn in reading the whole manuscript and improving its form is gratefully acknowledged. Franco A. Gianturco Bari, September 1978 CON TEN T S FOREWORD I NTRODUCTI ON Page 1. A RESUME OF QUANTUM MECHANICAL POTENTIAL SCATTERING 1. 1. General formulation of the problem Page 5 1. 2. Solutions of the radial equation 10 " 1. 3. The method of partial waves 13 1. 4. Some properties of 61. The Born appro~imation 18 1. 5. Properties of the S-matrix: bound states and resonances 23 1. 6. Classical and semiclassical scattering,a set of defi- tions 34 References 44 2. POTENTIAL ENERGY HYPERSURFACE CALCULATIONS FOR SIMPLE SYSTEMS 2. 1. Kinematic considerations 45 2. 2. General development of a priori method 52 2. 3. Some approximate treatments 68 2. 4.
Download or read book Semiclassical Theories of Molecular Scattering written by B. C. Eu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of molecular collisions at energies from less than about 100 eV 3 down to a few 10- eV, which is roughly the range of chemical interest, has greatly expanded in the last 10 to 20 years. As in many fields, this activity has been stimulated by parallel advances in theory which have triggered the autocatalytic positive feedback system of experiment challenging theory and vice versa. Possibly the biggest driving force, however, has been the growing awareness that molecular collisions are important in our understanding of na tural and man-made environments. Molecular collision dynamics is now studied in connection with molecular formation in interplanetary space, upper atmo sphere chemistry, plasmas, lasers and fusion reactors, and is crucial for understanding gas-dynamic flow processes, gas-phase chemical reactions and catalysis. Despite the great strides made in studying elementary collisions in laboratory scattering experiments, many of the processes in these areas are too complicated for us to hope ever to study them in detail in the labo ratory. Thus in the long run we shall have to rely on theory. Initially, I think many of us, like myself, had hoped that the development of fast compu ters would outpace the demands on computing time so that "brute force" quan tum-mechanical exact calculations would provide all the answers. Unfortunate ly this has not been the case and efficient approximations are needed. They can be broadly classified as classical, semiclassical or semiquantal.
Download or read book Scattering Theory written by Harald Friedrich and published by Springer. This book was released on 2015-11-20 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Download or read book Quantum Theory Of Tunneling written by Mohsen Razavy and published by World Scientific. This book was released on 2003-01-29 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications. The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral, Heisenberg's equations and the phase space method are all used to study the motion of a particle under the barrier. Extensions to the multidimensional cases and tunneling of particles with internal degrees of freedom are also considered. Furthermore, recent advances concerning time delay and tunneling times and some of the problems associated with their measurement are also discussed. Finally, some examples of tunneling in atomic, molecular, nuclear and condensed matter physics are presented.
Download or read book Theory and Application of Quantum Molecular Dynamics written by John Z. H. Zhang and published by World Scientific. This book was released on 1999 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an updated and detailed presentation of modern quantum-mechanical treatments and practical computational methods for dynamical processes of small molecular systems. The main emphasis is on the recent development of successful theories and computational methods for the reactive scattering process. Specific applications are given in detail for a number of benchmark chemical reaction systems in the gas phase and gas surface. Differing from traditional physics books focusing on abstract collision theory for elastic collisions, the book has been written in a fashion in which the development of general reactive or rearrangement scattering theory is accompanied by practical applications for realistic reaction systems.
Download or read book Selected Topics of the Theory of Chemical Elementary Processes written by E.E. Nikitin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction 1 1. 2. Basic Concepts and Phenomenological Description 6 2.1. Separation of the Center-of-Mass Motion 8 2.2. Separation of Electronic and Nuclear Motions. Interaction Potentials (Potential-Energy Surfaces) 11 2.2.1. Heuristic Considerations 11 2.2.2. Born-Oppenheimer Separation. Adiabatic Approximation, 16 Present State of Potential-Energy-Burface 2.2.3. Calculations 23 2.3. Scattering Channels ~6 2.4. Classification of Elementary Processes. Microscopic Mechanism 27 D.ynamics of Atomic and Molecular Collisions: 3. Electronically Adiabatic Processes 32 Classical Approach 3.1. 33 Some Arguments for the Reliability of the Classical Approach 33 Atom-Atom Collisions. Elastic Scattering 34 Quasiclassical Treatment of Elementary Processes in Triatomic Systems: Inelastic and Reactive Scattering 44 IV Examples of Results of Trajectory Calculations 59 3.1.4. 64 Elements of Quantum-Mechanical Methods 3.2. Correspondence of Classical and Quantum 3.2.1. 64 Mechanical Theories Time-Dependent Scattering Theory 71 3.2.2. Stationary Scattering Theory 77 3.2.3. One-Dimensional Scattering 78 3.2.3.1 • Three-Dimensional Elastic Scattering 83 3.2.3.2. Rearrangement Scattering (Reactions) 85 3.2.3.3. Examples of Quantum-Mechanical Calculations 3.2.4.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Atomic and Molecular Scattering written by Berni Alder and published by Elsevier. This book was released on 2012-12-02 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Computational Physics, Volume 10: Atomic and Molecular Scattering presents the digital methods used in producing quantitative results from the theory of atomic and molecular scattering. This volume contains seven chapters that specifically consider the methods that produce quantum mechanical wavefunctions from which cross sections are deduced. Chapter 1 covers the solutions of the systems of coupled integro-differential equations using the Hartree and Hartree-Fock methods for atomic structure calculations and the eigenfunction expansion method for electron-atom collision calculations. Chapter 2 treats the translation of the formal results into a generally applicable, efficient, and numerically stable method for solving quantum-mechanical scattering problems. Chapter 3 discusses the exponential method of solution as applied in inelastic scattering, the reaction coordinates for a collinear reactive system, and the modifications of the computational method required for reactive scattering. Chapter 4 outlines the theory and the calculational techniques involved in the use of algebraic expansions in scattering problems, while Chapter 5 deals with the solution of the close-coupled equations. Chapter 6 evaluates the collision between two quantum-mechanical systems with internal structure using the quantum-mechanical operator equations. Lastly, Chapter 7 focuses on the principles and applications of classical trajectory methods.
Download or read book Theory of Electron Atom Collisions written by Philip G. Burke and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors aim to hone the theory of electron-atom and electron-ion collisions by developing mathematical equations and comparing their results to the wealth of recent experimental data. This first of three parts focuses on potential scattering, and will serve as an introduction to many of the concepts covered in Parts II and III. As these processes occur in so many of the physical sciences, researchers in astrophysics, atmospheric physics, plasma physics, and laser physics will all benefit from the monograph.
Download or read book Low Energy Electron Scattering from Molecules Biomolecules and Surfaces written by Petr Carsky and published by CRC Press. This book was released on 2016-04-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the turn of the 21st century, the field of electron molecule collisions has undergone a renaissance. The importance of such collisions in applications from radiation chemistry to astrochemistry has flowered, and their role in industrial processes such as plasma technology and lighting are vital to the advancement of next generation devices. F
Download or read book Variational Methods in Electron Atom Scattering Theory written by Robert K. Nesbet and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of scattering phenomena is a major theme of modern physics. A scattered particle provides a dynamical probe of the target system. The practical problem of interest here is the scattering of a low energy electron by an N-electron atom. It has been difficult in this area of study to achieve theoretical results that are even qualitatively correct, yet quantitative accuracy is often needed as an adjunct to experiment. The present book describes a quantitative theoretical method, or class of methods, that has been applied effectively to this problem. Quantum mechanical theory relevant to the scattering of an electron by an N-electron atom, which may gain or lose energy in the process, is summarized in Chapter 1. The variational theory itself is presented in Chapter 2, both as currently used and in forms that may facilitate future applications. The theory of multichannel resonance and threshold effects, which provide a rich structure to observed electron-atom scattering data, is presented in Chapter 3. Practical details of the computational implementation of the variational theory are given in Chapter 4. Chapters 5 and 6 summarize recent appli cations of the variational theory to problems of experimental interest, with many examples of the successful interpretation of complex structural fea tures observed in scattering experiments, and of the quantitative prediction of details of electron-atom scattering phenomena.
Download or read book The Schr dinger Equation written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the 50th anniversary of the discovery of the Schrodinger equation a small symposium was organized in Vienna. It had mainly retrospective character, where after an appreciation of Schrodinger's scientific achievements the results were collected which one could extract from his equation. Of course not all the developments which originated in Schrodingers dis coveries could be included. Instead, it was attempted to present a review of the established predictions which follow directly from his equation. Despite the 50 years of its existence there are always new results of this sort being found, especially because the necessary mathe matical methods are being developed and become known to the physicists slowly only now .. I want to take the opportunity here to thank the lecturers for their efforts which they put into their excellent talks and their written versions. With their help this volume should become a useful document on the current mathematical art in the treatment of the Schrodinger equation. Finally it is my pleasant obligation to thank the Bundesministerium fUr Wissenschaft und Forschung and the Kulturamt der Gemeinde Wien for their financial support which made it possible to honor one of the great Austrian scientists.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1972 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt:
