This book is about the structure of multielectron atoms and predominantly adopts a perturbative approach to the total Hamiltonian. A key concept is the central-field approximation and, beyond the standard LS-coupling and jj-coupling schemes, intermediate cases are also treated. After that, the book covers hyperfine structure and other nuclear effects, as well as interactions with static external fields. Throughout the book, an analytical approach is adopted. Working knowledge of basic quantum mechanics (including the non-relativistic hydrogen atom, basic angular momentum and perturbation theory) is assumed, and it begins with a brief recap of the hydrogen orbitals, before turning towards the symmetry aspects of multi-electron atoms, spin-orbit interaction and couplings of angular momenta.

Stability and Transport in Magnetic Confinement Systems provides an advanced introduction to the fields of stability and transport in tokamaks. It serves as a reference for researchers with its highly-detailed theoretical background, and contains new results in the areas of analytical nonlinear theory of transport using kinetic theory and fluid closure. The use of fluid descriptions for advanced stability and transport problems provide the reader with a better understanding of this topic. In addition, the areas of nonlinear kinetic theory and fluid closure gives the researcher the basic knowledge of a highly relevant area to the present development of transport physics.

There is a growing need in both industrial and academic research to obtain accurate quantitative results from continuous wave (CW) electron paramagnetic resonance (EPR) experiments. This book describes various sample-related, instrument-related and software-related aspects of obtaining quantitative results from EPR expe- ments. Some speci?c items to be discussed include: selection of a reference standard, resonator considerations (Q, B, B ), power saturation, sample position- 1 m ing, and ?nally, the blending of all the factors together to provide a calculation model for obtaining an accurate spin concentration of a sample. This book might, at ?rst glance, appear to be a step back from some of the more advanced pulsed methods discussed in recent EPR texts, but actually quantitative "routine CW EPR" is a challenging technique, and requires a thorough understa- ing of the spectrometer and the spin system. Quantitation of CW EPR can be subdivided into two main categories: (1) intensity and (2) magnetic ?eld/mic- wave frequency measurement. Intensity is important for spin counting. Both re- tive intensity quantitation of EPR samples and their absolute spin concentration of samples are often of interest. This information is important for kinetics, mechanism elucidation, and commercial applications where EPR serves as a detection system for free radicals produced in an industrial process. It is also important for the study of magnetic properties. Magnetic ?eld/microwave frequency is important for g and nuclear hyper?ne coupling measurements that re?ect the electronic structure of the radicals or metal ions.

This book reviews the most significant advances in concepts, methods, and applications of quantum systems in a broad variety of problems in modern chemistry, physics, and biology. In particular, it discusses atomic, molecular, and solid structure, dynamics and spectroscopy, relativistic and correlation effects in quantum chemistry, topics of computational chemistry, physics and biology, as well as applications of theoretical chemistry and physics in advanced molecular and nano-materials and biochemical systems. The book contains peer-reviewed contributions written by leading experts in the fields and based on the presentations given at the Twenty-Fourth International Workshop on Quantum Systems in Chemistry, Physics, and Biology held in Odessa, Ukraine, in August 2019. This book is aimed at advanced graduate students, academics, and researchers, both in university and corporation laboratories, interested in state-of-the-art and novel trends in quantum chemistry, physics, biology, and their applications.

Quantum chromodynamics (QCD) is the fundamental quantum ?eld theory of quarks and gluons. In order to discuss it in a mathematically well-de?ned way, the theory has to be regularized. Replacing space-time by a Euclidean lattice has proven to be an e?cient approach which allows for both theor- ical understanding and computational analysis. Lattice QCD has become a standard tool in elementary particle physics. Asthetitlealreadysays: thisbookisintroductory Thetextisintendedfor newcomerstothe?eld, servingasastartingpoint.Wesimplywantedtohavea bookwhichwecanputintothehandsofanadvancedstudentfora?rstreading on lattice QCD. This imaginary student brings as a prerequisite knowledge of higher quantum mechanics, some continuum quantum ?eld theory, and basic facts of elementary particle physics phenomenology. In view of the wealth of applications in current research the topics p- sented here are limited and we had to make some painful choices. We discuss QCD but omit most other lattice ?eld theory applications like scalar th- ries, gauge-Higgs models, or electroweak theory. Although we try to lead the reader up to present day understanding, we cannot possibly address all on- ing activities, in particular concerning the role of QCD in electroweak theory. Subjects like glueballs, topological excitations, and approaches like chiral p- turbation theory are mentioned only brie?y. This allows us to cover the other topics quite explicitly, including detailed derivations of key equations. The ?eld is rapidly developing. The proceedings of the annual lattice conferences provide information on newer directions and up-to-date result

This book provides an exhaustive account of the origin and dynamics of cosmic rays. Divided into three parts, it first gives an up-to-date summary of the observational data, then -- in the following theory section -- deals with the kinetic description of cosmic ray plasma. The underlying diffusion-convection transport equation, which governs the coupling between cosmic rays and the background plasma, is derived and analyzed in detail. In the third part, several applications of the solutions of the transport equation are presented and how key observations in cosmic ray physics can be accounted for is demonstrated. The applications include cosmic ray modulation, acceleration near shock waves and the galactic propagation of cosmic rays. While the book is primarily of interest to scientists working at the forefront of research, the very careful derivations and explanations make it suitable also as an introduction to the field of cosmic rays for graduate students.

As a spectroscopic method, Nuclear Magnetic Resonance (NMR) has seen spectacular growth over the past two decades, both as a technique and in its applications. Today the applications of NMR span a wide range of scientific disciplines, from physics to biology to medicine. Each volume of Nuclear Magnetic Resonance comprises a combination of annual and biennial reports which together provide comprehensive of the literature on this topic. This Specialist Periodical Report reflects the growing volume of published work involving NMR techniques and applications, in particular NMR of natural macromolecules which is covered in two reports: "NMR of Proteins and Acids" and "NMR of Carbohydrates, Lipids and Membranes." For those wanting to become rapidly acquainted with specific areas of NMR, this title provides unrivalled scope of coverage. Seasoned practitioners of NMR will find this an in valuable source of current methods and applications. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis.

This book lays the foundations for you to understand all that you always wanted to know about radioactivity. It begins by setting out essential information about the structure of matter, how radiation occurs and how it can be measured. It goes on to explore the substantial benefits of radioactivity through its many applications, and also the possible risks associated with its use. The field of radioactivity is explained in layman's terms, so that everybody who is interested can improve their understanding of issues such as nuclear power, radiation accidents, medical applications of radiation and radioactivity from the environment. Everything is radioactive. There is natural radioactivity in the homes that we live in, the food that we eat and the air that we breath. For over 100 years, people have recognised the potential for radioactivity to help solve problems and improve our standard of living. This has led to the creation of radioactivity levels in some places that are much higher than naturally-occurring background levels. Such high levels of radiation can be harmful to people and the environment, so there is a clear need to manage this potential harm and to make the risk worth the benefits mankind can achieve from radioactive materials.

A comprehensive survey of recent theoretical and experimental progress in the area of electron-photon interaction and dense media. A state-of-the-art discussion of radiation production, with descriptions of new ideas and technologies that enhance the production of X-rays in the form of channelling, transition and parametric X-ray production. Progress in electron beam physics to produce sub-picosecond electron bunches from low-energy linear accelerators make it possible to produce coherent, high brightness, submillimeter radiation and sub-picosecond X-ray pulses. Micro-undulators in the form of bent crystalline structures hold great promise as future X-ray sources.

The dynamics of nuclear structures described in this book furnish the basis for a comprehensive understanding of how the higher-order organization and function of the nucleus is established and how it correlates with the expression of a variety of vital activities such as cell proliferation and differentiation. The resulting volume creates an invaluable source of reference for researchers in the field.

This Workshop was organized to bring once more tagether the scientists of the rather heterogeneaus field of exotic atoms. At present the main topic of the field seems to be the study of the atomic cascade. There are some who study it intentionally -Iet us call them cascadeurs -and others who think they investigate other features of the exotic atoms (like Coulomb capture, particle transfer, muon catalyzed fusion, chemical effects, fundamental properties, etc.) -users-while in fact they study some special consequences of the same atomic cascade. We decided to get cascadeurs and users discuss the problems of exotic atoms at wonderful Erice, at the 5th Course of the International School of Physics of Exotic Atoms. Our Workshop was quite successful, we have heard excellent talks from participants from a dozen countfies and most of them have prepared written contributions for this volume. The Organizers express their gratitude to all participants for their contributions, especially to David Measday for bis concluding remarks (not printed here) and to James Cohen for jumping in for Leonid Ponomarev who had to leave unexpectedly in the middle of the meeting. We greatly appreciate the enthusiastic help of Marianne Signer in every stage of the organization work. Am , of course, the Workshop could not happen at all without the incredibly efficient organization by the Ettore Majorana Centre of Scientific Culture. Leopold M. Simons Dezso Horvath Gabriele Torelli V CONTENTS OPENING ADDRESS . . . . . . . . . . . . . . . . . . . . . . . . . . xi . . . . . . ."

The development of linear-scaling density functional theory (LS-DFT) has made ab initio calculations on systems containing thousands of atoms possible. These systems range from nanostructures to biomolecules. These methods rely on the use of localized basis sets, which are optimised for the representation of occupied Kohn-Sham states but do not guarantee an accurate representation of the unoccupied states. This is problematic if one wishes to combine the power of LS-DFT with that of theoretical spectroscopy, which provides a direct link between simulation and experiment. In this work a new method is presented for optimizing localized functions to accurately represent the unoccupied states, thus allowing theoretical spectroscopy of large systems. Results are presented for optical absorption spectra calculated using the ONETEP code, but the method is equally applicable to other spectroscopies and LS formulations. Other topics covered include a study of some simple one dimensional basis sets and the presentation of two methods for band structure calculation using localized basis sets, both of which have important implications for the use of localized basis sets within LS-DFT.

Thermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data.
This book has the twofold aim to present coherently the relevant results coming from the recent scientific literature and to guide the readers through the process of deriving results, enabling them to explore the limits of the mathematical approximations and test the power of the method. The book is focused on the fundamental properties of nanosystems in the gas phase. For this reason there is a strong emphasis on microcanonical physics. Each chapter is enrichedwith exercises and 3 Appendices provide additional useful materials."

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics."

Neutron radiography has in recent years emerged as a useful and complementary technology for radiation diagnosis. It is now routinely used in industrial quality assurance and in support of selected research and developmental activities. Conferences are held on the subject, pertinent handbooks exist, and technical papers appear regularly reporting on new developments. While neutron radiography has indeed passed through the transition from a scientific curiosity to technological relevance, it is a sign of its continuing dynamic evolution that little material has appeared which provides an integrated mathematical and physical analysis of the subject possessing both an instructional as well as reference function. It is our hope that this monograph will fill this need. The distinctiveness of neutron radiography rests on the unique interactions between neutrons and nuclei. This leads to some special relationships between the material and geometrical properties of an object and the neutron radiographic image. The evolution of a technical discipline demands that specific conceptual constructs be developed and their mathematical representations examined and compared with controlled experiments. Experience has convinced us that a particular and substantial body of knowledge has accumulated endowing neutron radiography with the essential foundations of a unique mathematical and physical science. Our scientific and professional involvement in neutron radiography began some 15 years ago when the senior author (A.A.H.) found himself with convenient access to the McMaster University Nuclear Reactor and research support from the Government of Canada.

Although the fission of heavy nuclei was discovered over 75 years ago, many problems and questions still remain to be addressed and answered. The reader will be presented with an old, but persistent problem of this field: The contradiction between Prompt Fission Neutron (PFN) spectra measured with differential (microscopic) experiments and integral (macroscopic and benchmark) experiments (the Micro-Macro problem). The difference in average energy is rather small ~3% but it is stable and we cannot explain the difference due to experimental uncertainties. Can we measure the PFN spectrum with high accuracy? How may we compare results of different experiments to provide better accuracy? Are our traditional theoretical models correct? What can be done to solve the Micro-Macro problem in future? These questions are discussed in this monograph for the reader. The current work will be of interest to graduate students and researchers, particularly those working in nuclear and neutron physics.

I. Formal Methods.- Artificial Neural Networks that Learn Many-Body Physics.- Quantum Statistical Microdynamics and Critical Phenomena.- Quantum Spin Lattice Models: a Coupled-Cluster Treatment.- Time Dependent Mean Field Approximation in a Boson System.- Inhomogeneous Boson System Made Planar.- II. Quantum Fluids.- The Shape of Fluids.- Single Particle Properties of Atomic Deuterium.- Studies of the Critical Point of 4He.- The Spectral Function of Bose Superfluids: a Sum Rule Approach.- III. Electronic Systems, Atoms and Molecules.- Collective Spin Waves in Maxwellian Electron Plasma.- Test of Density Functional Approximation for an Atom in a Strong Magnetic Field.- Ionic Diffusion Phenomena in Superionic Conductors.- Electric Field Induced Solidification-Theory of Electro-Rheology Fluids.- Toward a Non-Born-Oppenheimer Density Functional Theory in the Context of Local-Scaling Transformations.- Bragg Intensities and Diffuse Scattering in Ag2Se: a Molecular Dynamics Study.- IV. High-Tc Superconductivity.- Dynamics of the Anderson Model for Dilute Magnetic Alloys: a Quantum Monte Carlo and Maximum Entropy Study.- High Temperature Superconductivity in an Exactly Solvable Model.- Cooper Pair Binding Energy and the BCS Gap Energy Revisited.- Coopers Pairs, Local Pairs, and TF-Scaled High-Tc Superconductivity.- Electron-Hole Liquid Model for High Tc-Superconductivity.- MEP Approach to the Anderson-Hubbard Model.- V. Lattice Theories.- Correlated Lattice Fermions in High Dimensions.- Cluster Gutzwiller Approximation.- The U(1)3 Lattice Gauge Vacuum.- Electronic Diamagnetism in Two-Dimensional Lattices.- Nuclear Physics and QCD.- Meson-Meson Scattering as a Many-Body Problem.- Alpha-Nucleus Interaction from an Inverse Scattering and Energy-Density Formalism.- Spin and Tensor Correlations in Model Nuclear Matter.- On Narrow ? Hypernuclear States with Positive Energy.- Electromagnetic Response in Nuclear Matter and Complex Nuclei.- Use of Correlated Hyperspherical Harmonic Basis for Strongly Interacting Systems.- Variational Cluster Methods in Coordinate Space for Small Systems: Center of Mass Corrections Made Easy.- Short-Range Correlations and Single-Particle Spectral Functions in Nuclear Matter.- Functional Techniques in the Many-Body Problem: the Longitudinal Nuclear Response function.- Contributors and Participants.

Taylor-Couette Flow, Experiment and Theory: Evolution of Instrumentation for Taylor-Couette Flow; R.J. Donnelly. Phase Dynamics in the Taylor-Couette System; M. Wu, C.D. Andereck. Taylor-Couette Flow Systems with Broken Rotational Symmetry: End Circulation in Non-Axisymmetrical Flows; C. Normand et, al. Turbulence in Taylor-Couette and Plane Couette Flow: Numerical Simulation of Turbulent Taylor-Couette Flow; S. Hirschberg. Instabilities, Pattern Formation, and Turbulence in Model Equations: Double Eigenvalues and the Formation of Flow Patterns; R. Meyer-Spache. Extensions of Taylor-Couette Flow: Taylor Vortex Flow with Superimposed Radial Mass Flux; K. Buehler. Open Flows: Structure and Perturbation in Gortler Vortex Flow; P. Petitjeans, J.E. Wesfreid. Appendix: A Guide to Literature Related to the Taylor-Couette Problem; R. Tagg. 24 additional articles. Index.

More than 50 years ago, in 1934, Chadwick and Goldhaber (ChG 34) published a paper entitled "A 'Nuclear Photo-effect' Disintegration of the Diplon by -y-Rays."l in the introduction: They noted "By analogy with the excitation and ionisation of atoms by light, one might expect that any complex nucleus should be excited or 'ionised', that is, disintegrated, by -y-rays of suitable energy," and furthermore: "Heavy hydrogen was chosen as the element first to be examined, because the diplon has a small mass defect and also because it is the simplest of all nuclear systems and its properties are as important in nuclear theory as the hydrogen is in atomic theory." Almost at the same time, in 1935, the first theoretical paper on the photodisinte gration of the deuteron entitled "Quantum theory of the diplon" by Bethe and Peierls (BeP 35) appeared. It is not without significance that these two papers mark the be ginning of photonuclear physics in general and emphasize in particular the special role the two-body system has played in nuclear physics since then and still plays. A steady flow of experimental and theoretical papers on deuteron photo disintegration and its inverse reaction, n-p capture, shows the continuing interest in this fundamental process (see fig. 1.1)."

In the50years since the first volume of "Progress in Optics" was published, optics has become one of the most dynamic fields of science. The volumes in this series that have appeared up to now contain more than 300 review articles by distinguished research workers, which have become permanent records for many important developments, helping optical scientists and optical engineers stay abreast of their fields.
Comprehensive, in-depth reviewsEdited by the leading authority in the field"