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This book presents basic principles and theories underlying elastic scattering of X-ray, light, and neutron. The book also presents applications of them to the explo ration of internal structures of soft matters in the length scale ranging from sub nanometers to a few ten-micron meters. The applications are based on the following fundamental concepts. Spatial variations of physical parameters relevant to internal structures of the matters, such as local mass density, can be generally decomposed into Fourier modes with wave vector q and amplitude of η(q): The scattered intensity I(q) from the matter at the scattering vector q is equal to the spectral intensity η(q) 2 of the Fourier mode with the wave vector q. Thus, I(q) is a fundamental quantity in physical science which investigates the relationship between structures and physical properties or functions of the matters. The matters include not only various materials studied in material sciences but also cells, basic units of living creatures studied in biology, and life sciences. Contents General Introduction Part I Fundamentals of X-ray, Light and Neutron Scattering Scattering Mechanism of X-ray, Light and Neutron Scattering Scattering of Schrödinger Wave: Interference of Scattered Waves and Born Approximation Scattering of X-ray and Visible Light Response of Electrons to X-ray and Visible Light: Thomson Scattering and Rayleigh Scattering Polarization of Scattered Electromagnetic Wave and Light Scattering from Optically Anisotropic Scattering Elements Rayleigh–Gans–Born–Debye Scattering from Large Particles Physics of Reciprocal Phenomena Scattering Structure Factor: Spectral Intensity Distribution of Fourier Modes of Structure Part II X-ray and Neutron Scattering: Isotropic Scattering Scattering from Isolated Particles Scattering from Fluctuations: Statistical Theory of Scattering Scattering from Thermal Concentration Fluctuations Interparticle Interference in Liquids Interparticle Interference in Solids: Diffraction from Paracrystal Lattice and Superlattice Scattering from Fractals Combined Small-Angle Scattering Methods for Analyses of Hierarchical Structures Statistical Mechanical Analyses of Hierarchically Self-Organized Nanoparticles Based on Scattering Methods Part III Light Scattering Light Scattering from Solids and Condensed Matters Experimental Methods and Apparatuses Light Scattering from Fluctuations in Solid and Condensed Matters Light Scattering from Fibrillar Crystalline Superstructures Light Scattering from Spherulitic Crystalline Superstructures Light Scattering from Paracrystal Superlattice Structures of Crystalline Superstructures Appendices