Multiple Scattering in Solids

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Antonios Gonis, William H. Butler

   Pages 1-5

3. Intuitive Approach to MST

   • Antonios Gonis, William H. Butler

   Pages 6-17

4. Single-Potential Scattering

   • Antonios Gonis, William H. Butler

   Pages 18-54

5. Formal Development of MST

   • Antonios Gonis, William H. Butler

   Pages 55-79

6. MST for Muffin-Tin Potentials

   • Antonios Gonis, William H. Butler

   Pages 80-121

7. MST for Space-Filling Cells

   • Antonios Gonis, William H. Butler

   Pages 122-160

8. Augmented MST(*)

   • Antonios Gonis, William H. Butler

   Pages 161-184

9. Relativistic Formalism

   • Antonios Gonis, William H. Butler

   Pages 185-202

10. The Poisson Equation

    • Antonios Gonis, William H. Butler

    Pages 203-225

11. Back Matter

    Pages 226-285

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The origins of multiple scattering theory (MST) can be traced back to Lord Rayleigh's publication of a paper treating the electrical resistivity of an ar­ ray of spheres, which appeared more than a century ago. At its most basic, MST provides a technique for solving a linear partial differential equa­ tion defined over a region of space by dividing space into nonoverlapping subregions, solving the differential equation for each of these subregions separately and then assembling these partial solutions into a global phys­ ical solution that is smooth and continuous over the entire region. This approach has given rise to a large and growing list of applications both in classical and quantum physics. Presently, the method is being applied to the study of membranes and colloids, to acoustics, to electromagnetics, and to the solution of the quantum-mechanical wave equation. It is with this latter application, in particular, with the solution of the SchrOdinger and the Dirac equations, that this book is primarily concerned. We will also demonstrate that it provides a convenient technique for solving the Poisson equation in solid materials. These differential equations are important in modern calculations of the electronic structure of solids. The application of MST to calculate the electronic structure of solid ma­ terials, which originated with Korringa's famous paper of 1947, provided an efficient technique for solving the one-electron Schrodinger equation.

• Helmholtz equation
• Muliple scattering theory
• electricity
• electronic structure of materials
• mechanics
• muffin-tin potentials
• partial waves
• scattering theory
• space-filling cells

• Chemistry and Materials Science Group, Lawrence Livermore Laboratory, Livermore, USA

  Antonios Gonis

• Metal and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, USA

  William H. Butler

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