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 atomic/molecular scattering from those of nuclear systems, are shown to be the same once physical units such as energy and 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 also lean heavily on semi-classical methods to explain the physics of quantum scattering - especially the interference seen in the angle dependence of the cross section. Having in mind a wide 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.

Description-Table Of Contents

1. Basic notions. 1.1. Introduction. 1.2. Several definitions. 1.3. Cross sections. 1.4. Classical scattering. 1.5. Stationary scattering of a plane wave. 1.6. Scattering of a wave packet. 1.7. Systems of units -- 2. The partial wave expansion method. 2.1. Free particle in spherical coordinates. 2.2. Numerical solutions of the radial equation. 2.3. Scattering amplitude and cross section. 2.4. Wronskian relations. 2.5. Integral formulae for the phase shifts. 2.6. Convergence of the partial-wave expansion. 2.7. Hard sphere scattering. 2.8. Absolute phase shifts - Levinson Theorem. 2.9. Resonances. 2.10. Scattering from a square-well. 2.11. Low energy scattering -- 3. Coulomb scattering. 3.1. Classical mechanics description of Coulomb scattering. 3.2. Quantum mechanical description. 3.3. Partial wave expansion. 3.4. Coulomb plus short-range potentials -- 4. Green's functions, T- and S-matrices. 4.1. Lippmann-Schwinger equations. 4.2. The transition and the scattering operators. 4.3. The time-dependent picture. 4.4. Scattering from non-local separable potentials. 4.5. Scattering from the sum of two potentials. 4.6. Partial-wave expansions. 4.7. Long range potentials. 4.8. Evaluation of partial-wave Green's functions -- 5. Approximate methods in potential scattering. 5.1. Perturbative approximations. 5.2. Semiclassical approximations -- 6. Spin and identical particles. 6.1. Collisions of particles with spin. 6.2. The scattering of a spin 1/2 particle. 6.3. Identical particles. ; 8 7. Scattering from complex potentials. 7.1. The absorption cross section. 7.2. Lippmann-Schwinger equations with complex potentials. 7.3. The scattering and the transition operators. 7.4. Partial-wave expansions. 7.5. Diffractive scattering. 7.6. Realistic treatments of elastic scattering with absorptive potentials -- 8. Additional topics. 8.1. Analytical properties of the S-matrix. 8.2. Quantum scattering in 1D and 2D. 8.3. The inverse scattering problem. 8.4. The Calogero equation for neutral particle scattering -- 9. The coupled channel formalism. 9.1. The close coupling approximation. 9.2. The Lippmann-Schwinger equations. 9.3. Partial-wave expansions. 9.4. Coupling with continuum states. 9.5. Solution of the coupled channel equations -- 10. Few-channel description of many-body scattering. 10.1. The Feshbach calculus. 10.2. Prompt processes, time delay and resonances. 10.3. Energy averages and the optical model. 10.4. Optical potentials. 10.5. Dynamic polarization potentials. 10.6. Scattering from energy-dependent potentials -- 11. Approximate methods in many-body scattering. 11.1. Perturbative approximations. 11.2. Semiclassical approximations -- 12. Selected topics in many-body scattering. 12.1. Doorway resonances. 12.2. Feshbach resonances in atom-atom collisions. 12.3. Statistical treatment of complex scattering: the compound nucleus. 12.4. Chaotic scattering. 12.5. Scattering in media and nuclear astrophysics. 12.6. Multiple scattering. 12.7. The three-body problem and Faddeev equations. 12.8. The R-matrix method.