Scattering Theory

A.G. Sitenko gives an introduction to nonrelativistic scattering theory. The presentation is mathematically rigorous, but is accessible to upper level undergraduates in physics. The relationship between the scattering matrix and physical observables, i.e., transition probabilities, is discussed in detail. Among the emphasized topics are the stationary formulation of the scattering problem, the inverse scattering problem, dispersion relations, three-particle bound states and their scattering, collisions of particles with spin and polarization phenomena. The analytical properties of the scattering matrix are discussed. Exercises are included to help the reader to gain some experience and more expertise in scattering theory.

This book is based on the course in theoretical nuclear physics that has been given by the author for some years at the T. G. Shevchenko Kiev State University. This version is supplemented and revised to include new results obtained after 1971 and 1975 when the first and second editions were published. This text is intended as an introduction to the nonrelativistic theory of po- tential scattering. The analysis is based on the scattering matrix concept where the relationship between the scattering matrix and observable physical quantities is considered. The stationary formulation of the scattering problem is presented; particle wave functions in the external field are obtained. A formulation of the optical theorem is given as well as a discussion on time inversion and the reci- procity theorem. Analytic properties of the scattering matrix, dispersion relations, and complex moments are analyzed. The dispersion relations for an arbitrary di- rection scattering amplitude are proven, and analytic properties of the amplitude in the plane of the complex cosine of the scattering angle are studied in detail.

This book is a mathematically rigorous introduction to nonrelativistic scattering theory. This theory, important for molecular, atomic, nuclear and particle physicists, is discussed in detail. Exercises are included.