Introduction

Abstract

This book is devoted to the theory of resonance states and processes expressed in terms of nonrelativistic quantum mechanics. There are already many excellent books on quantum mechanics and collision theory where, among other things, a description of general theory of resonance scattering may be found [1–6]. With rare exceptions, however, they usually discuss the parametrization of the scattering amplitude (or of the S-matrix) in the near-resonance region, for example the Breit-Wigner parametrization or the appropriate generalization to the case of many levels or many channels. At the same time, the basic problem nowadays is not to get a general parametrization of cross sections but to calculate the parameters of the resonance amplitudes (namely, widths, level shifts, S-matrix residues at resonance poles, etc.) proceeding from the fundamental interactions effective in a quantum system. It is the problem of the practical calculation of resonance parameters, however, that is explicitly given little consideration in the general-purpose manuals. They also usually omit the theory of many-body resonance states capable of decaying with emission of two or more particles, although such resonances are extensively used in atomic, molecular, nuclear and particle physics.