Extension theory approach to scattering and annihilation in the $$\bar p$$ d system

Abstract

We consider the problems of three-particle scattering and annihilation in a system of three strongly interacting charged particles (\(\bar p\)pn). We propose a model for the elastic scattering and the breakup process in the nucleon channel as well as for the annihilation into mesons. The mathematical foundation of the model is the extension theory of symmetrical operators. In the framework of this model, we construct the modified integral Faddeev equations with energy-dependent interactions taking the annihilation processes into account. These equations are uniquely resolvable for suitable classes of functions. On this basis, we deduce the corresponding differential Faddeev equations, construct asymptotic boundary conditions for wave function components, and formulate boundary problems for a system composed of nucleonic and mesonic channels. The results obtained are applied to scattering and annihilation processes in the three-particle system\(\bar p\).