Eur. Phys. J. A (2008) 38: 71-76
https://doi.org/10.1140/epja/i2008-10641-3

Regular Article - Theoretical Physics

Unitarization of the elastic amplitude on the SO(2, 1) group

¹ Department of Theoretical Physics, Irkutsk State University, 664003, Irkutsk, Russia
² Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Russia
³ Institut für Theoretische Physik II, Ruhr-Uni-Bochum, D-44780, Bochum, Germany

^* e-mail: avlad@theor.jinr.ru

Received: 25 May 2008
Accepted: 21 August 2008
Published online: 22 September 2008

Abstract

We obtain the solution of the unitarity equation for the elastic processes in terms of the expansion coefficients of the amplitude as a function on theSO(2, 1) group. This approach is a generalization of the eikonal representation to the case of small impact parameters and large transverse momenta. We show how the unitarity relation is modified when the contributions of the backward scattering are taken into account. We discuss the simplest models of the profile functions in the following cases: full reflection, full absorption and the combination of these two cases.