Eur. Phys. J. A (2016) 52: 358
https://doi.org/10.1140/epja/i2016-16358-8

Regular Article - Theoretical Physics

Three-body scattering problem in the fixed center approximation: The case of attraction

¹ Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, 117218, Moscow, Russia
² National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409, Moscow, Russia

^* e-mail: vagani@mephi.ru

Received: 11 September 2016
Accepted: 24 November 2016
Published online: 12 December 2016

Abstract

We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous --they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.