Boundary conditions for three-body scattering in configuration space

Abstract

where we investigate the free three-body propagation from sources with different spatial extents. In a forthcoming article this study will be improved by considering the three-body propagation including one pairwise finalstate interaction and finally the full treatment of the Faddeev equations. We summarize our results in Sec. V.Aside from the interest of gaining insight into these equations from the point of view of general scattering theory, the solution of this problem is also of practical interest. The possibility of solving the three-nucleon scattering equations in configuration space has important applications for nucleon-deuteron scattering and for the proper treatment of the final-state interaction of three nucleons in the disintegration of He caused by real or virtual photons. These processes provide very useful insights into the nuclear dynamics of few-body systems. In recent years the three-nucleon scattering problem has 1992 The American Physical Society 45 BOUNDARY CONDITIONS FOR THREE-BODY SCATTERING IN. . . 975 been solved in momentum space [3] and applied to elastic n-d scattering and n-d breakup processes; it is important to check these calculations by an independent method, which would be a configuration-space treatment.

Boundary conditions for three-body scattering in configuration space

“…(39) 1 An alternate derivation of this result is given in Section 6.3 of Ref. [2]; however, the solution g(x) = −1 of Eq.…”

Resonances in the three-neutron system

“…Ab initio it is not known at which ρ-value this form is valid with sufficient accuracy. For a recent discussion see [38]. Also it is a priori not known how many terms should be included One is intended to hope that SECSM which proved to be very efficient in the 2-body case will help here, too.…”

Three-body breakup within the fully discretized Faddeev equations

“…Now if one transforms the formulas for the breakup amplitudes A from [29] to the integral form one receives the following definition for the breakup amplitudes in the momentum hyperspherical representation…”

“…Using formulas (29) and (28) one can derive an alternative to formula (26) for the single-component breakup amplitude via the scattering functions of the channel Hamiltonian H 1…”