Analysis of the low-energy $\hat{I}\cdot$NN-dynamics within a three-body formalism

Abstract

The interaction of an $\hat{I}\cdot$-meson with two nucleons is studied within a three-body approach. The major features of the $\hat{I}\cdot NN$-system in the low-energy region are accounted for by using a s-wave separable ansatz for the two-body $\hat{I}\cdot N$- and $NN$-amplitudes. The calculation is confined to the $(J^{\ddot{I}}€;T)=(0^{-};1)$ and $(1^{-};0)$ configurations which are assumed to be the most promising candidates for virtual or resonant $\hat{I}\cdot NN$-states. The eigenvalue three-body equation is continued analytically into the nonphysical sheets by contour deformation. The position of the poles of the three-body scattering matrix as a function of the $\hat{I}\cdot N$-interaction strength is investigated. The corresponding trajectory, starting on the physical sheet, moves around the $\hat{I}\cdot NN$ three-body threshold and continues away from the physical area giving rise to virtual $\hat{I}\cdot NN$-states. The search for poles on the nonphysical sheets adjacent directly to the upper rim of the real energy axis gives a negative result. Thus no low-lying s-wave $\hat{I}\cdot NN$-resonances were found. The possible influence of virtual poles on the low-energy $\hat{I}\cdot NN$-scattering is discussed.

16 pages revtex including 10 figures