Interaction of Η Mesons with a Three-nucleon System * * *

A study of the η-3N interaction in the energy region near the η-3 H elastic scattering threshold is presented. The calculational scheme is based on the four-body scattering formalism. A manageable form of the integral equations is achieved by using a separable ansatz for the driving two-body ηN-and N N-forces as well as for the subamplitudes appearing in the (1+3) and (2+2) partitions of the η-3N system. Results presented for the η-3 H scattering length point to the existence of a virtual (antibound) s-wave η-3 H state. As a consequence, a large enhancement of the cross section for η-production from three-body nuclei is predicted. The experimental results for η-production from the lightest nuclei demonstrate a rather strong energy dependence in the region of a few MeV above threshold [1, 2, 3]. One observes a very rapid rise of the η-yields with energy , so that the predictions of simple models, neglecting any final state interaction, underestimate the data sizeably. Some of the models interpret this striking enhancement of the near-threshold η-production as an indirect indication that the η-meson can form bound states already with s-shell nu-clei. Whether the η-nuclear interaction allows the existence of such objects remains one of the most exciting but still unproven hypothesis of meson-nuclear physics. As for the η-3N system, several methods have been developed [4, 5, 6, 7, 8], where different approximations were used to circumvent the difficulties associated with a direct solution of the four-body problem. The crucial point of all these approaches is the neglect of the target excita-tion during the interaction with the η-meson, which may be too restrictive if few-nucleon targets are considered [9]. Therefore, our aim was to study the η-3N interaction within the formally exact four-body scattering theory. The formal basis of our calculation is described in detail in [10]. As a principal tool, we have employed the four-body integral equations which * Supported by Deutsche Forschungsgemeinschaft SFB 443.