Three-body potentials originating from cluster distortion.

The distortion of composite particles (clusters) during their mutual interaction leads to effective three-body forces. In a nonrelativistic theory, they originate from two sources. One is the coupling potential which couples a channel to a distortion channel. The second one is the energy denominator (propagator) which arises whenever a distortion channel is formally eliminated and represented by an elimination potential. In the present paper this second source is studied. A three-cluster system with only one distortion state in a two-cluster subsystem is considered. Two possibilities of defining a three-body potential from the three-cluster elimination potential are tested, namely (i) extraction of a two-body potential with ``frozen'' energy dependence and (ii) off-shell transformation and subsequent extraction of a two-body potential. The mathematical formalism is illustrated by a numerical example. In a simplified model of the triton, two \ensuremath{\Delta} particles and a nucleon form the distortion channel. It is seen that the interaction of the third nucleon with the two \ensuremath{\Delta} particles has a remarkable influence on the effective three-body potential. Considering the fact that excited nucleons like \ensuremath{\Delta} particles tend to interact more strongly with nucleons than nucleons interact among themselves, we find the overbinding problem of the triton becoming more serious. From the present microscopic study it also becomes clear that an N-body Schr\"odinger equation with purely phenomenological energy-dependent two-body potentials is in general undefined because of insufficient information.