S-matrix pole trajectory in a three-neutron model

The eigenvalue equation to the Faddeev kernel is analytically continued on to nonphysical sheets adjacent to the real energy axis of the physical sheet. The position of the pole of the three-body $S$ matrix corresponding to the deepest three-body bound state is calculated as a function of the two-body interaction strength. In a three-neutron model of pure ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ interaction and spectator angular momentum $\lambda =1\mathrm{}$ favored by the shell model, the very pattern of the pole trajectory rules out the possibility of a low-energy resonance.