The pending question of the existence of three-neutron resonances near the physical energy region is reconsidered. Finite rank neutron-neutron forces are used in Faddeev equations, which are analytically continued into the unphysical energy sheet below the positive real energy axis. The trajectories of the three-neutron S-matrix poles in the states of total angular momenta and parity $J^{\pi }={\frac{1}{2}}^{\pm }$ and $J^{\pi }={\frac{3}{2}}^{\pm }$ are traced out as a function of artificial enhancement factors of the neutron-neutron forces. The final positions of the S-matrix poles removing the artificial factors are found in all cases to be far away from the positive real energy axis, which provides a strong indication for the nonexistence of nearby three-neutron resonances. The pole trajectories close to the threshold $E=0\mathrm{}$ are also predicted out of auxiliary generated three-neutron bound state energies using the Padé method and agree very well with the directly calculated ones.

• Received 6 August 2002

DOI:https://doi.org/10.1103/PhysRevC.66.054001