Indications for the nonexistence of three-neutron resonances near the physical region

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 Jπ = 1/2± and Jπ = 3/2± 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 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.