We consider the theoretical possibility to generate a narrow resonance in the
four neutron system as suggested by a recent experimental result. To that end,
a phenomenological T=3/2 three neutron force is introduced, in addition to a
realistic NN interaction. We inquire what should be the strength of the 3n
force in order to generate such a resonance. The reliability of the
three-neutron force in the T=3/2 channel is exmined, by analyzing its
consistency with the low-lying T=1 states of 4H, 4He and 4Li and the
3H+n scattering.
The {\it ab initio} solution of the 4n Schr\"{o}dinger equation is obtained
using the complex scaling method with boundary conditions appropiate to the
four-body resonances. We find that in order to generate narrow 4n resonant
states a remarkably attractive 3N force in the T=3/2 channel is required.Comment: 11 pages, 11 figures, minor change, published version, to be
published in Physical Review