  We present quantum Monte Carlo calculations of few-neutron systems confined
in external potentials based on local chiral interactions at
next-to-next-to-leading order in chiral effective field theory. The energy and
radial densities for these systems are calculated in different external
Woods-Saxon potentials. We assume that their extrapolation to zero
external-potential depth provides a quantitative estimate of three- and
four-neutron resonances. The validity of this assumption is demonstrated by
benchmarking with an exact diagonalization in the two-body case. We find that
the extrapolated trineutron resonance, as well as the energy for shallow well
depths, is lower than the tetraneutron resonance energy. This suggests that a
three-neutron resonance exists below a four-neutron resonance in nature and is
potentially measurable. To confirm that the relative ordering of three- and
four-neutron resonances is not an artifact of the external confinement, we test
that the odd-even staggering in the helium isotopic chain is reproduced within
this approach. Finally, we discuss similarities between our results and
ultracold Fermi gases.
