  This work presents further analysis of the three- and four-neutron systems in
the low energy regime using adiabatic hyperspherical methods. In our previous
Phys. Rev. Lett. article (Phys. Rev. Lett. 125, 052501 (2020)), the low-energy
behavior of these neutron systems was treated in the adiabatic approximation,
neglecting the off-diagonal non-adiabatic couplings. A thorough analysis of the
density of states through a multi-channel treatment of the three-and
four-neutron scattering near the scattering continuum threshold is performed,
showing no evidence of a 4n resonance at low energy. A detailed analysis of the
long-range behavior of the lowest few adiabatic hyperspherical potentials shows
there is an attractive $\rho^{-3}$ universal behavior which dominates in the
low-energy regime of the multi-channel scattering. This long-range behavior
leads to a divergent behavior of the density of state for $E\rightarrow0$ that
could account for the low-energy signal observed in the 2016 experiment by
Kisamori et al. (Phys. Rev. Lett. 116, 052501 (2016)).
