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 $Erightarrow0$ that could account for the low-energy signal observed in the 2016 experiment by Kisamori et al. (Phys. Rev. Lett. 116, 052501 (2016)).
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