Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons*

Low-energy scattering of the three neutron (3$n)$ and four neutron (4$n)$ systems are studied in the framework of the adiabatic hyperspherical method in the symmetries $J^{\pi \thinspace }=$ 3/2$^{\mathrm{-}}$ and $J^{\pi \thinspace }=$ 0$^{\mathrm{+}}$, respectively. The nucleon-nucleon (NN) interaction considered in this work is the phenomenological AV8' potential and the resultant hyperspherical potentials are compared to those computed with the AV18 potential and other NN potentials with and without a three-nucleon force. The lowest hyperspherical potential for each system exhibits no features that indicate the existence of a low-energy resonance. This non-resonant behavior is further substantiated through an analysis of the elastic phaseshift and density of states or Wigner-Smith time delay. However, there is an enhancement of the density of states at low energies due to a universal long-range attraction in the hyperradial potential which could help explain the enhanced 4n signal observed in the experiment by Kisamori et al. [1]. [1] K. Kisamori, et al. ``Candidate Resonant Tetraneutron State Populated by the He-4 (He-8, Be-8) Reaction'', Phys. Rev. Lett. 116, 052501 (2016).