Universality in The Three- and Four-Neutron Systems*

This talk addresses the question of whether low energy bound or resonant states can possibly exist for a system of only three or four neutrons. Our exploration was trigged by an experiment published by Kisamori et al. [[Phys. Rev. Lett. 116, 052501 (2016)] which found an excess of low energy tetraneutron events in the nuclear reaction 8He+4He-->8Be+4n.  Prior to our work, a number of theoretical explorations were carried out, with several concluding that a tetraneutron resonance can emerge from solving the 4n Schroedinger equation with known nucleon-nucleon interaction potentials, and a comparable number of studies concluding that no tetraneutron resonance or bound state is possible.  Stimulated by these experimental and theoretical efforts, we have investigated this question using a theoretical technique with a well-proven track record for predicting resonances:  the adiabatic hyperspherical coordinate framework. The result of our calculations, after solving the Schroedinger equation in that framework, using a standard nuclear interaction Hamiltonian that either includes or neglects 3-body interactions, are a set of adiabatic potential curves.  Inspection of those potential curves makes it immediately and intuitively clear that no tetraneutron and no trineutron resonance can possibly exist.  Analysis of scattering phaseshifts in our treatment confirms the absence of any resonance, but it does indicate a possible interpretation of the unexpectedly large number of four neutron events at low energy (below 3 MeV) in the Kisamori et al. experiment.  Specifically we show that, consistent with 4-body universality studies, there is a long range attractive 4-body hyperradial potential proportional the inverse of the hyperradius cubed, which causes the 4n density of states to diverge at zero energy.  Accordingly, we conjecture that this divergent but nonresonant density of states is responsible for the excess low energy 4n events seen experimentally.