Influence of the tetraneutron on the EoS under core-collapse supernovae and heavy-ion collisions conditions

Recently, a resonant state of four neutrons (tetraneutron) with an energy of $E_{4n}=2.37\pm 0.38 \rm{(stat)} \pm 0.44 \rm{(sys)}$ MeV and a width of $\Gamma=1.75\pm 0.22 \rm{(stat)} \pm 0.30 \rm{(sys)}$ MeV was reported. In this work, we analyse the effect of including such an exotic state on the yields of other light clusters, that not only form in astrophysical sites, such as core-collapse supernovae and neutron star mergers, but also in heavy-ion collisions. To this aim, we use a relativistic mean-field formalism, where we consider in-medium effects in a two-fold way, via the couplings of the clusters to the mesons, and via a binding energy shift, to compute the low-density equation of state for nuclear matter at finite temperature and fixed proton fraction. We consider five light clusters, deuterons, tritons, heliums, $\alpha$-particles, and $^6$He, immersed in a gas of protons and neutrons, and we calculate their abundances and chemical equilibrium constants with and without the tetraneutron. We also analyse how the associated energy of the tetraneutron would influence such results. We find that the low-temperature, neutron-rich systems, are the ones most affected by the presence of the tetraneutron, making neutron stars excellent environments for their formation. Moreover, its presence in strongly asymmetric matter may increase considerably the proton and the $\alpha$-particle fractions. This may have an influence on the dissolution of the accretion disk of the merger of two neutron stars.