Structure of multi-$Λ$ hypernuclei with a Skyrme-type $ΛΛ$ interaction constrained by data on double-$Λ$ hypernuclei and neutron stars

Abstract

We investigate multi-$Λ$ hypernuclear systems with Skyrme-type $ΛΛ$ interactions constrained by the data on double-$Λ$ hypernuclei and neutron stars. The roles of the repulsive $p$-wave and density-dependent terms in the $ΛΛ$ interaction are examined by considering the homogeneous hyperonic matter around the normal density and finite multi-$Λ$ hypernuclei within the spherical Hartree-Fock approach. In homogeneous matter, the $Λ$ chemical potential and corresponding $Λ$ drip point depend strongly on the repulsive $p$-wave term, while the effect of density-dependent term is relatively weak in the density range relevant to finite nuclei. In the multi-$Λ$ hypernuclei built on doubly closed stable cores from light to heavy systems, $Λ$ radius, separation energy and single-particle structure show a clear dependence on the repulsive $p$-wave interaction, and this dependence becomes stronger as the number of $Λ$ hyperons increases. A second and distinct effect appears near the $Λ$ drip line: when the last occupied $Λ$ orbit approaches the continuum, the repulsive $p$-wave term shifts the state upward and can produce a weakly bound state with an extended radial distribution. As a result, $Λ$ radius can increase rapidly near the threshold. This threshold effect should be distinguished from the moderate enhancement of the dependence on $p$-wave interaction with increasing number of $Λ$ hyperons. These results indicate that the multi-$Λ$ hypernuclei are particularly useful for isolating the role of $p$-wave $ΛΛ$ interacion around the normal density, whereas the density-dependent term is expected to be more important interaction in the high-density domain relevant to neutron stars.