Background: A large number of hypernuclei, where a considerable fraction of nucleons is replaced with strange baryons, and even pure hyperonic species are expected to be bound. However, the hypernuclear landscape remains largely unknown because of scarce constraints on the and interactions.
Purpose: We want to estimate the number of potentially bound hypernuclei. To evaluate realistic error bars within the theoretical uncertainties associated with the spherical mean-field approach and the present information from already synthesized hypernuclei on the and channels, we limit ourselves to purely hypernuclei, to magic numbers of 's (for and ), and to even-even-even systems.
Method: We consider a density-functional approach adjusted to microscopic Bruckner-Hartree-Fock calculations, where the term is corrected in a phenomenological way, to reproduce present experimental constraints. Different models which strongly deviate at large densities, but giving the same bond energy, are generated to take into account the uncertainties related to the high-density equation of state.
Results: The number of bound even-even-even hypernuclei is estimated to . This relatively low uncertainty is attributable to the fact that the well-constrained low-density and highly unconstrained high-density behavior of the energy functional turn out to be largely decoupled. Results in hypernuclei appear to be almost independent of the choice for the high-density part of the interaction. The location of the hyperdriplines is also evaluated. Significant deviations from iron-nickel elements can be found for hypernuclei with the largest binding energy per baryon. Proton, neutron, and -hyperon magicity evolution and triple magic hypernuclei are studied. Possible bubble and halo effects in hypernuclei are also discussed.
Conclusions: The present results provide a first microscopic evaluation of the -hypernuclear landscape. They shall benefit from the more and more accurate design of the -based functionals. The measurements of and multi- hypernuclei together with additional constraints of the and interaction are mandatory to improve such critical information.