Microscopic evaluation of the hypernuclear chart with $Lambda$-hyperons

A large number of hypernuclei, where a considerable fraction of nucleons is replaced by strange baryons, and even pure hyperonic species are expected to be bound. Though, the hypernuclear landscape remains largely unknown because of scarce constraints on the $NY$ and $YY$ interactions. We want to estimate the number of potentially bound hypernuclei. In order to evaluate realistic error bars within the theoretical uncertainties associated to the spherical mean-field approach, and the present information from already synthetized hypernuclei on the $N-Y$ and $Y-Y$ channels, we limit ourselves to purely $Lambda$-hypernuclei, to magic numbers of $Lambda$s (for Z $leq$ 120 and $Lambda leq$70), and to even-even-even systems. We consider a density functional approach adjusted to microscopic Bruckner-Hartree-Fock calculations, where the $LambdaLambda$ term is corrected in a phenomenological way, to reproduce present experimental constraints. The number of bound even-even-even $Lambda$-hypernuclei is estimated to 491680 $pm$ 34400. This relatively low uncertainty is due 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 $Lambda$-hypernuclei appear to be almost independent of the choice for the high-density part of the $LambdaLambda$ interaction. The location of the $Lambda$-hyperdriplines is also evaluated. Significant deviations from Iron-Nickel elements can be found for $Lambda$-hypernuclei with the largest binding energy per baryon. Proton, neutron and $Lambda$-hyperon magicity evolution and triple magic $Lambda$-hypernuclei are studied. Possible bubbles and haloes effect in $Lambda$-hypernuclei are also discussed.