Quest for magicity in hypernuclei

In present study, we search the lambda magic number in hypernuclei within the framework of relativistic mean field theory (RMF) with inclusion of hyperon-nucleon and hyperon-hyperon potentials. Based on one- and two-lambda separation energy and two-lambda shell gap, 2, 8, 14, 18, 20, 28, 34, 40, 50, 58, 68, 70 and 82 are suggested to be the $\Lambda$ magic number within the present approach. The weakening strength of $\Lambda$ spin-orbit interaction is responsible for emerging the new lambda shell closure other than the model scheme. The predicted $\Lambda$ magic numbers are in remarkable agreement with earlier predictions and hypernuclear magicity quite resembles with nuclear magicity. %Our results also support the nuclear magicity, Our results are supported by nuclear magicity, where neutron number N = 34 is experimentally observed as a magic which is one of the $\Lambda$ closed shell in our predictions. In addition, the stability of hypernuclei is also examined by calculating the binding energy per particle, where Ni hypernucleus is found to be most tightly bound triply magic system in considered hypernuclei. Nucleon and lambda density distributions are observed and it is found that introduced $\Lambda$'s have significant impact on total density and reduces the central depression of the core nucleus. Nucleon and lambda mean field potentials and spin-orbit interaction potentials are also observed for predicted triply magic hypernuclei and the addition of $\Lambda$'s affect the both the potentials to a large extent. The single-particle energy levels are also analyzed to explain the shell gaps for triply magic multi-$\Lambda$ hypernuclei.