A Study of Multi$\Lambda$ hypernuclei within Spherical Relativistic Mean-field Approach

TL;DR

This study predicts potential lambda shell closures in superheavy hypernuclei using relativistic mean field theory, highlighting new magic numbers and the effects of weak spin-orbit coupling in hypernuclear systems.

Contribution

It extends previous work by predicting lambda magic numbers in superheavy hypernuclei using advanced relativistic mean field models with hyperon interactions.

Findings

Predicted lambda shell closures at specific nucleon numbers such as 92, 106, 126, 138, 184, 198, 240, and 258.

Identified weaker spin-orbit coupling effects in hypernuclei compared to normal nuclei.

Supported lambda shell closures with pairing energy and gap analyses.

Abstract

This research article is a follow up of earlier work by M. Ikram et al., reported in International Journal of Modern Physics E {\bf{25}}, 1650103 (2016) wherein we searched for $\Lambda$ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (ie.$^{16}O - ^{208}Pb$) by injecting $\Lambda$'s into them. In present manuscript, working within the state-of-art relativistic mean field theory with inclusion of $\Lambda N$ and $\Lambda\Lambda$ interaction in hypernuclei using the predicted doubly magic nucleonic cores ie. $^{292}$120, $^{304}$120, $^{360}$132, $^{370}$132, $^{336}$138, $^{396}$138 of elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicity are made on the basis of one-, two-$\Lambda$ separation energy ($S_\Lambda, S_{2\Lambda}$) and two lambda shell gaps ($\delta_{2\Lambda}$) in multi-$\Lambda$ hypernuclei. The calculations suggest that the $\Lambda$ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the $\Lambda$ shell closures after introducing the $\Lambda$'s in elusive superheavy nucleonic cores. Moreover, in support of $\Lambda$ shell closure the investigation of $\Lambda$ pairing energy and effective $\Lambda$ pairing gap has also been made. The appearance of new lambda shell closures other than the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of spin-orbit coupling in hypernuclei compared to normal nuclei.