$\Lambda\Lambda$ pairing in multi-strange hypernuclei

TL;DR

This paper investigates $\Lambda ext{-}\Lambda$ pairing in multi-strange hypernuclei using the Hartree-Fock-Bogoliubov method, providing an upper bound on the pairing gap and analyzing its effects on hypernuclear structure.

Contribution

It introduces a calibration method for the $\Lambda ext{-}\Lambda$ pairing strength based on uniform matter predictions, offering new insights into hypernuclear pairing effects.

Findings

Maximum $\Lambda ext{-}\Lambda$ pairing gap around 3 MeV.

Small corrections to density distributions and shell structure.

Nucleon-$\Lambda$ pairing is suppressed in most hypernuclei.

Abstract

Multi-strange Ca, Sn and Pb hypernuclei with $\Lambda\Lambda$ pairing interaction are investigated within the Hartree-Fock-Bogoliubov approach. The unknown $\Lambda\Lambda$ pairing strength is calibrated to match with the maximal value for the prediction of the $\Lambda$ pairing gap in uniform matter for densities and isospin asymmetries equivalent to those existing in multi-$\Lambda$ hypernuclei. In this way, we provide an upper bound for the prediction of the $\Lambda$ pairing gap and its effects in hypernuclei. The condensation energy is predicted to be about 3~MeV as a maximum value, yielding small corrections on density distributions and shell structure. In addition, conditions on both Fermi energies and orbital angular momenta are expected to quench the nucleon-$\Lambda$ pairing for most of hypernuclei.