Effects of Finite Temperature and Pairing Correlations in Multi-$Λ$ Hypernuclei

Abstract

The influence of finite temperatures and pairing correlations on the ground state properties of multi $Λ$- Ca, Sn and Pb hypernuclei is explored using finite temperature Hartree Fock Bogoliubov approach and contact pairing interaction. A critical temperature is predicted and is in agreement with the Bardeen Cooper Schrieffer relationship $k_B T_C^Λ\approx 0.5 Δ^{T=0}_Λ$, beyond which pairing correlations drop to zero. Particle densities, $Λ$ single particle energies, and nuclear radii are weakly impacted by pairing as well as by finite temperatures. However, other nuclear properties which are more sensitive to pairing correlations, such as $Λ$ pairing gaps, condensation energies, and abnormal densities are also more impacted by finite temperature, especially around the critical temperature. Furthermore, calculations show the occurrence of the pairing re-entrance effect in the $^{280}_{70Λ}$Pb hyperon drip line hypernucleus. Our study provides insight into the thermal evolution of $Λ$ pairing, i.e. the emergence and vanishing of pairing correlations in multi $Λ$ hypernuclei as a function of temperature.