Effects of finite temperature and pairing correlations in multi-Λ hypernuclei

The influence of finite temperatures and pairing correlations on the ground-state properties of multi-$\mathrm{\Lambda }$ Ca, Sn, and Pb hypernuclei is explored using the 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 $k_B{T}_C^{\mathrm{\Lambda }}\approx 0.5{\mathrm{\Delta }}_{\mathrm{\Lambda }}^{T=0}$, beyond which pairing correlations drop to zero. Particle densities, $\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }$-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 ${}_{70\mathrm{\Lambda }}{}^{280}\mathrm{Pb}$ hyperon drip-line hypernucleus. Our study provides insight into the thermal evolution of $\mathrm{\Lambda }$ pairing, i.e., the emergence and vanishing of pairing correlations in multi-$\mathrm{\Lambda }$ hypernuclei as a function of temperature.