Application of random phase approximation to vibrational excitations of double-$\Lambda$ hypernuclei

TL;DR

This study uses HF+RPA with Skyrme interactions to analyze how adding $\Lambda$ hyperons affects vibrational excitations and the incompressibility of double-$\Lambda$ hypernuclei, revealing increased resonance energies.

Contribution

It applies the HF+RPA method with Skyrme interactions to quantify the impurity effect of $\Lambda$ hyperons on vibrational modes in hypernuclei, a novel approach in this context.

Findings

Inclusion of $\Lambda$ hyperons shifts collective state energies higher.

Giant monopole resonance energies increase with $\Lambda$ hyperons.

Effective incompressibility modulus rises due to $\Lambda$ impurity effect.

Abstract

Using the Hartree-Fock plus random-phase-approximation (HF+RPA), we study the impurity effect of $\Lambda$ hyperon on the collective vibrational excitations of double-$\Lambda$ hypernuclei. To this end, we employ a Skyrme-type $\Lambda N$ and $\Lambda\Lambda$ interactions for the HF calculations, and the residual interactions for RPA derived with the same interactions. We find that inclusion of two $\Lambda$ hyperons in $^{16}$O shifts the energy of the collective states towards higher energies. In particular, the energy of the giant monopole resonance of $^{\,\,18}_{\Lambda\Lambda}$O, as well as that of $^{210}_{\Lambda\Lambda}$Pb, becomes larger. This implies that the effective incompressibility modulus increases due to the impurity effect of $\Lambda$ particle, if the $\beta$-stability condition is not imposed.