Beyond mean-field approach for pear-shaped hypernuclei
We develop both relativistic mean field and beyond approaches for hypernuclei with possible quadrupole-octupole deformation or pear-like shapes based on relativistic point-coupling energy density functionals. The symmetries broken in the mean-field states are recovered with parity, particle-number and angular momentum projections. We take $$\begin{array}{c}21\\ \Lambda\end{array}{\rm{Ne}}$$21ΛNe as an example to illustrate the method, where the Λ hyperon is put on one of the two lowest-energy orbits (labeled as Λs,Λp), respectively. We find that the Λ hyperon in both cases disfavors the formation of a reflection-asymmetric molecular-like 16O+α structure in 20Ne, which is consistent with the Nilsson diagram for the hyperon in (β2, β3) deformation plane. In particular, we show that the negative-parity states with the configuration 20Ne(Kπ = 0−) ⊗ Λs are close in energy to those with the configuration 20Ne(Kπ = 0+) ⊗ Λp, even though they have very different structures. The Λs (Λp) becomes more and more concentrated around the bottom (top) of the “pear” with the increase of octupole deformation.