Quadrupole deformation $(\beta,\gamma)$ of light $\Lambda$ hypernuclei in constrained relativistic mean field model: shape evolution and shape polarization effect of $\Lambda$ hyperon

TL;DR

This study uses a constrained relativistic mean field model to analyze the shape evolution and polarization effects of a $ ext{Lambda}$ hyperon in light nuclei, revealing subtle shape changes and significant polarization in specific cases.

Contribution

It introduces a new RMF approach to study shape deformation in hypernuclei and compares results with existing models, highlighting the polarization effects of $ ext{Lambda}$ hyperons.

Findings

$ ext{Lambda}$ hyperons slightly shift ground state shapes towards smaller $eta$ and softer $ extgamma$.

Most hypernuclei show minor shape changes due to $ extLambda$ addition.

Three hypernuclei exhibit strong shape polarization effects from $ extLambda$ hyperons.

Abstract

The shapes of light normal nuclei and $\Lambda$ hypernuclei are investigated in the $(\beta, \gamma)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $\gamma$ direction, differ a lot for several nuclei. For $\Lambda$ hypernuclei, in most cases, the addition of a $\Lambda$ hyperon alters slightly the location of the ground state minimum towards the direction of smaller $\beta$ and softer $\gamma$ in the potential energy surface $E \sim (\beta, \gamma)$. There are three exceptions, namely, $^{13}_\Lambda$C, $^{23}_\Lambda$C, and $^{31}_\Lambda$Si in which the polarization effect of the additional $\Lambda$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei.