We investigate the fission barriers of $\mathrm{\Lambda }$ hypernuclei using the multidimensionally constrained relativistic mean-field model, which incorporates both triaxial and octupole degrees of freedom. The effects of triaxial and octupole deformations on the inner and outer fission barriers of ${}^{240}\mathrm{Pu}$ are examined with different relativistic density functionals. Assuming that the $\mathrm{\Lambda }$ hyperon adiabatically follows the fission dynamics and occupies the lowest single-particle state, we analyze the fission barrier heights of ${}_{\mathrm{\Lambda }}{}^{239}\mathrm{U}$ and ${}_{\mathrm{\Lambda }}{}^{241}\mathrm{Pu}$. Our calculations indicate that the shape of the hypernuclei remains nearly identical to that of their core nucleus. The inner fission barrier of ${}_{\mathrm{\Lambda }}{}^{241}\mathrm{Pu}$ is influenced by triaxial deformation, whereas the outer barrier is affected by both triaxial and octupole deformations. The $\mathrm{\Lambda }$ hyperon increases both the inner and outer fission barrier heights due to the attractive $\mathrm{\Lambda }N$ interaction. With the specific $NN$ interaction DD-ME2, we observe that larger $\mathrm{\Lambda }N$ coupling constants correspond to lower inner and outer fission barrier heights. The $\mathrm{\Lambda }$ hyperon localizes at the nuclear center until the system reaches the fission isomer. After passes the outer barrier, it is attached to the heavy fission fragment. These findings are consistent with earlier Skyrme-Hartree-Fock studies, indicating that the influence of the hyperon on fission follows the same trend regardless of deformation degrees of freedom: even when triaxial deformations are included, the localization and attachment behavior of the $\mathrm{\Lambda }$ particle remain unchanged.

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• Fission
• Hypernuclei & mesic nuclei
• Nuclear shapes and moments
• Nuclear structure & decays
• Nucleon distribution