The addition of hyperons to nuclear systems presents a valuable avenue for exploring the interplay between strangeness and nuclear structure. In this work, we investigate the impact of one and two \(\Lambda \) hyperons on the properties of even-even deformed nuclear cores within the framework of the deformed Skyrme-Hartree-Fock (SHF)+BCS model. Incorporating a density functional approach \( \Lambda N \) and \(\Lambda \Lambda \) density-functional approach adjusted to microscopic Bruckner-Hartree-Fock calculations. For that, a new version of the ev8 code has been developed and adapted to solve the Hartree-Fock equations. Our calculations are performed for the two observed hyprnuclei \( _{\Lambda }^{9}Be \) and \( _{\Lambda \Lambda }^{10}Be \) that are predicted to have a deformed ground state. Our results reveal that the presence of a single \(\Lambda \) hyperon leads to a modest increase in one \(\Lambda \) binding energy and a slight reduction in quadrupole deformation. Inclusion of a second \(\Lambda \) hyperon enhances both the two \(\Lambda \) binding and bond energies. Furthermore, it is shown that DF-NSC89 + EmC is the most favored interaction in the description of deformed light hypernuclei. These findings provide insights into the structural modifications induced by strangeness in hypernuclei and contribute to a deeper understanding of hyperon-nucleon interactions in finite nuclear systems.
