Lambda binding energies in the Skyrme-Hartree-Fock approach with various $$\Lambda N$$ Λ N interactions

The Lambda binding energies $$B_\Lambda $$ of $$\Lambda $$ hypernuclei ranging from light to heavy masses are investigated systematically in the framework of the Skyrme-Hartree-Fock (SHF) approach. Calculations are performed with the combinations of the NN interactions SLy4 and SkI4 and various $$\Lambda N$$ interactions, including the Skyrme-type forces and the microscopic forces. It is demonstrated that the Skyrme-type SLL4 and YMR forces can well describe the experimental data overall better compared to other Skyrme-type forces, while the microscopic interaction results deviate a bit from the experimental data. In addition, the shrinkage effects caused by $$\Lambda $$ hyperon on the deformation indeed exist for the deformed light nuclei, while not for the heavy nuclei regardless of the $$\Lambda N$$ interactions.