Structure of single $\Lambda$-hypernuclei with Gogny-type $\Lambda$-nucleon forces

We study the structure of single $\Lambda$-hypernuclei using the Hartree--Fock--Bogoliubov method. Finite range Gogny-type forces are used to describe the nucleon-nucleon and $\Lambda$-nucleon interactions. Three different $\Lambda$-nucleon Gogny forces are built. The unknown parameters of these forces are obtained by fitting the experimental binding energies of the $1s$ $\Lambda$ single-particle state in various hypernuclei using the ``Simulated Annealing Method''. These forces are then used to calculate the binding energies of the other ($1p, 1d, 1f, 1g$) $\Lambda$ single-particle states in the different hypernuclei. The predicted values are found to be in good agreement with the experimental data for the three forces constructed. In addition, we calculate also the root-mean-square radii of ground state $\Lambda$ orbital, as well as several global properties of the hypernuclei considered such as their ground-state Hartree--Fock--Bogoliubov energy, their pairing energy and their quadrupole moment.