Data on $\Lambda\Lambda$ hypernuclei provide a unique method to learn details about the strangeness S =- 2 sector of the baryon-baryon interaction. From the free space Bonn-J\"ulich potentials, determined from data on baryon-baryon scattering in the S = 0, -1 channels, we construct an interaction in the S =-2 sector to describe the experimentally known LL hypernuclei. After including short-range (Jastrow) and RPA correlations, we find masses for these LL hypernuclei in a reasonable agreement with data, taking into account theoretical and experimental uncertainties. Thus, we provide a natural extension, at low energies, of the Bonn-J\"ulich one-boson exchange potentials to the S =-2 channel.

Comment: Contribution for the Conference Proceedings of the Compact Stars in the QCD Phase Diagram III (CSQCD III), December 12-15, 2012, Guaruj\'a, Brazil. http://www.astro.iag.usp.br/~foton/CSQCD3