Double $\Lambda$ Hypernuclei and the Nuclear Medium Effective $\Lambda \Lambda$ Interaction

Abstract

We fit the ${}^1{S}_0\Lambda \Lambda$ interaction in the nuclear medium to the masses of the experimentally known double-$\Lambda$ hypernuclei: ${}_{\Lambda \Lambda }^6$He, ${}_{\Lambda \Lambda }^{10}$Be and ${}_{\Lambda \Lambda }^{13}$B. We derive this effective interaction from OBE Jülich $\Lambda \Lambda$-type potentials and using both Hartree-Fock and variational approaches. We find that the inclusion of $\Lambda \Lambda$ correlations in the variational scheme leads to significant differences and a better understanding of the dynamical features of the system. We investigate the sensitivity of the binding energies and the mesonic decay widths of the above double-$\Lambda$ hypernuclei to the $\omega \Lambda \Lambda$ coupling and the form factor at the $\sigma \Lambda \Lambda$ vertex. We also use this effective interaction to predict binding energies and pionic decay widths of heavier double-$\Lambda$ hypernuclei, not discovered yet. Finally, we discard the existence of ${}^1{S}_0$ $\Lambda \Lambda$ bound states provided the $\Lambda \Lambda -\Xi N$ coupling can be neglected.

Comments: 49 pages, LaTeX + 8 ps-figure files