Variational approach to the calculation of the binding energy of sub(ΛΛ)31Si

The double hypernucleus sub(ΛΛ)31Si has been considered as a three-body system Λ-Λ-29Si and its binding energy calculated by a variational method using a trial wavefunction of the form F(rsub(c1)) F(rsub(c2)) G(r12), where the r are interparticle triangular coordinates and F and G are of the form zexp(-αr2) + exp(-βr2). These wavefunctions allow the description of strong Λ-Λ spatial correlations which are found to be quite significant. The parameters z, α, β for the two-body wavefunctions F and G are obtained by a variational procedure in order to find the binding energies of the two-body systems Λ-29Si and Λ-Λ. The parameters of the Λ-Λ wavefunction are adjusted so as to produce just a zero-energy Λ-Λ system. For the Λ-29Si system the interaction potential between Λ and 29Si is generated by folding a gaussian Λ-N potential into the density distribution of 29Si. Parameters for the Λ-29Si system are used in the three-body calculation, but those for the Λ-Λ system are kept free in the three-body variational calculation. In the first stage, our calculated value of the binding energy is 41.54 MeV, where we have used a gaussian Λ-Λ interaction having a volume integral of 610.8 MeV fm3. This volume integral is calculated from the two-body Λ-Λ system. In the second stage we have taken the volume integral as a free parameter also, and calculated the binding energy of sub(ΛΛ)31Si to be 39.7 MeV, for a volume integral of 356.5 MeV fm3 for the Λ-Λ potential. This value is compared with the experimental value of 38.2+-6.3 MeV found by Mondal et al. (1975). The dependence of the binding energy on the depth of the Λ-Λ interaction has also been investigated