Variational Approach to the Calculation of the Binding Energy of 31Si

Abstract

The double hypernucleus llsi has been considered as a three-body system A-A-29Si and its binding energy calculated by a variational method using a trial wavefunction of the form F(rCl) F(rC2) G(r12), where the r are interparticle triangular coordinates and F and G are of the form z exp( - rxr 2) + exp( - pr2 ). These wavefunctions allow the description of strong A-A spatial correlations which are found to be quite significant. The parameters z, rx, p 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 A_29Si and A-A. The parameters of the A-A wavefunction are adjusted so as to produce just a zero-energy A-A system. For the A _ 29Si system the interaction potential between A and 29Si is generated by folding a gaussian A-N potential into the density distribution of 29Si. Parameters for the A_29Si system are used in the three-body calculation, but those for the A-A 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 A-A interaction having a volume integral of 610'8 MeVfm3 ? This volume integral is calculated from the two-body A-A system. In the second stage we have taken the volume integral as a free parameter also, and calculated the binding energy of j~Si to be 39·7 MeV, for a volume integral of 356· 5 MeVfm3 for the A-A 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 A-A interaction has also been investigated.