Study of Light Lambda- and Lambda Lambda-Hypernuclei with the Stochastic Variational Method and Effective Lambda N Potentials

We first determine the Lambda-N S-wave phase shifts so as to reproduce the experimental Lambda separation energies of A=3, 4 Lambda-hypernuclei, and then construct three phase-equivalent Lambda-N potentials with different central repulsion. By the stochastic variational method with correlated Gaussian basis we perform an extensive calculation of ab initio type for the hypernuclei of up to A=6. The binding energies and the sizes of the Lambda-hypernuclei are very insensitive to the type of the phase-equivalent Lambda-N potentials. We use two different Lambda-Lambda potentials which both reproduce Delta B_{Lambda Lambda} of 6He_{Lambda Lambda} reasonably well. Any combination of these Lambda-N and Lambda-Lambda potentials predicts hitherto undiscovered particle-stable bound states, 4H_{Lambda Lambda}, 5H_{Lambda Lambda} and 5He_{Lambda Lambda}: Predicted values of B_{Lambda Lambda} are about 0.4, 5.5 and 6.3 MeV, respectively. The binding energy of 4H_{Lambda Lambda} is so small that its possibility crucially depends on the strength of the Lambda-Lambda interaction. The binding energies of both 5He_Lambda and 6He_{Lambda Lambda} are calculated to be strongly overbound compared to experiment. In relation to this well-known anomaly we examine the effect of the quark substructure of $N$ and Lambda on their binding energies. The effect is negligible if the baryon size in which three quarks are confined is smaller than 0.6 fm, but becomes appreciable, particularly in 6He_{Lambda Lambda}, if the size is taken to be as large as 0.7 fm. We discuss the extent to which the nucleon subsystem in the hypernuclei changes by the addition of Lambda particles. The charge symmetry breaking of the Lambda-N potential is phenomenologically determined and concluded to be weakly spin-dependent.