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

We first determine the Lambda-N S-wave phase shifts so as to reproduce theexperimental Lambda separation energies of A=3, 4 Lambda-hypernuclei, and thenconstruct three phase-equivalent Lambda-N potentials with different centralrepulsion. By the stochastic variational method with correlated Gaussian basiswe perform an extensive calculation of ab initio type for the hypernuclei of upto A=6. The binding energies and the sizes of the Lambda-hypernuclei are veryinsensitive to the type of the phase-equivalent Lambda-N potentials. We use twodifferent Lambda-Lambda potentials which both reproduce Delta B_{Lambda Lambda}of 6He_{Lambda Lambda} reasonably well. Any combination of these Lambda-N andLambda-Lambda potentials predicts hitherto undiscovered particle-stable boundstates, 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 itspossibility crucially depends on the strength of the Lambda-Lambda interaction.The binding energies of both 5He_Lambda and 6He_{Lambda Lambda} are calculatedto be strongly overbound compared to experiment. In relation to this well-knownanomaly we examine the effect of the quark substructure of $N$ and Lambda ontheir binding energies. The effect is negligible if the baryon size in whichthree 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 0.7fm. We discuss the extent to which the nucleon subsystem in the hypernucleichanges by the addition of Lambda particles. The charge symmetry breaking ofthe Lambda-N potential is phenomenologically determined and concluded to beweakly spin-dependent.Comment: 25 pages, 11 figures(15 eps files; each of Figs.1, 5, 6, and 11 contains two figures