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 (H-3 (Lambda), H-4(Lambda), He-4(Lambda), H-4(Lambda)* and He-4(Lambda)*), and w e then construct three phase-equivalent Lambda N potentials with different central repulsions. Using the stochastic variational method with a correlat ed Gaussian basis we perform an extensive calculation of an ab initio type for hypernuclei of up to A = 6. The binding energies and the sizes of the L ambda-hypernuclei are very insensitive to the type of the phase-equivalent Lambda N potentials employed. We use two different Lambda Lambda potentials , which both reproduce Delta B-Lambda Lambda(He-6(Lambda Lambda)) reasonabl y well. Any combination of these Lambda N and Lambda Lambda potentials pred icts hitherto undiscovered particle-stable bound states, H-4(Lambda Lambda) , H-4(Lambda Lambda) and He-5(Lambda Lambda): Predicted values of B-Lambda Lambda are about 0.4, 5.5 and 6.3 MeV, respectively. The binding energy of H-4(Lambda Lambda) is so small that its existence depends crucially on the strength of the nn interaction. The binding energies of both He-5(Lambda) a nd He-6(Lambda Lambda) are calculated to be strongly overbound compared to experiment. In relation to this well-known anomaly, we examine the effect o f the quark substructure of N and Lambda on their binding energies. The eff ect is negligible if the baryon size in which the three quarks are confined is smaller than 0.6 fm, but it becomes appreciable, particularly in He-6(L ambda Lambda), if the size is taken to be as large as 0.7 fm. We discuss th e extent to which the nucleon subsystem in the hypernuclei changes by the a ddition of Lambda particles. The charge symmetry breaking of the Lambda N p otential is phenomenologically determined and concluded to be weakly spin d ependent.