Study of Λ- and ΛΛ-hypernuclear structure and effective YN interaction

We first determine the ΛN S-wave phase shifts so as to reproduce the experimental Λ separation energies of A=3, 4 Λ-hypernuclei, and then construct some phase-equivalent ΛN potentials with different central repulsion. The 1S0 and 3S1 phase shifts predicted by the potentials grow up to 32 and 19 degrees, respectively. The scattering lengths and effective ranges are as=-2.52 fm, at=-1.20 fm, rs=3.08 fm and rt=4.26 fm, respectively. 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. We use two different ΛΛ potentials which both reproduce ΔBΛΛ(ΛΛ6He) reasonably well. Any combination of these ΛN and ΛΛ potentials predicts hitherto undiscovered particle-stable bound states, ΛΛ4H, ΛΛ5H and ΛΛ5He: Predicted values of BΛΛ are about 0.4, 5.5 and 6.3 MeV, respectively. The binding energies of both Λ5He and ΛΛ6He 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 Λ 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 ΛΛ6He, if the size is taken to be as large as 0.7 fm. (author)