Study of light Λ- and ΛΛ-hypernuclei with the stochastic variational method and effective ΛN potentials

Abstract

We first determine the ΛN S-wave phase shifts so as to reproduce the experimental Λ separation energies of A = 3, 4 Λ-hypernuclei (3ΛH, 4ΛH, 4ΛHe, 4ΛH* and 4ΛHe*), and we then construct three phase-equivalent ΛN potentials with different central repulsions. Using the stochastic variational method with a correlated 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 Λ-hypernuclei are very insensitive to the type of the phase-equivalent ΛN potentials employed. We use two different ΛΛ potentials, which both reproduce ΔBΛΛ(Λ6ΛHe) reasonably well. Any combination of these ΛN and ΛΛ potentials predicts hitherto undiscovered particle-stable bound states, Λ4ΛH, Λ5ΛH and Λ5ΛHe: Predicted values of BΛΛ are about 0.4, 5.5 and 6.3 MeV, respectively. The binding energy of Λ4ΛH is so small that its existence depends crucially on the strength of the ΛΛ interaction. The binding energies of both 5ΛHe and Λ6ΛHe 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 the three quarks are confined is smaller than 0.6 fm, but it becomes appreciable, particularly in Λ6ΛHe, 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 Λ particles. The charge symmetry breaking of the ΛN potential is phenomenologically determined and concluded to be weakly spin dependent.