Study of Light Λ-and ΛΛ-Hypernuclei with the Stochastic Variational Method and Effective ΛN Potentials

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We first determine the ΛN S-wave phase shifts so as to reproduce the experimental Λ separation energies of A=3, 4 Λ-hypernuclei (^3_ΛH, ^4_ΛH, ^4_ΛHe, ^4_ΛH^* and ^4_ΛHe^*), 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 ΔB_<ΛΛ>(^6_<ΛΛ>He) reasonably well. Any combination of these ΛN and ΛΛ potentials predicts hitherto undiscovered particle-stable bound states, ^4_<ΛΛ>H, ^5_<ΛΛ>H and ^5_<ΛΛ>He: Predicted values of B_<ΛΛ> are about 0.4, 5.5 and 6.3 MeV, respectively. The binding energy of ^4_<ΛΛ>H is so small that its existence depends crucially on the strength of the ΛΛ interaction. The binding energies of both ^5_ΛHe and ^6_<ΛΛ>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 ^6_<ΛΛ>He, 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.
理論物理学刊行会の論文
2000-05-25

Study of Light Λ-and ΛΛ-Hypernuclei with the Stochastic Variational Method and Effective ΛN Potentials

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