The α-cluster hypernuclei 5ΛHe, 6ΛΛHe, 9ΛBe, 10ΛΛBe and hypernuclear interactions

Abstract

Variational calculations for 6 ΛΛ He, 9 Λ Be and 10 ΛΛ Be have been made with n α α - n Λ Λ cluster models. Various αΛ potentials are considered, all of which reproduce B Λ ( 5 Λ He ) . Some of the V αΛ are obtained from an αΛ model by a folding procedure using effective ΛN and ΛNN forces; realistic V αΛ are also obtained from 4N-Λ Monte Carlo variational calculations of 5 Λ He. These MC V αΛ include many-body effects which give a central hump even with only Λ N forces. 9 Λ Be is overbound by about one MeV with realistic αα and αΛ potentials, even with reasonable estimates of ΛN exchange effects which give a reduction ≅0.5 MeV. Repulsive ΛNN forces which can account for the overbinding of 5 Λ He give rise to a repulsive ααΛ potential which brings the calculated B Λ ( 9 Λ Be ) into good agreement with the experimental energy. The ΛΛ interaction strengths are obtained from 6 ΛΛ He and 10 ΛΛ Be for a number of ΛΛ potential shapes. The strengths obtained from 10 ΛΛ Be underbind 6 ΛΛ He by more than one MeV for all our ΛΛ and αΛ potentials. The ΛΛ interaction obtained from the well established ΛΛ 10 Be event is found to be quite strongly attractive, comparable to the 1 S 0 NN interaction without OPE, with correspondingly large negative ΛΛ scattering lengths of ≅ −4 to −5 fm.