The p-shell hypernuclei and the Λ-N interaction

Abstract

The p shell hypernuclei have been studied in detail using two and three-body central Yukawa Λ-N interactions. Intermediate coupled wave functions and a range of density distributions are considered for the core nuclei. The Λ wave function and volume integrals are obtained by numerical solution of the appropriate two-body (Λ-core nucleus) eigenvalue problems, the results being most conveniently represented by the corresponding numerical spin-dependent and charge-independent two-body interaction turns out to be adequate to account for all the known B Λ. In particular, the values of the spin-averaged volume integral of the two-body interaction, which are obtained from ΛHe 5, ΛBe 9 and ΛC 13, agree very well in the absence of three-body forces. Further, quite small upper limits on the permissible strength of the latter are obtained. Almost nothing can be deduced about the range of the two-body forces or about their interactions in relative p states. The implications of our results for the well depth in nuclear matter are discussed. The spin-dependent interaction energy is found to be completely masked by quite small uncertainties in the core sizes, to a lesser extent, by uncertainties in the re-arrangement energies. Effectively nothing can at present be deduced from the p shell hypernuclei about the spin dependence which most plausible assumptions about the core sizes and re-arrangement energies can be made to agree with the values obtained from the s shell hypernuclei. Conversely assuming such values for the spin dependence can make the Λ into a quite sensitive probe into small size differences.