A generalized Bethe-Weizsäcker mass formula for strange hadronic matter

Abstract

We extend the Bethe-Weizsäcker nuclear mass formula to strange hadronic matter composed of nucleons, lambdas and cascade hyperons. The generalized formula contains several volume and symmetry terms constrained by phenomenologically determined Λ-nuclear, Ξ-nuclear and ΛΛ interaction parameters and by hyperon-hyperon ( ΛΛ, ΛΞ, ΞΞ) interaction parameters suggested by one-boson-exchange models. We confirm that multi-Λ hypernuclei are generally unstable to ΛΛ → ΞN conversion. For strange hadronic matter we determine, as function of the baryon number A, the line of strong-interaction stability, along which a large strangeness fraction |S| A − 0.5−1.1 and a low charge fraction q A < 0.2 hold, and no fission occurs. The binding energy per baryon increases monotonically to its bulk limit, B A → 38 MeV, |S| A → 1.1 and q A → 0 for the parameters adopted here assuming that the hyperon species saturate at densities similar to those of protons and neutrons in nuclei. Even in the extreme limit of vanishingly small hyperon-hyperon interaction strengths, strange hadronic matter with B A → 15 MeV, |S| A → 0.7 and q A → 0 in the bulk limit should exist and our mass formula reproduces semi-quantitatively recent mean-field calculations which implicitly assumed weak hyperon-hyperon interactions.