A single particle energies

We consider the binding energies of Λ hypernuclei (HN), in particular the single-particle (s.p.) energy data, which have been obtained for a wide range of HN with mass numbers A ≤ 89 and for orbital angular momenta ell Λ ≤ 4. We briefly review some of the relevant properties of A hypernuclei. These are nuclei ΛAZ with baryon number A in which a single Λ hyperon (baryon number = 1) is bound to an ordinary nucleus AZ consisting of A - 1 nucleons = Z protons + N neutrons. The Λ hyperon is neutral, has spin 1/2, strangeness S = -1, isospin I = O and a mass MΛ = 1116 MeV/c2. Although the Λ interacts with a nucleon, its interaction is only about half as strong as that between two nucleons, and thus very roughly VΛN ∼ 0.5 VNN. As a result, the two-body ΛN system is unbound, and the lightest bound HN is the three-body hypertriton Λ3H in which the Λ is bound to a deuteron with the Λ-d separation energy being only ∼ 0.1 MeV corresponding to an exponential tail of radius ∼ 15 fm exclamation point In strong interactions the strangeness S is of course conserved, and the Λ is distinct from the nucleons. In a HN strangeness changes only in the weak decays of the Λ which can decay either via ''free'' pionic decay Λ → N + π or via induced decay Λ + N → N + N which is only possible in the presence of nucleons. Because of the small energy release the pionic decay is strongly suppressed in all but the lightest HN and the induced decay dominates. However, the weak decay lifetime ∼ 10-10s is in fact close to the lifetime of a free Λ. Since this is much longer than the strong interaction time ∼ 10-22s we can ignore the weak interactions when considering the binding of HN, just as for ordinary nuclei