The binding of ΛΛ-hypernuclei

Abstract

The binding energy of the systems _ΛΛBe¹⁰ and _ΛΛHe⁶, considered as three-particle systems (Λ-Λ-nucleus), are calculated as function of the Λ-Λ potential strength by a variational procedure using a trial function of the form F(r₁)F(r₂)G(r₁₂), where the functions F, G are of the form (exp(-αr₂)+z exp (-βr₂)). This wave function allows the description of strong Λ-Λ spatial correlations, and these are found to be quite significant. With B_ΛΛ = 17.5±0.6 MeV for _ΛΛBe¹⁰, the volume integral found for the Λ-Λ potential is 322±26 MeV · fm³, leading to the scattering length a_ΛΛ = 1.76±0.33 fm; essentially the same result is obtained for the Λ-Λ potential if the Λ-Λ hypernucleus observed is interpreted as _ΛΛBe¹¹. The non-mesic and mesic decay rates for _ΛBe⁹ and _ΛΛBe¹⁰ are estimated; the (non-mesic)/(π‾mesic) ratio for _ΛΛBe¹⁰ is found to be about 25% higher than that estimated for _ΛBe⁹. For _ΛΛHe⁶, B_ΛΛ is computed and discussed as function of ν_ΛΛ for both attractive and repulsive Λ-Λ interactions. The calculation is discussed in some detail since it is likely that this trial function will prove both convenient and flexible for the discussion of a number of other three-particle systems of interest.