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 BΛΛ = 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 aΛΛ = 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, BΛΛ is computed and discussed as function of νΛΛ 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. © 1964.