ΛN and ΛΛ interactions

ΛN- and ΛΛ-interactions are studied from joint analysis of low-energy Λsub(p)-scattering cross sections and of binding energies of sub(Λ)sup(3)H, sub(Λ)sup(5)He, sub(Λ)sup(13)C hypernuclei, as well as of a double sub(ΛΛ)sup(6)He hypernucleus. sub(Λ)sup(5)He and sub(Λ)sup(13)C hypernuclei are calculated according to the two-body Λ+core model of nuclei. Binding energy of hypernuclei is found from the solution of Schroedinger equation for Λ particle in the field of nondeformed core. It is shown that agreement between basic hypernuclear data (binding energies of sub(Λ)sup(3)H, sub(Λ)sup(5)He, sub(Λ)sup(13)C hypernuclei and cross sections of low-energy Λsub(p) scattering) is possible within the framework of the central ΛN-potential only taking into account the spin dependence of ΛN interaction. Values of Vsub(i)sup(0), Vsub(i)sup(c), GITAsub(i)sup(c), GITAsub(i)sup(σ) parameters of volume Ωsub(ΛN)sup(c), Ωsub(ΛN)sup(0) integrals and Rsub(ΛN)sup(c), Rsub(ΛN)sup(σ) square-law radii for some of the found ΛN potentials are presented in the table. For the present potentials the values of singlet and triplet lengths of Λsub(p)-scattering and effective radii are within the range of asup(t)=-(0.6-0.65)fm, rsub(0)sup(t)=2.4-2.6 fm, sup(s)=-(3.2-3.6)fm, rsub(0)sup(s)=0.88-0.96 fm. Correct vinding energy of sub(ΛΛ)sup(6) He hypernucleus Bsub(ΛΛ)=10.8 MeV for chosen ΛN-potentials is received at the value of volume integral of ΛΛ-interaction equal to Ωsub(ΛΛ)sup(s)=(0.7-0.75) Ωsub(ΛN)sup(s)=188-194 MeV fm3. Thus, ΛΛ-interaction in singlet state is weaker than ΛN-interaction. Mean square distances between Λ-particle and α-particle rsub(Λα)=1.85 fm and between two Λ-particles Rsub(ΛΛ)=2.2 fm testify to the fact that sub(ΛΛ)sup(6)He hypernucleus sizes are comparable with α-particle sizes, and Λ-particles motion in sub(ΛΛ)sup(6)He hypernucleus is correlated obviously