Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei _ΛΛ ⁶ He, _ΛΛ ¹⁰ Be, _ΛΛ ¹⁴ C, _ΛΛ ¹⁸ O, _ΛΛ ²² Ne, _ΛΛ ²⁶ Mg, _ΛΛ ³⁰ Si, _ΛΛ ³⁴ S, _ΛΛ ³⁸ Ar, _ΛΛ ⁴² Ca, _ΛΛ ⁴⁶ Ti, _ΛΛ ⁵⁰ Cr, _ΛΛ ⁵⁴ Fe, _ΛΛ ⁵⁸ Ni, _ΛΛ ⁶² Zn, _ΛΛ ⁶⁶ Ge, _ΛΛ ⁷⁰ Se, _ΛΛ ⁷⁴ Kr, _ΛΛ ⁷⁸ Sr, _ΛΛ ⁸² Zr, _ΛΛ ⁸⁶ Mo, _ΛΛ ⁹⁰ Ru, _ΛΛ ⁹⁴ Pd, _ΛΛ ⁹⁸ Cd, _ΛΛ ¹⁰² Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. _ΛΛ ⁶ He and _ΛΛ ¹⁰ Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly Λ-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for K _max=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.