Study of the excited state of double-A hypernuclei by hyperspherical supersymmetric approach

Hyperspherical harmonics expansion (HHE) method has been applied to study the structure and Lambda Lambda dynamics for the ground and first excited states of low and medium mass double-Lambda hypernuclei in the framework of core+Lambda+Lambda three-body model. The Lambda Lambda potential is chosen phenomenologically while core-Lambda potential is obtained by folding the phenomenological LambdaN interaction into the density distribution of the core. The parameters of this effective LambdaN potential is obtained by the condition that they reproduce the experimental (or empirical) data for core-Lambda subsystem. The three-body (core+Lambda+Lambda) Schrodinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. This ground state energy and wave function are used to construct a partner potential. The three-body Schrodinger equation is solved once again for this partner potential. According to supersymmetric quantum mechanics, the ground state energy of this potential is exactly the wane as that of the first excited state of the potential used in the first step. In addition to the two-Lambda separation energy for the ground and first excited state, some geometrical quantities for the ground state of double-Lambda hypernuclei He-6(Lambda Lambda), Be-10(Lambda Lambda), C-14(Lambda Lambda), O-18(Lambda Lambda), Ne-22(Lambda Lambda), Mg-26(Lambda Lambda), Si-30(Lambda Lambda), S-34(Lambda Lambda), Ar-38(Lambda Lambda), (Lambda)Lambda Ca-42, Ti-46(Lambda Lambda), Cr-50(Lambda Lambda), Fe-54(Lambda Lambda), Ni-58(Lambda Lambda), Zn-62(Lambda Lambda), Ge-66(Lambda Lambda), Se-70(Lambda Lambda), Kr-74(Lambda Lambda), Zr-82(Lambda Lambda), Mo-86(Lambda Lambda), Ru-90(Lambda Lambda), Pd-94(Lambda Lambda), Pd-98(Lambda Lambda), Cd-102(Lambda Lambda), Sn-106(Lambda Lambda), Xe-132(Lambda Lambda), Ce-140(Lambda Lambda), Er-166(Lambda Lambda), Hf-180(Lambda Lambda), Pb-211(Lambda Lambda), Th-232(Lambda Lambda) are computed. These include the Lambda Lambda bond energy and various r.m.s. radii.