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Energies of the low-lying bound S-states (L=0) of exotic three-body systems,consisting a nuclear core of charge +Ze (Z being atomic number of the core) andtwo negatively charged valence muons, have been calculated by hypersphericalharmonics expansion method (HHEM). The three-body Schr\H{o}dinger equation issolved assuming purely Coulomb interaction among the binary pairs of thethree-body systems X$^{Z+}\mu^-\mu^-$ for Z=1 to 54. Convergence pattern of theenergies have been checked with respect to the increasing number of partialwaves $\Lambda_{max}$. For available computer facilities, calculations arefeasible up to $\Lambda_{max}=28$ partial waves, however, calculation for stillhigher partial waves have been achieved through an appropriate extrapolationscheme. The dependence of bound state energies has been checked againstincreasing nuclear charge Z and finally, the calculated energies have beencompared with the ones of the literature.

Application of hyperspherical harmonics expansion method to the low-lying bound S-states of exotic two-muon three-body systems