  In this paper, hyperspherical three-body model formalism has been applied for
the calculation energies of the low-lying bound $^{1,3}$S (L=0)-states of
neutral helium and helium like Coulombic three-body systems having nuclear
charge (Z) in the range Z=2 to Z=92. The calculation of the coupling potential
matrix elements of the two-body potentials has been simplified by the
introduction of Raynal-Revai Coefficients (RRC). The three-body wave function
in the Schr\H{o}dinger equation when expanded in terms of hyperpherical
harmonics (HH), leads to an infinite set of coupled differential equation
(CDE). For practical reason the infinite set of CDE is truncated to a finite
set and are solved by an exact numerical method known as renormalized Numerov
method (RNM) to get the energy solution (E). The calculated energy is compared
with the ones of the literature.
