Heavy ion-nucleus scattering is an excellent laboratory to probe high spin phenomena, exotic nuclei and for the analysis of various exit channels. The Strong Absorption Model or the generalized diffraction models, which are semi-classical in nature, have been employed in the description of various heavy ion-nucleus scattering phenomena with reasonable success. But one needs to treat the deflection function (scattering angles) quantum mechanically in the Wave Mechanical picture for the appropriate description of the heavy-ion nucleus scattering phenomena. We have brought the mathematics for the cross-section of the heavy-ion nucleus scattering to an analytic expression taking account of the deflection function (scattering angles) quantum mechanically. 9 Be, 16 O, ^Ne and 32 S heavy-ion beams elastic scattering from 28 Si, Mg and Ca target nuclei at various projectile energies over the range 20-151 MeV have been analysed in terms of the 2-parameter formalism of the present quantal formulation and from the Strong Absorption Model for comparison. Typical fits are shown and the nuclear parameters obtained from the analyses of both approaches are presented.