In this study, we calculate the scattering cross sections of two \(\Upsilon (1S)\) mesons using a potential model combined with the Resonating Group Method (RGM), employing the adiabatic approximation to characterize meson interactions. We investigate two scenarios: one with a point-like form factor ( \(f=1\) ) and another with a Gaussian form factor, to explore how the internal structure of the meson affects the interaction. At a center-of-mass kinetic energy of 0.01 GeV, the maximum value of total spin-averaged cross section comes out to be 0.3 mb for the point-like form and 0.19 mb for the Gaussian form with quadratic potential. For the Cornell potential, the values are 0.18 and 0.11 mb, respectively, with the same center-of-mass kinetic energy. This shows a reduction in the cross section when the internal structure of the mesons is taken into account. The small variation between these values indicates that the form factor has a limited effect on \(\Upsilon (1S)\) scattering, likely due to the larger mass of the mesons and smaller rms radii. In contrast, lighter mesons exhibit a more pronounced reduction in cross sections when the Gaussian form factor is applied, highlighting their greater sensitivity to the form factor’s detailed shape. This contrast opens up new avenues for future research and we discuss such possibilities at the end of the paper.
