This paper presents an analytical formula for the neutron scattering cross section on even-even heavy nuclei using the rotational model and some assumptions as a Yukawa potential shape for neutron-nucleon interaction, rigid rotor approximation, and nuclear matter uniformly distributed within the nuclear matter. The most important characteristic in this study is the avoidance of any approximation of central potential, opposed to what usually happens: the expansion of the potential according to the power of β2, over the Legendre polynomial basis or within Fourier-Bessel analysis. Satisfying and encouraging results have been acquired despite the simplicity of the chosen model (rigid rotor model and the two-parameter potential).