This paper is an effort to extract the structure function, the EMC ratio, and the lepton scattering cross section in the convolution nuclear theory framework for ⁴He and ¹²C nuclei. We suppose that, in conventional approach, based on harmonic oscillator model, one could consider for a nucleus shell different hw parameters which are associated with the square root of the mean radius of the nucleus shells. We use GRV free nucleon structure function, which has good agreement with the proton and neutron structure function, extracted from experimental results. In addition, the lepton scattering cross sections of ⁴He and ¹²C nuclei are calculated in energy higher than 1 GeV. The extracted results show good agreement with experimental data.