A theoretical model has been adopted to calculate the low energy electron of scattering quantities, such as differential cross section (DCS),phase shift (PS) ,and intensity of spectra. The total scattering potential in this model is the sum of coulomb interaction, exchange, correlation, and polarization potential. For exchange potential , a spin dependent Hara potential is used together with three spin dependent correlation potential, as follows :-Perdow -Wange , Perdow -Zange ,and Vosko- Wilk- Nusair . Two sets of wave functions have been used in these calculations, the result from different self- consistent method is used to solve Roothan - Hartree Fock equation. This model is used to determine the DCS, PS , total cross section and critical points of electron scattering from free ( Ar )atoms by using LEED technique. Electron scattering profiles are calculated for the electron scattering from the Al(l00), Ag(l00) and Au(100)surfaces, and for different beam directions. These calculations show that, Perdow -Wange Potential gave the best results, compared with experimental data. For the present results, it can be concluded that the relaxation value of the studying surface are: For Al is3%,for Agis 3% t0 6% and for Au is 6% .For the beam (11) and (θ = 0°,ψ = 0°) both of the theoretical and experimental data of AI and Ag have the same behavior and peak position.