Energies of K-shell for some atoms electrons

Abstract

Using the equation approximation of the Hartree-Fock (HF) method, the K-shell energies and atomic properties of the (Neon(Ne), sodium(Na), Magnesium(Mg), Aluminium (Al), and Silicon(Si)) atoms were calculated and compared with available experimental data from comprehensive studies. For atomic numbers in the range 10 ≤ Z ≤ 14, the computed atomic energies were thoroughly evaluated. The findings confirmed the reliability and accuracy of the approximations employed in determining these atomic characteristics. The single-particle radial density distribution function D(r₁) and the interparticle distribution function f(r₁₂) were among the atomic properties analysed and the associated statistical moments, where n is between -2 and 2, ⟨r₁ⁿ⟩ and ⟨r₁₂ⁿ⟩.Additionally, several key energy expectation values were computed, including the )electron-electron repulsion potential ⟨Vₑₑ⟩, the nucleus-electron attraction potential ⟨Vₑₙ⟩, the total potential ⟨V⟩, the kinetic ⟨T⟩, and the total (Hartree-Fock) ⟨E⟩) energies. In conclusion, all values of the examined energies rise as the atomic number increases. Ultimately, all computations were performed in atomic units, and the equations were programmed in Mathematics 2015.