Profiling the radial correlation factor of atoms

When shell density approximations are applied, the radial correlation factor of atoms is shown to be expressed by a block-diagonal step function composed of shell window functions. The step value in a shell region is determined by the number of electrons in that shell. The electron annihilation function, obtained from a particular case of the correlation factor, is given by the shell window function and the occupation number of the outermost shell. The accuracy of the present simple results is checked through comparison with the numerical Hartree–Fock results for 21 ground-state atoms selected from various groups of the first five periods. The effect of the electron correlation is examined for five light atoms. (paper)