Determination the Effect of the Coulomb Correlation for He And He-Like Ions Using Different Wave Functions

The aim of this work to evaluate electron correlation on the one-particle radial distribution function  used the uncorrelated wave function Hartree-Fock (HF) and correlated wave function Configuration-Interaction (CI). The effect of electron correlation on one-particle radial distributions is also demonstrated by comparison of expectation value for one-particle radial distribution function.we concludes that the one-particle radial distribution function increase as increase the atomic number Z, also increase the one-particle expectation value  when the Z increase when n=1, 2 but decrease when n=-1, -2. The electron correlation increase with increase the atomic number Z. the result of the one-particle expectation value for Hartree-Fock compared with the result of Bunge 1993 and for Configuration-Interaction compared with the result of A.Gupta and R.J.boyd in 1977.