Kerbala Universityjournal of kerbala university1813-04101020050301Radial expectation values and electron density at the nucleus of four electron systemsالقيم المتوقعة القطرية والكثافة النووية عند النواة للأنظمة الرباعية الإلكترون445476996ENRukia Jaber DoshQassim Shamkhi AL-KhafajiJournal Article20131201In this paper it is formulated the Hartree-Fock equations for multi-electron systems in terms of two electron density function Γ (r1,r2) in order to solve Hartree-Fock equations in the algebraic approximation which called Hartree-Fock-Roothaan (H-F-R) method using slater type atomic orbitals published by ref. [31] for Be atom and ref. [32] for B+1ion . The radial expectation values of one particle , two particles and inter particles where (n=-1,-2, 1,2) of Be atom and B+1 ion in its ground state are calculated using Hartree-Fock wave function with analysis the one electron radial density function D(r1) and inter electron density function f(r12) for each shell. Electron density at the nucleus ρ(o) also evaluated for each shell and for total systems , using partitioning technique ,were in these systems there are six shells : KαKβ(K(1S)),αLα (KL (3S)), βLα (KL (1S)), KαLβ (KL (3S)), KβLβ(KL(3S)), LαLβ (L(1S))https://kj.uokerbala.edu.iq/article_76996_0f400525d6d5cf94aab4a077e466bcaa.pdf