Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

摘要

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number Z is sufficiently large compared to the number N of electrons. More specifically, a two-electron atom with atomic number Z ≧ 35 has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some Z > 1, which exhibits a phase segregation.