Marcel Griesemer, Fabian Hantsch
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
(266K, pdf)

ABSTRACT.  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 $Z\geq 35$ 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.