- 10-206 Marcel Griesemer, Fabian Hantsch
- Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
Dec 23, 10
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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.