Existence of a solution to Hartree–Fock equations with decreasing magnetic fields

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge ZZ of KK nuclei exceeds N−1N−1, where NN is the number of electrons. In the opposite direction, no ground state exists if N>2Z+KN>2Z+K.