The states of the barrier D Ϫ center which consists of a positive ion located on the z axis at a distance from the x-y plane and two electrons in the same plane bound by the ion are investigated based on a direct diagonalization method in finite and relatively high magnetic fields. The energies of the barrier D Ϫ states, the binding energies for the barrier D Ϫ states, and the expectation values of both the distance of the electron from the origin and distance between two electrons are obtained as functions of the applied magnetic field strength ␥ perpendicular to the x-y plane and the distance between the positive ion and the x-y plane. The effects of the higher Landau levels become small as ␥ and increase. The change of symmetry of the barrier D Ϫ ground state is possible in finite magnetic fields. Both the distance of the electron from the origin and distance between two electrons vary discontinuously with the changes of symmetry of the barrier D Ϫ ground states. Our calculations indicate that the phase transitions of the barrier D Ϫ ground states can be observed in real systems.
The relation between the electron-electron correlations and magnetic-field-induced angular momentum transitions in the barrier D − centre is investigated based on a variational method. The Chandrasekhar-type variational wavefunctions for the barrier D − states are constructed based on the exact solutions in the strong-magnetic-field limit. The energies of the barrier D − states, the binding energies, the electron densities, the angular correlations, and the average distances between the two electrons are obtained as functions of the applied magnetic field strength γ and the distance ζ between the positive ion and the plane where the two electrons reside. When the transitions of the barrier D − ground state occur for finite ζ with increasing γ , the strong correlations appear in the electron densities, the angular correlations, and the average distances between the two electrons. As a consequence of detailed considerations of the relation between the angular correlations and the strength of binding, we find that the magnetic-fieldinduced angular-momentum transitions occur as a result of the strong correlations in the barrier D − states.
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