The case of (Q) over cap(chi 1).(Q) over cap(chi 1)-(Q) over cap(chi 2).(Q) over cap(chi 2) mixing in the interacting boson model is studied within its mean-field approximation. It is shown that the criticality conditions lead to two classes of solutions and that chi 1 and chi 2 need to have an opposite sign to allow for prolate-oblate shape coexistence. No evidence for a stable triaxial minimum is found. Phase diagrams for selected cases have been constructed.
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