The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present article we determine for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which the Efimov effect can exist for different values of the mass ratio $mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov discrete scaling factor, ${rm exp},(pi/s)$, as a function of a wide range of values of $mathpzc{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.
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