We have applied the Fonseca-Redish-Shanley solvable model for three bodies, two heavy and one light, in two dimensions for two types of Yamaguchi form factors in order to determine if the Efimov Effect exists there. The long-range effective heavy-heavy interaction which we extract in each case does not support an infinite number of bound states. Our results therefore indicate that the effect does not manifest itself in two dimensions.
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