The universal properties of a three-boson system with large scattering length are well understood within the framework of Eﬀective Field Theory. They include a geometric spectrum of shallow three-body bound states called “Eﬁmov states” and log-periodic dependence of scattering observables on the scattering length. We investigate the modiﬁcation of this spectrum in a ﬁnite cubic box using a partial wave expansion. The dependence of the binding energies on the box size is calculated for systems with positive and negative two-body scattering length. We compare the full results to results obtained using an expansion around the inﬁnite volume binding energy. The renormalization of the Eﬀective Field Theory in the ﬁnite volume is veriﬁed explicitly
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