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It is well-known that three-boson systems show the Efimov effect when thetwo-body scattering length $a$ is large with respect to the range of thetwo-body interaction. This effect is a manifestation of a discrete scalinginvariance (DSI). In this work we study DSI in the $N$-body system by analysingthe spectrum of $N$ identical bosons obtained with a pairwise gaussianinteraction close to the unitary limit. We consider different universal ratiossuch as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of theground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. Wediscuss the extension of the Efimov radial law, derived by Efimov for $N=3$, togeneral $N$.

Efimov spectrum in bosonic systems with increasing number of particles