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Since the $^4$He dimer supports only one weakly bound state with an averageinteratomic distance much larger than the van der Waals length and no deeplybound states, $^4$He$_N$ clusters with $N>2$ are a paradigmatic model systemwith which to explore foundational concepts such as large $s$-wave scatteringlength universality, van der Waals universality, Efimov physics, and effectivefield theories. This work presents structural properties such as the pair andtriple distribution functions, the hyperradial density, the probability to findthe $N$th particle at a given distance from the center of mass of the other$N-1$ atoms, and selected contacts. The kinetic energy release, which can bemeasured via Coulomb explosion in dedicated size-selected molecular beamexperiments -- at least for small $N$ -- , is also presented. The structuralproperties are determined for three different realistic $^4$He-$^4$Heinteraction potentials and contrasted with those for an effective low-energypotential model from the literature that reproduces the energies of $^4$He$_N$clusters in the ground state for $N=2$ to $N=\infty$ at the $\gtrsim95$~percent level with just four input parameters. The study is extended tounitarity (infinite $s$-wave scattering length) by artificially weakening theinteraction potentials. In addition to contributing to the characterization ofsmall bosonic helium quantum droplets, our study provides insights into theeffective low-energy theory's predictability of various structural properties.

Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity