Structural properties of HeN4 ( N=2–10 ) clusters for different potential models at the physical point and at unitarity

Abstract

Since the $^{4}\mathrm{He}$ dimer supports only one weakly bound state with an average interatomic distance much larger than the van der Waals length and no deeply bound states, $^{4}\mathrm{He}_{N}$ clusters with $N>2$ are a paradigmatic model system with which to explore foundational concepts such as large $s$-wave scattering length universality, van der Waals universality, Efimov physics, and effective field theories. This work presents structural properties such as the pair and triple distribution functions, the hyper-radial density, the probability to find the $N\mathrm{th}$ particle at a given distance from the center of mass of the other $N\ensuremath{-}1$ atoms, and selected contacts. The kinetic energy release, which can be measured via Coulomb explosion in dedicated size-selected molecular beam experiments---at least for small $N$ -- is also presented. The structural properties are determined for three different realistic $^{4}\mathrm{He}\ensuremath{-}^{4}\mathrm{He}$ interaction potentials and contrasted with those for an effective low-energy potential model from the literature that reproduces the energies of $^{4}\mathrm{He}_{N}$ clusters in the ground state for $N=2$ to $N=\ensuremath{\infty}$ at the $\ensuremath{\gtrsim}$95% level with just four input parameters. The study is extended to unitarity (infinite $s$-wave scattering length) by artificially weakening the interaction potentials. In addition to contributing to the characterization of small bosonic helium quantum droplets, our study provides insights into the effective low-energy theory's predictability of various structural properties.