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

TL;DR

This study investigates the structural properties of small bosonic helium clusters with N=2-10 atoms across different potential models, including at unitarity, to understand universality and effective field theories in quantum droplets.

Contribution

It provides detailed structural analysis of helium clusters using multiple potentials and compares them with an effective low-energy model, extending insights to the unitarity limit.

Findings

Structural properties vary with potential models.

Effective low-energy model reproduces energies with high accuracy.

Unitarity case reveals universal behavior.

Abstract

Since the $^4$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, $^4$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 hyperradial density, the probability to find the $N$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 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 $^4$He-$^4$He interaction potentials and contrasted with those for an effective low-energy potential 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 $\gtrsim 95$~percent 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.