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

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.

arXiv comment17 pages, 7 figures

References in corpus (48)

• Universality in Few-body Systems with Large Scattering Length
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Efimov Physics: a review
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Spectroscopy and dynamics in helium nanodroplets
• Helium nanodroplet isolation ro-vibrational spectroscopy: methods and recent results
• Structural and dynamical properties of superfluid helium: a density functional approach
• Momentum sharing in imbalanced Fermi systems
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Observation of the Efimov state of the helium trimer
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Introduction to the Diffusion Monte Carlo Method
• Efimov Physics in Cold Atoms
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Cold Physics and Chemistry: Collisions, Ionization and Reactions inside Helium Nanodroplets Close to Zero K
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• The structure of the atomic helium trimers: Halos and Efimov states
• Universal Relations for Identical Bosons from 3-Body Physics
• Weakly Bound Cluster States of Efimov Character
• Microscopic Origin and Universality Classes of the Efimov Three-Body Parameter
• Imaging the He${}_2$ quantum halo state using a free electron laser
• Generalized nuclear contacts and the nucleon's momentum distributions
• Scale and Scheme Independence and Position-Momentum Equivalence of Nuclear Short-Range Correlations
• Few-body physics in resonantly interacting ultracold quantum gases
• Physical Origin of the Universal Three-body Parameter in Atomic Efimov Physics
• Catching proteins in liquid helium droplets
• Variational description of the Helium trimer using correlated hyperspherycal harmonic basis functions
• Universality in the Three-Body Problem for 4He Atoms
• The few-body problem for trapped bosons with large scattering length
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• Variational calculation of 4He tetramer ground and excited states using a realistic pair potential
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Experimental evaluation of the nuclear neutron-proton contact
• The ^4He trimer as an Efimov system
• Universality and the three-body parameter of helium-4 trimers
• $N$-boson spectrum from a Discrete Scale Invariance
• Universality in Efimov associated tetramers in 4He
• Energy and structural properties of $N$-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator
• Efimov physics and the three-body parameter for shallow van der Waals potentials
• Saturation properties of helium drops from a Leading Order description
• Elusive structure of helium trimers
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Frustrated Coulomb explosion of small helium clusters
• Universal Short Range Correlations in Bosonic Helium Clusters
• Non-Universal and Universal Aspects of The Large Scattering Length Limit
• The van der Waals interaction as the starting point for an effective field theory

Cited by in corpus (2)

• Perspectives on few-body cluster structures in exotic nuclei
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters