From few to many bosons inside the unitary window: a transition between universal to non-universal behavior

Abstract

Universal behaviour in few-bosons systems close to the unitary limit, where two bosons become unbound, has been intensively investigated in recent years both experimentally and theoretically. In this particular region, called the unitary window, details of the inter-particle interactions are not important and observables, such as binding energies, can be characterized by a few parameters. With an increasing number of particles the short-range repulsion, present in all atomic, molecular or nuclear interactions, gradually induces deviations from the universal behaviour. In the present letter we discuss for the first time a simple way of incorporating non-universal behaviour through one specific parameter which controls the smooth transition of the system from universal to non-universal regime. Using a system of $N$ helium atoms as an example we calculate their ground state energies as trajectories within the unitary window and also show that the control parameters can be used to determine the energy per particle in homogeneous systems when $N\to \infty$.

arXiv comment6 pages, 3 figures

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• Subleading contributions to $N$-boson systems inside the universal window
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Improvement of the Envelope Theory for Systems with Different Particles
• A Many-Body Density Energy Functional
• Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters
• Compact equations for the envelope theory
• The excited state of the $\alpha$-particle: a benchmark study
• The role of the effective range in strongly-interacting few-body systems