Subleading contributions to $N$-boson systems inside the universal window

Abstract

We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of potential terms which have decreasing importance in the description of the binding energy of the systems. The leading order potential terms consist of a two-body term, usually attractive, plus a three-body term, usually repulsive; this last term is required to prevent the collapse of systems with more than two particles. At this order, the parametrization of the two-body potential is done to obtain a correct description of the scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a three-body datum. We investigate the role of the cut-off in the leading order description and we extend the exploration beyond the leading order by including the next-to-leading order terms in both, the two- and three-body potentials. We use the requirement of the stability of the N-body system, whose energy is variationally estimated, to introduce the three-body forces. The potential parametrization, as a function of the cut-off, is fixed to describe the energy of 4 He clusters up to seven particles within the expected accuracy. Finally, we also explore the possibility to describe at the same time the atom-dimer scattering length.

References in corpus (27)

• Universality in Few-body Systems with Large Scattering Length
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Efimov Physics: a review
• Effective Field Theory for Short-Range Forces
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Observation of the Efimov state of the helium trimer
• A renormalisation-group treatment of two-body scattering
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Spectra of helium clusters with up to six atoms using soft core potentials
• Four-Body Scale in Universal Few-Boson Systems
• Variational calculation of 4He tetramer ground and excited states using a realistic pair potential
• Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter and neutron stars
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• Effective Field Theory for Few-Boson Systems
• Efimov Physics and Connections to Nuclear Physics
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Nucleon-Nucleon Interaction and Isospin Violation
• Matching universal behavior with potential models
• Saturation properties of helium drops from a Leading Order description
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters
• Universal Short Range Correlations in Bosonic Helium Clusters
• Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics
• Universal behavior of few-boson systems using potential models
• A Many-Body Density Energy Functional

Cited by in corpus (2)

• Few-Nucleon Systems within Finite-Cutoff Pionless EFT
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters