Matching universal behavior with potential models

Abstract

Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed.

8 pages, 4 figures

References in corpus (30)

• Feshbach Resonances in Ultracold Gases
• Universality in Few-body Systems with Large Scattering Length
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Renormalization of the Three-Body System with Short-Range Interactions
• Effective Theory of the Triton
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• Efimov Resonances in Ultracold Quantum Gases
• Universality of the three-body Efimov parameter at narrow Feshbach resonances
• Analytical solution of the bosonic three-body problem
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Efimov physics beyond universality
• Finite range corrections near a Feshbach resonance and their role in the Efimov effect
• Association of Efimov trimers from a three-atom continuum
• Efimov physics in bosonic atom-trimer scattering
• Universality and scaling limit of weakly-bound tetramers
• Spectra of helium clusters with up to six atoms using soft core potentials
• Universal Equation for Efimov States
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Universality and scaling in the $N$-body sector of Efimov physics
• Momentum-space calculation of four-boson recombination
• $N$-boson spectrum from a Discrete Scale Invariance
• Universal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold
• The helium trimer with soft-core potentials
• Universality in Efimov associated tetramers in 4He
• Shallow Efimov tetramer as inelastic virtual state and resonant enhancement of the atom-trimer relaxation
• Universality in bosonic dimer-dimer scattering
• Efimov physics with $1/2$ spin-isospin fermions
• Universal range corrections to the Efimov trimer for a class of paths to the unitary limit
• Ultracold bosons in the vicinity of a narrow resonance: shallow dimer and recombination

Cited by in corpus (14)

• Efimov Physics and Connections to Nuclear Physics
• Embedding nuclear physics inside the unitary window
• Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
• 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
• More on the universal equation for Efimov states
• Neutron${-}^{19}$C scattering: emergence of universal properties in a finite range potential
• Subleading contributions to $N$-boson systems inside the universal window
• Resonant spectra of multipole-bound anions
• Mass Ratio Dependence of Three-Body Resonance Lifetimes in 1D and 3D
• Universal behavior of few-boson systems using potential models
• Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions
• The role of the effective range in strongly-interacting few-body systems
• Gaussian characterization of two-neutron halo nuclei