Multi-fermion systems with contact theories

Abstract

We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into clusters, if mixed-symmetry of its wave function is enforced. We claim that any theory in which the two-body scattering length is much larger than any other scale involved exhibits such instability. We exemplify this with the inability of the leading-order pionless effective field theory to describe stable states of $A>4$ nuclei. A finite interaction range is identified as a sufficient condition for a bound mixed-symmetry system. The minimal value of this range depends on the proximity of a system to unitarity, on the number of constituents, and on the particular realization of discrete scale invariance of the three-body spectrum.

15 pages, 3 figures

References in corpus (26)

• Universality in Few-body Systems with Large Scattering Length
• Weakly bound dimers of fermionic atoms
• Renormalization of the Three-Body System with Short-Range Interactions
• Nuclear effective field theory: status and perspectives
• Efimov Physics: a review
• Effective Theory of the Triton
• Effective Field Theory of Nuclear Forces
• Low-energy Universality and the New Charmonium Resonance at 3870 MeV
• Interference and binding effects in decays of possible molecular component of X(3872)
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• Effective field theory description of halo nuclei
• On the correlation between the binding energies of the triton and the alpha-particle
• Low-energy three-body dynamics in binary quantum gases
• alpha-alpha Scattering in Halo Effective Field Theory
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• Nuclear Physics Around the Unitarity Limit
• Weakly Bound Cluster States of Efimov Character
• Pion-less effective field theory for atomic nuclei and lattice nuclei
• Spectra of helium clusters with up to six atoms using soft core potentials
• Effective Field Theory for Few-Boson Systems
• How to Renormalize the Schrodinger Equation
• Embedding nuclear physics inside the unitary window
• Ground-state properties of unitary bosons: from clusters to matter
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Scattering of universal fermionic clusters in the resonating group method

Cited by in corpus (7)

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• Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Few nucleons scattering in pionless effective field theory
• The Four-Boson First-Excited State Near Two-Body Unitarity
• Feasibility of perturbative generation of bound-states from resonances or virtual states
• Machine learning the single-$\Lambda$ hypernuclei with neural-network quantum states