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arXiv:2401.15402

Universality for Three Bosons with Large, Negative Effective Range: Aspects and Addenda

Harald W. Grießhammer

Published Jan 27, 2024• 0 citations
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Abstract

Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its leading order is non-perturbative, and its observables depend only on the dimensionless ratio $ξ:=2r_0/a$ once $|r_0|$ is chosen as base unit. This presentation highlights aspects for three identical spinless bosons and adds details to a previous discussion [1]. At leading order, no three-body interaction is needed. A ground state exists only in the range $0.366\ldots\geξ\ge-8.72\ldots$, and excited states display self-similarity and Discrete Scale Invariance, with small corrections for nonzero $r_0$.

DOI
10.48550/arxiv.2401.15402

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Three- and four-boson systems expanded around the unitarity limit: Application to 4^44He molecules
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We develop an effective field theory (EFT) for strongly interacting bosonic clusters, using 4^44He as a paradigmatic example of universality in systems with large scattering length. At leading order (LO), two- and three-body zero-range interactions are entirely determined by the dimer and trimer ground-state energies. We show that ground-state energies for up to N=15N=15N=15 particles converge to cutoff-independent limits with extrapolation coefficients of natural size. At next-to-leading order (NLO), corrections stemming from the two-body interaction range and a four-body force, calibrated to the tetramer ground-state energy, reduce cutoff sensitivity. Close agreement with results from a realistic potential is found at LO and improved at NLO, demonstrating systematic convergence with few parameters at each order. The resulting EFT is directly applicable to larger clusters and bulk helium.