Three- and four-boson systems expanded around the unitarity limit: Application to 4He molecules
Abstract
The three- and four-boson systems with a large scattering length and a short effective range in the two-body sector are studied in the framework of Short-Range Effective Field Theory (SREFT). The starting point (leading order) of the EFT is taken to be the universal unitarity limit, where the two-body sector is parameter-free and only one three-body parameter enters. In this limit, physical systems manifest discrete scale invariance. Deviations from universality arising from finite scattering-length and effective-range corrections, as well as a four-body force required by renormalization, are included perturbatively at next-to-leading order. The three-body ground state and its associated four-body ground and first-excited states are studied using the Faddeev-Yakubovsky (FY) formalism and a complementary diagrammatic approach. By employing techniques to remove contributions from deep trimers in tetramer calculations, we extend our analysis to larger cutoffs than previously accessible within the FY approach to SREFT. Our results for binding energies and radii of 4He three- and four-atom systems converge well to results obtained with sophisticated phenomenological potentials. These successes suggest that the physics of 4He atomic clusters is governed by only small deviations from discrete scale invariance.
Versions
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BibTeX
@misc{wu2026three,
title = {{Three- and four-boson systems expanded around the unitarity limit: Application to $^4$He molecules}},
author = {Feng Wu and Xincheng Lin and Ubirajara van Kolck and Sebastian König},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.00854},
eprint = {2606.00854},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00854},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Three- and four-boson systems expanded around the unitarity limit: Application to ^4He molecules
AU - Feng Wu
AU - Xincheng Lin
AU - Ubirajara van Kolck
AU - Sebastian König
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.00854
UR - https://arxiv.org/abs/2606.00854
AB - The three- and four-boson systems with a large scattering length and a short effective range in the two-body sector are studied in the framework of Short-Range Effective Field Theory (SREFT). The starting point (leading order) of the EFT is taken to be the universal unitarity limit, where the two-body sector is parameter-free and only one three-body parameter enters. In this limit, physical systems manifest discrete scale invariance. Deviations from universality arising from finite scattering-length and effective-range corrections, as well as a four-body force required by renormalization, are included perturbatively at next-to-leading order. The three-body ground state and its associated four-body ground and first-excited states are studied using the Faddeev-Yakubovsky (FY) formalism and a complementary diagrammatic approach. By employing techniques to remove contributions from deep trimers in tetramer calculations, we extend our analysis to larger cutoffs than previously accessible within the FY approach to SREFT. Our results for binding energies and radii of ^4He three- and four-atom systems converge well to results obtained with sophisticated phenomenological potentials. These successes suggest that the physics of ^4He atomic clusters is governed by only small deviations from discrete scale invariance.
ER -