Numerical study of the three-boson bound-state problem in partial-wave and vector-variable formulations
Abstract
We present a systematic benchmark of the three-boson bound-state problem in momentum space, comparing one-dimensional (1D) spectator-amplitude, two-dimensional (2D) partial-wave, and three-dimensional (3D) vector-variable formulations. The benchmark controls the interaction representation by embedding the same finite partial-wave interaction space in each formulation, so that discrepancies reflect discretization, interpolation, and quadrature errors. This enables direct 1D--2D--3D comparisons for separable interactions, controlled 2D--3D tests for local interactions, and comparison with the full local interaction in the 3D vector-variable formulation. Binding energies agree at the 10−6~MeV level for the separable interactions. For the local interactions at lmax=12, the 2D--3D differences are 2.2×10−6~MeV for MT-V and 5.3×10−5~MeV for MT-IV. The 2D and 3D equations are also solved in both t-matrix-driven and bare-potential-driven forms, whose agreement validates the permutation geometry, quadrature, and interpolation. Fourier transforms to coordinate space yield consistent norm decompositions and spatial observables, providing an independent check of the momentum-space solutions.
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BibTeX
@misc{schadow2026numerical,
title = {{Numerical study of the three-boson bound-state problem in partial-wave and vector-variable formulations}},
author = {Wolfgang Schadow and Mohammadreza R. Hadizadeh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.05028},
eprint = {2606.05028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05028},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Numerical study of the three-boson bound-state problem in partial-wave and vector-variable formulations
AU - Wolfgang Schadow
AU - Mohammadreza R. Hadizadeh
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2606.05028
UR - https://arxiv.org/abs/2606.05028
AB - We present a systematic benchmark of the three-boson bound-state problem in momentum space, comparing one-dimensional (1D) spectator-amplitude, two-dimensional (2D) partial-wave, and three-dimensional (3D) vector-variable formulations. The benchmark controls the interaction representation by embedding the same finite partial-wave interaction space in each formulation, so that discrepancies reflect discretization, interpolation, and quadrature errors. This enables direct 1D--2D--3D comparisons for separable interactions, controlled 2D--3D tests for local interactions, and comparison with the full local interaction in the 3D vector-variable formulation. Binding energies agree at the 10^−6~MeV level for the separable interactions. For the local interactions at l_max=12, the 2D--3D differences are 2.2×10^−6~MeV for MT-V and 5.3×10^−5~MeV for MT-IV. The 2D and 3D equations are also solved in both t-matrix-driven and bare-potential-driven forms, whose agreement validates the permutation geometry, quadrature, and interpolation. Fourier transforms to coordinate space yield consistent norm decompositions and spatial observables, providing an independent check of the momentum-space solutions.
ER -