Abstract The spectrum of the 4He3 and 3He4He2 trimers are studied using the Faddeev differential equations with different realistic potentials. The influence assessment of a modern potential models on the binding energies of these systems is studied.

Physics of Particles and NucleiNov 29, 20231 citation

Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit

Lucas A. Souza

nucl-thCross-listedarXiv:2606.10343Few-Body SystemsJun 10, 20260 citations

Few-Body Systems

Symmetrized Faddeev Equations

Hiroyuki Kamada, J. Golak

Published Aug 20, 2021• 0 citations

Publisher

DOI: 10.1007/s00601-021-01664-7

Related papers

Adiabaticity in Faddeev Equations

BERTRAND G. GIRAUD, Jaume Carbonell, N. Takigawa

Few-body systems. SupplementumJan 1, 19990 citations

New variants of many-particle Faddeev equations

B.E. Grinyuk

Theoretical and Mathematical PhysicsJun 1, 19800 citations

Zero-energy scattering in symmetric Coulomb systems via Faddeev approach

Andrei A. Kvitsinsky, Chi‐Yu Hu

A method based on the modified Faddeev equations in the total-angular-momentum representation is developed to treat the zero-energy scattering in symmetric three-body Coulomb systems. The method is applied to calculate the s-wave scattering lengths of the systems ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$+(${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ ${\mathit{e}}^{+}$ ), p+(p\ensuremath{\mu}), and d+(d\ensuremath{\mu}). A large negative value of the even-parity p+(p\ensuremath{\mu}) scattering length indicates the presence of a virtual state near threshold.A method based on the modified Faddeev equations in the total-angular-momentum representation is developed to treat the zero-energy scattering in symmetric three-body Coulomb systems. The method is applied to calculate the s-wave scattering lengths of the systems ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$+(${\mathit{e}}^{\mathrm{\ensuremath{-}}}$${\mathit{e}}^{+}$), p+(p\ensuremath{\mu}), and d+(d\ensuremath{\mu}). A large negative value of the even-parity p+(p\ensuremath{\mu}) scattering length indicates the presence of a virtual state near threshold.

Physical Review AFeb 1, 199320 citations

THE APPLICATION OF THE FADDEEV EQUATIONS TO AN EXACTLY SOLUBLE MODEL.

Michael A. Hennell

Jan 1, 19680 citations

The Properties of the Symmetric and Asymmetric Helium Three-Atomic Systems

A. A. Korobitsin, Elena A. Kolganova

Physics of Particles and NucleiNov 29, 20231 citation

Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit

Lucas A. Souza

We apply a deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit. The network is trained by minimizing the residual of the discretized integral equation, while the positive binding scale associated with the three-body energy is treated as a trainable parameter. Deterministic diagonalization of the same discretized kernel is used only as an a posteriori numerical benchmark. As preliminary validation, the neural-solver strategy is tested on the analytically solvable hydrogen radial problem. At unitarity, the DNN reproduces the Efimov ground-state binding scale with a DNN--deterministic deviation of $0.022\%$ , while the first excited state is recovered to $0.002\%$ . The deterministic solver recovers the universal Efimov scaling ratio $e^{2π/s_0}\simeq 515.03$ , and the neural method traces the bound-state branches as a function of the inverse scattering length $1/a$ by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.We apply a deep-neural-network (DNN) ansatz to the symmetrized spectator vector of the subtracted three-body Faddeev integral equation for identical bosons near the Efimov limit. The network is trained by minimizing the residual of the discretized integral equation, while the positive binding scale associated with the three-body energy is treated as a trainable parameter. Deterministic diagonalization of the same discretized kernel is used only as an a posteriori numerical benchmark. As preliminary validation, the neural-solver strategy is tested on the analytically solvable hydrogen radial problem. At unitarity, the DNN reproduces the Efimov ground-state binding scale with a DNN--deterministic deviation of $0.022\%$, while the first excited state is recovered to $0.002\%$. The deterministic solver recovers the universal Efimov scaling ratio $e^{2π/s_0}\simeq 515.03$, and the neural method traces the bound-state branches as a function of the inverse scattering length $1/a$ by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.

nucl-thCross-listedarXiv:2606.10343Few-Body SystemsJun 10, 20260 citations

{\mathit{e}}^{+}

), p+(p\ensuremath{\mu}), and d+(d\ensuremath{\mu}). A large negative value of the even-parity p+(p\ensuremath{\mu}) scattering length indicates the presence of a virtual state near threshold.

0.022\%

, while the first excited state is recovered to

0.002\%

. The deterministic solver recovers the universal Efimov scaling ratio

e^{2π/s_0}\simeq 515.03

, and the neural method traces the bound-state branches as a function of the inverse scattering length

1/a

by continuation from the unitary solution. These results indicate that DNN-based residual minimization can provide a compact and differentiable representation of a renormalized few-body integral-equation solution in a regime governed by discrete scale invariance.