arXiv subjects

Wolfgang Schadow

Publications and source records attributed to Wolfgang Schadow.

4 recordsLinked to original sources

arXiv2026

Numerical study of the three-boson bound-state problem in partial-wave and vector-variable formulations

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 separable interactions and at the few-$10^{-6}$ to $10^{-5}$~MeV level for local interactions. 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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arXiv2026

Numerical study of the two-boson bound-state problem with and without partial-wave decomposition

The validation of numerical methods is a prerequisite for reliable few-body calculations, particularly when moving beyond standard partial-wave decompositions. In this work, we present a precision benchmark for the two-boson bound-state problem, solving it using two complementary formulations: the standard one-dimensional partial-wave Lippmann--Schwinger equation and a two-dimensional formulation based directly on vector variables. While the partial-wave approach is computationally efficient for low-energy bound states, the vector-variable formulation becomes essential for scattering applications at higher energies where the partial-wave expansion converges slowly. We demonstrate the high-precision numerical equivalence of both methods using rank-one separable Yamaguchi potentials and non-separable Malfliet--Tjon interactions. Furthermore, for the Yamaguchi potential, we derive exact analytical expressions quantifying the systematic errors introduced by finite momentum- and coordinate-space cut-offs. These analytical bounds provide a rigorous tool for disentangling discretization errors from truncation effects in few-body codes. The results establish a highly controlled methodological benchmark that provides a detailed baseline for vector-variable algorithms intended for more complex three- and four-body calculations.

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arXiv2002

Radiative Muon Capture by He-3

The rate of the nuclear reaction $^3He+μ^- \to ^3H+γ+ν_μ$ has been calculated using both the elementary particle model (EPM) approach and the impulse approximation (IA) approach. Using the EPM approach, the exclusive statistical radiative muon capture (RMC) rate for photon energy greater than 57 MeV is found to be $0.245 s^{-1}$ and the ordinary muon capture (OMC) rate to be $1503 s^{-1}$. The IA calculation exhibits a slight dependence on the type of trinucleon wave functions used. The difference between the IA and EPM calculation is larger for RMC than for OMC. To resolve the difference between the two approaches a more detailed investigation including meson exchange corrections will be required.

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arXiv1997

The pd <--> pi+ t reaction around the Delta resonance

The pd <--> pi+ t process has been calculated in the energy region around the Delta-resonance with elementary production/absorption mechanisms involving one and two nucleons. The isobar degrees of freedom have been explicitly included in the two-nucleon mechanism via pi-- and rho-exchange diagrams. No free parameters have been employed in the analysis since all the parameters have been fixed in previous studies on the simpler pp <--> pi+ d process. The treatment of the few-nucleon dynamics entailed a Faddeev-based calculation of the reaction, with continuum calculations for the initial p-d state and accurate solutions of the three-nucleon bound-state equation. The integral cross-section was found to be quite sensitive to the NN interaction employed while the angular dependence showed less sensitivity. Approximately a 4% effect was found for the one-body mechanism, for the three-nucleon dynamics in the p-d channel, and for the inclusion of a large, possibly converged, number of three-body partial states, indicating that these different aspects are of comparable importance in the calculation of the spin-averaged observables.

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