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From sparse measurements to dense DDX: Bayesian tensor analysis of proton-natPb for ADS source terms
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DOI：10.1007/s41365-026-02041-x.png)
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Abstract
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Accurate spallation-neutron source terms are essential for accelerator-driven systems (ADS), yet double-differential cross-section (DDX) data remain sparse, particularly for proton- $$^\text {nat}$$ Pb, a benchmark ADS target. We present a data-driven pathway from sparse measurements to dense DDX using a Bayesian tensor model together with a physics-consistent interpolation scheme tailored for ADS source-term construction. A total of 1,727 DDX points for proton– $$^\text {nat}$$ Pb, compiled from EXFOR and the literature, spanning eight incident energies (10 MeV–3 GeV) and seven angles (7.5– $$150^\circ$$ ), are used jointly to fit the tensor model. Under the selected hyperparameters, the model shows strong in-sample agreement on a logarithmic scale. For data-sparse checks, we compare predictions with the Bertini intranuclear-cascade model in Geant4 (and BERT_HP where available) on common discrete grids: Agreement is close below 10 MeV; in the 20–100 MeV band, where BERT/BERT_HP often underpredict the measurements, our predictions remain physically plausible. To deliver application-ready inputs, we construct a high-resolution dataset via bilinear interpolation in $$(E_\text {p},\theta )$$ on self-similar energy slices $$\kappa =\ln (E_\text {n}/E_\text {p})$$ , evaluated on a regular grid with 1 MeV spacing in $$E_\text {p}$$ and $$0.5^\circ$$ in $$\theta$$ , with a no-extrapolation policy. The interpolants preserve evaporation-like low-energy behavior and forward-peaked high-energy emission while remaining consistent with Geant4 trends. The resulting proton- $$^\text {nat}$$ Pb DDX dataset, covering the CiADS design point (500 MeV) and its neighborhood, can be coupled to transport codes (e.g., OpenMC) for anisotropic source-term calculations and can be extended to other targets and reactions.
Keywords:
Spallation neutrons
Double-differential cross-sections (DDX)
Bayesian tensor model
Proton-\(^{\text{nat}}\)Pb
ADS source terms
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