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Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

O. B. Tarasov

Abstract

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parameterizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion--ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the $^{78}$Kr and $^{124}$Xe projectiles. The resulting parameter trends are then propagated to the $^{92}$Mo and $^{144}$Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.

Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

Abstract

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parameterizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion--ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the Kr and Xe projectiles. The resulting parameter trends are then propagated to the Mo and Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.
Paper Structure (28 sections, 32 equations, 4 figures, 9 tables)

This paper contains 28 sections, 32 equations, 4 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Abrasion--ablation framework and fitting methodology
  3. Prefragment excitation-energy models
  4. AA model settings and fit parameters
  5. Objective function for AA minimization
  6. Quadratic component.
  7. Logarithmic component.
  8. Effective uncertainty for logarithmic weighting.
  9. Robust AA minimization for BMA-inspired fits
  10. Local-line cycling (mitigating local minima).
  11. Diagonal scaling (DSCL ) in levmar .
  12. Constraining the AA model with the $^{78}$Kr and $^{124}$Xe data
  13. BMA of the $^{78}$Kr and $^{124}$Xe data
  14. Extension to the $^{92}$Mo and $^{144}$Sm systems
  15. Propagation of the excitation-energy scale to additional projectiles
  16. ...and 13 more sections

Figures (4)

  • Figure 1: Measured production cross sections compared with the model-averaged abrasion--ablation (BMA-inspired) calculations and the EPAX3 parametrization. The isotopic distributions are shown as a function of mass number on a logarithmic cross-section scale. The left panel shows the $^{78}$Kr+$^{9}$Be reaction for fragments in the fitted range $26 \le Z \le 36$, while the right panel shows the $^{124}$Xe+$^{9}$Be reaction for fragments in the fitted range $44 \le Z \le 54$.
  • Figure 2: Model-averaged abrasion--ablation (BMA-inspired) production cross sections compared with the EPAX3 parametrization. Isotopic distributions are shown as a function of mass number on a logarithmic cross-section scale. The left panel corresponds to the $^{92}$Mo+$^{12}$C reaction for fragments in the range $32 \le Z \le 42$, while the right panel corresponds to the $^{144}$Sm+$^{12}$C reaction for fragments in the range $50 \le Z \le 62$. In both cases, the BMA predictions are obtained by propagating the trends and weights constrained by the $^{78}$Kr and $^{124}$Xe analyses.
  • Figure 3: BMA-inspired AA production cross sections for fragments with $Z=50$, 52, and 54, comparing projectile choices ($^{124}$Xe and $^{144}$Sm). The comparison illustrates how propagated BMA cross sections can guide projectile selection for targeted isotope production when combined with separator acceptance and transmission.
  • Figure 4: Global comparison of propagated BMA-inspired AA cross sections with the EPAX3 parametrization for all four projectiles considered in this work. Full isotopic distributions are shown on a logarithmic scale as a function of mass number for representative fragment chains with $Z=Z_{\rm proj}-8$, corresponding to $^{78}$Kr$\rightarrow$Ni, $^{92}$Mo$\rightarrow$Se, $^{124}$Xe$\rightarrow$Pd, and $^{144}$Sm$\rightarrow$Xe.