Measurements of Bremsstrahlung-Averaged Cross Sections for Reactions on Natural Nickel Targets at Eendpoint = 40MeV

Technical Summary: Measurements of Bremsstrahlung-Averaged Cross Sections for Reactions on Natural Nickel Targets at $E_{\text{endpoint}} = 40$ MeV

Problem Statement
The production of medical radioisotopes such as $^{57}\text{Ni}$, $^{56}\text{Ni}$, $^{58}\text{Co}$, $^{57}\text{Co}$, $^{56}\text{Co}$, and $^{55}\text{Co}$ via photonuclear reactions on natural nickel targets requires accurate knowledge of bremsstrahlung-averaged cross sections (BACS). While these isotopes have established roles in nuclear medicine (e.g., PET imaging and $\gamma$-ray spectrometry calibration), experimental data for nickel-based targets under production-relevant irradiation conditions remain limited. Existing evaluations, such as JENDL-5, and theoretical models like TALYS show discrepancies, particularly for charged-particle emission channels (e.g., $(\gamma, p)$ and $(\gamma, pn)$). A primary challenge in extracting reliable BACS values is the rigorous characterization of the incident photon flux, which is heavily influenced by the bremsstrahlung converter geometry and thickness. Without a validated photon flux model, quantitative interpretation of activation yields is compromised.

Methodology
The study employed a two-part experimental and analytical approach using the TT-300HE Rhodotron™ electron accelerator at NorthStar Medical Radioisotopes, LLC.

1. Experimental Setup:

   • Beam: A 40 MeV electron beam with a nominal current of 1 $\mu$A was directed onto a 6 mm thick water-cooled tantalum converter.
   • Targets: A high-purity natural nickel foil (0.449 g, 0.5 mm thick) served as the primary target. A natural tin foil (0.6186 g) was used as a flux monitor for model validation.
   • Irradiation: The nickel target was irradiated for 61 seconds. The tin target was irradiated for 10 seconds in a separate validation run.
   • Detection: Post-irradiation, samples were analyzed using high-purity germanium (HPGe) detectors. Counting for nickel began 1.37 hours after irradiation and lasted approximately 14 hours.

2. Monte Carlo Modeling and Validation:

   • Simulation: The bremsstrahlung photon flux was modeled using MCNP6.3 with an unstructured 3D mesh generated from CAD models via the Attila4MC interface. The geometry included the converter, shielding, and targets.
   • Flux Validation: To address uncertainties in the converter thickness and beam current, the simulated flux was validated against the natural tin activation data. A $\chi^2$-minimization procedure was applied to a two-energy-group flux parameterization (6–15 MeV and 15–40 MeV) using five independent tin activation products ($^{110}\text{Sn}$, $^{111}\text{Sn}$, $^{113}\text{Sn}$, $^{117\text{m}}\text{Sn}$, $^{123\text{m}}\text{Sn}$). This yielded correction factors ($p_{lo} = 27.06$, $p_{hi} = 6.10$) to align the simulation with experimental yields.

3. Cross Section Extraction:

   • Using the validated, corrected photon flux, BACS values were extracted from the measured end-of-irradiation (EOI) activities of the nickel reaction products.
   • For isotopes produced via both direct and indirect pathways (e.g., $^{57}\text{Co}$ from $^{58}\text{Ni}(\gamma, p)$ and $^{57}\text{Ni}$ decay; $^{56}\text{Co}$ from $^{58}\text{Ni}(\gamma, pn)$ and $^{56}\text{Ni}$ decay), the analysis explicitly accounted for time-dependent feeding and decay during the counting interval.
   • For $^{55}\text{Co}$, where no statistically significant signal was observed, a one-sided 90% confidence-level upper limit was established.

Key Results
The study determined the following bremsstrahlung-averaged cross sections (BACS) for reactions on natural nickel at a 40 MeV endpoint:

• $^{58}\text{Ni}(\gamma, n)^{57}\text{Ni}$: $8.983 \pm 0.028$ mb. This agrees well with the JENDL-5 evaluation ($10.293$ mb) when folded with the same flux.
• $^{58}\text{Ni}(\gamma, 2n)^{56}\text{Ni}$: $0.248 \pm 0.025$ mb. Consistent with the JENDL-5 prediction ($0.231$ mb).
• $\text{natNi}(\gamma, pxn)^{58}\text{Co}$: $0.704 \pm 0.218$ mb. The experimental value is higher than the JENDL-5 prediction ($0.216$ mb) but remains within experimental uncertainty.
• $^{58}\text{Ni}(\gamma, p)^{57}\text{Co}$: $9.192 \pm 0.386$ mb. This value is approximately two times larger than the JENDL-5 prediction ($4.600$ mb). However, TALYS-2.2 calculations reproduce the experimental value, suggesting an underestimation of the $(\gamma, p)$ channel strength in JENDL-5 under these conditions.
• $^{58}\text{Ni}(\gamma, pn)^{56}\text{Co}$: $2.239 \pm 0.355$ mb. This is approximately two times higher than the JENDL-5 prediction ($1.179$ mb) and TALYS-2.2 calculations, though the difference is attributed to larger associated uncertainties and sensitivity to the high-energy tail of the flux.
• $^{58}\text{Ni}(\gamma, p2n)^{55}\text{Co}$: A 90% confidence-level upper limit of $\langle\sigma\rangle < 0.021$ mb was established. This is lower than the JENDL-5 prediction ($0.035$ mb).

Significance and Claims
The paper claims to provide a quantitatively constrained methodology for extracting bremsstrahlung-averaged cross sections by integrating experimentally validated photon flux models with rigorous uncertainty propagation. Key contributions include:

1. Flux Validation: The use of natural tin activation to validate and correct the MCNP6.3 photon flux model, explicitly accounting for converter-induced spectral softening and geometric uncertainties.
2. Benchmarking: The results serve as a benchmark for modern photonuclear data libraries (JENDL-5) and reaction modeling codes (TALYS-2.2). The study highlights that while some channels agree well with evaluations, charged-particle emission channels (specifically $(\gamma, p)$ and $(\gamma, pn)$) exhibit significant discrepancies, with measured yields often exceeding evaluated predictions by a factor of two.
3. Spectral Dependence: The authors note that differences between their results and prior literature (e.g., Deiev et al.) are largely attributable to the converter thickness. The 6 mm tantalum converter used here produces a "softer" spectrum compared to the thin converters (1.05 mm) used in previous studies, altering the energy weighting of the cross sections.
4. Production Relevance: The work provides integral cross-section data under production-relevant conditions (thick converter, specific beam current), offering a more realistic assessment for medical isotope production than energy-dependent survey measurements.

The authors emphasize that this study is a precision benchmark at a fixed endpoint energy rather than a broad energy survey, aiming to improve the experimental database for nickel-based targets and refine the interpretation of bremsstrahlung-averaged measurements across different facilities.