2026.08 山西 · 太原

Fragmentation Cross-Sections of 130 A MeV ²⁸Si on

Carbon and Copper Targets

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Jing-Xiao Kang

Institute of Modern Physics, Shanxi Normal University

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The 8^th International Workshop on Nuclear Dynamics in Heavy-ion Reactions

August 21-25, 2026 Taiyuan, China

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• Projectile Fragmentation Reaction

• The nucleons in the overlapping region undergo intense collisions and are stripped off.
• The spectator region of the projectile nucleus forms highly excited primary fragments, which then decay into stable fragments through statistical processes like evaporation or fission.

• Two stages: the dynamic process and the statistical decay process.

• Extract the nuclear charge radius and study the exotic nuclear structure

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• Space radiation protection

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• Heavy-ion cancer therapy

• Construct and improve the nuclear databases

• Fragmentation cross-section — the core measurement quantity of the fragmentation reaction, is an indispensable basic parameter in various applications.

C. Zeitlin et al, Nuclear Physics A 784, 341 (2007).

• Experimental study

Most measurements of ²⁸Si fragmentation have been performed at energies above 200 A MeV.

For energies below 200 A MeV, data are very scarce, especially for heavy targets such as copper.

• Theoretical model

Empirical parameterizations, transport models, heavy ion transport codes, etc.

Most of these models are calibrated with high-energy data, their reliability at lower energies needs to be verified.

L. Sihver et al, Advances in Space Research 49, 812 (2012).

Measured the fragmentation cross sections of ²⁸Si on carbon and copper targets at 130 A MeV

• Beam Irradiation:

Facility : HIMAC in Japan

Initial beam energy : 135 A MeV

Effective energy at the target surface using the SRIM code : 130 A MeV

CR-39 nuclear track detector（HARZLAS TD - 1，Fukuvi，Japan）5×5×0.08cm

C target 5 mm ; Cu target 2 mm

• CR-39 nuclear track detector

Advantages：high charge resolution, small size, low cost, and high sensitivity；

Applications：measuring the angular distribution, neutron dosimetry, and biomedical research.

Limitations：only identify particles with Z ≥ 4, and the data analysis is quite time-consuming.

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• Chemical Etching：

7 N NaOH , 70°C ，30 h

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• Track Scanning：

HSP-1000 high-speed

imaging microscope

• Track Fitting: PitFit software

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• Track Reconstruction and Matching

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• Charged Particle Identification

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The distribution of dx and dy of the coordinate difference of the particle track coordinates.

• Total charge-changing cross-section

• Bradt-Peters semi-empirical formula：

（r₀=1.35fm, b₀=0.83）

Compared our results with data from other energies:

For the carbon target, the total charge-changing cross section does not change significantly with energy; For the copper target, all previous data are at energies above 200 A MeV. Our result fills the gap in the 100-200 A MeV region.

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Our results agree with the Bradt-Peters formula within experimental errors.

• Partial charge-changing cross-section

• The copper target cross sections are much larger than those for carbon.
• The overall trend is very similar for both targets. The cross section drops quickly and then becomes relatively flat between ΔZ = 4 and 10.

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This comes from the contribution of multifragmentation and splitting processes. The projectile nucleus can split into two fragments with charges between 4 and 10 through peripheral and semi-central collisions, as observed in our experimental data. These processes produce a broad distribution of fragments with similar probabilities, so the cross sections do not vary much.

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• Partial charge-changing cross-section

• Compared with the results for beam energies higher than 130 A MeV, the odd–even staggering effects are not observed in our results.
• Our experiment also measures the cross-sections of fragment products with Z = 4 and 5.

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At this low incident beam energy of 130 A MeV, the fragment production mechanism may be different from those at intermediate and high energies, which is the main reason for this experimental project.

• The results show obvious deviations between model predictions and experimental values, and most models systematically overestimate the fragmentation cross-sections.

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• Comparison with theoretical models

• Most theoretical models are calibrated by high-energy data and lack effective verification in the medium-low energy region, leading to prominent predictive deviations at low energies.

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• We have presented new measurements of fragmentation cross-sections for ²⁸Si on carbon and copper targets at 130 A MeV, reporting the latest experimental results of the total and partial charge-changing cross-sections at this energy, and comparing the experimental results with the theoretical model and other experimental results.

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Summary

Outkook

• We plan to continue measuring fragmentation cross-sections for other targets (Al and CH₂), to further complete the data set in this energy region.
• More experimental data are still needed below 200 A MeV to understand the complex reaction mechanisms and to improve theoretical models for radiation protection and heavy-ion therapy applications.

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Thank you for your attention!

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