Interplay between Charge-Changing Reactions�with Quantum Molecular Dynamics Models

• Introduction to experiments
• Exp. Data vs. IQMD+GEMINI predictions
• Summary

​

The 8th International Workshop on Nuclear Dynamics in

Heavy-ion Reactions, Taiyuan, 2026.08.21-24

Acknowledgment: Jun SU (SYSU)

Bao-Hua SUN

Rare-isotope groupp

bhsun@buaa.edu.cn

Beihang University

Charge-changing cross section

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• Experiment simple absolute xs

• High precision

• Bulk properties of nuclide

Transmission method

at ~ several 0.1-1 GeV/nucleon

The charge-changing cross section (σ_CC) is defined as the total cross section of removing at least one proton from the projectile nucleus during the collision with the target nucleus.

• Essential data for cosmic ray physics, reaction mechanism, and charge radius determination

3

Heavy Ion Research Facility in Lanzhou (HIRFL)

Xu et al., Science Bulletin 70, 1026 (2025)

BHS et al., Science Bulletin 63, 78 (2018)

Second Radioactive Ion Beam Line in Lanzhou (RIBLL2): the only

radioactive ion beam line at relativistic energy (300-500 MeV/nucleon) in China before 2025

Xia, Zhan, Wei, et al., NIMA 488 (2002) 11

Glance at data analysis

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Wang et al., Chin. Phys. C 47, 084001 (2023)

Incident particles before reaction target

Z distribution of reaction products

Z+1

Z-loss

²⁸Si

Z

σ_cc = σ_ΔZ>0

σ_ΔZ=1,2,3…

σ_ΔZ=-1

Si

Al

Mg

Na

σ_cc = σ_ΔZ>0

σ_ΔZ=1,2,3…

σ_ΔZ=-1

Charge-changing cross section

Partial charge-changing cross section

Charge pickup cross section

⁴⁰Ar(300 MeV/nucleon)+Be 🡪 ²⁸Si

²⁸Si+C

Consistent (and largest) database for σ_cc for systematic studies

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Xiao et al., PLB 880, 140787 (2026)

Xu et al., PRL. (2026) in press

Zhang et al., NIMA 1084,171267(2026)

Wei et al., Nucl. Sci. Tech. 36,195 (2025)

Wei et al., PRC 112, 064604(2025)

Liu et al., PRC 112, 014611 (2025)

Wu et al., ADNDT 165, 101733 (2025)

Zhang et al., PRX 15, 031004 (2025)

Xu et al., Sci. Bull. 70, 1026 (2025)

Li et al., PLB 859, 139143 (2024)

Zhao et al., PLB 858, 139082 (2024)

Zhang et al., Sci. Bull. 69, 1647 (2024)

Zhao et al., PLB 847, 138269 (2023)

Wang et al., Chin. Phys. C 47, 084001 (2023)

Li et al., PRC107, 024609 (2023)

Xu et al., PLB833, 137333 (2022)

Zhao et al., NIMA 930, 95 (2019)

BHS et al., Sci. Bull. 63, 78 (2018)

Lin et al., CPC41, 066001(2017)

Zhao et al., NIMA 823, 41(2016)

• Cross sections of >70 isotopes on C,

> 10 on H, Ag, Pb @ ~300 MeV/nucleon

• Cross sections of 24 isotopes on C and H @~900 MeV/nucleon (GSI)

Neutron number

Proton number

Instrumentation

Best paper award in 2023

Physics

Total beam time on target at HIRFL ~ 20 days

Interpreting the data using the IQMD+GEMINI model

COVER PAPER (2025.10)

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IQMD+GEMINI model

• Very good at revealing the dynamic process!

J. Su, F.S. Zhang et al., PRC 83, 014608 (2011)

J. Su et al., PRC 100, 014602 (2019)

J. Su et al., PRC 100, 014602 (2019)

J. Su et al., PRC 97, 054604 (2018)

Courtesy: Prof. Jun Su, SUSY

• Phase space density constraint
• Improved level densities
• IQMD–GEMINI Switching

Microscopic–Statistical Framework for Nuclear Reaction

Features

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Examples with interplay between data and IQMD models

Charge-changing cross sections

Reaction mechanism

Spectroscopic factor

One-nucleon removal reaction cross sections

Systematics in isospin-dep.

Partial charge-changing cross sections

Underproduction of charge-changing cross section data by 10%

²⁸Si + C

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Yamaguchi et al., PRC 82, 014609 (2010)

Wang et al., Chin. Phys. C 47, 084001 (2023)

Glauber model (only considering the collisions of projectile protons with target neutrons and protons) can reproduce about 90% of the experimental values: two decades of question

Chulkov et al., NPA 674, 330 (2000)

Meng, Zhou, Tanihata, PLB 532, 209 (2002)

Bhagwat & Gambhir, PRC 69, 014315 (2004)

Reaction mechanism of charge-changing reactions

Jian-Wei Zhao, BHS, Tanihata et al., PLB 847, 138269 (2023)

M. Tanaka et al., PRC 106 (2022) 014617

300 MeV/nucleon

A sophisticated model for charge particle evaporation after neutron removal was developed.

Key properties: excitation energy distribution of pre-fragments

Differences between theo. and exp. can be well explained by charge particle evaporation after neutron removal.

Liu et al., Phys. Rev. C 112(2025)014611; electromagnetic interaction

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Gaimard-Schmidt (GS) approach

e.g., one-neutron removal

e.g., one-proton evaporation

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Isospin-dependent charge-particle evaporation after pure neutron removal

• Isospin-dependent evaporation peaks at nuclei with isospin symmetry (T_z~0). NOT a CONSTANT!
• Peak values vary by up to ~16% for p-shell and ~10% for sd-shell nuclei
• Results employing EEDs of pre-fragments from IQMD agree well with the data.

Evaporation calculations rely on excitation energies, level densities, etc., for the pre-fragments.

Excitation energy distribution (EED) from an empirical formula (Gaimard-Schmidtapproach) requiring fine-tuning of the parameters and from IQMD

(σ^exp-σ^theo)/σ^exp

p-shell

sd-shell

Jian-Wei Zhao, BHS, Tanihata et al., PLB 847, 138269 (2023)

Discovery of a universal scaling with reaction targets

Jun-Yao Xu, BHS, Tanihata et al., PRL(2026)

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Heavy-isotope targets (Pb) instead of light-isotope targets (C, H) when inferring the charge radii of unstable isotopes from charge changing cross sections.

Two questions:

1. Heavy target

Electromagnetic dissociation (EMD)

2. Evaporation contributions

Getting smaller with increasing

target atomic number (Z)

σ^exp/σ^theo

Towards a complete mechanism of σ_cc and a view from IQMD+GEMINI

J.R. Liu, BHS, J.W. Zhao et al., PRC 112, 014611 (2025) Jun-Yao Xu, BHS, Tanihata et al., PRL(2026)

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• Negligible EM contributions to σ_cc

(γ, p) hardly occur except for proton-rich isotopes

• Less contribution ratio from CPE for heavy-isotope

target; can reproduce the target dependent pattern

​

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Examples with interplay between data and IQMD models

Subtle structure: OES

Charge-changing cross sections

Charge-pickup cross sections

Reaction mechanism

Spectroscopic factor

One-nucleon removal reaction cross sections

Systematics in isospin-dep.

Partial charge-changing cross sections

Partial charge-changing cross section�or elemental fragmentation cross sections (EFCSs)

²⁸Si+C: reference

^28-34Si+C , ^32-38S+C: isospin

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Wei et al., PRC(2025)

Zhang et al., PRX 15, 031004 (2025)

Li et al., PLB 859, 139143 (2024)

Li et al., PRC107, 024609 (2023)

Z → Z+1 of p-shell nuclei on C/H

• Charge pickup reaction

Complicity in extracting σ_ΔZ>4 due to

more reaction channel contributions

²⁸Si at 300 MeV/nucleon on C`

Impact parameter b

Central peripheral 

σ_ΔZ of ^28-33Si, ^32-38S @ 300 MeV/nucleon on C: isospin dependent

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Li, et al., PLB 859 (2024) 139143

Wei, et al., PRC (2025)

^28-33Si

^32-38S

With increasing removed protons (more central collisions),

σ_ΔZ shows different evolution.

σ_ΔZ globally decreases as ΔZ increases.

Pre-fragment

Fragment

1p+xn

2p+xn

3p+xn

4p+xn

IQMD+GEMIN reproduces the odd-even staggering (OES) in EFCS of ²⁸Si well

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²⁸Si@300 A MeV + C

Li, Su, BHS et al., PRC 107, 024609 (2023)

Odd-even staggering in EFCSs occurs in the sequential statistical decay stage rather than in

the initial dynamical collision stage. 

Evidence for a universal trend in odd-even staggering in EFCS of S isotopes

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X.L. Wei, G.S. Li, J. Su et al., PRC 112, 064604 (2025)

^32-38S @ 300 AMeV + C

• The odd-even staggering is generally reproduced with 3.5% accuracy by IQMD+GEMINI

• With increasing target nuclide isospin, OES is getting weaker

IQMD+GEMINI reproduces reaction energy-dependence of ETCS

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Also see works for stable isotopes done by Shanxi Normal University, Prof. Dong-Hai Zhang, Jun-Sheng Li

Chin. Phys. Lett. 34, 102501 (2017), J. Phys. G 39, 055104 (2012), J. Phys. G 42, 015102 (2015) ……

Although data are scattered at different energies, general trends are observed, decreasing to about a constant with increasing E, which can be captured by IQMD+GEMINI

²⁸Si @ 300 MeV/nucleon on C

²⁸Si: an important isotope in space science

IQMD

IQMD+GEMINI

Li, Su, BHS et al., PRC 107, 024609 (2023)

Charge pickup cross section: σ_ΔZ=-1 (Z🡪Z+1)

²⁸Si+C: reference

^28-34Si+C , ^32-38S+C: isospin

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Wei et al., PRC(2025)

Zhang et al., PRX 15, 031004 (2025)

Li et al., PLB 859, 139143 (2024)

Li et al., PRC107, 024609 (2023)

Z → Z+1 of p-shell nuclei on C/H

• Charge pickup reaction

Complicity in extracting σ_ΔZ>4 due to

more reaction channel contributions

Impact parameter b

²⁸Si at 300 MeV/nucleon on C

Central peripheral 

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Observation of rapid increase in the charge-pickup cross sections of neutron-rich projectile nuclei

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σ_ΔZ=-1 at E >700 MeV/nucleon

• 24 p-shell nuclei @ 900 MeV/nucleon + C/H

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• Charge-pick cross section: charge exchange

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See e.g., Lenske et al., PPNP109(2019)103716

Zhang, BHS, Tanihata et al., Phys. Rev. X 15, 031004 (2025)

^8,9Li, ^10–12Be, ^10,13–15B, ^12,14–19C, ^{14,15,17–22}N,

stable and neutron-rich isotopes: new data

• one-step charge-exchange via virtual pion

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A second look on Z🡪(Z+1): (n, p) exchange

At high energies (E/A ≫ E_b), the one-step charge-exchange via virtual pion comes into play.

Projectile nucleon

σ_CP: dominated by (p,n) charge-exchange reactions,

plus the sequential neutron emissions

Quasi-elastic process (NN^-1)

Ejectile nucleus

Target nucleon

Inelastic process (RN^-1)

Nucleon excitation

Spin-isospin excitation

See e.g., Lenske et al., PPNP109(2019)103716

R: Δ(1232)

π emission

Challenging nuclear reaction models

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• Predict different contributions of quasi-elastic over inelastic processes for C, H targets

C target data: Dominated by the inelastic

process (Δ resonance)

• Isospin dependence due to the statistical decay process

Jun Su et al., In prepration

IQMD+GEMINI calculations

(preliminary)

In preparation

• Such studies are important to reveal the baryonic resonances in nuclear medium/matter, π- productions in heavy-ion collisions

​

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Examples with interplay between data and IQMD models

Subtle structure: OES

Charge-changing cross sections

Charge-pickup cross sections

Reaction mechanism

Spectroscopic factor

One-nucleon removal reaction cross sections

Systematics in isospin-dep.

Partial charge-changing cross sections

24

Single-particle strength inferred from different reactions  

• Interpretations from nuclear reaction complex, nuclear structure models

• Quenching strength in heavy-ion (HI) induced strength on neutron-proton asymmetry:

one decade long question

HI-induced knockout reactions

on C/Be at intermediate energies

Transfer reactions

at low energies

Quasi-free knockout

at intermediate-high energies

N. Phuc et al., PRC 100, 064604 (2019)

Y.P. Xu et al., PLB 790, 308 (2019)

J. A. Tostevin et al,. PRC 103, 054610 (2021)

Negative corr.

(p,d)

(p,2p), (p,pn)

Guang-Shuai Li, BHS, Jun Su et al., PLB 859, 139143 (2024)

Erxi Xiao, Guangshuai Li, Yu Yang, Long Zhu, Jianwei Zhao, Jun Su, BHS, PLB 880, 140787 (2026)

Single-Nucleon Removal Beyond the Frozen-Core Picture

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Eikonal approximation:�Frozen internal core motion?

• IQMD+GEMINI framework�[Li, Sun, Su, PLB 859 (2024) 139143]

• Spectroscopic factors defined

using Eikonal model

Evaporation loss and feeding can be equally important in inclusive single-nucleon removal reactions

Final fragment

Single-Nucleon Removal Beyond the Frozen-Core Picture

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²⁸Si + C 🡪 ²⁷Al

• Proton knockout cross section stays almost constant
• Proton evaporation is predicted to be the primary mechanism, particularly for neutron-deficient Si isotopes.

Guang-shau Li, BHS, Jun Su et al., PLB 859, 139143 (2024)

Proton evaporation after inelastic scattering

charge-exchange (p,n), then decay by γ-rays `

Purifying one-neutron removal as a probe of single-particle strength

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Erxi Xiao, Guangshuai Li, Yu Yang, Long Zhu, Jianwei Zhao, Jun Su, Baohua Sun, PLB 880, 140787 (2026)

• Anomalous isospin trend in extracted Rs
• 73 one-neutron-removal data sets show that

The 𝑅_𝑠–Δ𝑆 trend correlates with evaporation feeding and evaporation loss.

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Proposed a purified reduction factor 𝑅_dir , assisted by IQMD+GEMINI, to associate with single-particle strength.

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𝑅_dir exhibits a much weaker Δ𝑆 dependence, consistent with nucleon-transfer and quasi-free knockout systematics

Summary & Outlook

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IQMD+GEMINI has been used to interpret new charge-changing cross-section data.

Nuclear structure is simplified when initializing the reaction nuclei.

e.g., a nuclide is defined by a Gaussian wavelet

IQMD+GEMINI may not be precise in absolute magnitudes; for example, it underestimates the total cross section by about 20-40% but gives reasonable partial cross sections. However, it is quantitatively very useful for examining the reaction dynamics.

It's interesting to see the capabilities of other transportation models.

THANK YOU!

Partial Charge-Changing Cross Sections as a Verifier of �Quantum Molecular Dynamics Models

• Introduction to experiments
• Exp. Data vs. IQMD+GEMINI predictions
• Summary

​

The 8th International Workshop on Nuclear Dynamics in

Heavy-ion Reactions, Taiyuan, 2026.08.21-24

Acknowledgment: Beihang ENP Group

Jun Su (SYSU)

Bao-Hua SUN

bhsun@buaa.edu.cn

Beihang University

Charge-changing cross section

30

• Experiment simple absolute xs

• High precision

• Bulk properties of nuclide

Transmission method

at ~ several 0.1-1 GeV/nucleon

The charge-changing cross section (σ_CC) is defined as the total cross section of removing at least one proton from the projectile nucleus during the collision with the target nucleus.

• Essential data for cosmic ray physics, reaction mechanism, and charge radius determination