Short-Range Correlations in Dynamical Intranuclear Cascade Models for Describing Nucleon Knockout and Fission Reactions

Short-Range Correlations in Dynamical Intranuclear
Cascade Models for Describing Nucleon Knockout and
Fission Reactions

1. José Luis Rodríguez-Sánchez
University of Coruña & USC
19
th
August 2024
Short-Range Correlations in Dynamical Intranuclear
Cascade Models for Describing Nucleon Knockout and
Fission Reactions

2. 2
Outline
J.L. Rodríguez-Sánchez
●
Introduction to intranuclear cascade models
●The Liège intranuclear cascade model INCL coupled to the de-excitation code ABLA
●Results for single-nucleon knockout cross sections
●
Results for fission reactions induced by quasi-free (p,2p) scattering collisions
●Conclusions and perspectives

3. 3
Introduction to intranuclear cascade models
J.L. Rodríguez-Sánchez
Intranuclear cascade models are used to describe nuclear reactions such as
spallation and fragmentation from few MeVs to tens of GeVs, where the reaction
process can be divided into two stages
R. Serber, Phys. Rev. 72, 1114 (1947)
First stage
- Cascade stage, ~10
-22
s
- Bertini, VEGAS, Isabel, INCL, ...
Second stage
- De-excitation of prefragments, ~10
-16
s
- Multi-fragmentation, Evaporation and Fission
- Gemini++, SMM, ABLA, ...
https://www-nds.iaea.org/spallations
J.-C.David, "Spallation reactions: A successful interplay between modeling and applications", Eur. Phys. J. A 51, 68 (2015)

4. 4
Introduction to intranuclear cascade models
J.L. Rodríguez-Sánchez
●
Interactions between high-energy incident particle and target nucleons are approximated
as individual nucleon-nucleon (NN) collisions, propagating the particles through the
nucleus
●
The scattered nucleons follow a straight-line
trajectory up to find another particle to interact
●The two-body collision is approximated as a
quasi-free scattering (QFS) interaction with
two-body cross sections
●
The nucleons with a momentum larger than the
Fermi momentum can be emitted, the others
are reflected at the surface of the nucleus
given place to the formation of a compound
nucleus or prefragment
General overview
J.-C.David, "Spallation reactions: A successful interplay between modeling and applications", Eur. Phys. J. A 51, 68 (2015)
Interaction channels:
NN → NN
NN → NΔ & Decay Δ → Nπ

5. 5
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Putting nuclear structure and SRC effects in the energy content (at the surface)
J.-L. Rodríguez-Sánchez et al., PRC 96, 054602 (2017)
Density profile parametrization depends on the mass (A) of the nucleus involved in the collision
(modified-harmonic-
oscilator)
Neutron skins (Hartree-Fock-Bogoliubov)
(Gaussian)
(Woods-Saxon)

6. 6
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Putting nuclear structure and SRC effects in the energy content (at the surface)
J.-L. Rodríguez-Sánchez et al., PRC 96, 054602 (2017) J.-L. Rodríguez-Sánchez et al., PLB 851, 138559 (2024)
Density profile parametrization depends on the mass (A) of the nucleus involved in the collision
(modified-harmonic-
oscilator)
Neutron skins (Hartree-Fock-Bogoliubov)
(Gaussian)
(Woods-Saxon)
Short range nucleon-nucleon correlations
The extra momentum gained by the nucleons due to the
presence of SRC is fixed by comparing the INCL nucleon
momentum distributions to experimental data
Electron-scattering dataSRC dominated by np pairs

7. 7
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Escaping particles
Quantum transmission
- Particle energy and momentum
- Nuclear potentials and separation energies
- Coulomb barriers
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
Neutron double-differential cross sections
in p +
208
Pb collisions at 1200 MeV
INCL++
The good description of particle double-differential
cross sections means that the excitation energy for
compound nuclei or remnants is well determined

8. 8
INCL coupled to the de-excitation model ABLA
J.L. Rodríguez-Sánchez
ABLA is used to describe the different de-excitation channels
→ Particle emission: γ-rays, neutrons, light charged particles, intermediate mass fragments (IMFs)
→ Fission decays
→ Multi-fragmentation
●Particle emission based on the Weisskopf’s approach including angular momentum corrections
●
Coulomb barriers calculated by the Bass’ model
●Particle separation energies obtained from the Atomic Mass Evaluation 2020
●Nuclear level densities – Ignatyuk’s parameterization
●
Fission barriers – Finite-range liquid-drop model
●Fission based on the Fokker-Planck equation
J.L. Rodríguez-Sánchez et al., Phys. Rev. C 105, 014623 (2022)
Fission cross sections
Isotopic cross sections of FFs
Production cross sections of ER
A. Boudard et al., PRC 87, 014606 (2013) J.L. Rodríguez et al., PRC 90, 064606 (2014) J.L. Rodríguez et al., PRC 91, 064616 (2015)
INCL++

9. 9
Single-nucleon knockout cross sections
J.L. Rodríguez-Sánchez
J.-L. Rodríguez-Sánchez et al., PLB 851, 138559 (2024)
The dependence on ΔS disappears when SRC correlations are included in the calculations, in particular
for Nucleus-Nucleus collisions where there are more data
Duer et al., Nature 560, 618 (2018)
Tostevin et al., PRC 90, 057602 (2014)
Electron-scattering reactions
The amount of SRC
increases with N/Z

10. 10
Single-nucleon knockout cross sections
J.L. Rodríguez-Sánchez
Triple-differential cross sections for (p,2p) reactions
measured at Grand-Raiden (Osaka) are also well
described by INCL given a better agreement for
neutron skins obtained with the HFBRAD model
200 MeV/u
J.-L. Rodríguez-Sánchez et al., PLB 851, 138559 (2024)
The dependence on ΔS disappears when SRC correlations are included in the calculations, in particular
for Nucleus-Nucleus collisions where there are more data

11. 11
Quasi-free (p,2p) collisions induced fission reactions
J.L. Rodríguez-Sánchez
Missing mass
Rest mass
QFS
Inelastic components
to (p,2p) collisions
The advantages of (p,2p) reactions and the inverse kinematics technique are combined to
induce fission and measure the E* of the compound nuclei
Coplanar reaction => ɸ1-ɸ2~180º
p(
238
U,
x
Pa)p @ 500 MeV/u

12. 12
Quasi-free (p,2p) collisions induced fission reactions
J.L. Rodríguez-Sánchez
The advantages of (p,2p) reactions and the inverse kinematics technique are combined to
induce fission and measure the E* of the compound nuclei
Missing mass
Rest mass
Selecting the QFS peak in the opening angle the excitation energy can be correlated with the
fission fragments to study the energy dependence of fission yields up to E* ~ 30MeV
p(
238
U,
237
Pa p)p
@ 500 MeV/u

13. 13
Quasi-free (p,2p) collisions induced fission reactions
J.L. Rodríguez-Sánchez
The advantages of (p,2p) reactions and the inverse kinematics technique are combined to
induce fission and measure the E* of the compound nuclei
Missing mass
Rest mass
Selecting the QFS peak in the opening angle the excitation energy can be correlated with the
fission fragments to study the energy dependence of fission yields up to E* ~ 30MeV
p(
238
U,
237
Pa p)p
@ 500 MeV/u
Fission yield
dependence on E*
Constraints
for the r-process

14. 14
Conclusions and perspectives
J.L. Rodríguez-Sánchez
The Liège intranuclear cascade model INCL has been improved in the last years to include
nuclear structure of nuclei, such as neutron skins and quantum effects
An implementation of short-range nucleon-nucleon correlations has also been developed in
the last year to improve the model predictions for nucleon-knockout reactions
→Results in very good agreement with experimental nucleon-knockout cross sections
→Showing a clear dependence with N/Z or ΔS, as also observed in electron-scattering experiments
Model validation for SRCs with other data, like pion-induced reactions
→New data from the HADES collaboration at GSI
Improvement and validation of the fission approach in ABLA++ using (p,2p)-fission reactions
performed at GSI in combination with previous data
Next steps
→ Validation for (p,3p), (p,4p), ..., reactions
→ Improvement of the fission model in ABLA++ including more fission channels (S3 & Z~43)
→ Implementation of the recent improvements in GEANT4

15. 15J.L. Rodríguez-Sánchez
Thanks to all my collaborators