Nucleon knockout reactions within the intranuclear cascade model INCL

Direct reactions and spectroscopy with hydrogen targets:
past 10 years at the RIBF and future prospects

1. José Luis Rodríguez-Sánchez
University of Coruña
2
nd
August 2023
Nucleon knockout reactions within the intranuclear
cascade model INCL
Direct reactions and spectroscopy with hydrogen targets:
past 10 years at the RIBF and future prospects

2. 2
Outline
J.L. Rodríguez-Sánchez
●Introduction to intranuclear cascade models
●The Liège intranuclear cascade model (INCL) coupled to the
deexcitation code ABLA
●Results for single-knockout cross sections (until 2021)
●Implementation of short-range nucleon-nucleon correlations in INCL
and new results for nucleon knockout cross sections
●Conclusions

3. 3
Introduction to intranuclear cascade models
J.L. Rodríguez-Sánchez
Intranuclear cascade models are used to describe nuclear reactions 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
- Deexcitation of prefragments, ~10
-16
s
- Multi-fragmentation, Evaporation and Fission
- Gemini++, SMM, ABLA, Fermi-breakup
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
Perfect
Very bad
https://www-nds.iaea.org/spallations
A model benchmark carried out by the international atomic energy organism in
2010 stated that the INCL-ABLA combination is the best one to describe residue
production cross sections, kinematics, ...
INCL: ~42000 lines
ABLA: ~13000 lines
Both models in C++
and in GEANT4

5. 5
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)

6. 6
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Particle interaction cross sections parametrized from elementary processes
π
⁺
p
π
⁻
p
π
⁺
p
NN → NN
NN → NΔ - Decay Δ → Nπ
Nπ → Nπ
Nπ → Δ
Nπ → Nρ
Nπ → Nω
Nπ → Nη
Nη → Nη
Nη →Nπ
Nη →N2π
NN → Nnω
NN → NNη + xπ
NN → NNη or dη
NN → NNη + NΔη + NNηπ
NN → NNη + NΔη + NNηπ + NNη2π + …
S
t
r
a
n
g
e

s
e
c
t
o
r
E
n
e
r
g
y

t
h
r
e
s
h
o
ld

~
1
.
2
G
e
V
/
u
M
e
s
o
n

s
e
c
t
o
r
E
n
e
r
g
y

t
h
r
e
s
h
o
ld

~
2
5
0

M
e
V
/
u
INCL energy range domain from few tens of MeV/u to 20 GeV/u
S. Pedoux and J. Cugnon, Nucl. Phys. A 866, 16 (2011)
D. Mancusi et al., Eur. Phys. J. A 53, 80 (2017)
J.-C. David et al., Eur. Phys. J. Plus 133, 253 (2018)
J. Hirtz et al., Phys. Rev. C 101, 014608 (2020)

7. 7
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Putting nuclear structure and quantum effects in the energy content (at the surface)
Classical
picture
Shell-model
picture
(fuzzy surface)
J.-L. Rodríguez-Sánchez et al., PRC 96, 054602 (2017) D. Mancusi et al., PRC 91, 034602 (2015)
●Density profile parametrization depends on the mass (A) of the nucleus involved in the collision
●Fuzzy surface random algorithm to mimic
quantum effects at the surface of nuclei,
validated with shell model calculations
(Gaussian)
(modified-harmonic-
oscilator)
(Woods-Saxon)
Neutron skins (Hartree-Fock-Bogoliubov)
HFBRAD model

8. 8
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
A. Boudard et al., Phys. Rev. C 66, 044615 (2002)
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
Coulomb energy
Conservation laws for the compound nucleus/pre-fragment formation
Vo calculated from the real part of optical potentials for
nucleons and baryonic resonances, for other particles
phenomenological values are used
Pauli blocking applied for ensuring energy conservation

9. 9
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

10. 10
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
Double-differential cross sections
for π production
⁺

Escaping particles
●Quantum transmission
- Particle energy and momentum
- Nuclear potentials and separation energies
- Coulomb barriers

11. 11
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
Proton double-differential cross sections
in p +
208
Pb @ 800 MeV and p +
197
Au @ 1200 MeV
Escaping particles
●Quantum transmission
- Particle energy and momentum
- Nuclear potentials and separation energies
- Coulomb barriers

12. 12
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
Quadruple-differential cross sections for two
coincident protons emitted in p +
197
Au @ 200 MeV
Escaping particles
●Quantum transmission
- Particle energy and momentum
- Nuclear potentials and separation energies
- Coulomb barriers

13. 13
The Liège intranuclear cascade model (INCL)
J.L. Rodríguez-Sánchez
Escaping particles
●Quantum transmission
●Coalescence approach in phase space
> Stable and unstable clusters
A. Boudard et al., Phys. Rev. C 87, 014606 (2013)
p +
197
Au collisions at 1200 MeV

14. 14
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
→ 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 2016
●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)
INCL
++INCL++
Fission cross sections
Isotopic cross sections of FFs
Production cross sections of ER
J.L. Rodríguez et al., PRC 90, 064606 (2014) A. Boudard et al., PRC 87, 014606 (2013) J.L. Rodríguez et al., PRC 91, 064616 (2015)

15. 15
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez
Triple-differential cross sections for (p,2p) reactions
INCL calculations for different density profiles
Proton-induced reactions
J.-L. Rodríguez-Sánchez et al., PRC 96, 054602 (2017)
238
U
208
Pb
197
Au
136
Xe
56
Fe
40
Ca
12
C
200 MeV/u
~1 GeV/u

16. 16
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez

17. 17
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez
First observation of a (p,2p) cross section splitting between even-Z and odd-Z nuclei
OES: data deviation with respect to the fit
INCL: Standard model without pairing effects for P.S.
Sn=Sp= 6.3 MeV
INCL-mod: Exp. particle separation energies

18. 18
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez

19. 19
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez
INCL (2015) without neutron skins
INCL (2019) with neutron skins

20. 20
Implementation of short-range correlations (SRCs) in INCL
J.L. Rodríguez-Sánchez
p
S. Stevens et al., PLB 777, 374 (2018)
SRCs are implemented in INCL only for np pairs taking into account this is the dominant
channel, assuming a back-to-back emission of the correlated nucleons in the c.m.
1) Algorithm to look for np pairs: d12 < 1.6 fm
2) Kinematics
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
Proj. Proton
P1,2
J.-L. Rodríguez-Sánchez et al., submitted to PLB
c.m.

21. 21
Results for nucleon-knockout reactions with SRCs
J.L. Rodríguez-Sánchez
INCL including SRCs provides a good description of single-proton removal cross
sections for neutron-rich Si and Sn isotopes
●ISGQR+GDR contributions are more important when the proton binding energy decreases
●The SRC contribution increases with the neutron excess (N/Z), as pointed out by the recent results
obtained by the CLAS collaboration M. Duer et al., Nature 560, 617 (2018)
C. A. Bertulani et al., PRL 94, 072701 (2005)

22. 22
Results for nucleon-knockout reactions with SRCs
J.L. Rodríguez-Sánchez
The new INCL approach provides better results for
single nucleon-knockout reactions induced by
protons (spallation) and light nuclei (fragmentation)
J.-L. Rodríguez-Sánchez et al., submitted to PLB

23. 23
Results for nucleon-knockout reactions with SRCs
J.L. Rodríguez-Sánchez
The new INCL approach provides better results for
single nucleon-knockout reactions induced by
protons (spallation) and light nuclei (fragmentation)
But also a better agreement with multi-nucleon
knockout cross sections of neutron-rich Sn nuclei
1p5n 1p4n 1p3n 1p2n 1p1n 1p
J.-L. Rodríguez-Sánchez et al., submitted to PLB

24. 24
Conclusions
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
The model has also been extended to the heavy mesonic and strange sectors by including
the ω, ρ and η mesons and the Λ and Σ hyperons
A first 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 the neutron excess (N/Z), as observed by the CLAS collaboration
Model validation for SRCs with other data, like pion-induced reactions
→ New data from the HADES collaboration at GSI
Next steps
→ Exclusive deuterium production in reactions involving SRCs
→ Validation for (p,3p),(p,4p), etc, reactions
→ Extension to neutrino, electron and antiproton induced reactions
→ Implementation of the recent improvements in GEANT4

25. 25
Collaboration
J.L. Rodríguez-Sánchez
The INCL team
Alain Boudard, Joseph Cugnon, Jean-Christophe David, Anna Ershova, Jason Hirtz,
Sylvie Leray and Davide Mancusi
RIKEN collaborators:
Andrea Jungclaus, Alexandre Obertelli, Nancy Paul and Victor Vaquero
Thank you for your attention!

26. 27
Results for nucleon-knockout reactions
J.L. Rodríguez-Sánchez
First observation of a (p,2p) cross section splitting between even-Z and odd-Z nuclei
OES: data deviation with respect to the fit
INCL: Standard model without pairing effects for P.S.
INCL-mod: Exp. particle separation energies