1. 12th Geant4 Space Users Workshop
Single scattering classes and NIEL computation within a Screened Relativistic treatment
M. Tacconi1,2,
P.G. Rancoita1, M. Gervasi2, V. Ivantchenko3
1INFN Milano Bicocca, 2University of Milano Bicocca, 3CERN
12th Geant4 Space Users Workshop
10-12 April 2017

2. Outline Single Scattering Models Cross Sections and NIEL Calculation
Results
Conclusions

3. Single Scattering Models
The scattering models are included in Geant4 and in 2 different physics classes:
Since Geant4 version 9.4 (February 2011)
G4IonCoulumbScatteringModel
G4IonCoulumbCrossSection
Since Geant4 version 9.5 (October 2012)
G4eSingleCoulumbScatteringModel
G4ScreeningMottCrossSection
G4MottCoefficients
For Protons and Ions Coulomb scattering
Electrons Coulomb scattering

4. Proton or nucleus Coulomb Cross Section on nuclei
It is based on the relativistic extension to ion-ion screened Coulomb scattering of the Wentzel-Moliere treatment - already used for electron and muon scattering in Geant4 –
with Moliere screening parameter
are the rest masses of the two particles
is the invariant mass
and with screening lengths as in ICRU-49 (1993)
If Z1 = for incident particle
If Z1 >1
References:
C. Leroy and P.G. Rancoita (2016), Principles of Radiation Interaction in Matter and Detection - 4th Edition -, World Scientific (Singapore), Sects
M.J. Boschini et al. "Nuclear and Non-Ionizing Energy-Loss for Coulomb
Scattered Particles from Low Energy up to Relativistic Regime in Space Radiation Environment." Proc. of the 12° ICATPP, Como 7-8/10/2010), World Scientific (Singapore) 2011, 9-23

5. Electron Cross Section on nuclei
Molier’s Screening
Coefficient:
Rutherford in the center of mass:
Nuclear Form Factor
Ratio of Mott cross section over Rutherford
Mott Cross Section fit:
bj,k are the fitting parameters
References:
C. Leroy and P.G. Rancoita (2016), Principles of Radiation Interaction in Matter and Detection - 4th Edition -, World Scientific (Singapore), Sects
M.J. Boschini et al."Nuclear and Non-Ionizing Energy-Loss of Electrons with low and Relativistic Energies in Materials and Space Environment" Proc. Of the 13th ICATPP (13th ICATPP, Como 3-7/10/2011).
M.J. Boschini et al “An Expression for the Mott cross section of electrons and positrons on nuclei with Z up to 118” Radiat. Phys. Chem. (2013),

6. Displacement Damage and NIEL
Incoming Particle
Frenkel-pairs:
Displacement threshold energy
Energy density which goes
into displacement [MeV/cm3]:
Non-Ionizing Energy Loss:
Minimum incoming energy
to generate displacement
F(E): Spectral Fluence [cm-2]
N : Number of Target Atoms [cm-3]
T: Target kinetic Energy
L(T): Lindhard’s partition function
differential cross section
Spectral fluence
Nuclear Stopping Power:

7. Code for NIEL Calculation
SR-NIEL: Screened Relativistic (SR) Treatment of the Displacement Damage
On line Calculators available at:
This is a C++ analytical code and has been developed to
calculate the Non Ionizing Energy Loss of electrons, protons, ions and neutrons with the possibility to change the displacement threshold energy
Also included:
Nuclear Stopping power calculator
Electronic stopping power calculator
Energetic nuclear recoil calculator

8. Geant4 Implementation (test58)
Using Geant4 transportation code the scattering of the incoming particle with the atoms of the materials is simulated with single scattering models
Projectile
Particle
What is calculated:
Scattering angle and new direction
Energy transferred to the target atom of the material.
If this energy is grater then Td a secondary particle is generated
Displaced
Atom
In an External Example (test58):
The secondaries are killed
The kinetic energies of secondary particle T are multiplied by L(T) and summed up
NIEL
The energies T transfered to target atoms are summed up
Nuclear Stopping Power

9. Results and Comparison
Total Cross Section
Differential Cross
Nuclear Stopping Power
NIEL
Testem0
test58

10. Total Cross Section
Calulated with Testem0 and method ComputeCrossSectionPerAtom
Average difference is less than 0.5%

11. Protons Differential Cross Section
test58 with only G4IonCoulumbScatteringModel (no other physic active)
107 Protons (E=10 MeV) on a slice of Silicon 0.1 nm thick*
3.8x105 interactions were produced
Y(q): Distribution of the deflection angle outside the target
particles deflected between θ and θ+dθ
Incident particles
Thickness of target
Number density of the taget
the solid angle between θ and θ+dθ
*The thickness was kept as thin as possible to reduce multiple scattering effects

12. Electrons Differential Cross Section
test58 with only G4eSingleScatteringModel (no other physic active)
107 Electrons (E=10 MeV) on a slice of Silicon 10 nm thick*
2.1x105 interactions were produced
Y(q): Distribution of the deflection angle outside the target
particles deflected between θ and θ+dθ
Incident particles
Thickness of target
Number density of the taget
the solid angle between θ and θ+dθ
*The thickness was kept as thin as possible to reduce multiple scattering effects

13. Electrons Differential Cross Section
command in macro file:
/process/em/setNuclearFormFactor formfactorname
None
Exponential
Gaussian
Flat
Available in Geant4 version 10.3
The experimental data are from:
G. C. Li, M. R. Yearian, and I. Sick,
Phys. Rev. C 9, 1861 (1974)

14. Nuclear Stopping Power
Calulated with test58
Electrons in Si - Nuclear Stopping Power

15. NIEL
Calulated with test58

16. Conclusions
Wentzel and Mott cross sections are well implemented in Single Scattering Models.
NIEL and Stopping Power calculation with test58 and Single Scattering models gives result in good agreement with analytical one.