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

Outline Single Scattering Models Cross Sections and NIEL Calculation Results Conclusions

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

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 =1 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. 2.2-2.2.2 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

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. 2.4-2.4.3 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), http://dx.doi.org/10.1016/j.radphyschem.2013.04.020

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:

Code for NIEL Calculation SR-NIEL: Screened Relativistic (SR) Treatment of the Displacement Damage On line Calculators available at: www.sr-niel.org 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

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

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

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

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

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

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)

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

NIEL Calulated with test58

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.