Single Scattering Models and NIEL Computation within Screened Relativistic Treatment
In this study, the focus is on single scattering models and NIEL computation within a screened relativistic treatment. The article delves into the classes and calculations involved, discussing cross sections, proton/nucleus coulomb interactions, electron cross sections, and more. Various models and methods are explored, referencing works by renowned researchers in the field. The content presents a detailed overview of theoretical frameworks and practical applications within the realm of radiation interaction and detection.
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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 2
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 For Protons and Ions Coulomb scattering Since Geant4 version 9.5 (October 2012) - G4eSingleCoulumbScatteringModel - G4ScreeningMottCrossSection - G4MottCoefficients Electrons Coulomb scattering 3
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 2 d 2 ( ) 1 d Z Z e = 1 pc 2 2 2 Z Z 1 + 2 2 ( 1 cos ) s A = + . 1 13 . 3 76 1 2 A s 4 pa , TF un 1,m m M are the rest masses of the two particles is the invariant mass 2 2 , 1 2 and with screening lengths as in ICRU-49 (1993) 2 1 c = + 1 If Z1=1 for incident particle If Z1>1 2 pc 88534 . 0 Z 88534 . 0 Z a a m m = aTF= 0 aun 0 = 1 2 ( ) 3 / 1 2 + 23 . 1 23 . 2 Z M 2 , 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 4
Electron Cross Section on nuclei ( ) 2 ( ) ( ) 1 cos d d = 2 ( ) R F q + 2 2 ( 1 cos ) d d A + + . ( . .) Mott Scrr NFF Ruth c m s Molier s Screening Coefficient: Rutherford in the center of mass: Nuclear Form Factor 2 d 2 ( ) 1 d Ze 2 2 = Z 1 ( )2 = + . 1 13 . 3 76 A 2 2 c 1 cos s 4 pa ( . ) Ruth c cm TF 88534 . 0 Z a aTF= 0 3 / 1 Ratio of Mott cross section over Rutherford ( ) d / 2 j Mott Cross Section fit: 4 j = 1 ( j cos ) R a d R Mott ( ) d = 0 1 k 6 d k bj,k are the fitting parameters = ( ) a b Ruth , j k j = 1 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 5
Displacement Damage and NIEL Incoming Particle Frenkel-pairs: E dis T FP 5 . 2 d Displacement threshold energy Energy density which goes into displacement [MeV/cm3]: E max min E = ( ) ( ) E NIEL E Minimum incoming energy to generate displacement E dE dis Non-Ionizing Energy Loss: T ( , ) d T E max = ( ) ( ) NIEL E N T L T dT (E): T: L(T): Spectral Fluence [cm-2] Number of Target Atoms [cm-3] Target kinetic Energy Lindhard s partition function dT Td Nuclear Stopping Power: T ( , ) dE d T E max = ( ) E N T dT ( , ) d T E differential cross section dx dT dT 6 0
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 7
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. Displaced Atom If this energy is grater then Td a secondary particle is generated 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 8
Results and Comparison Testem0 - Total Cross Section - - - Differential Cross Nuclear Stopping Power NIEL test58 9
Total Cross Section Calulated with Testem0 and method ComputeCrossSectionPerAtom Average difference is less than 0.5% 10
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( ): Distribution of the deflection angle outside the target particles deflected between and +d Incident particles Thickness of target Number density of the taget the solid angle between and +d 11 *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( ): Distribution of the deflection angle outside the target particles deflected between and +d Incident particles Thickness of target Number density of the taget the solid angle between and +d 12 *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) 13
Nuclear Stopping Power Calulated with test58 Electrons in Si - Nuclear Stopping Power 14
NIEL Calulated with test58 15
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. 16
