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  1. Geant4 DNA Physics processes overview and current statusY. Perrot, S. Incerti Centre d'Etudes Nucléaires de Bordeaux - Gradignan IN2P3 / CNRS Université Bordeaux 1 33175 Gradignan FranceZ. Francis,G. Montarou Laboratoire de Physique Corpusculaire IN2P3 / CNRS Université Blaise Pascal 63177 Aubière FranceR. Capra, M.G. Pia INFN Sezione di GenovaGeant4 DNA meeting Genova - July 13th-19th, 2005

  2. Aim • Extend Geant4 to simulate electron, proton and alpha electromagnetic interactions in liquid water down to ~7.5 eV • electrons : elastic scattering, excitation, ionization • p, H : excitation (p), ionization (p & H), charge transfer (p), stripping (H) • He++, He+, He : excitation, ionization, charge transfer • validation : two independent computations performed by LPC Clermont & CENBG from litterature • References used for the models : • - Dingfelder, Inokuti, Paretzke et al. (2000 for protons, 2005 for He) • Emfietzoglou et al. (2002 for electrons) • Friedland et al. (PARTRAC)

  3. Protons and Hydrogen

  4. List of processes

  5. Excitation by Protons (TXS) • function of t No experimental data, but semi-empirical relations with electron excitation cross sections s0 is a constant (s0 = 1E-20 m²)Z = 10 number of electrons in the crossed medium Ek excitation energy. a and W represent the energy superior limit so that this relation is in agreement with First Born Approximation (> 500 keV) n and J for low energy (FBA not valid) 5 excitation levels

  6. Ionisation by Protons (DXS) • function of E and t, for E>Ij • Nice agreement on TXS by Simpson integration • analytical formula also available for ionisation TCS • reproduces ICRU stopping powers 5 ionisation shells (K included) Rudd model E is the transfered energy t is the proton kinetic energy Ry = 13.606 eV (1 Ry -> eV) Ijionisation energy of shell j (liquid) Bj is the binding energy of shell j (vapour) Gj partitioning factor to adjust the shell contributions to the FBA calculations (Gjis 1 for K shell) Wj = E - Ij is the secondary electron kinetic energy w = Wj/Bj Nj is the number of electrons on shell j S = 4πα0²Nj(Ry/Bj)² T = (me/mp) t : kinetic energy of an electron traveling at the same speed as the proton n² = T/Bj wc = 4n²-2n-Ry/(4Bj) α related to the size of the target molecule Parameters from vapor data LE term HE term

  7. Ionisation by Protons (TXS) • function of t where T is the kinetic of an electron with the same speed as the proton

  8. Secondary electrons after ionisation Energy E is the transfered energy of an incident electron with kinetic energy T W = E - Ij is the secondary electron kinetic energy Angles • ifW > 100 eV • where Wmax = 4Telec and Telec is the kinetic energy of an electron with the same speed as the proton • ifW ≤ 100 eV, θ’ is uniformly shot within φuniformly shot within [0, 2π] • proton scattering neglected (nuclear scattering < 1 keV ?)

  9. Proton charge transfert (TXS) • function of t • plenty of experimental data • dominant at low energy t in eV for X<x0 a0 , b0 low energy line c0 , d0 intermediate power a1 , b1 high energy line Parameters calculated from vapor data and in order that stopping powers match recommendations for liquid water for X<x1

  10. Hydrogen stripping (TXS) • function of t • two contributions where T is the kinetic of an electron with the same speed as the proton Parameters adjusted to reproduce Dagnac & Toburen data, as well as stopping powers. (50)

  11. Ionisation by Hydrogen (DCS) • function of E and t • integration by Simpson • Differ from proton cross sections because of : • screening effect of the H electron • contribution of the stripping to the electron spectrum • interaction of H electron with water electrons • Obtained from proton spectrum taking into account Bolorizadeh and Rudd data, • as well as ICRU recommandations for liquid water. • t incident particle energy • at low energ, g(t) > 1 • at high energy, g(t) <1 to take into account • the screening effect by the Hydrogen electron

  12. He, He+, He2+

  13. List of processes

  14. Excitation & Ionisationfor He, He+ and He++ (DCS) • FBA • from p excitation or ionisation DXS • function of E and t Zeff = Z - S(R) • Takes into account the screening by the projectile’s electrons • We have : • Zeff : ion effective charge • S(R) : screening at distance R from nucleus • telec : kinetic energy of an electron with the same speed as the incident particle • E : transfered energy • Qeff : Slater effective charge for an electron on shell n for the considered ion Qeff = 2.0 for 1s electron, Qeff = 1.7 pour 2 electrons on 1s, Qeff = 1.15 for an electron on 2s or 2p

  15. Charge transfer for He, He+ and He++ (TXS) • from p charge transfer XS • function of t for X<x0 for X<x1

  16. electrons

  17. Oxygen K-shell ionisation (DXS) • Binary Encounter Approximation (BEA) • function of E and T, E and T > 540 eV • E integrated over [T, (T+540)/2] E : energy transfer (energy loss) T = mv 2 / 2 : electron kinetic energy R = 1RyN = 0.3343x1023 molecules.cm-3 for liquid H2OB = 537 eV : binding energy of the K-shelln = 2 : electron occupation numberU = 809 eV : average kinetic energy of electron in K-shell Contribution not neglected for T above 540 eV (~10% beyond 10 keV)

  18. Differential FBA cross section for a single excitation or ionisation • First Born Approximation • non relativisic limit • Dielectric Response Func Smearing of four outer shells Valence shells excitation and ionisation (DXS) • function of E and T • E integration over [7.5,max(T,0.5*(T+32.2)] ELFj (E,K) • Corrections at low energies (exchange and higher-order contributions) if Ej < T < 500 eV if 7.5 eV < T ≤ Ej if cut(j)<T<500 eV

  19. Valence shells excitation and ionisation • Dielectric formalism accounts for condensed-phase effects • Superposition of Drude functions : optical model of the liquid • Sum rule constraints • only if E>cut(j) • Real part of the DRF function (K=0) fj: ocillator strength Ej: transition energy gj: damping coefficient Ep = 21.46 eV plasmon energy • Imaginary part of the DRF function (K=0) • Dispersion to non-zero momentum transfers (K>0) Generalized Oscillator Strength functions Impulse approximation

  20. Valence shells excitation and ionisation partitioning • The energy loss function is cut just below the shell binding energy and redistributed over the lower shells, to prevent the contribution to the cross section below the binding energy : • if E>=13 eV and E<17 eV, shell 8 is redistributed on shells 6 and 7 • if E>=10 eV and E<13 eV, shells 7-8 are redistributed on shell 6 • if E>=7.5 eV and E<10 eV, shells 6-7-8 are redistributed on shells 1 & 2 • E is the transfered energy. Excitation Ionisation

  21. Elastic scattering DCS and TCS function of T Rutherford term Below 200 eV : Brenner-Zaider Above 200 eV : Rutherford « screened » for 0.35 eV ≤ T ≤ 10 eV for 10 eV < T ≤ 100 eV for 100 eV < T ≤ 200 eV • function of T • valid over whole enrgy range

  22. Secondary electrons after ionisation Energy E is the transfered energy of an incident electron with kinetic energy T The incident electron energy becomes T-E The secondary electron energy is W= E - Bj where Bj is the binding energy of the ejected electron. Angles • if W > 100 eV • if W ≤ 100 eV, θ shot uniformly within • j shot uniformly within • if W > 200 eV • if 50 ≤ W ≤ 200 eV : • if W < 50 eV, θ’ shot uniformly within

  23. Status : where are we now ? We have all C codes available for the following processes : Process DiffXS TotalXS Electron elastic (Brenner and Rutherford) A A Electron inelastic on valence T T Electron inelastic on Oxygen K shell A T Proton excitation T (>100keV*) A Proton ionisation A T or A Proton charge transfer - A Hydrogen ionisation A T Hydrogen stripping - A Helium excitation T (>100keV*) A Helium ionisation A T Helium charge transfer - A All analytical formulas (A) can produce tables (T)… * Tables for proton excitation > 100 keV from Dingfelder’s code

  24. e- ionisation+ excitation + elastic scattering p ionisation p excitation H ionisation + stripping He excitation + ionisation + charge transfer 10 102 103 104 105 106 107 eV Energy ranges (usual)

  25. Final states kinematics • Excitation (5 shells) • W + e → W* + e • W + p → W* + p • W + H → W* + H • W + a → W* + a • W + a+ → W* + a+ • W + a++ → W* + a++ • Outgoing direction same as incoming • E out = E in – E excitation for e, p, H, a • Ionisation (5 shells + K shell) • W + e → W+ + e + e • W + p → W+ + p + e • W + H → W+ + H + e • W + a → W+ + a + e • W + a+ → W+ + a+ + e • W + a++ → W+ + a++ + e • Outgoing electron : analytical (energy, angle) • Outgoing p, H, a : energy + momentum conservation • Charge changing and stripping • W + a++ → W+ + a+ s21 Ea+ = Ea++ - 1/2me(pa++/ma++)2 + C C = Ba+-Bw • W + a++ → W++ + a s20Ea = Ea++ - 2x1/2me(pa++/ma++)2 + C C = B*a-B*w • W + a+ → W + a++ + e s12 Ea++ = Ea+ - D D = Ba+ • W + a+ → W+ + a s10Ea = Ea+ - 1/2me(pa+/ma+)2 + C C = Ba-Bw • W + a → W + a+ + e s01 Ea+ = Ea - D D = Ba • W + a → W + a++ + e + e s02 Ea++ = Ea - D D = B*a • W + p → W+ + H s10 EH = Ep – 1/2me(pp/mp)2 + C C = BH-Bw • W + H → W + p + e s01 Ep = EH - D D = BH • Outgoing direction same as incoming

  26. Thank you for your attention

  27. Dielectric Response Function at the optical limit

  28. Energy Loss Function (ELF) without dispersion

  29. Energy Loss Function (ELF)with dispersion

  30. Bethe surface : ELF in two dimensions

  31. SP and MFP • Born-corrections included • no corrections

  32. Definitions (liquid H2O molecule) • Collision Stopping Power = average energy loss per unit path length dE : energy loss dS / dE : prob. per unit path length that an electronof kinetic energy T will experience an energy loss between E and E+dE T = mv 2 / 2 : electron kinetic energy • Inelastic Mean Free Path = distance between successive energy loss events Emin= 0, Emax = T / 2 • Valence and core (K shell) processes Justified by large difference in binding energy between valence and core shells

  33. Orders of magnitude For electrons,elastic collisions are increasingly the most probable interaction event below about 2 keV, while ionization takes over above that energy. For both protons and electrons(T > 100 eV) ionizations account for 75% of inelastic collisions, the remaining 25% being excitation events. For electron impact and as threshold energies are approached excitations become increasingly important and eventually dominate the inelastic scattering probability. Partial ionization cross section for each subshell of a water molecule as a function of impact energy for (full curves) electrons and (broken curves) protons. The 1a1 curve for electrons is multiplied by 100.

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