1. 1 Centre d’Etudes Nucléaires de Bordeaux - Gradignan G eant4 DNA Physics processes overview and current status Y. Perrot, S. Incerti Centre d'Etudes Nucléaires de Bordeaux - Gradignan IN2P3 / CNRS Université Bordeaux 1 33175 Gradignan France Z. Francis, G. Montarou Laboratoire de Physique Corpusculaire IN2P3 / CNRS Université Blaise Pascal 63177 Aubière France R. Capra, M.G. Pia INFN Sezione di Genova Geant4 DNA meeting Genova - July 13 th -19 th, 2005

2. 2 Centre d’Etudes Nucléaires de Bordeaux - Gradignan A im 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. 3 Centre d’Etudes Nucléaires de Bordeaux - Gradignan Protons and Hydrogen

4. 4 Centre d’Etudes Nucléaires de Bordeaux - Gradignan L ist of processes Processes p and H excitation : p + H 2 O → p + H 2 O * ionisation : p + H 2 O → p + e - + H 2 O + charge transfer : p + H 2 O → H * + H 2 O + stripping : H + H 2 O → p + e - + H 2 O * ionisation : H + H 2 O → H + e - + H 2 O + excitation neglected for H

5. 5 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E xcitation by Protons (TXS) No experimental data, but semi-empirical relations with electron excitation cross sections  0 is a constant (  0 = 1E-20 m²) Z = 10 number of electrons in the crossed medium E k excitation energy. a and  represent the energy superior limit so that this relation is in agreement with First Born Approximation (> 500 keV) and J for low energy (FBA not valid) ExcitationsE k (eV)a (eV)J (eV)Ων A B 1 8.17876198200.851 B A 1 10.132084234900.881 Ryd A+B11.311373277700.881 Ryd C+D12.91692308300.781 Diffuse bands14.50900330800.781 function of t 5 excitation levels

6. 6 Centre d’Etudes Nucléaires de Bordeaux - Gradignan I onisation by Protons (DXS) E is the transfered energy t is the proton kinetic energy Ry = 13.606 eV (1 Ry -> eV) I j ionisation energy of shell j (liquid) B j is the binding energy of shell j (vapour) G j partitioning factor to adjust the shell contributions to the FBA calculations (G j is 1 for K shell) W j = E - I j is the secondary electron kinetic energy w = W j /B j N j is the number of electrons on shell j S = 4πα 0 ²N j (Ry/B j )² T = (m e /m p ) t : kinetic energy of an electron traveling at the same speed as the proton ² = T/B j w c = 4 ²-2 -Ry/(4B j ) α related to the size of the target molecule Parameters from vapor data Shell jIj (eV)Bj (eV)NjGj 1a 1 539.00539.7021.00 2a 1 32.3032.2020.52 1b 2 16.0518.5521.11 3a 1 13.3914.7321.11 1b 1 10.7912.6120.99 ParameterValenceK-shell A1A1 1.02 1.25 B1B1 82.0 0.50 C1C1 0.45 1.00 D1D1 -0.80 1.00 E1E1 0.38 3.00 A2A2 1.07 1.10 B2B2 14.61.30 C2C2 0.601.00 D2D2 0.040.00 α 0.640.66 function of E and t, for E>I j Nice agreement on TXS by Simpson integration analytical formula also available for ionisation TCS reproduces ICRU stopping powers Rudd model LE term HE term 5 ionisation shells (K included)

7. 7 Centre d’Etudes Nucléaires de Bordeaux - Gradignan I onisation by Protons (TXS) where T is the kinetic of an electron with the same speed as the proton σ ioni A2.98 B4.42 C1.48 D0.75 F(4.80) function of t

8. 8 Centre d’Etudes Nucléaires de Bordeaux - Gradignan  if W > 100 eV where W max = 4T elec and T elec is the kinetic energy of an electron with the same speed as the proton  uniformly shot within [0, 2π] S econdary electrons after ionisation if W ≤ 100 eV, θ’ is uniformly shot within Angles Energy E is the transfered energy of an incident electron with kinetic energy T W = E - I j is the secondary electron kinetic energy proton scattering neglected (nuclear scattering < 1 keV ?)

9. 9 Centre d’Etudes Nucléaires de Bordeaux - Gradignan t in eV a 0, b 0 low energy line c 0, d 0 intermediate power a 1, b 1 high energy line Parameters calculated from vapor data and in order that stopping powers match recommendations for liquid water Parameters a0a0 -0.180 b0b0 -18.22 c0c0 0.215 d0d0 3.550 a1a1 -3.600 b1b1 -1.997 x0x0 3.450 x1x1 5.251 P roton charge transfert (TXS) function of t plenty of experimental data dominant at low energy for X<x 0 for X<x 1

10. 10 Centre d’Etudes Nucléaires de Bordeaux - Gradignan 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) H ydrogen stripping (TXS) σ 01 A2.835 B0.310 C2.100 D0.760 F- function of t two contributions

11. 11 Centre d’Etudes Nucléaires de Bordeaux - Gradignan I onisation by Hydrogen (DCS) 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 function of E and t integration by Simpson

12. 12 Centre d’Etudes Nucléaires de Bordeaux - Gradignan He, He +, He 2+

13. 13 Centre d’Etudes Nucléaires de Bordeaux - Gradignan Processes He ionisation : W + He → W + + He + e - excitation : W + He → W * + He charge transfer σ 01 : W + He → W + He + + e - charge transfer σ 02 : W + He → W + He ++ + e - + e - Processes He + ionisation : W + He + → W + + He + + e - excitation : W + He + → W * + He + charge transfer σ 12 : W + He + → W + He ++ + e - charge transfer σ 10 : W + He + → W + + He Processes He ++ ionisation : W + He ++ → W + + He ++ + e - excitation : W + He ++ → W * + He ++ charge transfer σ 21 : W + He ++ → W + + He + charge transfer σ 20 : W + He ++ → W ++ + He L ist of processes

14. 14 Centre d’Etudes Nucléaires de Bordeaux - Gradignan Zeff = Z - S(R) Qeff = 2.0 for 1s electron, Qeff = 1.7 pour 2 electrons on 1s, Qeff = 1.15 for an electron on 2s or 2p Takes into account the screening by the projectile’s electrons We have : Zeff : ion effective charge S(R) : screening at distance R from nucleus t elec : 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 E xcitation & Ionisation for He, He+ and He++ (DCS) FBA from p excitation or ionisation DXS function of E and t

15. 15 Centre d’Etudes Nucléaires de Bordeaux - Gradignan σ 01 σ 02 σ 12 σ 21 σ 20 σ 10 a0a0 2.25 0.95 0.65 b0b0 -30.93-32.61-32.10-23.00-23.73-21.81 a1a1 -0.75 -2.75 c0c0 0.5900.4350.6000.2150.2500.232 d0d0 2.352.702.402.953.552.95 x0x0 4.294.454.603.503.723.53 C harge transfer for He, He + and He ++ (TXS) from p charge transfer XS function of t for X<x 0 for X<x 1

16. 16 Centre d’Etudes Nucléaires de Bordeaux - Gradignan electrons

17. 17 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E : energy transfer (energy loss) T = mv 2 / 2 : electron kinetic energy R = 1 Ry N = 0.3343x10 23 molecules.cm -3 for liquid H 2 O B = 537 eV : binding energy of the K-shell n = 2 : electron occupation number U = 809 eV : average kinetic energy of electron in K-shell Contribution not neglected for T above 540 eV (~10% beyond 10 keV) 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]

18. 18 Centre d’Etudes Nucléaires de Bordeaux - Gradignan V alence shells excitation and ionisation (DXS) Corrections at low energies (exchange and higher-order contributions) Differential FBA cross section for a single excitation or ionisation Smearing of four outer shells First Born Approximation non relativisic limit Dielectric Response Func function of E and T E integration over [7.5,max(T,0.5*(T+32.2)] ELF j (E,K) if E j < T < 500 eV if 7.5 eV < T ≤ E j if cut(j)<T<500 eV

19. 19 Centre d’Etudes Nucléaires de Bordeaux - Gradignan Real part of the DRF function (K=0) Imaginary part of the DRF function (K=0) Dielectric formalism accounts for condensed-phase effects Superposition of Drude functions : optical model of the liquid Sum rule constraints only if E>cut(j) Dispersion to non-zero momentum transfers (K>0) f j : ocillator strength E j : transition energy  j : damping coefficient E p = 21.46 eV plasmon energy Generalized Oscillator Strength functions Impulse approximation V alence shells excitation and ionisation

20. 20 Centre d’Etudes Nucléaires de Bordeaux - Gradignan V alence shells excitation and ionisation partitioning shellCut (eV) 17.5 2 3 4 5 610 713 817 932.2 Excitation Ionisation 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.

21. 21 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E lastic scattering DCS and TCS for 0.35 eV ≤ T ≤ 10 eV for 10 eV < T ≤ 100 eV for 100 eV < T ≤ 200 eV function of T Rutherford term Below 200 eV : Brenner-ZaiderAbove 200 eV : Rutherford « screened » function of T valid over whole enrgy range

22. 22 Centre d’Etudes Nucléaires de Bordeaux - Gradignan S econdary electrons after ionisation 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 - B j where B j is the binding energy of the ejected electron.  if W > 100 eV  if W ≤ 100 eV, θ shot uniformly within   shot uniformly within  if W > 200 eV  if 50 ≤ W ≤ 200 eV :  if W < 50 eV, θ’ shot uniformly within Angles Energy

23. 23 Centre d’Etudes Nucléaires de Bordeaux - Gradignan S tatus : where are we now ? We have all C codes available for the following processes : ProcessDiffXSTotalXS Electron elastic (Brenner and Rutherford)AA Electron inelastic on valenceTT Electron inelastic on Oxygen K shellAT Proton excitationT (>100keV*)A Proton ionisationAT or A Proton charge transfer-A Hydrogen ionisationAT Hydrogen stripping-A Helium excitationT (>100keV*)A Helium ionisationAT Helium charge transfer-A All analytical formulas (A) can produce tables (T)… * Tables for proton excitation > 100 keV from Dingfelder’s code

24. 24 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E nergy ranges (usual) H ionisation + stripping 10 4 10 5 10 6 10 7 eV 10 3 10 2 10 p excitation p ionisation He excitation + ionisation + charge transfer e- ionisation+ excitation + elastic scattering

25. 25 Centre d’Etudes Nucléaires de Bordeaux - Gradignan F inal states kinematics Excitation (5 shells) W + e → W* + e W + p → W* + p W + H → W* + H W +  → W* +  W +  + → W* +  + W +  ++ → W* +  ++ Outgoing direction same as incoming E out = E in – E excitation for e, p, H,  Ionisation (5 shells + K shell) W + e → W + + e + e W + p → W + + p + e W + H → W + + H + e W +  → W + +  + e W +  + → W + +  + + e W +  ++ → W + +  ++ + e Outgoing electron : analytical (energy, angle) Outgoing p, H,  : energy + momentum conservation Charge changing and stripping W +  ++ → W + +  +  21 E  + = E  ++ - 1/2m e (p  ++ /m  ++ ) 2 + CC = B  + -B w W +  ++ → W ++ +  20 E  = E  ++ - 2x1/2m e (p  ++ /m  ++ ) 2 + CC = B*  -B* w W +  + → W +  ++ + e  12 E  ++ = E  + - D D = B  + W +  + → W + +  10 E  = E  + - 1/2m e (p  + /m  + ) 2 + CC = B  -B w W +  → W +  + + e  01 E  + = E  - D D = B  W +  → W +  ++ + e + e  02 E  ++ = E  - D D = B*  W + p → W + + H  10 E H = E p – 1/2m e (p p /m p ) 2 + C C = B H -B w W + H → W + p + e  01 E p = E H - DD = B H Outgoing direction same as incoming

26. 26 Centre d’Etudes Nucléaires de Bordeaux - Gradignan Thank you for your attention

27. 27 Centre d’Etudes Nucléaires de Bordeaux - Gradignan D ielectric Response Function at the optical limit

28. 28 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E nergy Loss Function (ELF) without dispersion

29. 29 Centre d’Etudes Nucléaires de Bordeaux - Gradignan E nergy Loss Function (ELF) with dispersion

30. 30 Centre d’Etudes Nucléaires de Bordeaux - Gradignan B ethe surface : ELF in two dimensions

31. 31 Centre d’Etudes Nucléaires de Bordeaux - Gradignan S P and MFP Born-corrections included no corrections

32. 32 Centre d’Etudes Nucléaires de Bordeaux - Gradignan D efinitions (liquid H 2 O molecule) Collision Stopping Power = average energy loss per unit path length Inelastic Mean Free Path = distance between successive energy loss events Valence and core (K shell) processes dE : energy loss d  / dE : prob. per unit path length that an electron of kinetic energy T will experience an energy loss between E and E+dE T = mv 2 / 2 : electron kinetic energy E min = 0, E max = T / 2 Justified by large difference in binding energy between valence and core shells

33. 33 Centre d’Etudes Nucléaires de Bordeaux - Gradignan 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 1a 1 curve for electrons is multiplied by 100. 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. O rders of magnitude