Diapositive 1

1
Geant4 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 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 (gt 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 EgtIj
• 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 -gt eV) Ij
ionisation 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 (Gj is 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
4pa0²Nj(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) a 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

• if W gt 100 eV

• where Wmax 4Telec and Telec is the kinetic
  energy of an electron with the same speed as the
  proton

• if W 100 eV, ? is uniformly shot within

f uniformly shot within 0, 2p

• proton scattering neglected (nuclear scattering
  lt 1 keV ?)

9
Proton charge transfert (TXS)

• function of t
• plenty of experimental data
• dominant at low energy

t in eV
for Xltx0
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 Xltx1
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) gt 1
• at high energy, g(t) lt1 to take into account
• the screening effect by the Hydrogen electron

12
He, He, He2
13
List of processes
14
Excitation Ionisation for 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
  projectiles 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 Xltx0
for Xltx1
16
electrons
17
Oxygen K-shell ionisation (DXS)

• Binary Encounter Approximation (BEA)

• function of E and T, E and T gt 540 eV
• E integrated over T, (T540)/2

E energy transfer (energy loss) T mv 2 / 2
electron kinetic energy R 1 RyN 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
Valence shells excitation and ionisation (DXS)

• function of E and T
• E integration over 7.5,max(T,0.5(T32.2)

ELFj (E,K)

• Corrections at low energies (exchange and
  higher-order contributions)

if Ej lt T lt 500 eV
if 7.5 eV lt T Ej
if cut(j)ltTlt500 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 Egtcut(j)

• Real part of the DRF function (K0)

fj ocillator strength Ej transition
energy gj damping coefficient Ep 21.46 eV
plasmon energy

• Imaginary part of the DRF function (K0)

• Dispersion to non-zero momentum transfers (Kgt0)

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 Egt13 eV and Elt17 eV, shell 8 is
  redistributed on shells 6 and 7
• if Egt10 eV and Elt13 eV, shells 7-8 are
  redistributed on shell 6
• if Egt7.5 eV and Elt10 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 lt T 100 eV
for 100 eV lt 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 gt 100 eV

• if W 100 eV, ? shot uniformly within

• j shot uniformly within

• if W gt 200 eV

• if 50 W 200 eV

• if W lt 50 eV, ? 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
(gt100keV) A Proton ionisation A T or
A Proton charge transfer - A Hydrogen
ionisation A T Hydrogen stripping - A Hel
ium excitation T (gt100keV) A Helium
ionisation A T Helium charge
transfer - A All analytical formulas (A)
can produce tables (T) Tables for proton
excitation gt 100 keV from Dingfelders code
24
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 s20 Ea Ea -
  2x1/2me(pa/ma)2 C C Ba-Bw
• W a ? W a e s12 Ea Ea - D D
  Ba
• W a ? W a s10 Ea 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
  Ba
• 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 EdE 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 gt 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.