Simulation of low energy nuclear recoils using Geant4

Simulation of low energy nuclear recoils using Geant4 [ heavy ions, T < 1 kev/amu ] Ricardo Pinho ricardo@lipc.fis.uc.pt 12th Geant4 Collaboration Workshop LIP - Coimbra Hebden Bridge 14 Set 2007

Outline 1. a review of Geant4 s models of stopping power 2. nuclear recoils full cascade 3. nuclear quenching estimates 4. summary and present work Versions used: geant4.8.2 and geant4.8.2.p01

Stopping power ion = projecticle particle Z 1 atom = target particle Z 2

Stopping power ion = projecticle particle Z 1 atom = target particle Z 2 G4hLowEnergyIonisation de dx = S e + S n (assuming no correlations) G4hBetheBlochModel G4hParametrisedLossModel G4hIonEffChargeSquare G4hNuclearStoppingModel

Stopping power ion = projecticle particle Z 1 atom = target particle Z 2 G4hLowEnergyIonisation de dx = S e + S n (assuming no correlations) Low energy extension Physics list: only G4hLowEnergyIonisation Very small step sizes ( 1% of the particle range) Continuous slowing down approximation: G4hBetheBlochModel G4hParametrisedLossModel G4hIonEffChargeSquare G4hNuclearStoppingModel Cut energy very high: no deltarays Actually no secondaries what so ever! Just follow our primary till it stops (default MinKineticEnergy = 10eV) No fluctuations

Stopping power ion = projecticle particle Z 1 atom = target particle Z 2 G4hLowEnergyIonisation de dx = S e + S n (assuming no correlations) Low energy extension Physics list: only G4hLowEnergyIonisation Very small step sizes ( 1% of the particle range) Continuous slowing down approximation: Geometry: just a square box, filled with pure material G4hBetheBlochModel G4hParametrisedLossModel G4hIonEffChargeSquare G4hNuclearStoppingModel Cut energy very high: no deltarays Actually no secondaries what so ever! Just follow our primary till it stops (default MinKineticEnergy = 10eV) No fluctuations shoot primary from the center of the box, random direction

de / dx (MeV cm 2 / g) 1000 100 10 Lindhard S e : proton -> Al, Cu, Pb GEANT4 (Lindhard+ICRU_R49p+Bethe-Bloch) T 1 T 2 parameterization Al Cu Pb T 1 = 0.25 kev T 1 = 10 kev T 2 = 2 MeV T 2 = 100 MeV Bethe-Bloch 1 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 1e+05 Energy T p (MeV)

de / dx (MeV cm 2 / g) 1000 100 10 Lindhard Min: 0.25keV 1keV S e : proton -> Al, Cu, Pb GEANT4 (Lindhard+ICRU_R49p+Bethe-Bloch) user s choice T 1 T 2 parameterization Al Cu Pb T 1 = 0.25 kev T 1 = 10 kev T 2 = 2 MeV T 2 = 100 MeV Bethe-Bloch Max: 2MeV 100MeV 1 1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 1e+05 Energy T p (MeV)

Geant4 Electronic stopping low energy stopping power is parameterized

Geant4 Electronic stopping low energy stopping power is parameterized parameterization is for protons and alphas only

Geant4 Electronic stopping low energy stopping power is parameterized parameterization is for protons and alphas only for other heavy ions, the stopping is scaled by:

Geant4 Electronic stopping low energy stopping power is parameterized parameterization is for protons and alphas only for other heavy ions, the stopping is scaled by: S ei (T ) = Z 2 eff S ep (T p ), T p = M p M T proton stopping parameterizations (default) ICRU_R49p Ziegler1977p Ziegler1985p SRIM2000p alpha stopping parameterizations ICRU_R49He Ziegler1977He

S e : Xe -> LXe Geant4 low energy 2 ICRU_R49p T 1 = 1 kev ICRU_R49p T 1 = 5 kev SRIM2000p T 1 = 1 kev SRIM2000p T 1 = 5 kev T p = 1 kev T p = 5 kev S e / Z 2 [MeV/cm] 1 Text parameterization T 1 < T p < T 2 T p < T 1 (default = 1 kev) ICRU_R49p 0 0 0.001 Ziegler1977p 0.002 0.003 S e = 0.004 A 1 Tp 0.005! SRIM2000p Ziegler1985p S e = A 1 Tp 0.25, Z 2 < 6 S e = A 1 T 0.375 S e = A 1 T 0.45 p T 2 = 10 kev p, Z 2 = 6, 14, 32, other S e = A 1 Tp S e = A T p

Geant4 Electronic stopping S e /! Z 2 p [MeV/cm] 10000 1000 all values are taken for v < v F Xe: v F = 610 kev (4,7 kev/amu) Ar: v F = 156 kev (4 kev/amu) Si: v F = 660 kev (24 kev/amu) Ge: v F = 1.6 MeV (22 kev/amu) LSS vs SRIM vs GEANT4 proportionality coefficient of S e #!v LSS Xe LSS Ar LSS Si LSS Ge SRIM Xe SRIM Ar SRIM Si SRIM Ge ICRU_R49p Xe ICRU_R49p Ar ICRU_R49p Si ICRU_R49p Ge Ziegler1985p Xe Ziegler1985p Ar Ziegler1985p Si Ziegler1985p Ge Ziegler1977p Xe Ziegler1977p Ar " ICRU_R49p Ziegler1977p Si Ziegler1977p Ge " ICRU_R49p ICRU_R49He Xe ICRU_R49He Ar ICRU_R49He Si ICRU_R49He Ge Ziegler1977He Xe Ziegler1977He Ar Ziegler1977He Si " ICRU_R49He Ziegler1977He Ge " ICRU_R49He 100 SRIM2000p Xe 1 1.5 2 2.5 3 Wigner-Seitz radius R s [a B ] SRIM2000p Ar SRIM2000p Si SRIM2000p Ge

Nuclear Stopping S n ion-atom interaction potencial

Nuclear Stopping S n ion-atom interaction potencial { lim Φ = 1 Φ r 0 lim Φ = 0 r V (r) = Z 1Z 2 e 2 r

ion-atom interaction potencial { lim Φ = 1 Φ r 0 lim Φ = 0 r Classical (or statistical) treatment: the Thomas-Fermi atom Approximations: elastic static (velocity independent) universal Nuclear Stopping S n V (r) = Z 1Z 2 e 2 Φ = Φ(r/a) r screening length no shell structure (as opposed to modern Hartree- Fock solid state models)

ion-atom interaction potencial { lim Φ = 1 Φ r 0 lim Φ = 0 r Classical (or statistical) treatment: the Thomas-Fermi atom Approximations: elastic static (velocity independent) universal V(r) Nuclear Stopping S n V (r) = Z 1Z 2 e 2 Φ = Φ(r/a) classical scattering dσ pertubation treatment r screening length no shell structure (as opposed to modern Hartree- Fock solid state models) S n = T dσ T = energy transfered to an atom at rest (target)

Universal screening functions proposed in the literature: Bohr Thomas-Fermi Lindhard (LSS) Lenz-Jensen Moliere Ziegler (ZBL) SRIM (a universal fit to 522 (!) solid state interatomic potencials)

Universal screening functions proposed in the literature: Bohr Thomas-Fermi Lindhard (LSS) Lenz-Jensen Moliere Geant4 Nuclear stopping Universal stopping in reduced units scales back to ion-atom dependent stopping in physical units. Available choices: (default) Ziegler (ZBL) SRIM (a universal fit to 522 (!) solid state interatomic potencials) ICRU_R49 - parameterization of Moliere s screening function Ziegler1977 the ZBL universal potencial Ziegler1985

Universal screening functions proposed in the literature: Bohr Thomas-Fermi Lindhard (LSS) Lenz-Jensen Moliere S n [MeV / (mg/cm 2 )] Geant4 Nuclear stopping Universal 2.5 stopping in reduced units scales back to ion-atom Ge Ziegler1977 Ar LSS dependent 2 stopping in physical units. Available choices: Ar SRIM (default) 4.5 4 3.5 3 1.5 Ziegler (ZBL) SRIM (a universal fit to 522 (!) solid state interatomic potencials) ICRU_R49 - parameterization of Moliere s screening Si function LSS 1 Si SRIM Si ICRU_R49 Ziegler1977 Si Ziegler1985 0.5 the ZBL universal potencial Si Ziegler1977 Ziegler1985 0 LSS vs. SRIM vs. GEANT4 nuclear stopping S n (E), E < 150 kev 0 20 40 60 80 100 120 140 ion energy E [kev] Xe LSS Xe SRIM Xe ICRU_R49 Xe Ziegler1985 Xe Ziegler1977 Ge LSS Ge SRIM Ge ICRU_R49 Ge Ziegler1985 Ar ICRU_R49 Ar Ziegler1985 Ar Ziegler1977

Nuclear recoil full cascade Note: the primary particle is already a recoil, doesn t matter if it originated from WIMPs or neutron scattering recoil CUT energy (default MinKineticEnergy = 10eV)

Nuclear recoil full cascade Note: the primary particle is already a recoil, doesn t matter if it originated from WIMPs or neutron scattering recoil CUT energy (default MinKineticEnergy = 10eV) Physics list: Introduced a new physical process for the recoils Had to make some changes to G4hLowEnergyIonisation:

Nuclear recoil full cascade Note: the primary particle is already a recoil, doesn t matter if it originated from WIMPs code structure or neutron based δ-electrons scattering emission, fluorescence and atom recoil deexcitation CUT of energy G4hLowEnergyIonisation (default MinKineticEnergy = 10eV) and on the continous photon generation Physics in list: G4Cerenkov Introduced a new physical process for the recoils Had to make some changes to G4hLowEnergyIonisation: don t deposit T when T < CUT changed CUT from T p to T SetNuclearStoppingOff() is mandatory

Geant4 Recoil cascade Geant4 has no nuclear recoils (at least heavy ion) It also doesn t have the respective cross sections (neither differential nor integrated)

Geant4 Recoil cascade Geant4 has no nuclear recoils (at least heavy ion) It also doesn t have the respective cross sections (neither differential nor integrated) 1st approximation, using only what Geant4 already has: the recoil atom kinetic energy is taken from the parameterized nuclear stopping power T = ( de dx ) n x = S n step size the so called continuous slowing down approximation (in a loosely sense) => a continuous process major disadvantage: very strong dependence on step size => an external parameter in need of fine tuning

Geant4 Recoil cascade Geant4 has no nuclear recoils (at least heavy ion) It also doesn t have the respective cross sections (neither differential nor integrated) 1st approximation, using only what Geant4 already has: the recoil atom kinetic energy is taken from the parameterized nuclear stopping power T = ( de dx ) n actually, we shouldn t even try to approximate nuclear collisions as a continuous process (as opposed to electronic stopping) as you re not supposed to get a recoil every step, just every now and then x = S n step size the so called continuous slowing down approximation (in a loosely sense) => a continuous process major disadvantage: very strong dependence on step size => an external parameter in need of fine tuning

Geant4 Nuclear quenching: Si Si: LSS vs. SRIM vs. GEANT4 vs. exp. data total fraction of energy transfered to electrons 0.7 0.6 E R = initial recoil energy η (E R ) = total energy given to electrons E R q n = η / E R = nuclear quenching 1 Nuclear quenching 0.5 0.4 0.3 0.2 0.1 0 TRIM LSS Sattler Gerbier 0.01 10eV ICRU_R49p ICRU_R49 0.025 10eV ICRU_R49p ICRU_R49 0.025 5eV ICRU_R49p ICRU_R49 0.025 5eV SRIM2000p Ziegler1985 0.025 5eV Ziegler1985p Ziegler1985 0.035 5eV Ziegler1985p Ziegler1985 0 20 40 60 80 100 120 140 Recoil energy (kev)

Scintillation efficiency or just nuclear quenching 0.5 0.4 0.3 0.2 0.1 Geant4 Nuclear quenching: LXe LXe: LSS, SRIM, Geant4, exp.data scintillation efficiency nuclear quenching LSS SRIM Arneodo Akimov Aprile Vitaly 0.0015 10eV ICRU_R49p ICRU_R49 0.01 10eV ICRU_R49p ICRU_R49 0.05 10eV ICRU_R49p ICRU_R49 0.035 5eV Ziegler1985p Ziegler1985 0 0 20 40 60 80 100 120 140 Recoil energy (kev)

Conclusions 1. Geant4 provides a good parameterization of both electronic and nuclear stopping powers (not shown here, is our validation of Geant4 s stopping by comparing with NIST databases as well as experimental data, in different target materials, besides SRIM and LSS) 2. The user has a total of 3x6 combinations of stopping parameterizations at his/her disposal 3. The continuous approximation provides a good prediction of the nuclear quenching of the recoils cascade, but also provides to much flexibility, by fine-tuning the total of 4 parameters that control the simulation: electronic S e : the parameterization step size nuclear recoils : the parameterization energy cut

dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect.

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect. numerical integration σ(t, T c )

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect. numerical integration To do: σ(t, T c ) put it in tables and load them in Geant4, with interpolation

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect. numerical integration To do: write the DiscreteProcess functions σ(t, T c ) put it in tables and load them in Geant4, with interpolation

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 implement the sampling Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect. numerical integration To do: write the DiscreteProcess functions σ(t, T c ) put it in tables and load them in Geant4, with interpolation

a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 implement the sampling T = γt sin 2 θ 2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect. numerical integration To do: write the DiscreteProcess functions ricardo@lipc.fis.uc.pt σ(t, T c ) put it in tables and load them in Geant4, with interpolation Opposed to the standard method of solving the scattering integral: SRIM/TRIM (the standard!) M.H. Mendenhalla and R.A. Weller, An algorithm for computing screened Coulomb scattering in GEANT4, Nuclear Instruments and Methods in Physics Research B227, 3 (2005) 420

Extras

Electronic Stopping S e Fermi-Teller: S e v (ion velocity) if v < v F v 0 Lindhard: uniform free electron gas, Thomas-Fermi atom, particleplasma interaction as a perturbation S e = kɛ 1/2 if v < Bragg peak ( v 0 Z 2/3 1 500MeV for Xe) 0.10 < k < 0.20 (reduced units) k Xe 0.166 SRIM: local density approximation using Hartree-Fock solid state atoms; semiempirical fit of charge state of the ion (de/dx)e/(β Z 2 P ) [MeV/cm] 5 5. 10 8 1. 10 5 1. 10 4 1. 10 3 1. 10 2 Fermi-Teller Lindhard-Winther Ritchie LSS SRIM A. Mangiarotti et al., 2007 Xe Ar Si 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Ge Wigner-Seitz radius r s [a B ]

Nuclear quenching?!

Nuclear quenching?! E = initial particle energy (e.g. Eᵧ = 122keV for Co57 or E R for recoils produced by neutrons or WIMPs)

Nuclear quenching?! E = initial particle energy (e.g. Eᵧ = 122keV for Co57 or E R for recoils produced by neutrons or WIMPs) η (E) = total energy ultimately given to electrons E (ηᵧ Eᵧ)

Nuclear quenching?! E = initial particle energy (e.g. Eᵧ = 122keV for Co57 or E R for recoils produced by neutrons or WIMPs) η (E) = total energy ultimately given to electrons E (ηᵧ Eᵧ) q n = η R / E R = nuclear quenching (of the recoils) 1 But what do we actually measure in the lab?! relative scintillation efficiency η R(E R ) E R W S(E γ ) W S (E R ) where we redefine: γ : W S = E γ /N ph R : W S = η R /N ph } W S now they refer to the energy transfered to electrons only! and are both just functions of LET

Nuclear quenching?! E = initial particle energy (e.g. Eᵧ = 122keV for Co57 or E R for recoils produced by neutrons or WIMPs) η (E) = total energy ultimately given to electrons E (ηᵧ Eᵧ) q n = η R / E R = nuclear quenching (of the recoils) 1 But what do we actually measure in the lab?! relative scintillation efficiency η R(E R ) E R W S(E γ ) W S (E R ) where we redefine: γ : W S = E γ /N ph R : W S = η R /N ph } W S { Hitachi gives constant < 1 now they refer to the energy transfered to electrons only! and are both just functions of LET

(relative) Scintillation efficiency q n W S(E γ ) W S (E R ) Is everybody clear about this definition?!

traditional definition of W S = E N ph for γ, Recoils, whatever! back

traditional definition of W S = E N ph for γ, Recoils, whatever! traditional/experimental definition of relative scintillation efficiency = W S(E γ ) W S (E R ) < 1 because it takes more energy to produce a photon in RC than in γ 2 quenching effects all mixed up! back

traditional definition of W S = E N ph for γ, Recoils, whatever! traditional/experimental definition of relative scintillation efficiency = W S(E γ ) W S (E R ) = E γ N ph E R N ph back

traditional definition of W S = E N ph for γ, Recoils, whatever! traditional/experimental definition of relative scintillation efficiency remember ηᵧ Eᵧ = W S(E γ ) W S (E R ) = E γ N ph E R N ph = E γ N ph η R /q n N ph remember our definition of q n = η R / E R back

traditional definition of W S = E N ph for γ, Recoils, whatever! traditional/experimental definition of relative scintillation efficiency we redefine: = W S(E γ ) W S (E R ) = E γ N ph E R N ph = E γ N ph η R /q n N ph = q n W S (E γ ) W S (E R ) γ : W S = E γ /N ph R : W S = η R /N ph back

Hitachi what we measure RC γ = q(r) n q (R) el q (γ) n q (γ) el back

Hitachi what we measure RC γ = q(r) n q (R) el q (γ) n q (γ) el q quenching or scintillation efficiency of the recoils back

Hitachi what we measure RC γ = q(r) n q (R) el 1 q (γ) n q (γ) el q quenching or scintillation efficiency of the recoils back

Hitachi what we measure RC γ = q(r) n q (R) el 1 q (γ) n = q (R) n q (γ) el q (R) el q (γ) el q quenching or scintillation efficiency of the recoils scintillation only back

Hitachi what we measure RC γ = q(r) n q (R) el 1 q (γ) n = q (R) n q (γ) el q (R) el q (γ) el q quenching or scintillation efficiency of the recoils scintillation only competition between recombination processes back