Simulation of low energy nuclear recoils using Geant4
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1 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
2 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
3 Stopping power ion = projecticle particle Z 1 atom = target particle Z 2
4 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
5 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
6 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
7 de / dx (MeV cm 2 / g) 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 e+05 Energy T p (MeV)
8 de / dx (MeV cm 2 / g) 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 e+05 Energy T p (MeV)
9 Geant4 Electronic stopping low energy stopping power is parameterized
10 Geant4 Electronic stopping low energy stopping power is parameterized parameterization is for protons and alphas only
11 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:
12 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
13 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
14 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
15 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 effective charge parameterization Z eff (v, v F ) Ziegler, 1985, Brandt and Kitagawa, 1982
16 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 Ziegler1977p S e = A 1 Tp 0.005! SRIM2000p Ziegler1985p S e = A 1 Tp 0.25, Z 2 < 6 S e = A 1 T 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
17 Geant4 Electronic stopping S e /! Z 2 p [MeV/cm] 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 Wigner-Seitz radius R s [a B ] SRIM2000p Ar SRIM2000p Si SRIM2000p Ge
18 Nuclear Stopping S n ion-atom interaction potencial
19 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
20 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)
21 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)
22 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)
23 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
24 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) 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 Ziegler the ZBL universal potencial Si Ziegler1977 Ziegler LSS vs. SRIM vs. GEANT4 nuclear stopping S n (E), E < 150 kev 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
25 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)
26 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:
27 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
28 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:
29 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: don t deposit T when T < CUT
30 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: don t deposit T when T < CUT changed CUT from T p to T
31 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: don t deposit T when T < CUT changed CUT from T p to T SetNuclearStoppingOff() is mandatory
32 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
33 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 nuclear quenching competition between total energy ultimately given to electrons and energy permanently lost to recoils
34 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)
35 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
36 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
37 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
38 Geant4 Nuclear quenching: Si Si: LSS vs. SRIM vs. GEANT4 vs. exp. data total fraction of energy transfered to electrons 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 TRIM LSS Sattler Gerbier eV ICRU_R49p ICRU_R eV ICRU_R49p ICRU_R eV ICRU_R49p ICRU_R eV SRIM2000p Ziegler eV Ziegler1985p Ziegler eV Ziegler1985p Ziegler Recoil energy (kev)
39 Scintillation efficiency or just nuclear quenching Geant4 Nuclear quenching: LXe LXe: LSS, SRIM, Geant4, exp.data scintillation efficiency nuclear quenching LSS SRIM Arneodo Akimov Aprile Vitaly eV ICRU_R49p ICRU_R eV ICRU_R49p ICRU_R eV ICRU_R49p ICRU_R eV Ziegler1985p Ziegler Recoil energy (kev)
40 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)
41 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
42 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
43 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 mean free path 1 σ nuclear recoils : the parameterization energy cut
44 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 screening parameterization function energy cut mean free path 1 σ a full discrete process (for the recoils) + dσ
45 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 mean free path 1 σ + dσ nuclear recoils : the screening parameterization function energy cut work in progress a full discrete process (for the recoils)
46 dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work
47 a F, a L, a U dσ = Πa 2 f(t1/2 ) 2t 3/2 Present work Thomas-Fermi, Lenz- Jensen, Moliere, ZBL, ect.
48 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 )
49 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
50 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
51 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
52 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 σ(t, T c ) put it in tables and load them in Geant4, with interpolation
53 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 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:
54 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 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!)
55 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
56 Extras
57 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/ MeV for Xe) 0.10 < k < 0.20 (reduced units) k Xe 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] Fermi-Teller Lindhard-Winther Ritchie LSS SRIM A. Mangiarotti et al., 2007 Xe Ar Si Ge Wigner-Seitz radius r s [a B ]
58 Nuclear quenching?!
59 Nuclear quenching?! E = initial particle energy (e.g. Eᵧ = 122keV for Co57 or E R for recoils produced by neutrons or WIMPs)
60 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)
61 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
62 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?!
63 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 )
64 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
65 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
66 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
67 (relative) Scintillation efficiency q n W S(E γ ) W S (E R ) Is everybody clear about this definition?!
68 traditional definition of W S = E N ph for γ, Recoils, whatever! back
69 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
70 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
71 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
72 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
73 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
74 Hitachi what we measure RC γ = q(r) n q (R) el q (γ) n q (γ) el back
75 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
76 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
77 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
78 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
79 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 electrons escaping recombination back
80 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 electrons escaping recombination back
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