Code DETEFF Influence of the electronic transport simulation on efficiency

Transcription

1 ICRM Gamma-Ray Spectrometry Working Group Meeting November 7-8, 006. Paris Code DETEFF Influence of the electronic transport simulation on efficiency Miguel Jurado Vargas Departamento de Física. Uex

2 DETEFF A simple MC code for the computation of efficiency in gamma-ray detectors Néstor Cornejo Díaz 1 & Miguel Jurado Vargas 1 Centro de Protección e Higiene de las Radiaciones. Ministerio de Ciencia, Tecnología y Medio Ambiente. Cuba Departamento de Física. Universidad de Extremadura. Spain

3 DETEFF characteristics Written in BORLAND DELPHI ( Version of Pascal ) Congruential random generator : 3 bit (period = 3 = 4.3 x 10 9 ) 10 8 random numbers: relative deviations of efficiency < 0.1% Simple variance-reduction techniques : photon E absorption (10 kev), limited space, total attenuation in sample (individual processes are not simulated) Sources: point, disk, cylindrical, rectangular, and Marinelli beakers (axially centered on the detector) Detectors: NaI, CsI, Ge and Si gamma-ray detectors Results: Peak efficiency ( intrinsic and S-D system ) Energy range: kev (bremstrahlung is not included) Specific code: much less time-consuming and more user-friendly than generalists codes

4 CS Interaction in sample, covers and sample PP PE shield In the sample, walls, covers and shield, the individual processes (PE, CS, PP) are not considered. We only take into account the photon attenuation. We only consider photons that reach the active crystal with the initial energy. detector It is assigned a statistic weight to each photon, which is reduced when it is crossing different attenuation layers before reaching the crystal. This weight is finally taken into account for the calculation of efficiency. We avoid individual simulation (photon by photon) Simulation time is greatly reduced Total efficiency cannot be calculated

5 SAMPLING EMISION POINT OF PHOTON IN THE SAMPLE V 1 = π.or (Hm Hd) V = π.hd (Or Ir ) V T = V 1 + V Y r 1, r,r 3,r 4 Hm > Hd No r 1, r,r 3 Z Y r 1 >V 1 /V T No u z = Hd.r u z = (Hd Hm).r u z = ( Hd Hm ) + Hm.r 1 Hm Hd ρ = (Ir +r 3 (Or -Ir )) 1/ ρ = Or.r 3 1/ ρ = (Ir +r (Or -Ir )) 1/ Ir Y ϕ =π.r 4 ϕ =π.r 3 X Marinelli Or u x = ρ.cos φ u y = ρ.sen φ

6 Photon interactions in the active detector crystal

7 Sampling of photon path t Sampling of interaction type r = t 0 µ x µ e dx = 1 e µ t t 1 = ln µ 1 () r µ = τ + σ + κ µ ( material, E): linear attenuation coefficient Photoelectric Effect τ, σ, κ µ =τ + σ + κ Generator r (0,1) r < τ /µ? τ P = τ + σ+ κ P σ σ = µ τ = P κ κ = µ τ /µ < r < (τ +σ )/ µ? τ µ t : path sampled for each photon τ, σ y κ : attenuation coefficients for PE, CS and PP, obtained by XCOM database (Berger et al. 1999). Compton scattering Pair Production

8 µ µ α α α α α α π µ α µ σ d r d e + + = ) 1, ( ' ' ' c m h e = υ α m x c m e r e e = ε π ( ) { } µ α α α + = 1 1 ' ( ) ( ) = 1 1, cos 1, µ µ α σ θ µ µ α σ d d r Sampling of the direction of the scattered photon after CS Sampling of the scattered angle θ. Expression without analytic solution r = random number (0,1). Probability density distribution (Klein Nishina formula) Cross section for scattering of a photon (E=h.v) with a free electron (µ=cos(θ)): EVERETT & CASHWELL method (1979)

9 w 1 ϕ uniformly sampled in (0,π) Photon Vector director director vector del fotón before antes CS de la interacción w Vector Photon director director del vector fotón después after CS de la interacción x z z θ ϕ w 1 x y w y Coordinate system X Y Z with origin at the Compton interaction point w 1 (0, 0, 0) w (sinθ cosϕ, sinθ sinϕ, cosθ) Change to the initial coordinate system X Y Z w 1 (a, b, c) w (a,b,c ) a.c 1 c b.c 1 c 1 c b 1 c a 1 c 0 a b c 1 a' = a cos 1 c ( θ ) + ( a c cos( ϕ) b sin( ϕ) ) sin( θ ) 1 b' = b cos 1 c ( θ ) + ( b c cos( ϕ ) a sin( ϕ )) sin( θ ) ( θ ) 1 c ( θ ) cos( ϕ) c' = c cos sin

10 CE e detector PE e X-ray Source E o DETECTOR Annihilation photons P.P e ADDITIONAL CONSIDERATIONS Secondarye - and e + are considered to be absorbed into the crystal After PE, the direction of X-ray is assigned isotropically. It is again simulated and can go out the detector (X-ray escape peak) Multiple Compton is considered until photon escapes from the detector or PE ocurrs After PP interaction, the direction of 1 st annihil. photon is assigned isotropically ( nd in opposite direction) Each annihilation photon can interact by PE or CS, or escape (single and double escape peaks) Energy for photon absorption: 10 kev FEPE: deposition of E from E 0-5 kev up to E 0

11 NaI & CsI DETECTORS Ge & Si DETECTORS

12 Cylindrical, disk, or point sources Marinelli samples

13 sample FILTER detector ATTENUATION COEFFICIENT LIBRARY

14 Input data Detector :Ge Detector Diameter [cm]: Detector Height [cm]: Frontal Al-Cover Thickness [cm]: Lateral Al-Cover Thickness [cm]: External Diameter of Detector Cover [cm]: Frontal Detector-Cover Gap [cm]: Detector Frontal Dead Layer [cm]: 3.00E-0003 Detector Lateral Dead Layer [cm]: 3.00E-0003 Diameter of Detector Internal Core [cm]: Deep of Detector Internal Core [cm]: 4.00 Diameter of Entrance Window [cm]: Thickness of Entrance Window [cm]: 5.00E-000 Entrance Window Lin. Att. Coeff. [cm-1]:.88e-0001 Energy Resolution in Photo-Peak [%]:.0 Detector Linear Att. Coefficient [cm-1]: 4.5E+0001 Al-Cover Linear Att. Coefficient [cm-1]: 1.69E+0000 Source Geometrie :Marinelli Source Height [cm]: Hole Deep [cm]: Source outer Diameter [cm]: Source inner Diameter [cm]: Source to Detector Distance [cm]: Photon Energy [KeV]: Source Lin. Attenuation Coefficient [cm-1]:.6e-0001 Source Wall Thickness [cm]: Lin. Att. Coefficient of Source Wall[cm-1]:.6E-0001 Results RESULTS Number of produced Photons : 0000 Pseudo-Random Numbers generated : Detector Total Efficiency : 9.96E % Detector Peak Efficiency : 9.93E % Total Efficiency of S-D System :.33E % Peak Efficiency of S-D System :.3E % Photofraction : % Filter Thickness [cm]: 0.00E+0000 Filter Lin. Attenuation Coefficient [cm-1]: 0.00E+0000

15 spectrum Single-escape peak 000 kev peak Compton edge Double-escape peak Multiple Compton COMPTON background COMPTON background

16 International Intercomparison (EUROMET 48) Point sources cylindrical sources

17 SELF-ABSORPTION CORRECTIONS

18 Future improvements Energy losses by electronic bremstrahlung Implementation of coherent scattering (Rayleigh) Interaction on the shields, covers, sample (back. peak, X-rays from shield, total efficiency ) Spectral spreading (more real gamma-spectrum) FWHM given by the user

19 Influence of electronic transport simulation on the efficiency calculation DETEFF: electronic transport is NOT included PENELOPE: electronic transport included Application of both codes to the MC exercise

20 CODE PENELOPE Lenguage: FORTRAN 77 Main program: written by user random generator : period aprox Variance-reduction techniques Complex Geometries: PENCYL Results: particle distributions (deposited energy, output angle, charge, dosis..) Main programs included: PENSLAB PENCYL

21 Conclusions GEOM1 GEOM GEOM3 At 000 KeV: FEPE values from DETEFF are overestimated, due to bremstrahlung losses are not considered. In general, FEPE values from DETEFF are similar to those from PENCYL. The influence of electronic transport must be less than 3% The total efficiency from DETEFF is in agreement (D < 0,7%) with PENCYL data for GEOM1 (point source and bare detector). The influence of electronic transport on total efficiency is negligible in this case. As expected, the total eficiency from DETEFF is greatly underestimated for the rest of geometries. The scattered radiation in sample and covers is significant. Simulation times : DETEFF: minutes PENCYL: days

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23 PENELOPE EUROMET48 (HpGe tipo p) Fuente puntual (distancia = cm) Pico escape Ge (60-11 kev) Fotones aniquilación

24 Z SAMPLING r 1 EMISION POINT OF PHOTON IN THE SAMPLE Dm Hm ϕ = π.r 1 r Y ρ =(D m /).r - 1 r 3 Z X u z = Hm (1 - r 3 ) / r 1 Am Hm u x = Lm.(r 1 1) / Y r u y = Am.(r 1) / r 3 u x = ρ.cos(ϕ) u y = ρ.sin(ϕ) X Lm u z = Hm.(r 3 1) /

25 r β=1/α γ=1 β(1+β) η=α+1 ξ=1/η λ=log η G=α(α+1)ξ +4β+γλ G F Yes α 7/ 6 No F = N 1 + β( N + N 3 β) J = F / G Y r J No EVERETT & CASHWELL method for the sampling of scattering angle θ after CS f = ξ+η f = N 4 + β( N 5 + N 6 β) Λ = (λ N 7 ) / (1 J) r R g = 3(1 ξ) h = (1 ξ) a = F / d = F / f b = F+ d g c = a d + h r / J R g =.1 h = 1.4 X = 0.3 exp[ Λ(r J)] α = X. α N 1 = N = N 3 = N 4 = N 5 = N 6 = N 7 = X = 1 + R[ a + R( b + R.c )]