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Detection efficiency calculation for photons, electrons and positrons in a well detector. Part II: Analytical model versus simulations
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Detection efficiency calculation for photons, electrons and positrons in a well detector. Part II: Analytical model versus simulations S. Pomme´ a,, G. Sibbens a, T. Vidmar a, J. Camps a,b, V. Peyres c a
European Commission, Joint Research Centre, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium SCK CEN, Belgian Nuclear Research Centre, Boeretang 200, B-2400 Mol, Belgium c Laboratorio de Metrologı´a de Radiaciones Ionizantes, Ed. 12, CIEMAT, Avda. Complutense 22, 28040 Madrid, Spain b
a r t i c l e in fo
abstract
Article history: Received 14 October 2008 Received in revised form 4 March 2009 Accepted 7 April 2009 Available online 18 April 2009
A comparison is made between the results of Monte Carlo simulations and a new analytical model (cf. Part I) for the detection efficiency of a well-type NaI detector for photons, electrons and positrons in the energy range of 0.01 MeV–10 MeV. Using MCNP 5.1.40, GEANT3 and PENELOPE simulation results as benchmark, it was found that the analytical model was quite successful at reproducing the total detection efficiency for photons and positrons, and at giving rough indications on the photon peak-tototal ratio and the electron detection efficiency. It was also able to deal with cylindrical volume sources and vials, eccentric positioning of the source inside the detector well and the possible contribution of scattering or pair production in the surrounding lead shield. & 2009 Elsevier B.V. All rights reserved.
Keywords: Well detector Efficiency Modelling Simulation Photons Nuclear
1. Introduction In Part I of this work [1], a new analytical model was presented to calculate the total detection efficiency of a well-type radiation detector for photons, electrons and positrons emitted from a radioactive source at an arbitrary position inside the well. The model was designed for typical configurations of a point source or cylindrical source and vial being measured in a NaI well detector, possibly with a surrounding lead shield. In this paper, part II of the work, the analytical model has been applied to the hypothetical cases of a 600 600 and a 300 300 NaI well detector, with or without lead shield, and the calculated detection efficiencies have been compared with the benchmark results of Monte Carlo simulation codes for combined electron-photon transport. The three codes used were MCNP 5.1.40 [2], GEANT3 [3] and, to a lesser extent, PENELOPE [4]. For one configuration, a comparison is also made with a simpler analytical model by Sima [5] with adaptations by Pomme´ et al. [6]. At this stage, no experimental verifications were done, only the level of equivalence of the models was examined. The final aim is to integrate the analytical model in a software package for 4pg counting, which is a convenient primary standardisation method for the activity of radionuclides that emit multiple g-rays per decay. By maximising the detection efficiency
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E-mail address: [email protected] (S. Pomme´). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.04.007
and the covered solid angle, one can minimise errors arising from the uncertainty on the calculated efficiencies and angular correlation effects. For radionuclides with a complex decay scheme, one can reach an overall combined efficiency of more than 99%, which significantly reduces the influence of possible errors on the calculated detection efficiency. Whereas the 4pg counting method is mainly based on the detection of the emitted g-rays, one should also take into account the contribution of other radiation, such as beta-particles, conversion electrons, positrons and their directionally correlated annihilation photons.
2. The source and detector geometries Two NaI well detector set-ups have been considered: the first is based on an existing 600 600 crystal at IRMM and the second on a 300 300 crystal at CIEMAT. A cross-section of the first geometry is shown in Fig. 1, together with an indication of the dimensional parameters involved. The detector crystal is represented by an outer cylinder with radius Ro ¼ 7.62 cm and height H ¼ 15.23 cm, and at the top side along the symmetry axis a cylindrical cavity with radius Ri ¼ 2.62 cm and depth Hh ¼ 9.80 cm. The detector cap surrounding the NaI crystal consists of Al and Al2O3 layers of equal thickness; each 0.06 cm for the inner cap and 0.16 cm for the outer cap. At the bottom side, however, a 1.05 cm layer of lightconducting gel is assumed, which was for convenience represented as acrylic glass in this simulation exercise.
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
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Fig. 1. Cross-section of the IRMM 600 600 NaI well detector set-up with indication of the relevant geometrical parameters.
Table 1 Hypothetical source and vial geometries investigated in combination with the IRMM (case 1–6) and CIEMAT (case 10 ) NaI well detector. ID
1 2 3 4 5 6 10
Geometry Description
cntr pnt src ecc pnt src+shld ecc vol src+vial cntr vol src+vial cntr pnt src+vial cntr pnt src+vial drop src+foils
Detector
600 600 300 300
Source
Vial
Rs
Hs
DRc
1 106 1 106 0.5 2 1 103 1 103 0.15
5 107 5 107 1 4 1 103 1 103 0
0 2.4 1.9 0 0 0 0
Vial
Acrylic Acrylic Acrylic Al Acrylic
NaI crystal
IRMM CIEMAT
Ro 7.62 3.81
Lead shield Rvi
0.5 2 1 103 1 103 1
Rvo
0.6 2.1 2.5 1 1
Inner cap H 15.23 7.62
Ri 2.62 1.45
h 5.43 2.54
Al 0.06 0.05
Tvt
0.1 0.1 2.499 0.2 0.0075
Tvb
zvb
0.1 0.1 2.5 0.199 0.0075
8.55 5.66 5.55 5.55 5.55 7.85 2.61
DZlt
DRl
0.3
0.3
Tl 0 1 0 0 0 0 0
Outer cap Al2O3 0.06 0.01
Al 0.16 0.05
Al2O3 0.16 0.01
The parameters are illustrated in Fig. 1. All dimensions are in centimetres.
For this detector, several source geometries have been tested. The discussion in this paper will be restricted to six particular cases, which may be representative for some realistic applications. The main geometrical characteristics of the considered geometries have been assembled in Table 1. The dimensions of the source are defined by the radius, Rs, and the height, Hs. The dimensions of the absorber or vial are defined by the inner and outer radius, Rvi and
Rvo, and the bottom and top thickness, Tvb and Tvt. The bottom side of the vial (or source if Tvb ¼ 0) is positioned at a distance zvb from the bottom side of the detector crystal and can have a radial displacement of the centre with respect to the symmetry axis of the detector by DRc. The lead shield has a thickness Tl and is at a distance DZlt and DRl away from the top and side of the outer cap, respectively.
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
The first geometry is the hypothetical case of a point source positioned on the symmetry axis inside the well, at three centimetre height above the bottom of the crystal well (z ¼ h+3 cm). The second case is a point source close to the crystal bottom (z ¼ h+0.23 cm) and the inner cap (zhdcap ¼ 0.11 cm). In this particular case, also a cylindrical lead shield of 1 cm thickness was included, at a distance of only 0.3 cm from the outer detector cap. The third case is a rather small water-based volume source of radius Rs ¼ 0.5 cm and height Hs ¼ 1 cm, contained in an acrylic vial of 0.1 cm thickness in all directions. The vial is placed directly on top of the inner cap, in the most extreme eccentric position at DRc ¼ 1.9 cm from the symmetry axis. In the fourth case, a bigger, centred water-based volume source of radius Rs ¼ 2 cm and height Hs ¼ 4 cm and 0.1-cm-thick acrylic vial was taken. The fifth and sixth cases concern a centred point source at z ¼ h+2.5 cm height, in the middle of a thick acrylic (height Hv ¼ 5 cm, Rvo ¼ 2.5 cm) and aluminium (Hv ¼ 0.4 cm, Rvo ¼ 1 cm) absorber, respectively. The second detector, referred to as the CIEMAT 300 300 detector, was represented by an outer cylinder radius of Ro ¼ 3.81 cm and height H ¼ 7.62 cm, and a cavity with radius Ri ¼ 1.45 cm and depth Hh ¼ 5.08 cm. The detector inner and outer caps consisted of a 0.05 cm Al layer and a 0.01 cm Al2O3 layer. The source was
100%
503
positioned at height z ¼ 2.6175 cm and its dimensions were Hs ¼ 0.2 cm and Rs ¼ 1 cm and the vial consisted of two foils of 0.0075 cm plastic. 2.1. Photons Fig. 2 shows the total photon detection efficiency of the IRMM detector for the six geometries mentioned, as calculated with the analytical model (full line) and simulated with MCNP5 (full circles) and GEANT3 (open circles). As the results often closely match, the absolute difference between simulations and analytical model is plotted in greater detail in Fig. 3. The first two cases, pertaining to point sources, demonstrate that the analytical model can reproduce the MCNP benchmark values with a precision of a few tenths of percent (typical errorE0.2%) at all photon energies in the 0.01–10 MeV range. This excellent result confirms the sound basis of the model, which could only be achieved by taking into account also secondary effects, such as energy degradation by inelastic scattering and effects on the travel path by elastic and inelastic interactions [1]. Also the inclusion of backscatter and pair production events in the outer cap and lead shield (cf. case 2) are essential elements at high energies. Calculations for point sources close to the inner cap, whether at the bottom or on the side of the well, show a crucial
80% (1) cntr pnt src
(1) cntr pnt src
2%
60%
0% -2%
40%
MCNP5 GEANT3
(2) ecc pnt src + shield
20%
2%
(2) ecc pnt src + shield
0%
0%
-2% (3) ecc vol src (3) ecc vol src
Absolute difference
Total efficiency
2%
(4) cntr vol src
(5) pnt src + acryl
100%
0% -2%
(4) cntr vol src
2% 0% -2%
80% 0% -2%
40% 20% PHOTONS 0% 0.01
(5) pnt src + acryl
2%
(6) pnt src + Al
60%
0.1 1 Photon Energy (MeV)
Pommé MCNP5 GEANT3
2%
(6) pnt src + Al
0%
10
Fig. 2. Total photon detection efficiency in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circle) and GEANT3 (open circle). The graphs are consecutively shifted by 40% on the y-axis.
-2% 0.01
PHOTONS 0.1 1 Photon Energy (MeV)
10
Fig. 3. Absolute difference between the total photon detection efficiency from simulations and the analytical model calculations displayed in Fig. 2.
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dependence on the exact calculation of the travel path through the cap material. Whereas the agreement with MCNP is very satisfactory (erroro0.6%), there is obviously a more significant discrepancy with the GEANT3 data, in particular at low energies (erroro2.8%). This is almost entirely due to the difference in attenuation coefficients used in the latter code. Indeed, the analytical model can reproduce the GEANT3 results when it applies the same attenuation coefficient input data set. At this point, one can already conclude that the choice of the input data set can be of higher importance than the choice of model by which the efficiency is calculated. The analytical model deals very well with an eccentric small volume source (case 3, erroro0.8%) and with a centred larger volume source (case 4, erroro0.5%). A point source in a big acrylic (case 5) and Al absorber (case 6) is reproduced with slight difficulty in the energy region where the efficiency changes steeply as a function of energy (erroro1.5%). The main weakness of the analytical model is related to multiple scattering interactions, which are obviously treated more rigorously in a simulation approach. Also when comparing the MCNP5 and GEANT3 results, it is clear that the mutual differences are the largest in the regions where the efficiency changes significantly with energy. A similar phenomenon may be expected when comparing with experimental data. At the top of the curve, the result is rather stable, because the penetration through the inner cap and the chance for interaction in the NaI crystal are both high. Excellent results were also obtained with the configuration of the CIEMAT 300 300 NaI detector. As shown in Fig. 4, the efficiency was simulated for a wide range of energies with the PENELOPE code. The attenuation coefficients of PENELOPE at the considered energies are not very different from the XCOM data [7] used in the
analytical model. The resulting efficiency values differ by typically 0.29% (median absolute deviation) with the analytical model calculations. The graph shows also a comparison with efficiencies calculated with an adapted version of Sima’s simple model [6]. Also this model performs surprisingly well, even though the deviation from simulations may amount to a few percent in the low-energy region. 2.2. Peak-to-total ratio The analytical model provides a rough estimate of the peak efficiency, via the peak-to-total ratio (P/T). The calculated P/T values are compared with simulated data in Fig. 5. There is a good agreement between the results from the MCNP5 and GEANT3 simulation codes if caution is taken to perform the simulations with sufficient energy resolution. For the peak efficiency, events are accepted only if the detected energy is equal to the initial energy within narrow margins (typically within 0.01%). The analytical model reaches a fairly acceptable approximation over a wide energy region, certainly in view of its simplicity. The model does not reproduce the high P/T values below 30 keV, nor does it predict the local dip around 33.2 keV. The latter corresponds to the K-shell electron binding energy in iodine, the 100% 80% 60% (1) cntr pnt src
40% 20% (2) ecc pnt src + shield
0%
0% Peak-to-Total ratio
difference
2%
-2%
100%
(3) ecc vol src
Total efficiency
80%
(4) cntr vol src
60%
100% (5) pnt src + acryl
80%
40%
20%
0% 0.01
60%
Pommé Pommé et al., based on Sima model Penelope
0.1 1 Photon Energy (MeV)
40%
10
Fig. 4. Bottom: total photon detection efficiency in the CIEMAT 300 300 NaI well detector for one source geometry. The full line corresponds with a spline interpolation between analytical model calculations. The open circles represent calculated values from an adaptation of Sima’s simple model, while the closed circles correspond to simulation results with PENELOPE. Top: absolute difference between simulated and calculated efficiencies.
20% 0% 0.01
Pommé MCNP5 GEANT3
(6) pnt src + Al
PHOTONS
0.1
1
10
Photon Energy (MeV) Fig. 5. Peak-to-total ratio for the photon detection efficiency of the IRMM 600 600 NaI well detector for the six source geometries (cf. Fig. 2). The graphs are consecutively shifted by 40% on the y-axis.
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
dip in the P/T being due to escape of KX-rays at the inside border of the NaI crystal. Simulated spectra indeed show escape peaks that corroborate this interpretation. In the frame of the simulations, the escape peaks were not included in the peak efficiency. In real experiments, however, the spectral resolution of the detector is rather bad and, at sufficiently high energies, the escape peaks will add up with the main photopeak. Therefore, also the simulated peak efficiencies should be interpreted with caution. At high energies (1 MeV–10 MeV), the simple model has some difficulty reproducing the benchmark P/T values, as it was not designed to deal in a rigorous manner with multiple interactions in the crystal. For the considered set-up, the simulation results between 0.5 MeV and 10 MeV show a rather linear behaviour as a function of the logarithm of the energy.
2.3. Electrons The penetration of electrons through the diverse absorber materials is very sensitive to the thickness, specific charge and mass of the absorber materials. Moreover, the deceleration of the 100% Pommé
80%
(1) cntr pnt src
MCNP5 GEANT3
60% 40% (2) ecc pnt src + shield
20% 0% Electron detection efficiency (%)
(3) ecc vol src
505
electrons in the materials leads to bremsstrahlung and secondary particles that can be detected in the NaI crystal. The analytical model uses an empirical formula for the transmission, with adaptations to deal with different absorber materials [1]. In order to partly compensate for the detection of secondary particles, the transmission probability was artificially increased using the CSDA range (continuous slowing down approximation) instead of the extrapolated range, and the dependence on the angle of incidence was switched off. In Fig. 6 the detection efficiency for electrons is shown as a function of their energy. The transmission functions show a rather steep transition between zero and the geometry factor ( ¼ O/4p) of the detector crystal. The MCNP5 and GEANT3 simulations show qualitatively a similar shape; however, the transmission functions are sometimes shifted along the energy axis by an amount of log(DE)E0.1. The analytical model generally reproduces the shape of the efficiency curves, yet the transition energies do not rigorously match those of the simulation results. The main difficulty with the different models seems to be related with the production of bremsstrahlung photons. In case 1, one can see that the transmission of the analytical model is slightly overestimated, due to the trick with the artificially enhanced electron transmission (cf. CSDA range). This approach works rather well in the second and third cases, of the eccentric point and volume source, which lead to more interaction with the inner cap and source material. In the last three cases, involving an excessive amount of source or vial absorber materials, the analytical model renders too low efficiency values. This is due to the missing contribution of bremsstrahlung, which penetrates the absorber materials much more easily than electrons. The proof can be seen in the bottom of Fig. 6 for case 5 (point source in acrylic vial), where the simulated transmission of the electrons, represented by a dash–dotted curve, is indeed somewhat lower than the predicted detection efficiency from the analytical model. In general, one can conclude that the calculation of detection efficiencies for electrons does not offer the same level of accuracy as for photons. The calculations may be trusted at the extremes of low or high energy and can be used for an indicative value with high uncertainty in the transition range.
2.4. Positrons
100%
(6) pnt src + Al
80% 60% (4) cntr vol src
40% ELECTRONS
20%
(5) pnt src + acryl
0% 1
10 Electron Energy (MeV)
Fig. 6. Total electron detection efficiency in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The positions of geometries 4–6 have been switched, in order to avoid mutual interference in the graph. The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circle) and GEANT3 (open circle). The graphs are consecutively shifted by 40% on the y-axis.
Positron emitters can be conveniently measured in a 4pg detection geometry. In particular, the annihilation photons of 511 keV have a high probability of being detected. The fact that they are emitted in opposite direction ensures that at most one of them can escape through the hole of the well. In the presence of a top lead shield, there is even a chance that the escaped photon is nevertheless detected after a backward scattering interaction in the shield. Also the positron may reach the crystal, provided that it has enough energy to pass the absorbers. The analytical model takes into account the angular correlation between both annihilation quanta; hence, it does not treat them as two independent, randomly emitted g-rays. Calculations show that this leads to significantly different results in asymmetric configurations, i.e. for a source that is situated close to the hole of the well. The effect is almost insignificant for a point situated near the bottom of the well. This is illustrated in Fig. 7 for a point source moving along the symmetry axis of the IRMM NaI well detector. The bottom side of the graph shows that the model reproduces rather accurately the simulated efficiencies for single and double 511 keV photons as well as for positrons. The top side of the graph shows the distinct difference in detection efficiency for low-energy positrons and two directionally uncorrelated 511 keV photons.
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
506
99%
difference
15% positron minus 2 x 511 keV Pommé MCNP5 GEANT3
10% 5%
(1) cntr pnt src
96% 93% 99%
0%
(2) ecc pnt src + shield
96% 93%
100%
99% 96% (3) ecc vol src
Total efficiency
Total efficiency
90%
80%
70%
Pommé MCNP5 + GEANT3: 1 x 511 keV 2 x 511 keV low-energy positron
60%
93% 99% 96% (4) cntr vol src
93% 99% 96%
50% 0
2
4
6
8
(5) pnt src + acryl
93%
source position height (cm) Fig. 7. Bottom: calculated (line) and MCNP5 (closed symbols) and GEANT3 (open symbols) simulated detection efficiencies in the IRMM NaI well detector for single 511 keV photons (diamonds), two simultaneous but directionally uncorrelated 511 keV photons (circles) and low-energy positrons and their oppositely emitted annihilation photons (triangles) as a function of height of the source point in the well. Top: difference in detection probability of low-energy positrons and uncorrelated 511 keV photons.
99%
(6) pnt src + Al
96% 93%
Pommé MCNP5 GEANT3
POSITRONS
90%
Fig. 8 gives an overview of the positron detection efficiency as a function of positron energy for the six geometries in the IRMM detector. In the first case, the positron starts from a centred point at 3 cm height, the first absorber being the air in the well. The lowenergy positrons annihilate close to the source point and the detection efficiency corresponds to that of the annihilation photons. With increasing energy, the annihilation zone expands around the source point and the efficiency corresponds to a mean. In the analytical model, the efficiency value at source point is taken instead of the mean. As the range of the positron increases with energy, some will escape through the hole and annihilate outside the well, leading to a drop in the detection efficiency. At even higher energies, a fraction of the positrons can penetrate the inner cap and thus increase the overall probability for detection, which levels off at the solid angle covered by the crystal. The simulations confirm the qualitative behaviour of the energy dependence of the detection efficiency. However, they do not agree quantitatively at intermediate energies, probably due to differences in electron transport handling. The analytical model does not reproduce the rise between 30 keV and 70 keV, owing to annihilations taking place deeper inside the well. In the second case, that of an eccentric point source close to the bottom of the well, the detection efficiency is higher because of the higher mean travelling path of the photons in the crystal, the higher solid angle covered by the crystal and the stopping of escaped positrons in the lead shield. The point source is very close to the bottom of the well, which reduces the expansion of the annihilation zone with increase in positron energy. These conditions are favourable for the analytical model, which indeed reproduces the counting efficiency satisfactorily at all energies.
0.01
0.1 1 Positron Energy (MeV)
10
Fig. 8. Total detection efficiency for positrons and their annihilation photons in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circles) and GEANT3 (open circles).
Some of the arguments mentioned for case two are also valid for case three, where the source and vial material act as additional absorbers that retain most of the annihilation inside the well. In cases five and six, the positrons have little chance of leaving the acrylic or aluminium absorbers, leading to a fairly constant efficiency as a function of energy. The analytical model and simulations show good agreement in all cases where the majority of the positrons are stopped inside the well. The agreement is even better for source points closer to the bottom of the well, as could be observed in Fig. 7. 2.5. b-particles For b-particles, the analytical model adopts a simplified energy distribution and derives a type of attenuation coefficient associated with the absorber (and its approximate thickness) to be used in an exponential transmission formula. This leads to rough approximations of the total detection efficiencies for b-particles and rather good approximations for b+-particles, as the annihilation radiation is dominant for the latter. Alternatively, one can calculate the detection efficiency for b and b+-particles from a normalised multiplication of the beta-particle energy spectrum
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
100%
98% β+-particles
96%
Total efficiency
100% Pommé, exponential model Pommé, convolution GEANT3, simulation MCNP5, convolution
80%
60%
40%
20% β--particles 0% 0.01
0.1 1 Beta Particle Energy (MeV)
10
Fig. 9. Total detection efficiency for b-particles (bottom of graph) and for b+particles and their annihilation photons (top of graph) in the IRMM 600 600 NaI well detector for an eccentric point source close to the bottom of the well (case 2), as calculated with the analytical model (line) and GEANT3 (open circles) or MCNP (closed circles). The dashed line shows the convolution of the efficiency curves for mono-energetic particles (cf. Figs. 6 and 8) and a simplified beta-particle energy spectrum.
and the corresponding (interpolated) efficiencies for monoenergetic electrons and positrons, respectively. An example is presented in Fig. 9, corresponding to geometry case 2.
507
The simulated total photon detection efficiencies with GEANT3 deviate at low energies from the other codes, because it applies significantly different attenuation coefficients. As a result, one can conclude that the choice of the input data can be more critical than the choice of the model by which the efficiency is calculated. When comparing with reality, also the uncertainty on actual dimensions and material composition may be decisive factors in the uncertainty budget, rather than the model itself. The analytical model is also very successful in reproducing the detection efficiency for positrons and their annihilation photons, including the important angular effect owing to the opposite emission direction of the latter. With increase in positron energy, the result is generally more stable and accurate for configurations with sufficient absorber material to ensure that the annihilation takes place close to the source. Differences among the different models were mainly due to uncertainty in the positron transport, which is decisive for the expansion of the annihilation zone, the fraction of positrons escaping through the hole of the well and the detection probability of positrons in the crystal. The different codes show difficulty to simulate the detection efficiency of electrons, which is not only determined by the transmission of the primary particles but also greatly influenced by secondary particles. The analytical model does not adequately take into account bremsstrahlung, which can significantly increase the detection efficiency of high-energy electrons passing through thick absorbers. The detection efficiency for beta-particles can be calculated in two ways: via an exponential transmission formula or by combining the mono-energetic efficiency curves with the normalised energy spectrum of the beta-particle. This leads to rough approximations of the total detection efficiencies for b-particles and rather good approximations for b+-particles, as the annihilation radiation is dominant for the latter. As an overall conclusion, one can say that the analytical model is somewhat less rigorous and flexible than the simulation codes, but on the other hand it is easy to use, relatively fast and sufficiently complete and accurate for many applications. References
3. Conclusions The analytical model of Pomme´ [1] gives an accurate account of the total photon detection efficiency for point sources in a welltype NaI detector, when compared with the outcome of the MNCP5, GEANT3 and PENELOPE simulation codes. It was also able to deal with cylindrical volume sources and vials, eccentric positioning of the source inside the detector well and the possible contribution of scattering or pair production in the surrounding lead shield. Its accuracy is generally best for sources with a minimum of absorber materials and situated rather deep into the well. It can also provide a rough indication of the peak-to-total ratio, which may be useful to estimate the relative count loss caused by setting a discriminator threshold at a fixed energy level.
[1] S. Pomme´, Detection efficiency calculation for photons, electrons and positrons in a well detector; Part I: Analytical Model, Nucl. Instr. and Meth. (2009); doi:10.1016/j.nima.2009.03.076. [2] MCNP Team, MCNP—A General Monte Carlo N-Particle Transport Code—Version 5, MCNP 5.1.40 RSICC Release Notes, 2005 /http://mcnp-green.lanl.gov/ index.htmlS. [3] R. Brun, F. Bruyant, M. Maire, A.C. McPherson, P. Zanarini, GEANT3, CERN Data Handling Division, Geneva, 1987. [4] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE—A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD Nuclear Energy Agency, Issy-les-Moulineaux, France, 2003. [5] O. Sima, Nucl. Instr. and Meth. A 450 (2000) 98. [6] S. Pomme´, J. Camps, G. Sibbens, T. Vidmar, Y. Spasova, J. Radioanal. Nucl. Chem., in press. [7] M.J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S. Zucker, XCOM: Photon Cross Sections Database, 2007 /http://physics.nist.gov/ PhysRefData/Xcom/Text/XCOM.htmlS.
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Detection efficiency calculation for photons, electrons and positrons in a well detector. Part II: Analytical model versus simulations S. Pomme´ a,, G. Sibbens a, T. Vidmar a, J. Camps a,b, V. Peyres c a
European Commission, Joint Research Centre, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium SCK CEN, Belgian Nuclear Research Centre, Boeretang 200, B-2400 Mol, Belgium c Laboratorio de Metrologı´a de Radiaciones Ionizantes, Ed. 12, CIEMAT, Avda. Complutense 22, 28040 Madrid, Spain b
a r t i c l e in fo
abstract
Article history: Received 14 October 2008 Received in revised form 4 March 2009 Accepted 7 April 2009 Available online 18 April 2009
A comparison is made between the results of Monte Carlo simulations and a new analytical model (cf. Part I) for the detection efficiency of a well-type NaI detector for photons, electrons and positrons in the energy range of 0.01 MeV–10 MeV. Using MCNP 5.1.40, GEANT3 and PENELOPE simulation results as benchmark, it was found that the analytical model was quite successful at reproducing the total detection efficiency for photons and positrons, and at giving rough indications on the photon peak-tototal ratio and the electron detection efficiency. It was also able to deal with cylindrical volume sources and vials, eccentric positioning of the source inside the detector well and the possible contribution of scattering or pair production in the surrounding lead shield. & 2009 Elsevier B.V. All rights reserved.
Keywords: Well detector Efficiency Modelling Simulation Photons Nuclear
1. Introduction In Part I of this work [1], a new analytical model was presented to calculate the total detection efficiency of a well-type radiation detector for photons, electrons and positrons emitted from a radioactive source at an arbitrary position inside the well. The model was designed for typical configurations of a point source or cylindrical source and vial being measured in a NaI well detector, possibly with a surrounding lead shield. In this paper, part II of the work, the analytical model has been applied to the hypothetical cases of a 600 600 and a 300 300 NaI well detector, with or without lead shield, and the calculated detection efficiencies have been compared with the benchmark results of Monte Carlo simulation codes for combined electron-photon transport. The three codes used were MCNP 5.1.40 [2], GEANT3 [3] and, to a lesser extent, PENELOPE [4]. For one configuration, a comparison is also made with a simpler analytical model by Sima [5] with adaptations by Pomme´ et al. [6]. At this stage, no experimental verifications were done, only the level of equivalence of the models was examined. The final aim is to integrate the analytical model in a software package for 4pg counting, which is a convenient primary standardisation method for the activity of radionuclides that emit multiple g-rays per decay. By maximising the detection efficiency
Corresponding author. Tel.: +32 14 571289; fax: +32 14 571864.
E-mail address: [email protected] (S. Pomme´). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.04.007
and the covered solid angle, one can minimise errors arising from the uncertainty on the calculated efficiencies and angular correlation effects. For radionuclides with a complex decay scheme, one can reach an overall combined efficiency of more than 99%, which significantly reduces the influence of possible errors on the calculated detection efficiency. Whereas the 4pg counting method is mainly based on the detection of the emitted g-rays, one should also take into account the contribution of other radiation, such as beta-particles, conversion electrons, positrons and their directionally correlated annihilation photons.
2. The source and detector geometries Two NaI well detector set-ups have been considered: the first is based on an existing 600 600 crystal at IRMM and the second on a 300 300 crystal at CIEMAT. A cross-section of the first geometry is shown in Fig. 1, together with an indication of the dimensional parameters involved. The detector crystal is represented by an outer cylinder with radius Ro ¼ 7.62 cm and height H ¼ 15.23 cm, and at the top side along the symmetry axis a cylindrical cavity with radius Ri ¼ 2.62 cm and depth Hh ¼ 9.80 cm. The detector cap surrounding the NaI crystal consists of Al and Al2O3 layers of equal thickness; each 0.06 cm for the inner cap and 0.16 cm for the outer cap. At the bottom side, however, a 1.05 cm layer of lightconducting gel is assumed, which was for convenience represented as acrylic glass in this simulation exercise.
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Fig. 1. Cross-section of the IRMM 600 600 NaI well detector set-up with indication of the relevant geometrical parameters.
Table 1 Hypothetical source and vial geometries investigated in combination with the IRMM (case 1–6) and CIEMAT (case 10 ) NaI well detector. ID
1 2 3 4 5 6 10
Geometry Description
cntr pnt src ecc pnt src+shld ecc vol src+vial cntr vol src+vial cntr pnt src+vial cntr pnt src+vial drop src+foils
Detector
600 600 300 300
Source
Vial
Rs
Hs
DRc
1 106 1 106 0.5 2 1 103 1 103 0.15
5 107 5 107 1 4 1 103 1 103 0
0 2.4 1.9 0 0 0 0
Vial
Acrylic Acrylic Acrylic Al Acrylic
NaI crystal
IRMM CIEMAT
Ro 7.62 3.81
Lead shield Rvi
0.5 2 1 103 1 103 1
Rvo
0.6 2.1 2.5 1 1
Inner cap H 15.23 7.62
Ri 2.62 1.45
h 5.43 2.54
Al 0.06 0.05
Tvt
0.1 0.1 2.499 0.2 0.0075
Tvb
zvb
0.1 0.1 2.5 0.199 0.0075
8.55 5.66 5.55 5.55 5.55 7.85 2.61
DZlt
DRl
0.3
0.3
Tl 0 1 0 0 0 0 0
Outer cap Al2O3 0.06 0.01
Al 0.16 0.05
Al2O3 0.16 0.01
The parameters are illustrated in Fig. 1. All dimensions are in centimetres.
For this detector, several source geometries have been tested. The discussion in this paper will be restricted to six particular cases, which may be representative for some realistic applications. The main geometrical characteristics of the considered geometries have been assembled in Table 1. The dimensions of the source are defined by the radius, Rs, and the height, Hs. The dimensions of the absorber or vial are defined by the inner and outer radius, Rvi and
Rvo, and the bottom and top thickness, Tvb and Tvt. The bottom side of the vial (or source if Tvb ¼ 0) is positioned at a distance zvb from the bottom side of the detector crystal and can have a radial displacement of the centre with respect to the symmetry axis of the detector by DRc. The lead shield has a thickness Tl and is at a distance DZlt and DRl away from the top and side of the outer cap, respectively.
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The first geometry is the hypothetical case of a point source positioned on the symmetry axis inside the well, at three centimetre height above the bottom of the crystal well (z ¼ h+3 cm). The second case is a point source close to the crystal bottom (z ¼ h+0.23 cm) and the inner cap (zhdcap ¼ 0.11 cm). In this particular case, also a cylindrical lead shield of 1 cm thickness was included, at a distance of only 0.3 cm from the outer detector cap. The third case is a rather small water-based volume source of radius Rs ¼ 0.5 cm and height Hs ¼ 1 cm, contained in an acrylic vial of 0.1 cm thickness in all directions. The vial is placed directly on top of the inner cap, in the most extreme eccentric position at DRc ¼ 1.9 cm from the symmetry axis. In the fourth case, a bigger, centred water-based volume source of radius Rs ¼ 2 cm and height Hs ¼ 4 cm and 0.1-cm-thick acrylic vial was taken. The fifth and sixth cases concern a centred point source at z ¼ h+2.5 cm height, in the middle of a thick acrylic (height Hv ¼ 5 cm, Rvo ¼ 2.5 cm) and aluminium (Hv ¼ 0.4 cm, Rvo ¼ 1 cm) absorber, respectively. The second detector, referred to as the CIEMAT 300 300 detector, was represented by an outer cylinder radius of Ro ¼ 3.81 cm and height H ¼ 7.62 cm, and a cavity with radius Ri ¼ 1.45 cm and depth Hh ¼ 5.08 cm. The detector inner and outer caps consisted of a 0.05 cm Al layer and a 0.01 cm Al2O3 layer. The source was
100%
503
positioned at height z ¼ 2.6175 cm and its dimensions were Hs ¼ 0.2 cm and Rs ¼ 1 cm and the vial consisted of two foils of 0.0075 cm plastic. 2.1. Photons Fig. 2 shows the total photon detection efficiency of the IRMM detector for the six geometries mentioned, as calculated with the analytical model (full line) and simulated with MCNP5 (full circles) and GEANT3 (open circles). As the results often closely match, the absolute difference between simulations and analytical model is plotted in greater detail in Fig. 3. The first two cases, pertaining to point sources, demonstrate that the analytical model can reproduce the MCNP benchmark values with a precision of a few tenths of percent (typical errorE0.2%) at all photon energies in the 0.01–10 MeV range. This excellent result confirms the sound basis of the model, which could only be achieved by taking into account also secondary effects, such as energy degradation by inelastic scattering and effects on the travel path by elastic and inelastic interactions [1]. Also the inclusion of backscatter and pair production events in the outer cap and lead shield (cf. case 2) are essential elements at high energies. Calculations for point sources close to the inner cap, whether at the bottom or on the side of the well, show a crucial
80% (1) cntr pnt src
(1) cntr pnt src
2%
60%
0% -2%
40%
MCNP5 GEANT3
(2) ecc pnt src + shield
20%
2%
(2) ecc pnt src + shield
0%
0%
-2% (3) ecc vol src (3) ecc vol src
Absolute difference
Total efficiency
2%
(4) cntr vol src
(5) pnt src + acryl
100%
0% -2%
(4) cntr vol src
2% 0% -2%
80% 0% -2%
40% 20% PHOTONS 0% 0.01
(5) pnt src + acryl
2%
(6) pnt src + Al
60%
0.1 1 Photon Energy (MeV)
Pommé MCNP5 GEANT3
2%
(6) pnt src + Al
0%
10
Fig. 2. Total photon detection efficiency in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circle) and GEANT3 (open circle). The graphs are consecutively shifted by 40% on the y-axis.
-2% 0.01
PHOTONS 0.1 1 Photon Energy (MeV)
10
Fig. 3. Absolute difference between the total photon detection efficiency from simulations and the analytical model calculations displayed in Fig. 2.
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dependence on the exact calculation of the travel path through the cap material. Whereas the agreement with MCNP is very satisfactory (erroro0.6%), there is obviously a more significant discrepancy with the GEANT3 data, in particular at low energies (erroro2.8%). This is almost entirely due to the difference in attenuation coefficients used in the latter code. Indeed, the analytical model can reproduce the GEANT3 results when it applies the same attenuation coefficient input data set. At this point, one can already conclude that the choice of the input data set can be of higher importance than the choice of model by which the efficiency is calculated. The analytical model deals very well with an eccentric small volume source (case 3, erroro0.8%) and with a centred larger volume source (case 4, erroro0.5%). A point source in a big acrylic (case 5) and Al absorber (case 6) is reproduced with slight difficulty in the energy region where the efficiency changes steeply as a function of energy (erroro1.5%). The main weakness of the analytical model is related to multiple scattering interactions, which are obviously treated more rigorously in a simulation approach. Also when comparing the MCNP5 and GEANT3 results, it is clear that the mutual differences are the largest in the regions where the efficiency changes significantly with energy. A similar phenomenon may be expected when comparing with experimental data. At the top of the curve, the result is rather stable, because the penetration through the inner cap and the chance for interaction in the NaI crystal are both high. Excellent results were also obtained with the configuration of the CIEMAT 300 300 NaI detector. As shown in Fig. 4, the efficiency was simulated for a wide range of energies with the PENELOPE code. The attenuation coefficients of PENELOPE at the considered energies are not very different from the XCOM data [7] used in the
analytical model. The resulting efficiency values differ by typically 0.29% (median absolute deviation) with the analytical model calculations. The graph shows also a comparison with efficiencies calculated with an adapted version of Sima’s simple model [6]. Also this model performs surprisingly well, even though the deviation from simulations may amount to a few percent in the low-energy region. 2.2. Peak-to-total ratio The analytical model provides a rough estimate of the peak efficiency, via the peak-to-total ratio (P/T). The calculated P/T values are compared with simulated data in Fig. 5. There is a good agreement between the results from the MCNP5 and GEANT3 simulation codes if caution is taken to perform the simulations with sufficient energy resolution. For the peak efficiency, events are accepted only if the detected energy is equal to the initial energy within narrow margins (typically within 0.01%). The analytical model reaches a fairly acceptable approximation over a wide energy region, certainly in view of its simplicity. The model does not reproduce the high P/T values below 30 keV, nor does it predict the local dip around 33.2 keV. The latter corresponds to the K-shell electron binding energy in iodine, the 100% 80% 60% (1) cntr pnt src
40% 20% (2) ecc pnt src + shield
0%
0% Peak-to-Total ratio
difference
2%
-2%
100%
(3) ecc vol src
Total efficiency
80%
(4) cntr vol src
60%
100% (5) pnt src + acryl
80%
40%
20%
0% 0.01
60%
Pommé Pommé et al., based on Sima model Penelope
0.1 1 Photon Energy (MeV)
40%
10
Fig. 4. Bottom: total photon detection efficiency in the CIEMAT 300 300 NaI well detector for one source geometry. The full line corresponds with a spline interpolation between analytical model calculations. The open circles represent calculated values from an adaptation of Sima’s simple model, while the closed circles correspond to simulation results with PENELOPE. Top: absolute difference between simulated and calculated efficiencies.
20% 0% 0.01
Pommé MCNP5 GEANT3
(6) pnt src + Al
PHOTONS
0.1
1
10
Photon Energy (MeV) Fig. 5. Peak-to-total ratio for the photon detection efficiency of the IRMM 600 600 NaI well detector for the six source geometries (cf. Fig. 2). The graphs are consecutively shifted by 40% on the y-axis.
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dip in the P/T being due to escape of KX-rays at the inside border of the NaI crystal. Simulated spectra indeed show escape peaks that corroborate this interpretation. In the frame of the simulations, the escape peaks were not included in the peak efficiency. In real experiments, however, the spectral resolution of the detector is rather bad and, at sufficiently high energies, the escape peaks will add up with the main photopeak. Therefore, also the simulated peak efficiencies should be interpreted with caution. At high energies (1 MeV–10 MeV), the simple model has some difficulty reproducing the benchmark P/T values, as it was not designed to deal in a rigorous manner with multiple interactions in the crystal. For the considered set-up, the simulation results between 0.5 MeV and 10 MeV show a rather linear behaviour as a function of the logarithm of the energy.
2.3. Electrons The penetration of electrons through the diverse absorber materials is very sensitive to the thickness, specific charge and mass of the absorber materials. Moreover, the deceleration of the 100% Pommé
80%
(1) cntr pnt src
MCNP5 GEANT3
60% 40% (2) ecc pnt src + shield
20% 0% Electron detection efficiency (%)
(3) ecc vol src
505
electrons in the materials leads to bremsstrahlung and secondary particles that can be detected in the NaI crystal. The analytical model uses an empirical formula for the transmission, with adaptations to deal with different absorber materials [1]. In order to partly compensate for the detection of secondary particles, the transmission probability was artificially increased using the CSDA range (continuous slowing down approximation) instead of the extrapolated range, and the dependence on the angle of incidence was switched off. In Fig. 6 the detection efficiency for electrons is shown as a function of their energy. The transmission functions show a rather steep transition between zero and the geometry factor ( ¼ O/4p) of the detector crystal. The MCNP5 and GEANT3 simulations show qualitatively a similar shape; however, the transmission functions are sometimes shifted along the energy axis by an amount of log(DE)E0.1. The analytical model generally reproduces the shape of the efficiency curves, yet the transition energies do not rigorously match those of the simulation results. The main difficulty with the different models seems to be related with the production of bremsstrahlung photons. In case 1, one can see that the transmission of the analytical model is slightly overestimated, due to the trick with the artificially enhanced electron transmission (cf. CSDA range). This approach works rather well in the second and third cases, of the eccentric point and volume source, which lead to more interaction with the inner cap and source material. In the last three cases, involving an excessive amount of source or vial absorber materials, the analytical model renders too low efficiency values. This is due to the missing contribution of bremsstrahlung, which penetrates the absorber materials much more easily than electrons. The proof can be seen in the bottom of Fig. 6 for case 5 (point source in acrylic vial), where the simulated transmission of the electrons, represented by a dash–dotted curve, is indeed somewhat lower than the predicted detection efficiency from the analytical model. In general, one can conclude that the calculation of detection efficiencies for electrons does not offer the same level of accuracy as for photons. The calculations may be trusted at the extremes of low or high energy and can be used for an indicative value with high uncertainty in the transition range.
2.4. Positrons
100%
(6) pnt src + Al
80% 60% (4) cntr vol src
40% ELECTRONS
20%
(5) pnt src + acryl
0% 1
10 Electron Energy (MeV)
Fig. 6. Total electron detection efficiency in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The positions of geometries 4–6 have been switched, in order to avoid mutual interference in the graph. The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circle) and GEANT3 (open circle). The graphs are consecutively shifted by 40% on the y-axis.
Positron emitters can be conveniently measured in a 4pg detection geometry. In particular, the annihilation photons of 511 keV have a high probability of being detected. The fact that they are emitted in opposite direction ensures that at most one of them can escape through the hole of the well. In the presence of a top lead shield, there is even a chance that the escaped photon is nevertheless detected after a backward scattering interaction in the shield. Also the positron may reach the crystal, provided that it has enough energy to pass the absorbers. The analytical model takes into account the angular correlation between both annihilation quanta; hence, it does not treat them as two independent, randomly emitted g-rays. Calculations show that this leads to significantly different results in asymmetric configurations, i.e. for a source that is situated close to the hole of the well. The effect is almost insignificant for a point situated near the bottom of the well. This is illustrated in Fig. 7 for a point source moving along the symmetry axis of the IRMM NaI well detector. The bottom side of the graph shows that the model reproduces rather accurately the simulated efficiencies for single and double 511 keV photons as well as for positrons. The top side of the graph shows the distinct difference in detection efficiency for low-energy positrons and two directionally uncorrelated 511 keV photons.
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99%
difference
15% positron minus 2 x 511 keV Pommé MCNP5 GEANT3
10% 5%
(1) cntr pnt src
96% 93% 99%
0%
(2) ecc pnt src + shield
96% 93%
100%
99% 96% (3) ecc vol src
Total efficiency
Total efficiency
90%
80%
70%
Pommé MCNP5 + GEANT3: 1 x 511 keV 2 x 511 keV low-energy positron
60%
93% 99% 96% (4) cntr vol src
93% 99% 96%
50% 0
2
4
6
8
(5) pnt src + acryl
93%
source position height (cm) Fig. 7. Bottom: calculated (line) and MCNP5 (closed symbols) and GEANT3 (open symbols) simulated detection efficiencies in the IRMM NaI well detector for single 511 keV photons (diamonds), two simultaneous but directionally uncorrelated 511 keV photons (circles) and low-energy positrons and their oppositely emitted annihilation photons (triangles) as a function of height of the source point in the well. Top: difference in detection probability of low-energy positrons and uncorrelated 511 keV photons.
99%
(6) pnt src + Al
96% 93%
Pommé MCNP5 GEANT3
POSITRONS
90%
Fig. 8 gives an overview of the positron detection efficiency as a function of positron energy for the six geometries in the IRMM detector. In the first case, the positron starts from a centred point at 3 cm height, the first absorber being the air in the well. The lowenergy positrons annihilate close to the source point and the detection efficiency corresponds to that of the annihilation photons. With increasing energy, the annihilation zone expands around the source point and the efficiency corresponds to a mean. In the analytical model, the efficiency value at source point is taken instead of the mean. As the range of the positron increases with energy, some will escape through the hole and annihilate outside the well, leading to a drop in the detection efficiency. At even higher energies, a fraction of the positrons can penetrate the inner cap and thus increase the overall probability for detection, which levels off at the solid angle covered by the crystal. The simulations confirm the qualitative behaviour of the energy dependence of the detection efficiency. However, they do not agree quantitatively at intermediate energies, probably due to differences in electron transport handling. The analytical model does not reproduce the rise between 30 keV and 70 keV, owing to annihilations taking place deeper inside the well. In the second case, that of an eccentric point source close to the bottom of the well, the detection efficiency is higher because of the higher mean travelling path of the photons in the crystal, the higher solid angle covered by the crystal and the stopping of escaped positrons in the lead shield. The point source is very close to the bottom of the well, which reduces the expansion of the annihilation zone with increase in positron energy. These conditions are favourable for the analytical model, which indeed reproduces the counting efficiency satisfactorily at all energies.
0.01
0.1 1 Positron Energy (MeV)
10
Fig. 8. Total detection efficiency for positrons and their annihilation photons in the IRMM 600 600 NaI well detector for six source and vial geometries (see text). The full line corresponds with a spline interpolation between analytical model calculations, while the circles correspond to simulation results with MCNP5 (closed circles) and GEANT3 (open circles).
Some of the arguments mentioned for case two are also valid for case three, where the source and vial material act as additional absorbers that retain most of the annihilation inside the well. In cases five and six, the positrons have little chance of leaving the acrylic or aluminium absorbers, leading to a fairly constant efficiency as a function of energy. The analytical model and simulations show good agreement in all cases where the majority of the positrons are stopped inside the well. The agreement is even better for source points closer to the bottom of the well, as could be observed in Fig. 7. 2.5. b-particles For b-particles, the analytical model adopts a simplified energy distribution and derives a type of attenuation coefficient associated with the absorber (and its approximate thickness) to be used in an exponential transmission formula. This leads to rough approximations of the total detection efficiencies for b-particles and rather good approximations for b+-particles, as the annihilation radiation is dominant for the latter. Alternatively, one can calculate the detection efficiency for b and b+-particles from a normalised multiplication of the beta-particle energy spectrum
ARTICLE IN PRESS ´ et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 501–507 S. Pomme
100%
98% β+-particles
96%
Total efficiency
100% Pommé, exponential model Pommé, convolution GEANT3, simulation MCNP5, convolution
80%
60%
40%
20% β--particles 0% 0.01
0.1 1 Beta Particle Energy (MeV)
10
Fig. 9. Total detection efficiency for b-particles (bottom of graph) and for b+particles and their annihilation photons (top of graph) in the IRMM 600 600 NaI well detector for an eccentric point source close to the bottom of the well (case 2), as calculated with the analytical model (line) and GEANT3 (open circles) or MCNP (closed circles). The dashed line shows the convolution of the efficiency curves for mono-energetic particles (cf. Figs. 6 and 8) and a simplified beta-particle energy spectrum.
and the corresponding (interpolated) efficiencies for monoenergetic electrons and positrons, respectively. An example is presented in Fig. 9, corresponding to geometry case 2.
507
The simulated total photon detection efficiencies with GEANT3 deviate at low energies from the other codes, because it applies significantly different attenuation coefficients. As a result, one can conclude that the choice of the input data can be more critical than the choice of the model by which the efficiency is calculated. When comparing with reality, also the uncertainty on actual dimensions and material composition may be decisive factors in the uncertainty budget, rather than the model itself. The analytical model is also very successful in reproducing the detection efficiency for positrons and their annihilation photons, including the important angular effect owing to the opposite emission direction of the latter. With increase in positron energy, the result is generally more stable and accurate for configurations with sufficient absorber material to ensure that the annihilation takes place close to the source. Differences among the different models were mainly due to uncertainty in the positron transport, which is decisive for the expansion of the annihilation zone, the fraction of positrons escaping through the hole of the well and the detection probability of positrons in the crystal. The different codes show difficulty to simulate the detection efficiency of electrons, which is not only determined by the transmission of the primary particles but also greatly influenced by secondary particles. The analytical model does not adequately take into account bremsstrahlung, which can significantly increase the detection efficiency of high-energy electrons passing through thick absorbers. The detection efficiency for beta-particles can be calculated in two ways: via an exponential transmission formula or by combining the mono-energetic efficiency curves with the normalised energy spectrum of the beta-particle. This leads to rough approximations of the total detection efficiencies for b-particles and rather good approximations for b+-particles, as the annihilation radiation is dominant for the latter. As an overall conclusion, one can say that the analytical model is somewhat less rigorous and flexible than the simulation codes, but on the other hand it is easy to use, relatively fast and sufficiently complete and accurate for many applications. References
3. Conclusions The analytical model of Pomme´ [1] gives an accurate account of the total photon detection efficiency for point sources in a welltype NaI detector, when compared with the outcome of the MNCP5, GEANT3 and PENELOPE simulation codes. It was also able to deal with cylindrical volume sources and vials, eccentric positioning of the source inside the detector well and the possible contribution of scattering or pair production in the surrounding lead shield. Its accuracy is generally best for sources with a minimum of absorber materials and situated rather deep into the well. It can also provide a rough indication of the peak-to-total ratio, which may be useful to estimate the relative count loss caused by setting a discriminator threshold at a fixed energy level.
[1] S. Pomme´, Detection efficiency calculation for photons, electrons and positrons in a well detector; Part I: Analytical Model, Nucl. Instr. and Meth. (2009); doi:10.1016/j.nima.2009.03.076. [2] MCNP Team, MCNP—A General Monte Carlo N-Particle Transport Code—Version 5, MCNP 5.1.40 RSICC Release Notes, 2005 /http://mcnp-green.lanl.gov/ index.htmlS. [3] R. Brun, F. Bruyant, M. Maire, A.C. McPherson, P. Zanarini, GEANT3, CERN Data Handling Division, Geneva, 1987. [4] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE—A Code System for Monte Carlo Simulation of Electron and Photon Transport, OECD Nuclear Energy Agency, Issy-les-Moulineaux, France, 2003. [5] O. Sima, Nucl. Instr. and Meth. A 450 (2000) 98. [6] S. Pomme´, J. Camps, G. Sibbens, T. Vidmar, Y. Spasova, J. Radioanal. Nucl. Chem., in press. [7] M.J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S. Zucker, XCOM: Photon Cross Sections Database, 2007 /http://physics.nist.gov/ PhysRefData/Xcom/Text/XCOM.htmlS.