The active area shadow-shielding effect on detection efficiencyof collimated broad energy germanium detectors

Massimo Altavilla a, Romolo Remetti b,n

a High Institute for Environmental Protection and Research (ISPRA), Department for Nuclear, Technological and Industrial Risk, Via Vitaliano Brancati 48,00144 Rome, Italyb “Sapienza”—University of Rome, Department BASE—Basic and Applied Sciences for Engineering, Via Antonio Scarpa 14, 00161 Rome, Italy

a r t i c l e i n f o

Article history:Received 10 July 2013Received in revised form4 December 2013Accepted 4 December 2013Available online 18 December 2013

Keywords:Broad energy germanium detectorGamma-ray spectrometryMCNPXISOCSCollimator algorithmsActive area

a b s t r a c t

The ISOCS calibration, when utilized for a BEGe detector with a small angled collimator, producesinaccuracies of about 19% for gamma rays with energies greater than 0.4 MeV. Such a discrepancy iscaused by the collimator algorithms currently utilized in the ISOCS software which, originally developedfor HPGe detectors, are less suited for BEGe detectors. ISOCS's errors are due to the different crystalconfigurations of broad energy detectors compared to coaxial detectors, i.e. to a different importance ofthe active area portion obscured by the collimator. This work proposes some solutions for the problem,either using the ISOCS software or implementing a stochastic calibration procedure. In particular, thepresent work considers a virtual collimator that, maintaining its angular aperture, is capable ofcontinuously enlarging its bottom collimator's aperture cone radius, to expose growing active areaportions. In such a way two goals may be achieved: the mathematical characterization of ISOCS’ errorsand the minimization of observed errors by means of the stochastic calibration procedure.

Different reference set-ups are considered in order to test source geometry effects, source materialsand different detectors. In particular, a 220 L drum, a 2 m3 box filled with uniformly contaminatedcellulose or PVC, and small BE3825 and large BE5030 Canberra detectors are considered. Detectionefficiencies calculated by ISOCS software are compared against a completely stochastic MCNPXsimulation procedure, that is unaffected by any algorithmic correction. MCNPX simulations demonstrate,when widening collimators’ cone but maintaining the angular aperture unchanged, that ISOCS andMCNPX difference percentage between efficiency data points reduces, depending on energy, by morethan 50%. This happens as far as the shadow-shielded portion of detector's active area reduces.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

As is well known, the potentialities of in situ gamma-rayspectrometry have been strongly enhanced by the introductionof BEGe detectors, which join together the spectral advantages oflow energy and coaxial detectors to extend assay energy rangefrom 3 keV to 3 MeV in the same measurement. Accurate descrip-tions of these kinds of detectors are given by Luis et al. [1], Muelleret al. [2], Budjas et al. [3], and Barrientos et al. [4]. For in situapplications the natural complements of BEGe detectors are thesoftware tools based on mathematical models aimed at simulatinga wide variety of sample shapes, which eliminate the need ofradionuclide standards for detector's efficiency calibration, such asthe well known ISOCSs software [5].

ISOCSs systems (ISOCS software and Canberra's detectors) areprobably the most widely used detectors all over the world fortheir unique characteristics; an average of 150–200 detectors’

characterizations is performed yearly which means that 150–200ISOCS detectors are used in several fields like waste characteriza-tion, clearance measurements, decommissioning activities, landfield remediation and radionuclide laboratories activities coveringthe nuclear research field. Considering the year of its invention(1998–1999), approximately 1500/2000 ISOCS detectors have beenused in all the previous fields.

The advantage of using ISOCS efficiency calibration software canbe translated to allowing the elimination of traditional calibrationsources, providing significant savings in cost and measurement time.In addition the flexibility of this tool allows excellent replication ofthe measured sample geometry, resulting in improved accuracy overindustrial calibration source standards.

The traditional efficiency calibration of a high purity germa-nium detector needs an accurate selection of the sources (energyrange, half-life, cascade effects and activity) and the measurementgeometry (beakers and vials in case of laboratory measurementsand 3D models in case of in situ measurements) requiring a lotof money. On the contrary, using the ISOCS software, the costof source-based calibration (purchase of sources, replacement,disposal, licensing, calibration program and sample preparation)

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n Corresponding author. Tel.: þ390649766538; fax: þ390644240183.E-mail address: romolo.remetti@uniroma1.it (R. Remetti).

Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20

can be completely avoided. Detection efficiency responses, based onthe physical parameters of the experimental set-up, can be calcu-lated using mathematical models to accurately compute the trans-port of gamma-rays through different media and geometries.Further, with software modeling it is possible to rapidly producegeometries that represent many real shapes for which sourcestandards may not be readily available. In particular, as describedby Venkataraman et al. [6,7] the ISOCS calibration method is basedon a detailed Monte Carlo radiation transport model of a specificgermanium detector created using the nominal dimensions providedby the production facility. The detector model is validated bycomparing Monte Carlo detection efficiencies to measured efficien-cies for several source geometries and ranges of energies. These twoefficiency data sets are then meshed together into a single char-acterization file, which contains a series of equations defining thedetector response that are then implemented in the ISOCS software.

Recently, authors have pointed out [8] that with a BEGe detectorhaving a small angled collimator, the ISOCS calibration producesinaccuracies of about 19% for gamma rays with energies greaterthan 0.4 MeV. Authors have suggested that such a discrepancy maybe caused by the collimator algorithms [9] currently utilized in theISOCS software which, originally developed for HPGe detectors, seemto be less suited for BEGe detectors. Authors advanced the hypothesisthat ISOCS’ errors might be due to the different crystal configurationsof broad energy detectors compared to coaxial detectors, i.e. to adifferent importance of the active area portion obscured by thecollimator. To stress such a hypothesis, the present work considers avirtual collimator that, maintaining its angular aperture, is capable ofcontinuously enlarging its bottom collimator's aperture cone radius,to expose growing active area portions. Such a virtual collimator ispart of a reference geometry that has been modeled by means ofboth ISOCS Geometry Composer [10] and the completely stochasticMCNPX™ [11] simulation procedures that authors have describedand validated against experimental data in Ref. [8]. In the presentwork different reference set-ups were considered in order to testsource geometry effects, source materials and different detectors. Inparticular, a 220 L drum, a 2 m3 box filled with uniformly contami-nated cellulose or PVC, and small BE3825 and large BE5030 Canberradetectors [12] were considered. The detectors’ simulation methodol-ogy by MCNPX code is the same as that considered in Ref. [8].

The tests carried out have allowed quantifying the mathema-tical trend of ISOCS’ errors and proposing some solutions of theproblem, either using the ISOCS software or implementing thestochastic calibration procedure; further, an example of correctionfactor for ISOCS’ errors is given.

2. Simulation procedure

The outstanding feature of all the simulations carried out forthis work consisted in considering a virtual collimator capable ofassuming different geometries to change the shadow-shieldingdegree on detector's active area; i.e. a conical collimator thatstarting from its real dimensions and maintaining its angle of view

is able to move its cone vertex position away from the detector'swindow, to consider different values of the radius of its bottomaperture, as depicted in Fig. 1 for the case of BE3825 detector; notethat the largest R value is able to expose the entire active area(89 mm diameter).

In order to account for eventual perturbing effects, sources ofdifferent geometries and materials have been considered, as wellas different detectors’ dimensions. Henceforth different measure-ment set-ups have been evaluated, and each one has beenreproduced by both MCNPX and ISOCS’ Geometry Composersoftware, to obtain couples of detection efficiency values forcomparison. For each test the source term given in Table 1 isconsidered. It is worth remarking that ISOCS’ Geometry Composergives values that are subjected to the deterministic correctionoperated by the ISOCS’ collimator algorithms [5,6], while MCNPXgives purely stochastic values.

All MCNPX simulations were completely analog; no variancereduction technique has ever been used. Number of histories rangedfrom 400�106 to 2�109, depending on the simulated radionuclide'senergy: low energy gamma rays simulations required higher numberof histories to maintain a constant relative error in the whole energyrange. Simulations’ relative errors were always far below 4%.

3. Simulation tests

Considering the source term of Table 1 homogeneously dis-persed amid the matrix material, the following simulation testshave been carried out:

� 3825 detector○ 220 L drum filled with cellulose;○ 220 L drum filled with PVC.

� 5030 detector○ 220 L drum filled with PVC;○ 2 m3 box filled with PVC.

Fig. 1. The virtual collimator capable of assuming different values of the bottom collimator's aperture cone radius, to expose growing portions of the detector's active area.Numerical values are referred to a BE3825 detector

Table 1220 L drum source term.

Radionuclide Energy (MeV) Yield

210Pb 0.04650 0.04050241Am 0.05954 0.35780109Cd 0.08803 0.0362657Co 0.12206 0.85510139Ce 0.16585 0.79900113Sn 0.39169 0.6494085Sr 0.51400 0.98500137Cs 0.66165 0.8499054Mn 0.83490 0.9997588Y 0.89802 0.9390065Zn 1.11560 0.5060060Co 1.17322 0.9985060Co 1.33249 0.9998388Y 1.83610 0.99380

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20 11

3.1. Drum with cellulose—3825 detector

The measurement set-up is composed of a 220 L drum parti-ally filled with uniformly contaminated cellulose and a BE3825Canberra detector positioned at 25 cm away from the drum sur-face. The drum is characterized by an internal height of 85.3 cm,57.1 cm internal diameter and 0.1 cm wall thickness. The linerwalls are made up of iron with a density of 7.86 g/cm3. It is filled,starting from its baseline to a height of 51.2 cm, with uniformlycontaminated cellulose (0.45 g/cm3—C6H10O5).

The following cases have been considered:

i. not collimated detector;ii. detector with Canberra's old 50 mm 301 lead shield collimator.

Case ii has been divided into five subcases, and for each of theseones the collimator's 301 aperture was maintained constant butthe cone vertex position was moved away from the detector'swindow to consider different values for the bottom collimator'saperture cone radius, R, as follows:

ii.a. R¼0.68 cm (real Canberra's collimator);ii.b. R¼1.55 cm (virtual Canberra's collimator);ii.c. R¼2.55 cm (virtual Canberra's collimator);ii.d. R¼3.55 cm (virtual Canberra's collimator);ii.e. R¼4.55 cm (virtual Canberra's collimator).

The situation is depicted in Fig. 1: as R increases, a greaterportion of detector's active area is exposed to radiation.

For each one of the cases two detector's efficiency data setshave been generated: one by ISOCS’ Geometry Composer, usingthe Simple Cylinder Template, and the other by MCNPX code. Fig. 2shows the graphic outputs of ISOCS and MCNPX for case 1. Fig. 3,obtained by MCNP Visual Editor [19], shows gamma-ray trackssimulated by MCNPX.

3.1.1. Without collimationThe first run has been carried out without collimated geometry,

as in Fig. 2, with the source term presented in Table 1. Results ofISOCS Geometry Composer and MCNPX stochastic simulation, interms of detection efficiency, are quite similar, as described in Fig. 4.

The interpolating functions are of the type

ε¼ aþb lnðenergyÞþc ln ðenergyÞ2þd ln ðenergyÞ3þe ln ðenergyÞ4þ f ln ðenergyÞ5 ð1ÞWhen interpolating ISOCS’ efficiency points the coefficients a,

b, c, d, e and f are, respectively, 5.1984E�005, �9.8142E�006,3.1285E�005, �7.6510E�005, �5.5329E�005 and �8.5852E�006with an R2 of 0.9928; in the case of MCNPX's efficiency points thesame coefficients are, respectively, 5.5031E�005, �1.1032E�005,3.2253E�005, �7.9144E�005, �5.7619E�005 and �9.0008E�006with an R2 of 0.9938.

3.1.2. Canberra's old 50 mm 301 lead shield collimatorWhen a detector is collimated using a real Canberra's old

50 mm 301 lead shield collimator, as described in Fig. 1 (caseR¼0.68 cm), the situation changes drastically, and the detectionefficiencies calculated by ISOCS’ Geometry Composer and MCNPXexhibit significant differences, as shown in Fig. 5. It is worthremarking that such a collimator has the characteristic of shieldingthe detector itself all around except a small open cone in the frontwindow, leaving exposed only a small fraction of detector's active

Fig. 2. Measurement set-up without collimation. (a) The graphic output of ISOCS’ Geometry Composer and (b) the graphic output of MCNPX Visual Editor.

Fig. 3. Gamma-ray tracks simulated by MCNPX from uniformly contaminatedcellulose inside the 220 L drum to the BEGe detector. The graphical representationis obtained by means of MCNP Visual Editor.

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–2012

area. Supposing that the cause of the discrepancy shown in Fig. 5 isthe shadow-shielding effect of the active area, a series of simula-tion runs with different values of the bottom collimator's aperturecone radius R were carried out to confirm the hypothesis.

3.1.3. Increasing bottom collimator's aperture cone radiusAs already introduced, the bottom collimator's aperture cone

radius has been increased in length, in steps of approximately 1 cm,till approaching the extreme radius of Canberra's BEGe 3825 endcap(4.55 cm). Virtual Canberra's old 50 mm 301 lead shield collimatorangle has not been changed and has been fixed so that only bottomcollimator's aperture cone radius is changed. As shown in Fig. 6, thecomplete stochastic simulation carried out with MCNPX is able tofollow detection efficiency variations as expected.

By considering the percentage difference of ISOCS efficiencyvalues vs. MCNPX ones, for each energy value of the source term,

the situation shown in Fig. 7 is obtained. How the differencedrastically reduces as greater portion of detectors’ active area isexposed is evident. To better appreciate detection efficiency varia-tions vs. energy, in Table 2, for an immediate and easier reading,representatives values for low, medium, and high energy ranges areshown. In particular, the percentage difference between ISOCS andMCNPX efficiency data vs. bottom collimator's aperture is reportedfor the energies of gamma-rays emitted by 139Ce (165.85 keV), 137Cs(661.65 keV) and 60Co (1332.49 keV). The same data can be fittedwith a simple second order polynomial curve, as shown in Fig. 8,obtaining R2 values ranging from 96% to 99%.

3.2. 220 L drum filled with a PVC-contaminated source—BEGe 3825detector

In order to verify the influence of the source matrix, thesame geometry considered in Section 3.1 has been replicated by

Fig. 5. Detector with Canberra's old 50 mm 301 lead shield collimator. Detection efficiencies from ISOCS’ Geometry Composer and MCNPX stochastic simulation. 220 L drumfilled with a cellulose contaminated source, BEGe 3825 detector.

Fig. 4. Detector without collimation. Detection efficiencies from ISOCS’ Geometry Composer and MCNPX stochastic simulation. 220 L drum filled with cellulose.

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20 13

substituting cellulose with PVC (1.4 g/cm3—H3C2Cl), to significantlyincrease matrix density from the previous value of 0.45 g/cm3

to 1.4 g/cm3. As may be seen fromTable 3 and Fig. 9 percentage

difference between ISOCS’ and MCNPX's efficiency data pointsis practically independent of source material. For this case onlythe real Canberra's old 50 mm 301 lead collimator and the

Fig. 7. Percentage difference of ISOCS vs. MCNPX efficiency values for different values of bottom collimator's aperture. 220 L drum filled with a cellulose contaminatedsource, BEGe 3825 detector.

Fig. 6. Detector with Canberra's old 50 mm 301 lead shield collimator with different apertures. Detection efficiencies from MCNPX stochastic simulation. 220 L drum filledwith a cellulose contaminated source, BEGe 3825 detector.

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–2014

energy lines ranging from 59.54 keV to 1836.10 keV have beenconsidered because the MCNPX simulation of very low energies,for the Canberra's old 301 lead shield collimator, did not allowreliable results considering the fact that MCNPX associatedrelative errors are always far above 5%.

3.3. 220 L drum with a contaminated PVC source—BEGe 5030detector

In order to verify the influence of detector's dimensions, thesame drum considered in Section 3.2 has been measured with adifferent detector, a Canberra's BEGe 5030, characterized by largerdimensions than those of BEGe 3825 one. Due to its larger endcapdiameter (102 mm vs. 89 mm) this kind of detector needs adifferent collimator, identified in the following as the “Canberra'snew 50 mm 301 lead shield collimator” and produced by Canberraitself. Such a kind of collimator has the same 301 cone angleaperture of the previous one but different lateral dimensions forallowing complete shielding of BEGe 5030 model that is muchbigger than BEGe 3825 one. According to the simulation metho-dology described in Section 2, in order to account for a widerportion of the active area, a virtual collimator capable of exposingthe whole active area, i.e. to reach 5.2 cm of bottom aperture'scone radius, is considered, as shown in Fig. 10.

In Table 4 and Fig. 11 results obtained from the real and virtualcollimators are presented; as in the previous sections; these onesare expressed in terms of percentage difference between detectionefficiencies obtained by ISOCS and MCNPX.

For a 5030 BEGe detector, simulated ISOCS and MCNPX differ-ence percentages between efficiency data points are lower than the

Fig. 8. Percentage difference of ISOCS and MCNPX efficiency values at low, medium, and high energies vs. bottom collimator's radius aperture. 220 L drum filled with acellulose contaminated source, BEGe 3825 detector.

Table 3Comparison of ISOCS/MCNPX percentage difference for two different matrix densities.

Radionuclide Energy(MeV)

Real Canberra's old 50 mm 301 lead shield

Δε [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX]PVC (1.4 g/cm3) [%]

Δε [ISOCS/MCNPX] cellulose(0.45 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX]cellulose (0.45 g/cm3) [%]

210Pb 0.04650 �4.7 19.3241Am 0.05954 �5.0 14.0 �7.1 14.5109Cd 0.08803 �3.6 12.3 �5.4 13.057Co 0.12206 �2.8 12.6 �3.6 12.7139Ce 0.16585 �8.3 10.5 �9.7 10.8113Sn 0.39169 �17.6 10.6 �17.0 10.785Sr 0.51400 �20.7 10.7 �20.2 11.0137Cs 0.66165 �18.3 8.7 �17.6 9.254Mn 0.83490 �19.1 8.5 �18.8 9.088Y 0.89802 �19.6 8.5 �17.6 8.865Zn 1.11560 �19.1 6.4 �17.3 7.760Co 1.17322 �18.1 6.5 �17.2 6.660Co 1.33249 �17.8 6.4 �15.9 6.288Y 1.83610 �15.8 6.3 �14.5 6.2

Table 2Percentage difference of ISOCS and MCNPX efficiency values at low, medium, andhigh energies vs. virtual bottom collimator's radius aperture. 220 L drum filled witha cellulose-contaminated source, BEGe 3825 detector.

Virtual bottomcollimator's radiusaperture (cm)

139Ce 137Cs 60Co

(εISOCS�εMCNPX)/εMCNPX

(εISOCS�εMCNPX)/εMCNPX

(εISOCS�εMCNPX)/εMCNPX

[%] Uncert.[%]

[%] Uncert.[%]

[%] Uncert.[%]

0.68 �9.7 10.1 �17.6 8.2 �15.9 5.91.55 �6.5 9.3 �13.4 7.5 �14.9 5.62.55 �6.5 8.8 �10.3 7.2 �10.6 5.33.55 �5.4 8.6 �7.0 7.0 �8.7 5.14.55 �5.0 8.6 �6.2 7.0 �7.6 5.0

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20 15

ones obtained by the BEGe 3825 detector. Moreover, consideringthe virtual Canberra's new 50 mm 301 lead shield collimator, ISOCSand MCNPX difference percentages between efficiency data pointsare far below 5%.

From the above MCNPX simulations it has been demonstrated,once again, considering two opposite BEGe detectors (a smaller anda bigger one), that widening collimators’ cone and fixing 301 angle,so that detectors’ active area is not covered by any lead shield, ISOCS

Fig. 9. Percentage difference of ISOCS vs. MCNPX efficiency values for two different matrix densities. 220 L drum filled with a cellulose contaminated source and 220 L drumfilled with a PVC contaminated source, BEGe 3825 detector.

Fig. 10. The real (on the left) and the virtual (on the right) collimators for BEGe 5030 detector.

Table 4Comparison of ISOCS/MCNPX percentage difference for real and virtual collimators. 220 L drum with PVC, 5030 detector.

Radionuclide Energy(MeV)

Real Canberra's new 50 mm 301 lead shield Virtual Canberra's new 50 mm 301 lead shield [bottomcollimator's aperture cone radius, R¼5.2 cm]

Δε [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Δε [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX]PVC (1.4 g/cm3) [%]

241Am 0.05954 1.8 13.9 1.1 10.5109Cd 0.08803 2.5 12.7 2.6 10.957Co 0.12206 4.3 12.5 1.0 10.8139Ce 0.16585 �0.6 12.5 0.2 10.7113Sn 0.39169 �12.7 10.5 �0.8 8.985Sr 0.51400 �14.5 8.5 �1.0 7.0137Cs 0.66165 �16.1 8.5 �1.8 7.054Mn 0.83490 �13.0 8.5 �4.0 7.160Co 1.17322 �10.8 6.2 �4.0 5.260Co 1.33249 �10.2 6.1 �3.9 4.888Y 1.83610 �10.1 5.9 �3.7 4.9

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–2016

and MCNPX difference percentage between efficiency data pointsreduces, depending on energy, by more than 50%.

3.4. Box filled with a PVC contaminated source—BEGe 5030 detector

To test the influence of source geometry the case of a 2 m3 ironbox, with a 0.3 cm liner, with the same source term of Table 1uniformly dispersed amid PVC matrix, has been considered. Bysupposing to divide box's surface into four equal sections, theBEGe 5030 detector has been placed at the center of the topleft part, 25 cm far away the box surface (see Fig. 12). Such aconfiguration is typical when assaying clearance of various mate-rials in decommissioning activities.

Two simulations have been performed implementing a differentvirtual collimator, identified in the following as the “virtual modified50 mm 251 lead shield collimator”. Such a kind of collimator imple-ments a 251 cone angle aperture and thicker lateral dimensions withrespect to the previous ones for allowing complete shielding of aBEGe 5030 model from the high background that could be found indecommissioning activities. The 251 collimator's cone angle aperturehas been considered for effectively viewed masses, contained into a

2 m3 box, not exceeding 1 m3 at a fixed distance in observing buildingmaterials’ clearance levels established in the UE publication “Radia-tion Protection No. 113” [13] and various materials’ clearance levelsestablished in the UE publication “Radiation Protection No. 122 part I”[14]. Results are reported in Table 5 and Fig. 13.

As can be seen, ISOCS and MCNPX percentage difference betweenefficiency data points exceeds 20% several times; moreover, con-sidering the virtual modified 50 mm 251 lead shield collimator with5.2 cm bottom collimator's aperture cone radius, the percentagedifferences have been reduced, in some energy lines, by more than50%. For this case only the energy lines ranging from 165.85 keV to1836.10 keV have been considered, because the MCNPX simulationof very low energies, for the virtual modified 50 mm 251 lead shieldcollimator, did not allow reliable results considering the fact thatMCNPX associated relative errors are always far above 5%.

4. Practical application

The previous section shows that changes to the collimatoropenings are dramatic (Fig. 1) and substantially affect the detectionefficiency (Fig. 6). Apart from equipping current ISOCS systems withnew collimators, the next logical step, given that typical ISOCS userswould likely consider performing additional MCNPX simulations tobe overly burdensome, is trying to find a simple correction capableof being implemented in operation with the existing hardware. Inpractice, Canberra, following the same philosophy already adoptedfor HPGe detectors [9] should try to introduce new collimationalgorithms for each one of the Geometry Composer referencegeometries, for each specific detector and collimator. The followingsection gives an example of obtaining such a correction factor for avery common situation: the characterization of a 220 L drum.

4.1. Correction factor for a 220 L drum

Considering the same situation described previously in Section3.1, i.e. a 220 L drum partially filled with uniformly contaminatedcellulose (drum filled, starting from its baseline, to a height of51.2 cm) and a BE3825 detector with real Canberra's old 50 mm301 lead shield collimator, positioned at a distance of 25 cm fromthe drum itself, the correction factor may be obtained by means of

Fig. 11. Comparison of ISOCS/MCNPX percentage difference for real and virtual collimators. 220 L drum filled with PVC, 5030 detector.

Fig. 12. 2 m3 box with iron walls partially viewed by a BEGe 5030 detector. Thesource term of Table 1 is homogenously dispersed amid PVC matrix.

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20 17

a fifth order polynomial fit of the percentage difference of ISOCSand MCNPX efficiency values.

The fifth order polynomial fit is of the type

f αðEÞ ¼ ∑j ¼ 0;⋯;5

aαj Ej ð2Þ

where fα(E) is the percentage correction factor, E representsdifferent energy values in MeV, α¼301, 901, and 1801 is thecollimator's open angle, and j¼0,…,5 is the jth polynomial term.

Correction of ISOCS’ data is obtained as follows:

ϵðEÞα;corrected ¼ ϵðEÞα;ISOCS�½ϵðEÞα;ISOCSf αðEÞ=100� ð3Þ

Table 6Percentage difference of ISOCS and MCNPX efficiency values at low, medium and high energies vs. test cases 1.a, 1.b, 1.c, 2 and 3. 220 L drum and a BE3825 detector withCanberra's old 50 mm 301 lead shield collimator.

220 L drum—BE3825 with real Canberra's old 50 mm 301 collimator—tests: 139Ce [165.85 keV] 137Cs [661.65 keV] 60Co [1332.49 keV]

(εISOCS�εMCNPX)/εMCNPX

(εISOCS�εMCNPX)/εMCNPX

(εISOCS�εMCNPX)/εMCNPX

[%] Uncert. [%] [%] Uncert. [%] [%] Uncert. [%]

1.a PVC matrix, partial filling to a height of 51.2 cm, source–detector distance of 25 cm �8.3 10.5 �18.3 8.7 �17.8 6.41.b Cellulose matrix, partial filling to a height of 51.2 cm, source–detector distance of 25 cm �7.8 10.8 �18.2 9.2 �16.5 6.21.c Aluminum matrix, partial filling to a height of 51.2 cm, source–detector distance of 25 cm �7.0 11.2 �16.6 9.3 �17.2 6.62 Cellulose matrix, partial filling to a height of 51.2 cm, source–detector distance of 50 cm �3.7 10.6 �18.3 8.7 �16.3 6.83 Cellulose matrix, partial filling to a height of 70 cm, source–detector distance of 25 cm �6.1 10.7 �14.4 8.7 �13.5 6.3

Fig. 13. Comparison of ISOCS/MCNPX percentage difference for real and virtual collimators. 2 m3 box filled with a PVC contaminated source, BEGe 5030 detector.

Table 5Comparison of ISOCS/MCNPX percentage difference for virtual modified 50 mm 251 lead shield collimator and virtual modified 50 mm 251 lead shield collimator withbottom collimator's aperture cone radius, R¼5.2 cm. 2 m3 box with PVC, 5030 detector.

Radionuclide Energy(MeV)

Virtual modified 50 mm 251 lead shield collimator Virtual modified 50 mm 251 lead shield collimator [bottomcollimator's aperture cone radius, R¼5.2 cm]

Δε [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Δε [ISOCS/MCNPX] PVC(1.4 g/cm3) [%]

Uncertainty (Δε) [ISOCS/MCNPX]PVC (1.4 g/cm3) [%]

241Am 0.05954 16.9 14.2109Cd 0.08803 9.1 12.957Co 0.12206 �1.7 11.9139Ce 0.16585 �17.8 14.0 �4.7 11.7113Sn 0.39169 �23.9 11.4 �7.1 9.985Sr 0.51400 �22.0 9.2 �8.2 8.0137Cs 0.66165 �23.4 9.3 �8.4 8.054Mn 0.83490 �20.9 9.1 �8.7 8.160Co 1.17322 �20.6 6.9 �10.1 5.960Co 1.33249 �19.5 6.8 �11.6 5.988Y 1.83610 �18.1 6.7 �9.4 6.2

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–2018

where ϵ Eð Þα; corrected represents the corrected efficiency valuedepending on energy and lead shield collimator's open angle,and ϵ Eð Þα; ISOCS is the ISOCS efficiency calculated using Canberra'ssoftware.

On considering the specific case with α¼301, the fifth orderpolynomial fit will have the form

f 301 Eð Þ ¼ 85:6E5�300:0E4þ353:5E3�132:2E2�22:4E�1:9 ð4Þ

with an R2¼0.973.

4.1.1. Correction factor confidence limitThe same correction factor obtained for the case specified

above (source–detector distance of 25 cm, and partially cellulosefilling), within a certain confidence limit, can be applied in all theother cases involved with 220 L drums, i.e. all the situations that acommon ISOCS’ user can find in a typical waste characterizationmeasurement: a different matrix present in the drum, a detectorpositioned at a different distance from the source or a differentmatrix filling of the drum itself.

To demonstrate such an assumption the following simulationtests have been carried out:

1) 220 L drum partially filled (drum filled, starting from its base-line, to a height of 51.2 cm) with different matrixes and aBE3825 detector with Canberra's old 50 mm 301 lead shieldcollimator, positioned at a distance of 25 cm from the drumitself, for investigating influence coming from materials’ cross-sections and densities such as1.a. PVC matrix [1.40 g/cm3];1.b. cellulose matrix [0.45 g/cm3];1.c. aluminum matrix [2.69 g/cm3];

2) 220 L drum partially filled with uniformly contaminated cellu-lose (drum filled, starting from its baseline, to a height of51.2 cm) and a BE3825 detector with Canberra's old 50 mm 301lead shield collimator, positioned at a distance of 50 cm from

the drum itself, for investigating influence coming from detec-tor's position with respect to the drum;

3) 220 L drum partially filled with uniformly contaminated cellu-lose (drum filled, starting from its baseline, to a height of70.0 cm) and a BE3825 detector with Canberra's old 50 mm 301lead shield collimator, positioned at a distance of 25 cm fromthe drum itself for investigating influence coming from differ-ent matrix filling heights into the drum.

For all the simulation tests the same source term was con-sidered: 137Cs, 60Co (limiting to 1.33 MeV gamma-ray emission),and 139Ce. Cesium and cobalt were chosen because they are usuallyconsidered as “Key Nuclides” for other “Hard to Measure” nuclides,while 139Ce was chosen to account for the low energy range.

Table 6 shows the results in terms of percentage differencebetween the detection efficiency calculated with ISOCS and MCNPXdetection efficiency. Practically, these results represent the devia-tions from the reference situation described in Section 3.1, i.e. a220 L drum partially filled with uniformly contaminated cellulose(drum filled, starting from its baseline, to a height of 51.2 cm) and aBE3825 detector with real Canberra's old 50 mm 301 lead shieldcollimator, positioned at a distance of 25 cm from the drum itself.

As can be seen in Table 6, either for the three identified energyranges or different test cases, the 220 L drum and the BE3825detector with real Canberra's old 50 mm 301 lead shield collimatorshow a percentage difference in the same ranging values and inthe same uncertainty; in particular, the difference between themaximum and minimum values of each column never exceeds 5%.

Data of Table 6 can be best fitted by a fifth order polynomial, asshown in Fig. 14. The fifth order polynomial is derived from theanalysis of results of the reference situation described in Section 3.1in which the BE3825 detector is collimated implementing a realCanberra's old 50 mm 301 lead shield collimator. For this referencesituation several efficiency points, with associated uncertainties,covering an extended energy range, have been fitted for extrapolat-ing the fifth order polynomial curve itself. On considering real

Fig. 14. Percentage difference of ISOCS and MCNPX efficiency values considering a 220 L drum and a BE3825 detector with Canberra's old 50 mm lead shield collimator (301,901 and 1801) vs. energy.

M. Altavilla, R. Remetti / Nuclear Instruments and Methods in Physics Research A 739 (2014) 10–20 19

common collimators provided with ISOCS systems (01, 301, 901, and1801), such a figure also shows that the same trend can bedemonstrated for 901 and 1801 BE3825 collimations (the 01 collima-tion has not been considered because efficiency data values startfrom medium to high energies, taking into account the attenuationof the lead shield for low energies).

Given previous results it may be asserted that the correctionfactor given in Section 4.1, within a limit of 5%, is able to cover all thesituations encountered when assaying a 220 L drum implementing aBE3825 detector with the real old 50 mm 301 lead shield collimator.

5. Conclusions

Starting from the observation that ISOCS’ calibration producesremarkable inaccuracies when applied to BEGe detectors with asmall angled real collimator, this work verifies that this is dueto the shadow-shielding of detector's active area caused by thecollimator itself. Further, the collimator algorithms currentlyutilized in the ISOCS software, having been originally develo-ped for HPGe detectors, are not able to operate a deterministiccorrection of such an effect. This is due to the different crystalconfigurations of broad energy detectors compared to coaxialdetectors, i.e. to a different importance of the active area portionobscured by the collimator.

The present work has considered a virtual collimator that,maintaining its angular aperture, was capable of continuouslyenlarging its bottom collimator's aperture cone radius, to exposegrowing active area portions. Results have been obtained in termsof couples of detection efficiency values obtained both fromCanberra's Geometry Composer and MCNPX. MCNPX results werecompletely stochastic, while Canberra's ones were affected bythe deterministic correction for collimation. Different referenceset-ups involving source geometry effects, source materials anddifferent detectors were considered.

MCNPX simulations demonstrated when widening collimators’cone but maintaining the angular aperture unchanged that ISOCSand MCNPX difference percentage between efficiency data pointsreduced, depending on energy, by more than 50%. This happens as far

as the shadow-shielded portion of detector's active area reduces. Onthe basis of MCNPX simulations, it is possible to develop correctionfactors for ISOCS’ detection efficiencies obtained with the current realcollimators. In other words, the better ISOCS and MCNPX agreementpresented for larger bottom collimator aperture cone radii allowedcorrection factors to be estimated for real collimator dimensions.

References

[1] R. Luis, J. Bento, G. Carvalhal, P. Nigeria, L. Silva, P. Teles, P. Vaz, NuclearInstruments and Methods in Physics Research A 623 (2010) 1014.

[2] W.F. Mueller, F. Bronson, M. Field, K. Morris, D. Nakazawa, R. Venkataraman,V. Atrashkevitch, Journal of Radioanalytical and Nuclear Chemistry 282 (2009)217, http://dx.doi.org/10.1007/s10967-009-0273-6.

[3] D. Budjas, M.B. Heider, O. Chkvorets, N. Khanbekova, S. Schoenert, Journal ofInstrumentation 4 (2009) 1001, http://dx.doi.org/10.1088/1748-0221/4/10/P10007.

[4] D. Barrientos, A.J. Boston, H.C. Boston, B. Quintana, I.C. Sagrado, C. Unsworth,S. Moon, J.R. Cresswell, Nuclear Instruments and Methods in Physics ResearchA 648 (2011) S228.

[5] ⟨http://www.canberra.com/products/insitu_systems/isocs.asp⟩ (accessed 07.11.13).[6] R. Venkataraman, F. Bronson, V. Alrashkevich, B.M. Young, M. Field, Nuclear

Instruments and Methods in Physics Research A 422 (1999) 450.[7] R. Venkataraman, F. Bronson, V. Atrashkevich, M. Field, B.M. Young, Improved

detector response characterization method in ISOCS and LabSOCS, in: Proced-ings of Methods and Applications of Radioanalytical Chemistry (MARC VI)Conference, Kailua-Kona, Hawaii, 2003.

[8] M. Altavilla, R. Remetti, Nuclear Instruments and Methods in Physics ResearchA 712 (2013) 157.

[9] R. Venkataraman, F. Bronson, Implementation and testing of the new colli-mator algorithm in ISOCS (In Situ Object Calibration Software), in: Proceedingsof Health Physics Society 33rd Annual Midyear Meeting on Instrumentation,Measurements, and Electronic Dosimetry, Virginia Beach, VA, Laboratory UseSession, 2000.

[10] ⟨http://www.canberra.com/products/insitu_systems/pdf/ISOCS-SS-C40166.pdf⟩(accessed 06.11.13).

[11] D.B. Pelowitz (Ed.), MCNPX™ User's Manual Version 2.7.0, LA-CP-11-00438,Los Alamos, 2011.

[12] ⟨http://www.canberra.com/products/detectors/germanium-detectors.asp?Accordion1=1⟩ (accessed 20.10.13).

[13] Radiation Protection 113: Recommended Radiological Protection Criteria forthe Clearance of Buildings and Building Rubble from the Dismantling ofNuclear Installations, European Communities, Luxembourg, 2000.

[14] Radiation Protection 122: Practical Use of the Concepts of Clearance andExemption—Part I. Guidance on General Clearance Levels for Practices,European Communities, Luxembourg, 2000.

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