The photoionization-reduced energy in LSC

ARTICLE IN PRESS

Applied Radiation and Isotopes 64 (2006) 43–54 www.elsevier.com/locate/apradiso

The photoionization-reduced energy in LSC A. Grau Carlesa,, E. Gu¨ntherb, A. Grau Malondac a IMAFF/CSIC, Dcho. 211, C/ Serrano 113b, 28006 Madrid, Spain Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany c Laboratorio Nacional de Fusio´n, Edif. 6, Dcho. 16, Avda. Complutense 22, 28040 Madrid, Spain b

Received 16 September 2004; received in revised form 10 June 2005; accepted 10 June 2005

Abstract The atomic rearrangement cascade that follows the electron-capture decay process in low-Z radionuclides involves Xrays which have high photoelectric interaction probabilities. When the K-shell binding energy of the ionized atom (e.g., hydrogen) is significantly lower than the energy of the X-ray photon, the detector response to a photon-equivalent energy electron and the whole photoionization process are very similar. This is not the case when the scintillator cocktail contains larger atoms (e.g., oxygen and phosphorus in Ultima GoldTM ). For larger Z atoms, the reduced energy of the whole photoionization process is less than the reduced energy of the interacting photon due to the nonlinear effects of ionization quenching. This paper shows the convenience of including a more detailed simulation of the photoionization process in the atomic rearrangement detection model for electron-capture nuclides such as 55Fe, 51 Cr and 54Mn. The need for more elaborate atomic rearrangement models is a consequence of the analysis of 125I data. r 2005 Elsevier Ltd. All rights reserved. Keywords: Liquid Scintillation counting; Photoionization; Electron-capture

1. Introduction The early idea of the first developers of the CIEMAT/ NIST method was to build a general standardization method for any radionuclide (Grau Malonda, 1982; Coursey et al., 1986) Basically, the procedure consists of a combination of experimental and theoretical work. Firstly, the assay of the tracer (commonly 3H) characterizes the detection system and the free parameter of the sample, and secondly, the comparison of the computed efficiencies of the nuclide and the tracer

Corresponding author. Tel.:+34 1 561 68 00 x-3211; fax: +34 1 585 48 94. E-mail address: [email protected] (A. Grau Carles).

gives the counting efficiency for the nuclide (Grau Malonda and Garcı´ a-Toran˜o, 1982; Coursey et al., 1989; Gu¨nther, 2002a; Zimmerman et al., 2002). Although many laboratories apply the method to bray nuclide standardizations, its generalization to electron-capture nuclides has not reached the required degree of accuracy. The uncertainties in nuclear and atomic data cannot explain the discrepancies of 3% for low-Z EC nuclides in comparison with other measurement methods (Gu¨nther, 2002b). Also, the apparent oversimplification of the atomic rearrangement detection models (i.e., KLM, KLMN or KL1L2L3M) cannot explain such a discrepancy (Grau Malonda and Grau Carles, 2004). For low-Z nuclides, we propose to include in the model the nonlinear response of the scintillator to low-energy X-ray photoionizations. The lack of this

0969-8043/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2005.06.005

ARTICLE IN PRESS 44

A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

correction can lead to an overestimation in the counting efficiency approaching 3% for moderately quenched samples. Obviously, the detailed simulation of each photoionization process is not feasible. The number of possible combinations between the atomic rearrangement pathways due to photoionization and the EC primary pathways is huge. Fortunately, the influence of the nonlinear effects of photoionization on the counting efficiency is only corrective. To simplify the process, the energy involved in the K-shell photoionization process is separated into a sum of only three terms: the photoelectron energy, the KXY Auger electron mean energy and the remaining atom de-excitation energy. When the K-shell-binding energy is significantly less than the energy of the incident photon, the influence of the three-term correction is negligible. Therefore, the three-term correction is unnecessary for large-Z EC nuclides or when the scintillator has only light elements (i.e., hydrogen and carbon). On the contrary, the standardization of low-Z EC nuclides in scintillator cocktails with heavier elements (e.g., oxygen and phosphorus in Ultima GoldTM ) should provide for the correction. The pathway modifications induced by the separation of the photoionization-reduced energy into a sum of three terms may look trivial. However, the extensive range of photon interaction possibilities generate the split of the atomic rearrangement detection pathways. The LM photons can be photoabsorbed by the atomic K- and L-shells of the scintillator elements without distinction. In addition, a number of pathways refer to the simultaneous interaction of two LM photons with the scintillator, increasing the pathway split significantly. Contrary to LM photons, for which the Compton interaction probability is negligible for a wide range of Z, the Compton and photoelectric interaction probabilities can be of the same order for KL photons. Consequently, the simultaneous collision of KL and LM photons with the scintillator into the resolving time of the spectrometer can follow both the Compton–photoelectric and the photoelectric–photoelectric alternatives. In this article we study how the nonlinear response of the scintillator to photoionization affects the counting efficiency for 55Fe, 51Cr, 54Mn, 65Zn and 125I. We prove experimentally that the nonlinear effects decrease in importance with Z. The discrepancies between uncorrected and corrected counting efficiencies can be from 3% for 55Fe ðZ ¼ 25Þ to less than 0.5% for 125I ðZ ¼ 52Þ. Also, we study how the accuracy of the counting efficiency depends on the quality of the atomic model. The obvious conclusion of this study is that the more we increase Z, the more the quality of the atomic rearrangement model is justified. The recently revised version of the program EMI, now called EMILIA (Grau Carles, 2004), considers the nonlinear correction.

2. Parameters affecting the counting efficiency 2.1. The atomic model Good knowledge of the limitations of the available atomic models is basic to improve the simulations and reduce the uncertainty. The three-shell KLM model involves averaged values for the Li - and Mi -subshells. However, the criterion of averaging is certainly ambiguous, and depends on the magnitude we need to evaluate. To compute the mean value of the Auger LMM energy, we do not have to average the three subshells L1 , L2 and L3 , but the transitions Li Xj Yk with their respective weights. Grau Carles and Grau Malonda (1996) give details on the computation of the mean LMM Auger transition energy for 125I. On computing the Auger LMM energy a question arises on how to include the Coster–Kronig transition energies: should the low-energy Coster–Kronig transition energies be averaged together with the higherenergy Auger–electron transitions? Obviously, energy is an additive magnitude for which the standard deviation contributes to the uncertainty without affecting the mean value. Although, in principle, Coster–Kronig and Auger energies can be averaged in the way reported by Grau Carles and Grau Malonda (1996), what finally matters in the determination of the counting efficiency is the response of the scintillator. This can be summarized in a mathematical way as follows: to find the average energy of a transition (e.g., PN LXY) we must use reduced electron energies instead of 1 wi E i QðE i Þ=N PN 1 wi E i =N, where QðEÞ is the ionization quench function, N is the total number of Auger (e.g., Lj Xk Yl ) and Coster–Kronig (e.g., Lj Lk Xl ) electrons involved and wi is the relative emission probability for each electron. Therefore, the models KLM and KL1 L2 L3 M must give similar counting efficiencies if averaged in the proper way. The pathway energies of both models gather sums of simultaneous processes, clearly pointing out what really matters in the computation of the counting efficiency is the nonlinear response of the scintillator (Grau Malonda and Grau Carles, 2004). Gu¨nther (2002b) reports the importance of a wellaveraged Auger LMM energy to reduce the counting efficiency uncertainty for nuclides in the range 50oZo90. 2.2. Atomic and nuclear data The origin and quality of the atomic and nuclear data are essential for obtaining acceptable results. The comparison of the simple KLM model with the more elaborated KL1 L2 L3 M and KLMN requires parameter groups taken from the same data base. Tables 1 and 2 list the nuclide data for the KL1 L2 L3 M atomic rearrangement models, respectively. The references for

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54 Table 1 Atomic and nuclear data of

55

Fe,

54

Mn and

45

51

55

Fe

Cr for the KL1 L2 L3 M model 54

51

Mn

Cr

Reference

$K ; $L1 $L2 ; $L3

.321,.00084 .005,.005

.289,.00071 .0037,.0037

.256,.00058 .0026,.0026

Bambynek et al. (1972)

f 12 ; f 13 ; f 23

.30,.58,.0

.31,.57,.0

.31,.58,.0

Bambynek et al. (1972)

pKL1 L1 ; pKL1 L2 ; pKL1 L3 pKL2 L2 ; pKL2 L3 ; pKL3 L3 pKL1 M ; pKL2 M ; pKL3 M pKMM

.0666,.0742,.1362 .0136,.3247,.1818 .0465,.0490,.0961 .0113

.0666,.0741,.1367 .0136,.3258,.1827 .0460,.0482,.0956 .0107

.0686,.0763,.1416 .0139,.3373,.1896 .0468,.0491,.0658 .0110

pL1 L1 M ; pL1 L3 M ; pL2 L3 M

1.,1.,1.

1.,1.,1.

1.,1.,1.

pL1 MM ; pL2 MM ; pL3 MM

1.,1.,1.

1.,1.,1.

1.,1.,1.

E KL1 L2 ; E KL1 L2 ; E KL1 L3 E KL2 L2 ; E KL2 L3 ; E KL3 L3 E KL1 M ; E KL2 M ; E KL3 M E KMM

5.001,5.119,5.130 5.236,5.247,5.258 5.710,5.835,5.847 6.428

4.600,4.711,4.720 4.822,4.831,4.840 5.242,5.359,5.369 5.892

4.209,4.316,4.324 4.424,4.432,4.439 4.595,4.632,4.679 5.378

E L1 L2 M ; E L1 L3 M ; E L2 L3 M

.078,.091,0.

.0633,.0848,.0

.0746,.0840,.0

Beardem and Burr (1967)

E L1 MM ; E L2 MM ; E L3 MM

.661,.575,.557

.593,.507,.494

.537,.454,.447

Larkins (1977)

pKL2 ; pKL3 ; pKM pL1 M ; pL2 M ; pL3 M E KL2 ; E KL3 ; E KM E L1 M ; E L2 M ; E L3 M

.3017,.5936,.1047 1.,1.,1. 5.888,5.899,6.490 .720,.639,.628

.3020,.5968,.1012 1.,1.,1. 5.406,5.415,5.947 .652,.542,.565

.3007,.5979,1.021 1.,1.,1. 4.945,4.952,5.427 .590,.473,.498

Browne and Firestone (1986)

EC to ground state pK ; pL1 ; pL2 pM

.8844,.0988,.0005 .0163

.8919,.0930,.0004 .0147

Firestone and Shirley (1996)

Chen et al. (1979)

Beardem and Burr (1967)

Beardem and Burr (1967) Beardem and Burr (1967)

EC to excited state pK ; pL1 ; pL2 pM

.8886,.0955,.0004 .0155

.8910,.0937,.0004 .0149

Firestone and Shirley (1996)

pg ; E g

1.,834.85

.0989,320.08

Be´ et al. (2004)

the data are given in the last column (Tables 1 and 2). The group of data elements related to probability are correlated, and consequently have been normalized to one. The Auger LMM energies have been corrected according to Larkins’ (1997) approximation. To compute the mean L-shell fluorescence yield $L , in Tables 3 and 4, we followed the recipe of Grau Malonda (1999). 2.3. Ionization quenching In general, the response of a liquid scintillator to ionizing particles is not a linear function of the particle energy. The loss of fluorescence photons increases with the ionization power of the particle. The term ‘reduced energy’ is used to define how the response of the scintillator is affected by ionization quenching. The concept of reduced energy is in fact an artifice that allows one to assume a linear response of the scintillator

by only decreasing the particle energy from E to EQðEÞ. The factor QðEÞ is consequently called the ionization quench correction factor or the ionization quench function. In the past, many efforts were devoted to the determination of the function QðEÞ that provides the best agreement between the experimental and computed counting efficiencies (Grau Malonda and Coursey, 1988; Peron, 1995; Grau Malonda and Grau Carles, 1999). However, a procedure based on the counting efficiency has the inconvenience of incorporating the deficiencies of the atomic model and the inaccuracies of the tracer activity, both of which obviously can distort the results of QðEÞ. The study of the ionization quench function is frequently based on Birks’ formula (Birks, 1964) for which accurate values of the scintillator stopping power are essential. Although we can use the Bethe theory to derive the stopping power as a function of energy, the

ARTICLE IN PRESS 46 Table 2 Atomic and nuclear data of

A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

65

Zn and

125

I for the KL1 L2 L3 M model

65

Zn

125

I

Reference

$K ; $L1 $L2 ; $L3

.454,.016 .01,.011

.875,.041 .074,.074

Bambynek et al. (1972)

f 12 ; f 13 ; f 23

.30,.54,.028

.18,.28,.155

Bambynek et al. (1972)

pKL1 L1 ; pKL1 L2 ; pKL1 L3 pKL2 L2 ; pKL2 L3 ; pKL3 L3 pKL1 M ; pKL2 M ; pKL3 M pKMM

.0682,.0738,.1350 .0136,.3208,.1777 .0485,.0516,.0990 .0118

.0776,.0925,.1153 .0119,.2517,.1280 .0848,.0780,.1336 .0266

pL1 L1 M ; pL1 L3 M ; pL2 L3 M

1.,1.,1.

1.,1.,1.

pL1 MM ; pL2 MM ; pL3 MM

1.,1.,1.

1.,1.,1.

E KL1 L2 ; E KL1 L2 ; E KL1 L3 E KL2 L2 ; E KL2 L3 ; E KL3 L3 E KL1 M ; E KL2 M ; E KL3 M E KMM

6.736,6.915,6.864 7.003,7.059,7.031 7.752,7.759,7.797 8.812

21.935,22.263,22.533 22.590,22.860,23.131 26.126,26.490,26.758 30.272

E L1 L2 M ; E L1 L3 M ; E L2 L3 M

.1090,.1207,.0

.212,.509,.196

Beardem and Burr (1967)

E L1 MM ; E L2 MM ; E L3 MM

.9701,.8899,.840

3.523,3.312,3.076

Larkins (1977)

pKL2 ; pKL3 ; pKM pL1 M ; pL2 M ; pL3 M E KL2 ; E KL3 ; E KM E L1 M ; E L2 M ; E L3 M

.3023,.5910,.1067 1.,1.,1. 8.028,8.048,8.905 1.022,.900,.921

.290,.536,.174 1.,1.,1. 27.202,27.472,31.095 4.240,4.077,3.822

Browne and Firestone (1986)

EC to ground state pK ; pL1 ; pL2 pM

.8853,.0881,.0096 .0170

EC to excited state pK ; pL1 ; pL2 pM

.8794,.0926,.0101 .0179

.8170,.1449,.0037 .0344

Firestone and Shirley (1996)

pg ; E g

0.5023,1115.54

.0683,35.49

Be´ et al. (2004)

.8718,.1042,.0096 .0038,.0106

Karttunen et al. (1969)

pICK ; pICL1 ; pICL2 pICL3 ; pICM pbþ

0.0142

zero in the lower integration limit of the semiempirical equation of Birks indicates that we cannot achieve the numerical integration of the function without knowing the stopping power values in the low-energy range. Since the validity of the Rohrlich and Carlson (1953) equation is restricted to energies greater than 1 keV, we have extrapolated the stopping power to infinity by assuming the functional behavior AE a for Eo1 keV. The coefficient, A, is derived from the Rohrlich and Carlson equation for E ¼ 1 keV, while the divergence parameter a is assumed to be 1.0. The hypothesis of an infinity value of the stopping power at E ¼ 0 has no physical basis, as was discussed in a previous article (Grau Malonda and Grau Carles, 1999), but it leads to a good

Chen et al. (1979)

Beardem and Burr (1967)

Beardem and Burr (1967) Beardem and Burr (1967) Firestone and Shirley (1996)

Helmer (2002)

agreement with experiment. Since the available stopping power data are almost entirely based on molecules in gas state, this apparent contradiction could find the following explanation: for condensed matter, other physical processes exist which can significantly increase the values of the stopping power in the low-energy region compared to the gas phase (e.g., molecular excitation). 2.4. Nonlinear response of the scintillator to photoionization The detection of the emitted radiation subsequent to EC involves two different types of atomic rearrangement processes. The first process is generated by the capture

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54 Table 3 Atomic and nuclear data of

55

Fe,

54

Mn and

47

51

Cr for the three-shell KLM model

55

54

Fe

51

Mn

Cr

Reference

$K $L

.321,.00496

.289,.0045

.256,.0045

Bambynek et al. (1972)

pKLL pKLM pKMM

.7971,.1916,.0113

.7995,.1898,.0107

.8273,.1617,.0110

Chen et al. (1979)

E KLL E KLM E KMM E LMM

5.24,5.80 6.45,.62

4.784,5.323 5.892,.53

4.385,4.641 5.378,.48

Beardem and Burr (1967)

pKL pKM E KL E KM E LM

.8953,.1047 5.895,6.490,.635

.8988,.1012 5.412,5.947,.57

.8979,.1021 4.951,5.427,.59

Beardem and Burr (1967)

EC to ground state pK pL pM

.8844,.0993,.0163

.8919,.0934,.0147

Firestone and Shirley (1996)

EC to excited state pK pL pM

.8886,.0959,.0155

.8910,.0941,.0149

Firestone and Shirley (1996)

pg E g

1.,834.85

.0989,320.08

Be´ et al. (2004)

Table 4 Atomic and nuclear data of

65

Zn and

125

I for the three-shell KLM model

65

Zn

125

I

Reference

$K $L

.454,.0050

.875,.0730

Bambynek et al. (1972)

pKLL pKLM pKMM E KLL E KLM E KMM E LMM pKL pKM E KL E KM E LM

.7891,.1991,.0118 6.98,7.90 8.82,.89 .8933,.1067 8.040,8.905,.93

.6770,.2964,.0266 22.6,25.5 30.27,3.3 .826,.174 27.3,31.10,4.2

Chen et al. (1979) Beardem and Burr (1967)

EC to ground state pK pL pM

.8853 .0977 .0170

EC to excited state pK pL pM pg E g

.8794 .1027 .0179 .5023,1115.54

pICK pICL pICM pbþ

.0142

of one electron in the nuclide atom, while the second is due to photoionization, and occurs in a different atom of the scintillator. The available computer codes EMI (Grau Carles et al., 1994), CAPMULT (Galiano Casas et al., 1995) and EMI2 (Grau Malonda et al., 1999) use the reduced energies EQðEÞ to simulate the response of the scintillator to photoionization, where E is the energy of the incident photon. The energy conservation law states that photoionization total energy must be equal to the incident photon energy. However, the nonlinear response of the scintillator causes the sum of all emitted components to be slightly less than the reduced energy of the incident photon. To make clear the influence of

Beardem and Burr (1967)

Firestone and Shirley (1996) .8170.1486 .0344 .0683,35.49

Firestone and Shirley (1996) Be´ et al. (2004)

.8718,.1176,.0106

Karttunen et al. (1969) Helmer (2002)

the nonlinear effects on the counting efficiency we propose to compare the response to one low-energy 4 keV electron with the response of two simultaneously interacting electrons of 2 keV. If the response of the scintillator were linear with energy, the number of emitted fluorescence light photons would be the same in both cases. On the contrary, the nonlinear effects in the low-energy region make significantly less the reduced energy of the 2 keV electrons 2EQðEÞ ¼ 4Qð2Þ ¼ 1:83 when compared to the reduced energy of the 4 keV electron EQðEÞ ¼ 4Qð4Þ ¼ 2:27. The detection probabilities in a system of two photomultiplier tubes in coincidence are 26% and 34% for a free parameter of

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

48

1.3. Therefore, the counting efficiency of a set of lowenergy electrons can be significantly lower than the energy of one electron of kinetic energy equivalent to the sum. The whole photoionization process not only involves the ejection of one photoelectron but also the emission of Auger electrons and X-rays in the atomic rearrangement cascade. When the binding energy of the atom is substantially lower than the energy of the incident photon, the reduced energy of the whole process approaches the reduced energy of the photoelectron, and the separation of the photoionization-reduced energy into a sum of terms becomes unnecessary. On the contrary, when the energy of the colliding photon gets closer to the binding energy of the shell from where the photoelectron is ejected, the reduced energy of the whole process must be separated into a sum of several terms to take into account the nonlinear effects of similar low-energy simultaneous events. Since the simulation of all possible combinations between the EC and photoionization pathways is not manageable, especially for the most elaborated atomic KLMN and KL1 L2 L3 M models, we have transformed the reduced energy of K-shell photoionizations into a sum that includes only the three terms: ðE XY  E sK ÞQðE XY  E sK Þ þ E sKXY QðE sKXY Þ þ E sR QðE sR Þ;

E XY 4E sK .

ð1Þ

On the other hand, for L-shell photoionizations, the following two-term sum yields a good approximation: ðE XY  E sL ÞQðE XY  E sL Þ þ E sR QðE sR Þ;

E XY 4E sL ,

daughter nuclide release but also to how the linear behavior in the response of the scintillator can be lost for low-energy electrons or how X-ray collisions may vary due to changes in the composition or volume of the sample. One direct consequence of applying Eqs. (1) and (2) to low-energy X-rays is the splitting of the detection pathways which contain interacting KL-, KM- and LMphotons. Obviously, since photoabsorption processes can take place both in the K- and L-shells, the number of possible different pathways increases significantly. By using the subindexes i and k to label scintillator elements and the different type of interactions, we have, for the KLM model and Ultima GoldTM , the complete set of elements listed in Table 7. Table 8 illustrates how the 22 pathways of the KLM model are affected by the photoionization process. The pathway splitting becomes particularly significant when two photons interact simultaneously with the scintillator or when the scintillator cocktail contains a number of different elements. To prove the influence of large-Z elements in the scintillator (e.g., oxygen and phosphorus) on the counting efficiency for low-Z EC nuclides we list the counting efficiencies computed with EMILIA in Table 9, with and without applying the photoelectric correction, for the three scintillators: toluene, dioxanenaphthalene and Ultima GoldTM . Since toluene only contains carbon and hydrogen atoms, the application of the photoelectric correction has negligible consequences. On the contrary, dioxane-naphthalene and Ultima Gold exhibit non-negligible deviations.

(2)

where the superindex s denotes that energies are relative to the atoms of the scintillator, E XY is the energy of the incident photon, E sKXY is the K-Auger-electron mean energy for each one of the atoms in the scintillator and E sR is the remaining energy of the rearrangement process, which can take the values E sK  E sKXY and E sL for the K- and L-shell photoionizations, respectively. Table 5 lists the energies required in equations (1) and (2) for Ultima GoldTM . By substituting the data of Table 5 into Eq. (1) we can derive for each element of Ultima GoldTM the implications of dividing the photoionization process into three components. Table 6 illustrates how the reduced energy of 55Fe KL photoelectrons can be overestimated for Ultima GoldTM when the photoionization process of Eq. (1) is ignored. The pathway equations applied to EC nuclides in LSC standardizations include not only the probabilities and energies of the radiation (electrons and X-rays) released in the rearrangement of the daughter nuclide but also other radiation–matter interaction aspects, e.g., the probability of interaction for X-rays and the reduced energy for electrons. In other words, the 22 equations of the KLM rearrangement model refer not only to the

3. Experimental The measurements were carried out in two different spectrometers: a Wallac Guardian 1414 and a Camberra Packard 2200CA, both working at controlled temperatures of 18 and 12 1C, respectively. The quench parameters of these spectrometers (i.e., SQP(E) for Wallac and tSIE for Packard) were measured with external g-ray sources of 152Eu (Wallac) and 133Ba (Packard). All samples were prepared with the same total volume of 15 ml of Ultima GoldTM . To avoid the adsorption of the radioactive substance on the vial walls, 1 ml 0.05 mol/l of EDTA solution with 0.4 mg of Mn2þ and Zn2þ as carrier was incorporated. The samples of each nuclide set were gradually quenched by adding increasing volumes of nitromethane (0–100 ml). The samples were shaken and centrifuged to avoid drops on the top of the vials. After waiting for cooling in the spectrometer, the stability of the samples was monitored for three days. To check the chemical stability, we also included samples with a lower content of water or EDTA solution. In the case of 55Fe, 0.2 ml diethylhexyl

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

phosphoric acid (HDEHP) or 30 mg tri-n-octylphosphinoxide (TOPO) were used as complexing agents. The radionuclide solutions applied in the experiments were calibrated solutions. The activity of the tritiated water was measured by internal gas counting, and compared with the activities obtained by other laboratories within the scope of a EUROMET intercomparison Makepeace et al. (1998). The 55Fe solution was measured in a EUROMET intercomparison (Cassette et al., 1998). The specific activities of the standard solutions of 54Mn and 65Zn were obtained by using an ionization chamber, which was calibrated with solutions of these nuclides traceable to the International Reference System (SIR) (Ratel and Michotte, 2003a, 2004). The solution of 51Cr was calibrated by 4pb  g coincidence and traced to SIR in 1998 (Ratel and Michotte, 2003b), while the specific activity of the 125I solution was measured by photon–photon coincidence in 1987 (Schrader and Walz, 1987).

4. Results and discussion Tables 10–14 compare the counting efficiencies derived from the standard activities (experimental) with the efficiencies obtained by the CIEMAT/NIST method (computed). We include both the KL1 L2 L3 M and KLM

Table 5 Inner shell energies and K-Auger electron energy for Ultima GoldTM Atom

Carbon Oxygen Phosphorus Nitrogen Sodium Sulfur

49

models for which we study the results of either applying or ignoring corrections (1) and (2) for photoionization. The experimental counting efficiencies in the sense defined above are given in the second column. Columns 3 and 7 show the counting efficiencies computed with the program EMILIA (Grau Carles, 2004) when the photoelectric correction option is enabled, while columns 5 and 9 show the efficiencies when the same option is disabled. The relative discrepancies between experimental and computed efficiencies are given in columns 4, 6, 8 and 10. Table 10 shows the results obtained for twenty samples of 55Fe. The first 10 samples were measured in the Wallac spectrometer, while for the last 10, the Packard spectrometer was used. The KL1 L2 L3 M model, with the photoelectric correction enabled, shows discrepancies which are always less than 1, including both positive and negative values. However, when the photoelectric correction is disabled, the discrepancies increase significantly, obtaining a systematic uncertainty of 2% for the uncorrected efficiencies. By applying the photoelectric correction to the KLM model, all discrepancies fall into the range between 1% and 2.2%. However, the uncertainty increases by 2.5% for the uncorrected samples. From these results we can extract three consequences. First, the photoelectric correction improves the results of both atomic models by 2%. Second, the comparison of the models KL1 L2 L3 M and KLM

Table 7 Subindex notation used to describe the splitting of the atomic rearrangement pathways

E sK (keV)

E sL (keV)

E sKLL (keV)

i

Element

k

Interaction

0.284 0.532 2.14 0.40 1.073 2.472

0.018 0.0285 0.189 0.018 0.063 0.227

— — 1.851 — — 2.01

1 2 3 4 5 6

C O P N Na S

1 2 3 4 5 6

KL photon vs. K-shell KL photon vs. L-shell KM photon vs. K-shell KM photon vs. L-shell LM photon vs. K-shell LM photon vs. L-shell

Table 6 According to Eq. (1), the sum of the reduced energies of the three terms is always less than the reduced energy of the incident photon Atom

E KL QðE KL Þ (keV)

ðE KL  E sK ÞQðE KL  E sK Þ (keV)

E sKLL QðE sKLL Þ (keV)

E sR QðE sR Þ (keV)

D

C O P N Na S

3.739 3.739 3.739 3.739 3.739 3.739

3.514 3.319 2.098 3.422 2.900 1.857

— — 0.795 — 0.307 0.895

0.031 0.101 0.032 0.059 0.002 0.078

0.194 0.319 0.823 0.258 0.530 0.909

ARTICLE IN PRESS 50

A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

Table 8 Splitting of the pathway equations of the KLM model according to the different X-ray interactions with the scintillator j

Split

Interaction with the scintillator

1–18 3; 5; 9; . . . 6 19–20 21

None P P pj ¼ pj k i pk pi P PP P pj ¼ pj k i k0 i0 pk pi pk0 pi0 P P pj ¼ pj pc þ pj ð1  pc Þ k i pk pi PP pk pi pj ¼ pj pc P PP P þpj ð1  pc Þ k i k0 i0 pk pi pk0 pi0 P P pj ¼ pj pc þ pj ð1  pc Þ k i pk pi

LM photon does not interact LM photon interacts Two LM photons interact KL photon interacts Both KL and LM photons interact

22

KM photon interacts

Table 9 The counting efficiencies computed with the program EMILIA exhibit discrepancies between the corrected and uncorrected data for Ultima GoldTM and dioxane-naphthalene. These discrepancies are due to the presence of larger-Z elements such as oxygen and phosphorus in the scintillator Scintillator

Composition

Free param.

Eff. 3 H

Eff. 55 Fe uncorrect.

Eff. 55 Fe correct.

Toluene Dioxane-naphth. Ultima GoldTM

C7H8 C4.6H9.2O2.3 C16.8H24.5O1.52P0.11

1.3 1.3 1.3

0.477 0.478 0.476

0.487 0.494 0.491

0.484 0.487 0.481

shows that Li -subshells play an important role in the accuracy of the simulations. Third, the uncertainties in the experimental counting efficiencies of both spectrometers are quite similar when the CIEMAT/NIST method is applied. Table 11 compares the experimental and the computed counting efficiencies for sixteen samples of 54Mn. The first eight and the last eight samples were measured separately in the Wallac and the Packard spectrometers. The results of Table 11 show that the photoelectric correction improves the results of both atomic models by 2%. Also, both spectrometers provide similar uncertainties in the counting efficiency. Table 12 shows the results of 51Cr. The first set of ten samples was measured in the Wallac spectrometer, while the Packard spectrometer was used for the rest of the samples. There are two essential characteristics of Table 12 to be remarked upon. First, the photoelectric correction improves the results of both atomic models by 2.5%, the uncertainties in the counting efficiency being slightly higher for the KLM model than for the KL1 L2 L3 M. Second, the uncertainties of both spectrometers do not differ significantly. The computed efficiencies for 65Zn are given in Table 13. The Packard spectrometer was used to assay the first ten samples and the Wallac spectrometer was utilized for the rest. The photoelectric correction improves the uncertainties of the KL1 L2 L3 M model by 2%, and the

uncertainties of the KLM model by 2.5%. In addition, the uncertainties in both corrected and uncorrected efficiencies are about 1% lower for the KL1 L2 L3 M than for the KLM model. As Table 14 shows, the counting efficiency of the large-Z nuclide 125I is not affected by the photoelectric correction. However, the presence of uncertainties greater than 4% in the quenched samples presumably indicates that the KL1 L2 L3 M model is not sufficiently accurate for the simulation of such nuclides.

5. Conclusions We proved the convenience of including nonlinear effects of the spectrometer in the computation of the photoionization-reduced energy. The photoelectric correction was found to be necessary when the binding energy of the atomic shell was similar to the energy of the incident photon, i.e., when low-Z electron capture nuclides were incorporated into organic liquid scintillation cocktails containing atoms heavier than carbon or hydrogen. The obvious consequence of including nonlinearities in the X-ray reduced energies was the significant increase of the detection pathways, and the complexity of the simulation method. However, the convenience of the photoelectric correction was demonstrated for 55Fe, 54Mn, 51Cr and 65Zn for

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54 Table 10 Comparison between the experimental and computed counting efficiencies of Sample

Experim.

KL1 L2 L3 M model

46.95 38.01 34.88 31.82 30.73 26.52 24.26 20.28 18.66 16.44 51.42 45.46 42.92 36.07 35.22 30.49 28.26 24.01 19.82 7.31

55

Fe KLM model

Correct.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

51

Uncorrect.

Correct.

Uncorrect.

Comput.

D%

Comput.

D%

Comput.

D%

Comput.

D%

47.37 38.01 35.07 31.95 30.84 26.54 24.24 20.21 18.58 16.39 51.85 45.63 43.89 36.23 35.42 30.59 28.20 23.93 19.71 7.24

0.9 0.0 0.5 0.4 0.4 0.1 0.1 0.3 0.4 0.3 0.8 0.4 0.9 0.4 0.6 0.3 0.2 0.3 0.5 1.0

48.40 38.90 36.00 32.84 31.71 27.34 24.99 20.87 19.20 16.96 52.87 46.65 44.30 37.17 36.36 31.46 29.06 24.67 20.36 7.35

3.1 2.3 3.2 3.2 3.2 3.0 3.0 2.9 2.9 3.2 2.8 2.6 3.2 3.0 3.2 3.2 2.8 2.8 2.7 3.0

47.97 38.57 35.60 32.46 31.33 26.99 24.67 20.58 18.93 16.41 52.45 46.22 43.87 36.77 35.96 31.09 28.67 24.35 20.07 7.40

2.2 1.5 2.1 2.0 1.9 1.8 1.7 1.5 1.5 0.2 2.0 1.7 2.2 1.9 2.1 2.0 1.5 1.4 1.3 1.2

49.04 39.57 36.57 33.38 32.24 27.82 25.45 21.26 19.57 17.30 53.52 47.29 44.93 37.76 36.93 31.99 29.54 25.12 20.74 7.69

4.4 4.1 4.8 4.9 4.9 4.9 4.9 4.8 4.9 5.2 4.1 4.0 4.7 4.7 4.9 4.9 4.5 4.6 4.6 5.2

The application of the photoelectric correction to both atomic models makes discrepancies to fall below 2%.

Table 11 Experimental and computed counting efficiencies of Sample

Experim.

47.36 40.41 32.34 33.56 29.42 26.81 22.81 19.16 51.55 44.69 36.07 37.32 32.84 30.14 25.67 21.53

Mn

KL1 L2 L3 M model Correct.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

54

KLM model Uncorrect.

Correct.

Uncorrect.

Comput.

D%

Comput.

D%

Comput.

D%

Comput.

D%

47.67 40.52 32.31 33.72 29.51 26.77 22.68 18.92 51.98 44.84 38.10 37.41 32.86 29.92 25.52 21.36

0.6 0.3 0.1 0.5 0.3 0.1 0.6 1.3 0.8 0.3 0.1 0.2 0.1 0.7 0.6 0.8

48.71 41.51 33.17 34.61 30.32 27.51 23.32 19.45 53.04 45.87 37.03 38.36 33.72 30.74 26.23 21.97

2.9 2.7 2.6 3.1 3.1 2.6 2.2 1.5 2.9 2.6 2.7 3.0 2.7 2.0 2.2 2.0

47.86 40.70 32.46 33.88 29.65 26.89 22.78 18.99 52.19 45.04 36.26 37.58 33.01 30.06 25.63 21.41

1.1 0.7 0.4 1.0 0.8 0.3 0.1 0.9 1.2 0.8 0.5 1.0 0.5 0.3 0.2 0.4

48.75 41.51 33.11 34.56 30.23 27.41 23.18 19.27 53.11 45.90 37.00 38.33 33.67 30.66 26.12 21.81

2.9 2.7 2.4 3.0 2.7 2.2 1.6 0.6 3.0 2.7 2.6 3.0 2.5 1.7 1.8 1.3

The best results are obtained for the KL1 L2 L3 M model when the photoelectric correction is applied. The uncertainty is reduced by 2% for the corrected results.

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

52

Table 12 Experimental and computed counting efficiencies for Sample

Experim.

51

Cr

KL1 L2 L3 M model

KLM model

Correct.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

36.83 33.72 30.83 27.23 25.30 23.10 20.78 18.17 16.18 41.85 39.13 36.31 32.90 30.91 28.55 26.17 23.46 21.06 16.26

Uncorrect.

Correct.

Uncorrect.

Comput.

D%

Comput.

D%

Comput.

D%

Comput.

D%

36.88 33.75 30.98 27.44 25.48 23.27 20.96 18.29 16.08 41.90 39.11 36.42 33.00 30.98 28.60 26.23 23.46 20.96 16.19

0.1 0.1 0.5 0.8 0.7 0.7 0.9 0.7 0.6 0.1 0.1 0.3 0.3 0.2 0.2 0.2 0.0 0.5 0.4

37.80 34.63 31.83 28.21 26.21 23.97 21.61 18.88 16.61 42.87 40.06 37.37 33.86 31.83 29.40 27.00 24.17 21.61 16.72

2.6 2.7 3.2 3.6 3.6 3.8 4.0 3.9 2.7 2.4 2.4 2.8 2.9 3.0 3.0 3.2 3.0 2.6 2.8

37.06 33.92 31.14 27.59 25.62 23.40 21.09 18.41 16.19 42.08 39.29 36.60 33.16 31.14 28.76 26.37 23.60 21.09 16.30

0.6 0.6 1.0 1.3 1.3 1.3 1.5 1.3 0.1 0.5 0.4 0.8 0.8 0.7 0.7 0.8 0.6 0.1 0.3

37.99 34.81 32.00 28.38 26.37 24.11 21.48 19.00 16.71 43.07 40.25 37.53 34.05 32.00 29.57 27.14 24.31 21.67 16.82

3.1 3.2 3.8 4.2 4.2 4.4 3.4 4.6 3.3 2.9 2.9 3.4 3.5 3.5 3.6 3.7 3.6 2.9 3.4

The photoelectric correction reduces the uncertainties of both models from 3% to 1%.

Table 13 Experimental and computed counting efficiencies for Sample

Experim.

64.78 55.96 51.72 49.95 48.81 44.09 43.45 40.05 37.48 30.38 68.15 63.19 59.95 54.35 53.21 48.62 47.59 44.59 41.86 34.04

Zn

KL1 L2 L3 M model Correct.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

65

KLM model Uncorrect.

Correct.

Uncorrect.

Comput.

D%

Comput.

D%

Comput.

D%

Comput.

D%

65.30 56.37 52.14 50.25 49.08 44.22 43.68 40.27 37.61 30.63 68.90 63.63 60.54 54.80 53.67 48.99 47.78 45.01 42.20 34.25

0.8 0.7 0.8 0.6 0.6 0.3 0.5 0.5 0.4 0.8 1.1 0.7 1.0 0.8 0.9 0.8 0.4 0.9 0.8 0.6

66.12 57.31 53.10 51.21 50.04 45.16 44.62 41.18 38.48 31.39 69.66 64.49 61.45 55.72 54.62 49.94 48.73 45.93 43.12 35.07

2.1 2.5 2.7 2.5 2.5 2.4 2.7 2.8 2.7 3.3 2.2 2.1 2.5 2.5 2.7 2.7 2.4 3.0 3.0 3.0

65.67 56.77 52.55 50.65 49.48 44.60 44.06 40.65 37.96 30.94 69.27 64.02 60.93 55.21 54.08 49.39 48.17 45.38 42.61 34.58

1.4 1.4 1.6 1.2 1.4 1.2 1.4 1.5 1.3 1.8 1.6 1.3 1.6 1.6 1.6 1.6 1.2 1.8 1.8 1.6

66.54 57.77 53.57 51.68 50.52 45.64 45.09 41.65 38.96 31.84 70.04 64.91 61.51 56.22 55.10 50.42 49.21 46.42 43.60 35.53

2.7 3.2 3.6 3.5 3.5 3.5 3.8 4.0 3.9 4.8 2.8 2.7 2.6 3.4 3.5 3.7 3.4 4.1 4.2 4.4

The photoelectric correction slightly reduces the uncertainties of the KL1 L2 L3 M model from 2% to1%.

ARTICLE IN PRESS A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54 Table 14 Comparison between the experimental and computed counting efficiencies for the large-Z nuclide Sample

Experim.

KL1 L2 L3 M model Correct.

1 2 3 4 5 6 7 8 9

80.46 80.54 75.80 72.51 69.65 65.63 63.06 59.94 56.70

53

125

I

KLM model Uncorrect.

Correct.

Uncorrect.

Comput.

D%

Comput.

D%

Comput.

D%

Comput.

D%

81.06 81.25 76.67 73.37 70.83 66.59 64.44 61.58 59.22

0.8 0.9 1.2 1.2 1.7 1.5 2.2 2.7 4.4

81.09 81.28 77.67 73.34 70.78 66.50 64.34 61.47 59.10

0.8 0.9 1.2 1.1 1.6 1.3 2.0 3.6 4.2

81.95 82.14 77.62 74.33 71.78 67.49 65.32 62.41 60.00

1.9 2.0 2.4 2.5 3.1 2.8 3.6 4.1 5.8

81.97 82.16 77.62 74.32 71.76 67.46 65.27 62.36 59.94

1.9 2.0 2.4 2.5 3.0 2.8 3.5 4.0 5.7

The photoelectric correction does not affect the uncertainties of both models.

which an excellent agreement between the experimental and computed counting efficiencies was achieved. The use of the photoelectric correction for large-Z nuclides was experimentally demonstrated to be unimportant for 125 I. For such a nuclide, new more complete atomic models and elaborated simulations will be necessary to achieve satisfactory calibrations by the CIEMAT/NIST method.

Acknowledgements The first author would like to acknowledge the financial support of the Education and Science Ministry of Spain through the Ramo´n y Cajal Programme.

References Bambynek, W., Crasemann, B., Fink, R.W., Freund, H.U., Mark, H., Swift, C.D., Price, R.E., Venugopala Rao, P., 1972. X-ray fluorescence yields, Auger and Coster–Kronig transition probabilities. Rev. Mod. Phys. 44, 716. Be´, M.M., Chiste´, C., Dulieu, C., Browne, E., Chechev, V., Kuzmenko, N., Helmer, R., Nichols, A., 2004. In: Scho¨nfeld, E., Dersch, R. (Eds.), Table of Radionuclides. BIPM, Sevres. Beardem, J.A., Burr, A.F., 1967. Reevaluation of X-ray atomic energy levels. Rev. Mod. Phys. 39, 125. Birks, J.B., 1964. The Theory and Practice of Scintillation Counting. Pergamon Press, Oxford. Browne, E., Firestone, R.B., 1986. Table of Radioactive Isotopes, Appendix C. Atomic Data. Wiley, New York. Cassette, T., Altzitzoglou, T., Broda, R., Colle, R., Dryak, P., de Felice, P., Gu¨nther, E., Los Arcos, J.M., Ratel, G., Simpson, B., Unterwerger, M., 1998. Appl. Radiat. Isot. 49, 1403.

Chen, M.H., Craseman, B., Mark, H., 1979. Relativistic radiationless transition probabilities for atomic K- and Lshells. At. Data Nucl. Data Tables 24, 13. Coursey, B.M., Mann, W.B., Grau Malonda, A., Garcı´ aToran˜o, E., Los Arcos, J.M., Gibson, J.A.B., Reher, D., 1986. Standardization of 14C by 4pb liquid scintillation efficiency tacing with 3H. Appl. Radiat. Isot. 37, 403. Coursey, E., Lucas, L.L., Grau Malonda, A., Garcı´ a-Toran˜o, E., 1989. The standardization of 241Pu and 63Ni. Nucl. Instrum. Methods A 279, 603. Firestone, R.B., Shirley, V.S., 1996. Table of Isotopes, Appendix F. Atomic Data. Wiley, New York. Galiano Casas, G., Grau Carles, A., Grau Malonda, A., 1995. CAPMULT, the counting efficiency for electron-capture by a KLMN model. Comput. Phys. Commun. 87, 432. Grau Carles, A., 2004. EMILIA, the LS counting efficiency for electron-capture and capture-gamma emitters, Comp. Phys. Commun., to be published. Grau Carles, A., Grau Malonda, A., 1996. Ca´lculo de la energı´ a media de emisio´n electro´nica LXY. CIEMAT Report 792 (Madrid). Grau Carles, A., Grau Malonda, A., Grau Carles, P., 1994. EMI, the counting efficiency for electron capture, electron capture-gamma and isomeric transitions. Comput. Phys. Commun. 123, 114. Grau Malonda, A., 1982. Counting efficiency for electron capture nuclides in liquid scintillator solutions. Appl. Radiat. Isot. 33, 371. Grau Malonda, A., 1999. Free Parameter Models in Liquid Scintillation Counting. CIEMAT, Madrid. Grau Malonda, A., Coursey, B.M., 1988. Calculation of beta counting efficiency for liquid-scintillation systems with three phototubes. Appl. Radiat. Isot. 12, 1191. Grau Malonda, A., Garcı´ a-Toran˜o, E., 1982. Evaluation of counting efficiency in liquid scintillation counting of pure b-ray emitters. Appl. Radiat. Isot. 33, 249. Grau Malonda, A., Grau Carles, A., 1999. The ionization quench factor in liquid-scintillation counting standardizations. Appl. Radiat. Isot. 51, 183.

ARTICLE IN PRESS 54

A. Grau Carles et al. / Applied Radiation and Isotopes 64 (2006) 43–54

Grau Malonda, A., Grau Carles, A., 2004. Averaging the reduced Auger electron energies in LSC simulations. Appl. Radiat. Isot., to be published. Grau Malonda, A., Grau Carles, A., Grau Carles, P., Galiano Casas, G., 1999. EMI2, the counting efficiency for electroncapture by a KL1L2L3M model. Comput. Phys. Commun. 123, 114. Gu¨nther, E., 2002a. Determination of the 32P activity in angioplastic balloons by LSC. Appl. Radiat. Isot. 56, 291. Gu¨nther, E., 2002b. What can we expect from the CIEMAT/ NIST method? Appl. Radiat. Isot. 56, 357. Helmer, R.G., 2002. Table des Radionuclides. BNM-CEA/ LNMB. Karttunen, E., Freund, H.U., Fink, R.W., 1969. The Kfluorescence yield of Te and the total and K-shell conversion coefficients of the 35.48 keV transition in I-125. Nucl. Phys. A 131, 343. Larkins, F.P., 1977. Semiempirical Auger-electron energies for elements 10pZp100. At. Data Nucl. Data Tables 20, 311. Makepeace, J., Altzitzoglou, T., Cassette, P., Dryak, P., Gu¨nther, E., Verrezen, F., Broda, R., Simpson, B., Unterwerger, M., 1998. International comparison of measurements of the specific activity of tritiated water. Appl. Radiat. Isot. 49, 1411.

Peron, M.N., 1995. Etude de la re´ponse lumineuse de scintillateurs liquides a´ des e´lectrons monoe´nergetiques de base e´nergie. Ph.D. Thesis, Paris-Sud University. Ratel, G., Michotte, C., 2003a. BIPM comparison BIPM.RI(II)-K1.Mn-54 of activity measurements of the radionuclide 54Mn. Metrologia 40, 06 025. Ratel, G., Michotte, C., 2003b. BIPM comparison BIPM.RI(II)-K1.Cr-51 of activity measurements of the radionuclide 51Cr. Metrologia 40, 06 008. Ratel, G., Michotte, C., 2004. BIPM comparison BIPM.RI(II)K1.Zn-65 of activity measurements of the radionuclide 65 Zn. Metrologia 41, 06014. Rohrlich, F., Carlson, B.C., 1953. Positron–electron differences in energy loss and multiple scattering. Phys. Rev. 93, 38 ICRU Report 37. 1984. Stopping powers for electrons and positrons. Bethesda. Schrader, H., Walz, K.F., 1987. Standardization of 125I by photon–photon coincidence counting and efficiency extrapolation. Appl. Radiat. Isot. 38, 763. Zimmerman, B.E., Cessna, J.T., Unterwerger, M.P., 2002. The standardization of 188W/ 188Re by 4p liquid scintillation spectrometry with the CIEMAT/NIST 3H standard efficiency tracing method. Appl. Radiat. Isot. 56, 315.