The ionization quench factor in liquid-scintillation counting standardizations

Applied Radiation and Isotopes PERGAMON

Applied Radiation and Isotopes 51 (1999) 183±188

The ionization quench factor in liquid-scintillation counting standardizations A. Grau Malonda *, A. Grau Carles Centro de Investigaciones EnergeÂticas Medioambientales y TecnoloÂgicas, Av. Complutense 22, 28040 Madrid, Spain Received 15 June 1998; received in revised form 21 September 1998; accepted 24 September 1998

Abstract We present a new detailed analysis of the ionization quench function Q(E) used in calculating the counting eciency in liquid-scintillation counting (LSC), which shows that Q(0) = 1, and permits one to derive Q(E) as a function of the electron energy and the parameter kB. The coecients are tabulated by applying a new empirical formula of Q(E) for kB values in the range between 0.001 and 0.20 gMeVÿ1 cmÿ2. We demonstrate the convenience of applying 3 H and 54 Mn for b-ray and electron capture standardizations, respectively. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction The results of the last EUROMET comparison of Fe activity, under the coordination of Laboratoire Primaire des Rayonnements Ionisants (France), showed important discrepancies among the computed activity concentrations provided by the 10 participant laboratories. In the data evaluation analysis, carried out by Cassette (1997), he pointed out a correlation between the applied scintillators and the obtained activities. The liquid scintillation measurements of 55 Fe gave lower activities when 55 Mn was used as a tracer. The general feeling among the participants was that the main reason for such discrepancies was uncertainly in a correction factor for the ionization quenching process. In this paper a new analysis of the ionization quench function Q(E) is proposed. The computation procedures applied up to now assume a zero value for the quench function when E = 0. This contradicts the experimental evidence. To compute the ionization quench function we apply the Birks' formula, the integration range is divided in subintervals, and the stopping power is approximated to a polynomial equation. In 55

* Corresponding author.

such a way, Q(E) is evaluated in an analytical form, and the function Q(E) is expressed in terms of the parameter kB. The empirical equation of Q(E) is expressed as a quotient of polynomial equations, which are ®tted for kB values between 0.001 and 0.020 gMeVÿ1 cmÿ2 in steps of 0.001. We consider of great interest to analyze the in¯uence of the tracer on the accuracy of the counting eciency computation, and to compare the experimental and the computed counting eciencies for extreme values of kB, e.g. kB = 0 and 0.020 gMeVÿ1cmÿ2. We observe that tritium is a good tracer for b-ray nuclides, while 54 Mn is better suited for electron capture nuclides when the atomic number is close to that of iron. The conclusions we derive for the CIEMAT/NIST method (Grau Malonda and Garcõ aToranÄo, 1982; Coursey et al., 1986) are also valid for TDCR three phototube liquid scintillation systems (Broda et al., 1988; Pochwalski et al., 1988; Grau Malonda and Coursey, 1988; Grau Carles and Grau Malonda, 1989). At the end of the paper, we illustrate the consequences of an extended inadequate application of the ionization quench function Q(E) to the CIEMAT/NIST method, which consists on taking a di€erent Q(E) function for the tracer and the for the radionuclide to be standardized.

0969-8043/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 9 8 ) 0 0 1 7 9 - 1

184

A. Grau Malonda, A. Grau Carles / Applied Radiation and Isotopes 51 (1999) 183±188

2. Computation of the ionization quench factor The ionization quench factor is usually computed in terms of the semiempirical formula of Birks (1964) Q…E † ˆ

1 E

…E 0

dE , 1 ‡ kB dE=dx

…1†

where dE/dx is the stopping power of the liquid scintillator for one electron of energy E and kB is a parameter independent of the electron energy. To calculate the integral in Eq. (1), the stopping power function must be well-known for low-energy electrons. Among the expressions available in the literature we should mention those reported by GarcõÂ a-ToranÄo and Grau Malonda (1981), Los Arcos et al. (1987) and Los Arcos and Ortiz (1997). All these equations assume Q(0) = 0, and consequently suppose an in®nite stopping power for vanishing electron energies. However, since experimentally the stopping power decreases with energy for energies below 60 eV, we are forced to assume a zero stopping power for E = 0. The experimental data of Cole (1969) include stopping power values in the low energy region. He studied the absorption for 20±50 keV monoenergetic electrons in air and plastic, and a maximum point between 60 and 100 eV is clearly observed. In this paper the stopping power, expressed in MeVcm2 gÿ1 units, is calculated for toluene (Table 1). For energies above 1 keV, the stopping power values are available in the ICRU 37 data tables (ICRU 37, 1984). These tables were computed from the Bethe formula by Berger and Seltzer (1983) and afterwards recalculated by Peron (1995). For electron energies Table 1 Energies stopping powers for toluene Energy (keV) 4000 2000 1000 800 600 400 200 100 70 50 40 30 20 15 10

Stopping power (MeVcm2 gÿ2)

Energy (keV)

1.898 1.823 1.840 1.876 1.956 2.149 2.797 4.127 5.228 6.637 7.823 9.722 13.29 16.64 22.86

8.0 6.0 5.0 4.0 3.0 2.0 1.0 0.6 0.4 0.2 0.1 0.06 0.04 0.02 0.0

between 20 eV and 1 keV, we adopt the experimental values of Cole (1969), corrected by a factor of 1.179, normalized at 1 keV, to achieve the toluene values from collodion. Between 0 and 20 eV a linear variation of the stopping power is assumed. The maximum point of the stopping power curve reveals a minimum point for the ionization quench function Q(E) when the electron energy vanishes, i.e. we have Q(0) = 1. The di€erent behavior of the stopping power in the energy interval between 0 and 4000 keV requires one to divide Eq. (1) into di€erent subintervals: (0, 0.1), (0.1, 1), (1, 10) and (10, 4000). This permits one, for each selected subinterval, to ®t the stopping power curve to a function of computable inde®nite integral. For energies into the interval 0 R E < 4000 keV, the ionization quench function is 1 …I1 ‡ I2 ‡ I3 ‡ I4 †, E

Q…E † ˆ

where … 0:1 I1 ˆ F…E 0 †dE 0 , 0

I2 ˆ

I3 ˆ

I4 ˆ

…1

…4†

F…E 0 †dE 0 ,

…5†

F…E 0 †dE 0 ,

…6†

1 : 1 ‡ kB dE=dx

…7†

… 10 1

10

…3†

F…E 0 †dE 0 ,

0:1

…E

…2†

and Stopping power (MeVcm2 gÿ2) 27.2 34.0 39.1 46.4 57.6 77.4 125 171 200 271 307 200 165 130 0

F…E † ˆ

The limit of integration E in Eq. (6) determines the last integration subinterval and the number of integrals Ii to be taken. For instance, if E is within the energy interval between 1 and 10 keV, we should write Q(E) as follows: Q…E † ˆ

1 …I1 ‡ I2 ‡ I3 †, E

…8†

where the integrals I1 and I2 were de®ned above, while I3 is now given by …E I3 ˆ F…E 0 †dE 0 : …9† 1

We can ®t the stopping power into the integral I1 to the linear function

A. Grau Malonda, A. Grau Carles / Applied Radiation and Isotopes 51 (1999) 183±188 Table 2 Coecients a, b and c of the stopping power equation dE/ dx = a + b/E + c/E 2 Energy range (keV)

a

10RE < 4,000 1RE < 10 0.1RE < 1

1.66688 8.03871 67.3517

b

dE 1 ‡ kB…a ‡ b=E ‡ c=E 2 †  1 E b ˆ ÿ ln…aE 2 ‡ bE ‡ c† kB a 2a

F…E, a, b, c† ˆ

c

b2 ÿ 2ac p 2a2 b2 ÿ 4ac p  2aE ‡ b ÿ b2 ÿ 4ac p ,  ln 2aE ‡ b ‡ b2 ÿ 4ac ‡

253.991 161.846 60.6538

ÿ423.253 ÿ45.2347 ÿ3.68220

…10†

Hence for the ®rst subinterval (E1<0.1 keV) we have … E1 0

…13†

where

dE ˆ a0 E: dx

I1 …E1 † ˆ

185

…

dE 1 ˆ ln…1 ‡ a0 kBE1 †: 1 ‡ a0 kBE a0 kB

…11†

The stopping power for the rest of integration subintervals can be ®tted to the following equation: dE b c ˆa‡ ‡ 2: dx E E

…12†

By inserting Eq. (12) into Eq. (1) we have for the inde®nite integral

aˆa‡

1 : kB

…14†

Therefore, the solutions of the integrals I2, I3, and I4 are the following: I2 …E2 † ˆ F…E2 , a, b2 , c2 † ÿ F…0:1, a, b2 , c2 †,

…15†

I3 …E3 † ˆ F…E3 , a, b3 , c3 † ÿ F…1, a, b3 , c3 †,

…16†

I4 …E4 † ˆ F…E4 , a, b4 , c4 † ÿ F…10, a, b4 , c4 †:

…17†

The coecients a, b and c listed in Table 2 may be applied to compute the ionization quench function Q(E), which is expressed as follows for the four subintervals:

Table 3 Coecients Ai for di€erent kB values when the ionization Q(E) = (A1+A2 ln E + A3(ln E)2+A4(ln E)3)/(1 + A5ln E + A6(ln E)2+A4(ln E)3)

quench

function

is

®tted

to

kB

A1

A2

A3

A4 (10ÿ3)

A5

A6

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.020

0.84859 0.73916 0.65585 0.58917 0.53551 0.49041 0.45355 0.42149 0.39439 0.36851 0.34793 0.32903 0.31231 0.29668 0.28281 0.27020 0.25863 0.24808 0.23832 0.22933

0.38579 0.33815 0.30430 0.26473 0.23970 0.21600 0.20231 0.18731 0.17372 0.16398 0.15193 0.14404 0.13664 0.12872 0.12259 0.11663 0.11133 0.10646 0.10192 0.09784

0.15528 0.14114 0.13198 0.12173 0.11401 0.10725 0.10137 0.09624 0.09129 0.08816 0.08427 0.08059 0.07744 0.07477 0.07235 0.06985 0.06764 0.06576 0.06363 0.06184

ÿ5.91812 ÿ4.12402 ÿ4.75264 ÿ2.54649 ÿ1.95557 ÿ1.46804 ÿ0.79200 ÿ0.52346 ÿ0.57124 ÿ0.45562 ÿ0.05526 ÿ0.04536 ÿ0.04306 0.15992 0.30371 0.34938 0.41188 0.46844 0.51606 0.56027

0.38996 0.34586 0.31382 0.27388 0.24956 0.22468 0.21445 0.19977 0.18524 0.17582 0.16443 0.15623 0.14961 0.14091 0.13539 0.12933 0.12414 0.11938 0.11493 0.11096

0.15143 0.13451 0.12344 0.11198 0.10317 0.09544 0.08880 0.08311 0.07784 0.07431 0.07002 0.06611 0.06284 0.05978 0.05725 0.05453 0.05218 0.04998 0.04793 0.04604

186

A. Grau Malonda, A. Grau Carles / Applied Radiation and Isotopes 51 (1999) 183±188 Table 4 Computed counting eciencies for

14

C, when kB = 0 and 0.020 gMeVÿ1 cmÿ2. The tracer is 3 H

e (3 H) exp

e (14 C) exp

e (14 C) comp (kB = 0)

Disc. (%)

e (14 C) comp (kB = 0.020)

Disc. (%)

0.4431 0.4216 0.3960 0.3604 0.3107 0.2796 0.2408 0.1954

0.9330 0.9293 0.9241 0.9159 0.9017 0.8907 0.8765 0.8532

0.9275 0.9228 0.9167 0.9072 0.8911 0.8790 0.8631 0.8347

ÿ0.6 ÿ0.7 ÿ0.8 ÿ0.9 ÿ1.2 ÿ1.3 ÿ1.5 ÿ2.2

0.9343 0.9305 0.9259 0.9191 0.9059 0.8971 0.8837 0.8640

0.1 0.1 0.2 0.4 0.5 0.7 0.8 1.3

Q…E1 † ˆ

1 I1 …E1 † E1

0RE1 <0:1 keV,

Q…E2 † ˆ

1 ‰I1 …0:1† ‡ I2 …E2 †Š E2

Q…E3 † ˆ

1 ‰I1 …0:1† ‡ I2 …1† ‡ I3 …E3 †Š E3

3. Experimental

0:1RE2 <1 keV, …18†

1RE3 <10 keV, Q…E4 † ˆ

1 ‰I1 …0:1† ‡ I2 …1† ‡ I3 …10† ‡ I4 …E4 †Š E4

10RE4 <4000 keV: A code was applied to compute the ionization quench for kB values in the range between 0.001 and 0.02 gMeVÿ1 cmÿ2 with steps of 0.001. The energy interval was from 0 to 4 MeV. The Q(E) function was ®tted to the equation Q…E † ˆ

A1 ‡ A2 ln E ‡ A3 …ln E †2 ‡ A4 …ln E †3 , 1 ‡ A5 ln E ‡ A6 …ln E †2 ‡ A4 …ln E †3

…19†

in which the coecients Ai are shown in Table 3 for di€erent kB values. Table 5 Computed counting eciencies for

55

All liquid scintillation measurements were carried out in a Canberra Packard scintillation spectrometer, model 2500 TR, which uses a 133 Ba external g-ray source for quench monitoring. The quench parameter is tSIE (transformed spectral index of the external standard). All samples were prepared by dispensing 15 mL of Insta Gel Plus (Packard Instruments) into low potassium content standard glass vials. Four sets of eight vials of the radioactive substances: 3 H2O, 14 C in n-hexadecane, 54 Mn in 1 M HCl and 55 FeCl dissolved in 1 M HCl; were prepared by adding gravimetrically amounts between 50 and 150 mg into the vials containing the scintillator. The samples were monitored for two weeks in order to detect possible instabilities. None were observed. Afterwards, increasing amounts of nithromethane were added to the scintillators to achieve the required level of quench.

4. Results and discussion The best kB value must be derived from experimental data (Grau Malonda and Coursey, 1987). For bray emitters, the counting eciency is obtained by

Fe, when kB = 0 and 0.020 gMeVÿ1 cmÿ2. The tracer is

54

Mn

e (54 Mn) exp

e (55 Fe) exp

e (55 Fe) comp (kB = 0)

Disc. (%)

e (55 Fe) comp (kB = 0.020)

Disc. (%)

0.4703 0.4448 0.4206 0.3795 0.3450 0.2918 0.2101 0.1864

0.4697 0.4414 0.4142 0.3676 0.3274 0.2643 0.1657 0.1369

0.4591 0.4306 0.4035 0.3577 0.3188 0.2568 0.1605 0.1309

ÿ2.3 ÿ2.4 ÿ2.6 ÿ2.7 ÿ2.6 ÿ2.8 ÿ3.1 ÿ4.4

0.4750 0.4467 0.4194 0.3723 0.3333 0.2688 0.1684 0.1385

1.1 1.2 1.3 1.3 1.8 1.7 1.6 1.2

A. Grau Malonda, A. Grau Carles / Applied Radiation and Isotopes 51 (1999) 183±188 Table 6 Computed counting eciencies for

55

187

Fe, when kB = 0 and 0.020 gMeVÿ1 cmÿ2. The tracer is 3 H

e (3 H) exp

e (55 Fe) exp

e (5 Fe) comp (kB = 0)

Disc. (%)

e (55 Fe) comp (kB = 0.020)

Disc. (%)

0.4789 0.4571 0.3811 0.3296 0.2986 0.2764 0.2467 0.2055

0.5055 0.4751 0.3730 0.3083 0.2706 0.2456 0.2128 0.1695

0.5346 0.5106 0.4119 0.3479 0.3100 0.2833 0.2487 0.2027

5.8 7.4 10.4 12.8 14.6 15.4 16.9 19.6

0.4933 0.4612 0.3629 0.2990 0.2516 0.2264 0.1942 0.1528

ÿ2.4 ÿ2.9 ÿ2.7 ÿ3.0 ÿ7.0 ÿ7.8 ÿ8.7 ÿ9.9

Table 7 Computed counting eciencies for 55 Fe, when di€erent kB values of 0 and 0.020 gMeVÿ1 cm are used for 3 H and 55 Fe, respectively e (3 H) exp.

e (55 Fe) exp.

e (55 Fe) comp.

Discrepancy (%)

0.4789 0.4571 0.3811 0.3296 0.2986 0.2764 0.2467 0.2055

0.5055 0.4751 0.3730 0.3083 0.2706 0.2456 0.2128 0.1695

0.1797 0.1649 0.1196 0.0936 0.0797 0.0709 0.0599 0.0460

ÿ65 ÿ65 ÿ68 ÿ70 ÿ71 ÿ71 ÿ72 ÿ73

applying 3 H as a tracer. Table 4 shows the experimental and computed counting eciency for 14 C for extreme kB values of 0 and 0.02 gMeVÿ1 cmÿ2. The relative discrepancies between the computed and the experimental eciencies were slight in all cases, and become worse for lower eciency values (the maximum discrepancy is 2% when the counting eciency for 3 H is 20%). Therefore, the in¯uence of the kB value on the counting eciency is barely detectable. This explains how values of kB of 0.007 and 0.009 gMeVÿ1 cmÿ2 can give similar results. In a previous article (Grau Malonda and Garcõ aToranÄo, 1982) proved that 3 H is the most adequate bray tracer for the application of CIEMAT/NIST method, because the uncertainties on 3 H activity are slightly transmitted to the majority of b-ray nuclides. In addition, 3 H has an acceptable long half-life, commercial standardized solutions are easily available and evaporation does not ruin the standards. However, if the radionuclide to be standardized decays by electron capture, we should take 54 Mn as the reference nuclide. This radionuclide can be standardized with great accuracy by direct coincidence measurements. Table 5 shows the results when we apply 54 Mn to standardize 55 Fe. In this case the discrepancies between computed

and experimental counting eciencies are comparable to those obtained for 3 H for b-ray emitters. In Table 6 the experimental counting eciencies for 3 H and 55 Fe are listed for the same tSIE value. The discrepancies depend in this case very much on the kB value. For the unquenched samples, the uncertainty on the counting eciency for 3 H is multiplied by a factor 1.5 for 55 Fe, but this factor increases appreciably with chemical quench. An additional problem is the relatively large discrepancies in 3 H activity when we compare standards from di€erent laboratories. It should be remarked that both the Q(E) formula and the kB value must be the same for the tracer and the radionuclide. Table 7 shows the results when this condition is not ful®lled. In this example, we apply the same expressions of Q(E), but the kB value is modi®ed (0.020 and 0 gMeVÿ1 cmÿ2 for 3 H and 55 Fe, respectively). The obtained discrepancies are quite impressive.

5. Conclusions A new procedure to compute the ionization quenching function as a function of E and kB is presented, which applies a polynomial equation for the stopping

188

A. Grau Malonda, A. Grau Carles / Applied Radiation and Isotopes 51 (1999) 183±188

power. This permits the analytical integration of the Birks formula, and additionally to demonstrate that Q(0) must be 1. Also we prove the feasibility of 3 H when b-ray nuclides are calibrated, with a maximum discrepancy of 2% between extreme kB values. For electron capture nuclides such as 55 Fe the use of 54 Mn as a tracer gives a 5% discrepancy for extreme kB values, while 3 H generates a variation of the counting eciency of nearly 20%. This fact supports the necessity of carrying out intercomparisons of 3 H and 55 Mn to make available more reliable standards of these radionuclides. Finally, we insist that the Q(E) expression and the kB value must be the same for both the tracer and the radionuclide. One of the largest discrepancies observed into the last 55 Fe intercomparison was generated by the application of di€erent Q(E) expressions for 3 H and 55 Fe. References Berger, M.J., Seltzer, S.M., 1983. Stopping Powers and Ranges of Electrons and Positrons. NBSIR 82-2550-A. Birks, J.B., 1964. The Theory and Practice of Scintillation Counting. Pergamon Press, Oxford, p. 187. Broda, R., Pochwalski, K., Rodozewski, T., 1988. Calculation of liquid-scintillation detector eciency. Appl. Radiat. Isot. 39, 159. Cassette, P., 1997. Comparison of activity measurement of 63 Ni and 55 Fe in the framework of the EUROMET 297 project. Conference on Radionuclide Metrology and its applications. ICRM'97, Gaithersburg, MD. Cole, A., 1969. Absorption of 20 to 50,000 eV electron beams in air and plastic. Rad. Res. 38, 7.

Coursey, B.M., Mann, W.B., Grau Malonda, A., Garcõ aToranÄo, E., Los Arcos, J.M., Gibson, J.A.B., Reher, B., 1986 Appl. Radiat. Isot. 37, 403. ICRU 37, 1984. Stopping Powers for Electrons and Positrons, p. 43. Garcõ a-ToranÄo, E., Grau Malonda, A., 1981. EFFY, a program to calculate the counting eciency of beta-particles in liquid scintillation. Comp. Phys. Commun. 23, 385. Grau Malonda, A., Coursey, B.M., 1987. Standardization of isomeric-transition radionuclides by liquid scintillation eciency tracing with hydrogen-3: application to technetium99m. Appl. Radiat. Isot. 38, 695. Grau Malonda, A., Coursey, B.M., 1988. Calculation of bparticle counting eciency for liquid-scintillation systems with three photobubes. Appl. Radiat. Isot. 39, 1191. Grau Carles, A., Grau Malonda, A., 1989. Electron-capture standardization with triple phototube system. Anales de Fisica B85, 160. Grau Malonda, A., Garcia-ToranÄo, E., 1982. Evaluation of counting eciency in liquid scintillation counting of pure bray emitters. Appl. Radiat. Isot. 33, 249. Los Arcos, J.M., Grau Malonda, A., Fernandez, A., 1987. VIASKL: a computer program to evaluate the liquid scintillation counting eciency and its associated uncertainty for K±L-atomic shell electrocapture nuclides. Comp. Phys. Commun. 44, 209. Los Arcos, J.M., Ortiz, F., 1997. KB: a code to determine the ionization quenching function Q(E) as a function of the kB parameter. Comp. Phys. Commun. 103, 83. Peron, M.N., 1995. Etude de la reÂponse lumineuse des scintellateours liquids a des eÂlectrons monoeÂnergetiques de basse eÂnergie. Ph.D thesis, Paris-Sud University. Pochwalski, K., Broda, R., Rodozewski, T., 1988. Standardization of pure beta-emitters by liquid-scintillation counting. Appl. Radiat. Isot. 39, 165.