Appl. Radiat. 1.w~ Vol. 39, No. 3. pp. 253-256. 1988 hf. J. Radiur. Appl. Instrum. Parr A Printed in Great Britain. All nghts reserved

0883-2X89/88 $3.00 + 0.00 Copyright c; 1988 Pergamon Journals Ltd

Optimum Geometry of Large Marinelli-Type

Vessels for In -situ Environmental Sample

Measurements with Ge(Li) Detectors

TAKASHI SUZUKI, YUKIO INOKOSHI, HARUO CHISAKA and TAKASHI NAKAMURA’

Tokyo Metropolitan Isotope Research Center, 2-l I-l Fukazawa. Setagaya-ku, Tokyo 158, Japan and ‘Cyclotron and Radioisotope Center, Tohoku University. Sendai 980, Japan

(Receiwd 26 May 1987; in revised jorm 13 July 1987)

Using the peak efficiencies calculated by the PEAK code for 8 and 18% Ge(Li) detectors, the optimum geometry of large Marinehi-type vessels (5-60 L), under which the peak efficiency has its maximum value, was obtained in the energy region from 365 to 1332 keV. The result showed that the optimum geometry holds when the sample thickness in the axial and radial directions are equal.

1. Introduction

Two methods are used to measure the, usually low, radioactivity concentration of environmental sam- ples. One is to measure a large volume sample directly and the other is to concentrate the large volume sample. The former method, without the need for complicated chemical treatment makes rapid quan- titative analysis possible and is suitable for in-situ

measurement. Using a 5 L comparatively large cylin- drical vessel, we measured the concentration of radio- activities in the waste water and the return sludge of waste water treatment plants without chemical treat- ment (Chisaka et al., 1982).

As a more efficient method for low-level radio-

activity measurement, the geometry surrounding a detector with the vessel filled with a sample was first suggested by Marinelli et al. (Hill et al., 1950) for Geiger-Miiller counters. This type of vessel is called a Marinelli beaker. It has since been applied to scintillation counters by Verheijke (1970). Further, optimum geometries of Marinelli beakers below 10 L capacity for Ge(Li) detectors were reported experi- mentally by Bonfanti and Dora (198 I).

Although the optimum geometry of the large vol- ume Marinelli-type vessel (5-100 L) having two vari- ables has already been obtained (Suzuki et al., 1984) by calculating the values of their peak efficiencies by the Monte Carlo code PEAK (Nakamura and Suzuki, 1983) in this paper, we considered the more ideal case in which the arm length of the Marinelli- type vessel is not restricted by attachments such as pre-amplifier or high voltage supply, and has three variables.

2. Definition of Optimum Geometry

The performance of a detector has often been compared by using the fi ure-of-merit (FOM) which

can be expressed as t 1 Jg B or E’/B, where c is the peak

efficiency and B is the background counts. To opti- mize the geometry of samples, Sugiyama et aI. (1976) modified the FOM derived mathematically by Cooper (1970), as follows:

FOM = t V/dm (1)

where V is the volume of the measuring vessel, B, is the natural background of the measuring system and B, is the Compton background of the nuclides other than the relevant nuclide in the sample. In the previous work (Suzuki et al., 1984) this FOM was applied to obtain the optimum volume and the optimum geometry of a Marinelli-type vessel having two variables Tand R (see Fig. I). Since we failed to obtain the optimum volume in our previous work, the optimum geometry of the Marinelli-type vessel was sought in more general cases where V = constant and R, T and Tw are the three variables. When the volume V is constant, B, is considered almost con- stant from the results of the measured background counts in each Marinelli-type vessel (Suzuki, 1987) and B, is ignored in the in-situ environmental sample measurement. Then equation (I) becomes

FOM 3~ c. (2)

As a result, the optimum values of the three variables R, T, TM? of the Marinelli-type vessel can be obtained at the maximum value of peak efficiency.

253

254 TAKASHI SUZUKI et al

3 3.46cm * \I

T A

GdLi); 0

SSD d TV

End- Cap 2

Fig. I. Calculational geometry of source and detector. r, source thickness; R. source radius; TJ~, arm length of Marinelli-type source; CI, distance between source surface

and detector center.

3. Calculational Geometry

Two true coaxial-type Ge(Li) detectors having 8 and 18% relative peak efficiencies and four Marinelli- type vessels with different volumes of 5, 10, 30 and 60 L were considered. Both detectors are encap- sulated in an end-cap 3.46 cm in radius. The calcu- lational geometry is shown in Fig. 1. In order to calculate the peak efficiency with high accuracy, it is necessary to know the sensitive zone of the Ge(Li) detector as accurately as possible. The shape of the sensitive zone was measured in the previous paper (Nakamura and Suzuki, 1983). The source was as- sumed to be a uniformly distributed aqueous y-ray source whose center was on the axis of the detector. The inner source surface was closely contacted with an end-cap. The peak efficiencies to the Marinelli- type sources were calculated with the FACOM M- 160F computer for 365, 661 and 1332 keV y rays at about 50,000 histories.

4. Results and Discussion

4.1. Relation between T and Tw

Under the condition that the parameters of the source volume v, the source radius R and the y-ray energy were fixed, the ratio between the distance from the detector center to the upper source surface and that to the bottom source surface. (T + a)/( Tw - (I), was varied, where N = 2.73 and 3.03 cm for 8 and 18% Ge(Li) detectors, respectively.

For 96 combinations (two detectors x three energies x four source volumes x four source radii) the peak efficiencies were calculated at various (r+u)/(Trr -u) values. The calculated peak efficiencies are shown as a function of the (T + u)/(Ttr - u) ratio in Fig. 2, as examples. With increases in the volumes of the Marinelli-type vessels. the calculated values of the peak efficiencies were scattered but fitted smoothly to a parabolic function by the least square method. On almost all of the 96

combinations, the optimum values of the (T + a)/(Tw - a) ratio at which the peak efficiency has the maximum value could be obtained. The results are shown in Table 1 for 8 and 18% Ge(Li) detectors. The optimum values of (T + u)/(TH, - (1) are almost independent of the y-ray energy and the volume, and the mean values are 1 .Ol and 1.06 for 8 and 18% Gc(Li) detectors, respectively.

4.2. Optimum c&es of R. T und Tw

As a next step, the optimum values of the source radius R were obtained for each of 24 combinations (two detectors x three energies x four volumes) by fitting the peak efficiencies as a function of R to a parabolic function. The optimum R values are almost constant independently of two detectors and three y-ray energies. The mean values of the optimum radii for four volumes of 5, IO, 30 and 60 L were 9.8. 12. I. 17.7 and 21.7 cm, respectively. Figure 3 shows the optimum radius as a function of volume. From this figure the optimum radius of any volume from 5 to 60 L can be estimated. The optimum values of the radius R and the (T + u)/(Tr~ - a) ratio lead to the optimum values of T and TLC for each volume.

4.3. Relution hetbt,een radial und u.Cal sizes

Using the optimum values of r, TL~’ and R obtained for four vessel volumes, the ratio of radial and axial distances from the detector center to the outer surface of the vessel, R/(7% - a) and (T + a)/R, were ob- tained for 8 and 18% Ge(Li) detectors and are shown in Table 1. The mean values of R/(Tw - u) for two detectors are about 1. I. which are greater than unity. The mean values of the (T + u)/R ratio for two detectors are 0.94, which are a little smaller than unity. Since the optimum (T + a)/(Tbr - u) value is a little larger than unity, the optimum values of R, (T + a) and (Trv - u) are in descending order. This may be explained by the fact that the optimum R and T values become larger because the sample cannot be set beneath the Ge(Li) detector. A slight difference in the optimum values of (T + u)/( TN, - n). R!(Tw - a) and (T + a)/R may come from the difference in the ‘a’ values for 8 and 18% Ge(Li) detectors. The ratios of the sample thickness in the axial direction to that in the radial one, T/(R - Rw), are also shown in Table 1; the mean values arc quite close to unity. This means that the directional de- pendence of these two detectors does not exist for the large Marinelli-type source, just as it does not for a point source, (Takata, 1987) and supports Ver- heijke’s supposition (Verheijke, 1970).

5. Conclusion

In the case of in-situ environmental sample mea- surement, the optimum geometries of Marinelli-type vessels of four capacities (5, IO, 30 and 60 L) for 8 and 18% coaxial-type Ge(Li) detectors were investigated using the PEAK Monte Carlo code. It was confirmed

Environmental sample measurement 255

5 L vessel

3.oL---- 0.5 1.0 2.0

(Tt2.73)/(G-2.73)

7C) 16 Ge (Li)

30 L vessel 0 661 keV o

2.5 - (b) 6% Ge iLi)

10 L vessel

1.5 I I I 0.5 1.0 2.0

(Tt 2.73) / ( T, - 2.73 1

(d) 16%Ge (Li)

60 L vessel

1332 keV 0.

3.5

Fig. 2. Variation of peak efficiency with the (T + u)/(Tw -u) ratio for four radii R in two detectors and some cases of y-ray energy. and the vessel volume V.

2(

E

”

z .- D Y

E 1c

; .- ‘a 0

C

/ .A**

/’ ,

10 20 30 40 50 60

Volume (L)

Fig. 3. Optimum radius of Marinelli-type vessels as a function of the sample volume.

256 TAKASHI SUZUKI et rrl.

Table I. Optimum values of (T+n):(7‘11 u), R’(Tw -II). (T+ OR and T’(R RN ) rat,os for X and IX". Ge(1.1)

detecrors m vessels of various capacities

(Tfa):(Tn,-o) R ‘(TM ~ 11) (T+ <r)‘R T(R -RN) Volume ~~~~~~

(L) 8% G?(LI) 18% Ge(L1) X% Ge(L1) IX%ck(LI) 8% Ck(LI) IX?,, ck(LI) 8",, Gc (1.1) IX"?, Ck(LI)

5 I .O3 I .Oh I.10 I ox 0.93 0.9X IO1 I 04

IO I .os 1.07 IO6 I I5 O.YY 0 93 I nx 0 05 30 0.9 I I .oo I I2 I I? 0 XI 0 YO 0 x2 I) YO

60 I .06 I IO I 0') I II 0 YX 0 YY I 111 I O?

MeaIl I.01 I06 I 00 I.12 O.Y3 0 Y5 0 YX 0 YX

that the distance from the detector center to the upper source surface and that to the bottom source surface are almost equal, and that the source thickness in the axial direction is almost equal to that in the radial direction. This means that the Marinelli-type vessel shaped as close as possible to the sphere and the optimum and the highest peak efficiency.

References Bonfanti G. and Dora G. D. (1981) Optimum counting

geometries of uniform and large Y-sources for Ge(Li) detectors. An experimental study. Radiochml. Radiomol. Left. 49, 215.

Chisaka H., Suzuki T., Inokoshi Y., Okano Y.. Horiguchi Y. and Yamamoto T. (1982) Radioactivities at a mega- lopolis waste water treatment plants. Hokm Bur.vuri 17,

521.

Cooper J. A. (1970) Factors determining the ultimate

detection sensitivity of Ge(Li) gamma-ra) spectromc1cr5. ,Yucl. Instrum. Meriwd~ 82, 273.

Hill R. F.. Hine G. J. and Marinelli L. D. (1950) The quantitative determination of gamma-ray radlatlon 111 biological research. An?. .I. Rook/., Rodiunl Thcrrrp). 63, 160.

Nakamura T. and Suzuki T. (19X3) Monte Carlo calculation of peak efficiencies of Ge(Li) and pure Ge detector:, IO voluminal sources and comparison with environmental radioactivity measurement, .Ytrc/. Im~rurm M~~t/wt/.~, 205. 21 I.

Sugiyama T.. Hirayama H., Hasebe N.. Kikuchl J. ,md Doke T. (1976) Optimization of the sample geometry In low level gamma-ray measurement. 0,~ Bururi 45, 632.

Suzuki T.. Inokoshi Y. and Chisaka H. (1984) Optimum geometry of a large Marinelli-type vessel and its applica- tion to environmental aqueous samples. Irfl. J. .I/)~I/. Radiut. Isor. 35, 1029.

Suzuki T. (1987) Unpublished data. Takata S. (1987) Private commumcation. Verheijke M. L. (1970) Calculated efficiencies of Nal(T-I)

scintillation crystals for Marlnelli beakerr uith aqueous sources. fnr. J. Appl. R&u/. f.vo/. 21, I I9