Radionuclide standardization by Cherenkov counting

Pergamon

0969-8043(%)ooo19-4

Appl. Radial. Isor. Vol. 46. No. 6. pp. 799-803, 1995 Copyright Q 1995 ElscvierScience Ltd

Printed in Greet Britain. All rights reserved 0969-8043/95 39.50 + 0.00

Radionuclide Standardization Cherenkov Counting

bY

A. GRAU CARLES and A. GRAU MALONDA Instituto de Investigacibn Basica, CIEMAT, Avda Complutense 22, E-28040 Madrid, Spain (Received

I2 December

1994; in revised from

18 January 1995)

We present a new method for the standardization of pure /? and B-r nuchdes based on Cherenkov counting. This method uses standards of %3 and 32P for obtaining a general curve that relates the detection probability to the kinetic energy of the electron. The test of the method shows an excellent agreement with experiment for *04T1,‘?3r. %r + 9oY,@Co and “‘Cs. We also analyze the influence of the B-spectrum shapefactors on the results.

1. Introduction

We can find in the literature several expressions to compute the Cherenkov counting efficiency. HowCherenkov radiation may be employed for the ever, the results frequently show important disefficient measurement of radioactivity as was first crepancies between predictions and experiment demonstrated by Belcher (1953). Cherenkov radiwhich have not conveniently been explained. In that ation is independent of the liquid scintillation prosense, the discrepancies for J6C1and 204Tlare always cess. However a conventional liquid scintillation remarkable. Experiment shows that counting counter can be used as a Cherenkov light detector to efficiency for “Cl is 70% greater than counting count high energy /?-ray nuclides in water or other efficiency for %Tl. This result is quite surprising transparent liquids without the use of scintillators. because 2vl maximum b-ray energy (763 keV) is Since counting efficiency is always higher for greater than that of ‘6Cl (710 keV). liquid scintillation than for Cherenkov light, liquid An explanation for the very different behavior scintillation counting is commonly preferred for of ?ZI and 20LTlrequires us to introduce two new p-ray nuclide standardizations. However, Cherenkov concepts: the intrinsic Cherenkov counting efficiency counting can be advantageous in the calibration of and the Cherenkov yield. The intrinsic Cherenkov certain nuclides in which the detection of low-energy counting efficiency is defined as the ratio between electrons complicates considerably the elaboration counted particles and emitted particles over the of the standardization model. The idea is to use the Cherenkov threshold as a discriminator for Iow- Cherenkov threshold, while the Cherenkov yield expresses the ratio between emitted particles over energy electrons. For instance, the genetic mixture the Cherenkov threshold and total number of emitted 234Th+ 234mPahas a complex decay scheme in which particles. We will show in this paper that although many p particles and conversion electrons are emitted the intrinsic Cherenkov counting efficiency is quite with energies below the Cherenkov threshold of water similar for 36CIand 2wTl (IO%), the Cherenkov yield (263 keV). Only the two p-branches of 234mPawith differs significantly for these nuclides (40% for 204TI maximum-energies 2.3 and 1.5 MeV can be detected and 65% for 36C1). with appreciable efficiency. We will emphasize the importance of the shapeThe available Cherenkov counting standardization factor in the computation of the counting efficiency. techniques require the use of a standardization solThe large sensitivity of the Cherenkov counting ution to obtain the counting efficiency. Therefore, efficiency to any variation of the /?-ray distribution, they are only valid for a given nuclide. In this work especially for maximum p-ray energies less than we present a new method, which only requires the prior calibration with two standards, i.e. ‘6Cl and 32P, 700 keV, permits one to confirm shapefactors for forbidden transitions. Sadler and Behrens (1993) to determine the counting efficiency of any radionuclide with electron emission over the Cherenkov demonstrated that the so-called two-parameter threshold. These two radionuclides permit one to equation, which is often applied to second noncharacterize the detection system and Cherenkov unique forbidden transitions, was not correct in light anisotropy. general. The particular case of 36C1requires a more 799

A. Grau Carles and A. Grau Malonda

800

complicated expression which we can verify by analyzing the Cherenkov light emission. Also we will see that shapefactors of other radionuclides can be improved by this technique.

2. Description of the Method As we mentioned above, an adequate analysis of the counting efficiency for Cherenkov light emitters requires one to relate the counting efficiency with the ratio of fl-particles emitted over the Cherenkov threshold. The idea is to separate counting efficiency into two terms. On the one hand, the intrinsic Cherenkov counting efficiency ck, i.e. the ratio between counted pulses and emitted particles over the Cherenkov threshold; and the Cherenkov yield rk, i.e. the ratio of /l-spectrum of the Cherenkov threshold, on the other. These two new parameters will be used throughout this work. From above, the counting efficiency is expressed as follows: .5c= r,c,.

(1)

The Cherenkov yield rk is obtained directly from the g-ray distribution by: wnl

N(W)dW rk = I Wk (2) W, N(W)dW’ II where W, and W, are the maximum B-ray energy and

the Cherenkov threshold energies, respectively, and N(W) is the /l-ray distribution. The achievement of the intrinsic Cherenkov efficiency requires counting pulses. However, the expression: ck =

W0ll N(Wzf(W) dW, s WA

(3)

permits one to relate the number of counted pulses with the detection probability f( W). We assume that the response of the spectrometer to monoenergetic radiation is unique for electrons with kinetic energies over the Cherenkov threshold. Therefore, the detection of high-energy electrons by Cherenkov light only depends on the measurement conditions we established. Equation (3) permits one to achieve immediately the counting efficiency of any /I-emitter [with known N(W)] over the Cherenkov threshold by only knowing the function off(W). A rapid view of the function f( W) shows that it is zero for energies below W, and unity for electrons which have sufficient energy for total detection (the detection probability is nearly I for electrons over 1 MeV in water). In the intermediate region, detection probability augments exponentially. The functionf( W) can be fitted with good accuracy to the expressions: f(W)=a(Wf(W)=

w,)n,

w,<

1,

w > w,,

w<

w,, (4)

where W, is the minimum energy that corresponds to total detection. a and n are both parameters to be determined by least square fitting. If all electrons are partially detected W,,, < W,, the minimum condition is: Y W, N,(W)(W - W,)ldW ‘, (5) min C tk, -a i-l [ s Wk

1

where v is the total number of radionuclides involved in the fitting. However, if W, > W, the minimum condition is: Y W” min C tk, - a N,(W)(W - W,)“dW i-l [ s Wh

-

I

W,

W”

N,(W)dW

2 1 .

(6)

Thus we can use both conditions to iterate the parameter n, and obtain a and W, by least square fitting. Since @‘Coand 13’Cs both present y-ray emission over the Cherenkov threshold, the contribution of photoelectric and Compton electrons must be evaluated. For these nuclides we simulate by Monte-Carlo techniques the interaction of y-rays to achieve the Compton spectrum. Finally, we apply conditions (5) and (6) to determine the y-ray contribution to the counting efficiency for @Co and “‘Cs. The detection probability function f( W) is also valid for Compton electrons. The contribution of the B-ray emission to the counting efficiency for @‘Cois negligible. The maximum /?-ray energy (317.9 keV) is slightly over the Cherenkov threshold. Therefore, the double y-ray emission of @‘Co is the only contribution to Cherenkov light. We assume for @Co that: 6 =~(r,)+E(YI)-~(Y,)E(Y2),

(7)

where 6 ( y, ) and F.( y2) are the counting efficiencies for the Compton electrons generated by each one of the two y-rays. The product of both efficiencies considers the simultaneous Compton interaction of the two y-rays. The situation is more complicated for 13’Cs.Besides the two b-branches over the Cherenkov threshold, we have a 662 keV y-ray transition from ‘37mBawhich is 10% converted.

3. Experimental We carried out all measurements in a LKB 1219 Rack Beta counter. The radioactive solutions for the nuclides 36Cl, 2?‘l, 32P,*9Sr,‘?Sr + 9, @‘Coand ‘)‘Cs were all prepared in 1 M HCI with adequate amounts of carrier to avoid adsorption in vial walls. Since the counting efficiency for 36Cl, 204Tl, ‘Yo and 13’Cs in 1 M HCI is less than lo%, the activity of the samples must be high. An activity greater than 5 kBq for each sample is recommended to obtain good statistics. We prepared four samples for each nuclide by dispensing

Radionuclide standardization

15 mL of the radioactive solution into glass vials, Cherenkov background was subtracted from the average counting rate. A crude estimation for the Cherenkov background for 15 mL of 1 M HCI indicates counting rates about l/2 of the liquid scintillation background for unquenched samples. The computation of the counting efficiency for 6oCo and 13’Csrequires some more empirical work because y-radiation produces extra Cherenkov light into vial walls and other glass components of the detection system. We covered with reflectant paint the internal and external surface of the vial walls to determine this extra Cherenkov counting rate. The experiment was repeated afterwards using black paint with similar results.

by Cherenkov counting Table

Efficiency Nuclide

2. Cherenkov

yield

shapefactors

r*,

exp.

camp.

“Cl

0.0666

0.0666

‘VI

0.0402

0.0404

“?Yr

0.374

0.377

0.9

‘2P

0.468

0.468

0.0

WSr+WY

0.620

0.63

I

1.8

*co

0.0561

0.0556

0.7

‘)‘CS

0.0493

0.0475

3.7

Cherenkov

Discrepancies

Discrepancy 0.0 0.6

function f(W)

1.5004 < W < 2.9662, W 2 2.9662,

which is valid for any other nuclide over the Cherenkov threshold in 15 mL of 1 M HCI. The use of 1 M HCl instead of water reduces the Cherenkov threshold from 263 to 255.7 keV. The consequence is an enhancement of the counting efficiency respect with water. Table 1 shows that the discrepancies for counting

are relative

efficiency

6) and counting

to the shapefactor

which

efficiency

c, for

agrees the best with

experiment Shapefactor

q2 + q2+ q2 + q*+

Q

6,

Ar,

I .67p2

0.5945

0.0971

0.0566

- 10.7

-4.7

-15.0

I

1.75p2

0.5995

0.0974

0.0573

- 10.0

-4.4

- 14.0

2

-3.4

-

10.4

3

-4.6

- 14.9

4

0.0

5

efficiency

L, for

lp2

1.68$

0.6187

0.0984

0.0597

0.5951

0.0972

0.0567

0.6661

0.1019

0.0666

C(W) I.

Feldmann

2. Johnson 3. Willett 4.

and

5. Sadler

Wu

-7.1 -

10.7 0.0

A&

0.0

(1952).

el al. (1956). and

Reich

Table

and

AC,

Ref.

‘k

2.1

Spcjewski

(1967).

Schiipferling

and

Behrens

3. Cherenkov

(1974).

(1993).

yield

rli, intrinsic

Cherenkov

counting

different

shapefactors

efficiency

cL and counting

of *@?I

Shapefactor l.161q’+l,p2

0.4334

0. I020

0.043 I

4.4

2.1

7.2

I

1.097qz + I,p’ 1.45q*+p* I.792 +p’ q2+&p2

0.4264

0.1012

0.042 1

2.7

1.3

4.7

2

0.43 I6

0.1012

0.0426

0.4109

0.0988

0.0396

0.4150

0.0999

0.0404

1. Park

and Christmas

2. Flothmann 3. Sastry 4. Grau

Table

4.0 -1.0 0.0

Caries

4

0.6

5

(1995).

yield

rk, intrinsic

Cherenkov

counting

shapefactors

efficiency

r, 0.7876

0.4664

0.3674

q2+p2

0.7965

0.4737

0.3773

0.0

I -0.Ol12W

0.7986

0.4282

0.3420

2.6

I - 0.022 w

0.7967

0.4261

0.3394

0.7903

0.4193

0.3314

Konopinski

(1966).

and Tabert

3. Nagarajan

(1970).

et al. (1971).

er al. (1964).

efficiency

c, for

Ref.

Ar,

I-

0.054 w

c1 and counting

of s9Sr

Shaoefactor

Daniel

3

I.5

(1966).

cl2+ &P2

4.

0.0

5.9

(1967).

different

I

-

et al. (1969).

4. Cherenkov

2. Wohn

1.3 -1.1

(1972).

5. Konopinski

(%)

f(W) = 0.5424( W - 1.5004)‘.60,

f(W) = 1,

intrinsic

of ‘6CI.

efficiencies

Efficiency

and 32P gives a detection probability for our spectrometer:

The experimental and computed counting efficiencies for 36C1,‘“Tl, “P, 89Sr, 90Sr+ 9oY, @‘Coand 13’Cs are compared in Table 1. Since we used the standards 36C1and 32Pto achieve the parameters a, W, and n of equation (4), the discrepancies for these nuclides are zero. The application of expressions (l-6) for “Cl

different

Experimental and computed counting

I.

4. Results and Discussion

Table

801

-1.1

0.0 -0.8

-

I.5

-1.8

0.0

0.9

-9.6

-8.6

- 10.0 -11.5

-9.2 -

I

I .4

I I 2 3 4

A. Grau Caries and A. Grau Malonda

802

Table 5. Cherenkov yield r,, intrinsic Cherenkov counting etliciency ci and counting etIiciency L, for different shamfactors of q Shapefactor

q2+ 0.91p2 q2+p2

I + 0.025/W 1 - 0.0047 w I +0.26/W I - 0.0072W I -0.0064w I - 0.0050w I - 0.0010w 1-0.0114w I. 2. 3. 4. 5. 6. 7. 8. 9. IO.

c,(“Sr + 9oy)

fk 0.6935 0.7026 0.6926 0.6922 0.6842 0.6915 0.6917 0.6921 0.6933 0.6903

rlr 0.8910 0.8955 0.9088 0.9090 0.9015 0.9087 0.9088 0.9090 0.9095 0.9080

A% - 1.2 -0.7 0.8 0.8 0.0 0.8 0.8 0.8 0.9 0.7

0.6321 0.6434 0.6436 0.6434 0.6310 0.6425 0.6428 0.6433 0.6447 0.6410

hfh I .4 2.7 1.2 I .2 0.0 I.1 I.1 1.2 1.3 0.9

Ref.

& 2.0 3.8 3.8 3.8 1.8 3.6 3.7 3.8 4.0 3.4

1

2 3 4 5 6 7 8 9 IO

Sunier and Berthier (1969) Konopinski (1966). Yuasa et al. (1957). Nichols et cl. (1961). AndrC and Depommier (1964). Daniel t-r al. (1964). Riehs (1966). Agarwal ef al. (1969). Nagarajan er al. (1971). Flothmann er al. (1975).

all the nuclides are less than 2%, except for 13’Cs, which is greater than 3%. Two critical aspects that affect the computed counting efficiency are the maximum-energy and the shapefactor. From Tables 2-6 we analyse this influence for diverse shapefactors we can find in the literature. The discrepancies for all these shapefactors are computed relative to the shapefactor that is in better agreement with the experimental counting efficiency of Table 1. For ‘Q (Table 2), only the shapefactor recently proposed by Sadler and Behrens (1993) can conveniently explain the great difference between the counting efficiencies of “Cl and -1. Sadler and Behrens use the impulse approximation theory to demonstrate that the shapefactor coefficients for 36Cl cannot be expressed as constants. In general, for second forbidden non-unique transitions, we need

Table 6. Cherenkov yield Shapefactor 1

1 +0.0300/w

I + 0.041ow 1- 0.0133w 1 - 0.042OW

I + 0.001 w 1 - 0.017ow

I - 0.0060w I - 0.018OW 1 - 0.0100w 1+0.0001w

I - 0.019ow 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

r, ,

expressions for the shapefactor coefficients that depend on the energy of the p-particle. Shapefactors in Table 3 give too high counting efficiencies for 2”“Tl. Only 1.7q2 +p* (Grau Caries, 1995) and q2 + I,p2 (Konopinski, 1966) agree with the experiment. The very similar intrinsic Cherenkov counting efficiency, and the very different Cherenkov yield for 36Cl and 2”“Tl indicate that Cherenkov counting is a suitable method for the verification of current /&spectrum shapefactors. The discrepancies in Table 4 for the counting efficiency for *9Sr show that the intrinsic Cherenkov counting efficiency discrepancy is transmitted almost entirely to the counting efficiency for shapefactors of the form 1 + aW. However, for shapefactors of the form q* +p* the discrepancy for the counting efficiency discrepancy shares between the Cherenkov yield and the intrinsic Cherenkov counting efficiency.

intrinsic Cherenkov counting efficiency ct and counting efficiency L, for different shapefactors of ‘*P

f-k

Ck

0.8709 0.8697 0.8646 0.8690 0.8645 0.8711 0.8685 0.8701 0.8683 0.8695 0.8709 0.8682

0.5378 0.5368 0.5279 0.5349 0.5276 0.5381 0.5340 0.5365 0.5338 0.5356 0.5379 0.5335

Grau Caries (1995). Prohm et al. (1956). Daniel and Schmidt-Rohr (1958). Nichols er al. (1961). Fehrentz and Daniel (1961). Persson and Reynolds (1965). Fischbeck (1968). Nagarajan et al. (1971). Booij er al. (1971). Persson er al. (1971). Zemann ef al. (1971). Wiesner t-f al. (1973).

cc

Ark

A.5

A%

0.4684 0.4668 0.4564 0.4648 0.4561 0.4687 0.4637 0.4668 0.4635 0.4657 0.4684 0.4632

0.0 -0.1

0.0

0.0

I

-0.2 -1.8 -0.5 -1.9 0.0 -0.7 -0.2 -0.7 -0.4 0.0 -0.8

-0.3 -2.5 -0.7 -2.5 0.0 -0.9 -0.3 -1.0 -0.5 0.0 - I.0

2 3 4 5 6 7 8 9 10 II 12

-0.7 -0.2 -0.7 0.0 -0.3 0.1 -0.3 -0.2 0.0 -0.3

Ref.

Radionuclide standardization by Cherenkov counting Table 7. Discrepancies for the Cherenkov yield r,. the

References

intrinsic Cherenkov

efficiency Lo and the counting efficiency cc when the maximum p-ray energy E, has an uncertainty of 1%

Nuclide ‘%I *D+T1 Ysr ‘2P 9oy

E,,, (keV)

Ar,

A%

A%

709.5 763.4 1492 1710.4 2284

1.3 1.2 0.3 0.3 0.2

3.1 2.5 1.4 1.2 0.6

4.2 3.7 1.7 1.5 0.8

Since ?3r maximum B-ray energy is over the Cherenkov threshold, we need to include %Sr for the calculation of the counting efficiency of the genetic mixture ?Sr +“Y. However, Table 5 shows that none of the current shapefactors permit one to obtain a discrepancy less than 1.5%. Finally, Table 6 shows that we do not need to assume any special shapefactor for the allowed transition of 32P. In Table 7 we consider an uncertainty of 1% for the maximum b-ray energy. The discrepancies for 89Sr, %Y and 32P are less than for “Cl and 204Tl,but they are too high to be acceptable from an experimental point of view. Also, we see that an uncertainty on the maximum energy affects more the intrinsic Cherenkov counting efficiency than the Cherenkov yield. 5. Conclusions The standardization of nuclides with /? or y-emission over the Cherenkov threshold was studied. We used 36C1and 32P as standards to obtain a detection probability function valid for any other nuclide. This function was tested for 204Tl, *‘Sr, 9oY and 32Pwith excellent results. The y-emitters @‘Coand 13’Cs were also standardized by applying the same detection probability function to the Compton spectrum. Finally, the analysis of the counting efficiency for the different shapefactors permitted one to explain the large difference between the Cherenkov counting efficiencies for 36C1and *04Tl.

803

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