Measurement of @Emitting Nuclides Using Cerenkov Radiation H. H. Ross Analytical Chemistry Division, Oak Ridge National Laboratory, O a k Ridge, Tenn. The variables that determine the Cerenkov counting response of small liquid systems are presented. A control of these variables will permit the optimization of Cerenkov measurements with any conventional liquid scintillation counter. The design of a counter specifically for Cerenkov emission is also suggested. A new calculation of the photon yield of electrons passing through water indicates the requirements of the electronic counting system.
THEPRACTICAL application of Cerenkov radiation represents one of the most interesting new developments in liquid scintillation technology. This familiar phenomenon, now being applied to the assay of radioisotopes used in biology, medicine, and in physical and chemical research, has many advantages over conventional liquid scintillation procedures, not the least of which is the ability to count in completely aqueous systems without the use of organic fluors. Other properties of Cerenkov radiation enable the simplification of many currently used liquid scintillation techniques. The early applications of Cerenkov radiation were primarily concerned with high energy physics measurements. Only recently has the technique been applied to radioisotope assay. Already, many nuclides including lalI, Z4Na, VoY, 42K, aC1, and 1n6Ru-106Rhhave been determined in a variety of samples with good results (1-3). Sample handling procedures are both simple and reproducible. The purpose of the present investigation is to examine some of the experimental and theoretical parameters that determine Cerenkov response to @emitting radioisotopes in small liquid counting systems. The results are used to delineate the unique advantages of the Cerenkov technique and provide a sound experimental basis for optimizing these measurements.
0 x GLYCEROL H20
56%(wt.)
GLYCEROC 75%(wt.l GLYCEROL 95%(Wt.) A SUCROSE 8 5 % 0
Y
E E 1.3
f.4
1.5
1.6
REFRACTIVE I N D E X
Figure 1. Cerenkov threshold energy as a function of solvent index of refraction
In water, where n = 1.332,p must exceed 0.7508 for the generation of Cerenkov radiation by electrons. Substituting p = 0.7508 in Equation 2 and solving for E gives 263 KeV as the lower energy threshold. The Cerenkov energy threshold for electrons as a function of refractive index is illustrated in Figure 1 ; the positions of several solvent systems are indicated. An important property of Cerenkov radiation is that it is emitted at an angle 0 with respect to the direction of the particle where:
THEORETICAL
Cerenkov radiation is produced when a charged particle passes through a transparent medium at a velocity greater than the speed of light in the same medium. The photons produced have a continuous spectral distribution and a defined geometrical configuration. The photon emission has been described as the particle electro-magnetic “shock wave” that is analogous to the sonic boom created by hypersonic aircraft. The threshold condition for the formation of Cerenkov radiation is: pn
where: (3
=
1
(1)
particle relative phase velocity; velocity of particle (v)/speed of light (c) n = refractive index of the transparent medium For relativistic electrons, ,B is related to electron energy ( E ) by: =
Photons generated by electrons just above the threshold energy will be emitted in a very narrow cone. As electron energy increases, @ approaches 1 and cos 0 approaches 0.7508 from Equation 3. Thus, the maximum angle of emission caused by any singly charged particle in water is 41.3’. Figure 2 illustrates the calculated relationship between Oa,o and p for electrons in water. The detection sensitivity parameters of a Cerenkov system are based primarily on the number and spectral distribution of the generated photons and the conversion characteristics of the photon detector. From the theory of Frank and Tamm (4), the number of photons per unit path length of an electron over a selected spectral region is: dN
- -- 2xa du
(1) K . Haberer, Atom Wirtsclz. 10, 36 (1965). (2) R. P. Parker, and R. H. Elrick, bit. J. Appl. Radial. Isotopes 17, 361 (1966). (3) R. H. Elrick, and R. P. Parker, ibid., 19,263 (1968). 1260
ANALYTICAL CHEMISTRY
(i i) &) -
(1 -
photons/cm
(4)
(4) I. M. Frank, and I. G. Tamm, Dokl. Akad. Nauk SSSR, 14,
109 (1937).
4 1
E
I
I
I
L -
.50
5
10
15
20
SAMPLE VOLUME (ml)
Figure 3. Volume response of Cerenkov emission
30 O 200 100 Figure 2. Cerenkov emission angle as a function of electron relative velocity, /3
where CY
= fine structure constant = e2/hc = 11137 XI = upper limit of selected wavelength region (cm) Xs = lower limit of selected wavelength region (cm)
For example, over the wavelength region 400 to 600 nm, (5)
In order to determine the total photon yield from a given Cerenkov event, Equation 4 would normally be integrated over the limits of x,the particle path length. However, for the case of electrons in water, this simple solution cannot be used because x is a function of the original electron energy; @ also becomes a variable because energy degradation of the electron occurs during its passage through the liquid. Finally, the low energy Cerenkov cutoff at 263 KeV must be considered. We have developed a calculation of photon yield in water that incorporates these factors for the specific case of electrons up to 4 MeV. The variables x and /3 were established in terms of electron energy (E) and Equation 4 was transposed to the dN/ dE form. Empirical range-energy relationships for electrons in water were generated based on the techniques of Glendenin (5). These slightly modified forms are in good agreement with experimental data.
R
=
[(-5.08 X lO-’OE)
R R
=
+ 3.72 X - 0.098
= (4.82 X lOU4E)
(6) (7)
range of electron in water, cm
E = energy of electron, KeV Equation 6 is used for electron energies up to 1 MeV and Equation 7 between 1 and 4 MeV. Although the actual experimental values for the ranges of electrons could have been used in the calculation to be described, the above equations provided a convenient entry into the computer program and were also used in the energy calculations. Electron energy degradation as a function of distance traveled (dE/dx) can be evaluated from theoretical equations (6) but their use is somewhat cumbersome. Also, a significant ( 5 ) L. E. Glendenin, Nucleonics, 2, (1) 12 (1948). (6) R. D. Evans, “The Atomic Nucleus,” McGraw Hill, New York, 1955, Chap 18, p 567.
deviation between the theoretical and experimental result is observed at low electron energies. Therefore, a linear regression technique was applied to Equations 6 and 7 for the dEjdx calculation. The results obtained in this way were in good agreement with the experimental values and had the advantage that they could be easily generated in the computer program. A simple analytical solution for dN/dE using Equations 4, 6, and 7 did not appear to be likely. Thus, a numerical integration procedure was developed using both Simpson and trapezoidal methods (for comparison). In addition to the range and energy degradation factors, the low energy cutoff at 263 KeV was included in the calculation as the lower integration limit. Table I shows the results of the photon yield integration. For an electron having an original energy E, the total number of photons produced in each of seven spectral ranges is indicated. Photon yields over wider spectral segments are obtained by simply adding the results of each individual segment. For example, a 1-MeV electron (p) creates 23.4 photons in the 400- to 600-nm spectral range before degrading to the 263KeV threshold level. An experimental verification of the photon yield calculation is shown in the results section. We admit that additional refinements could have been included in the calculation, but we did not feel that the calculated response would be changed significantly. Because a large number of radioactive nuclides exhibit p emission above the 263-KeV threshold, we can expect Cerenkov response from these nuclides when their radiation passes through water. All the decay events cannot be detected; however, there is always a finite number that fall below the Cerenkov threshold. The maximum theoretical detection efficiency in water for a given nuclide can be calculated by integrating the number of events above 263 KeV and comparing this to the total emission. This calculation was carried out for the nine nuclides used in this study; distributions were taken from Hogan, Zigman, and Mackin (7). The results for this calculation are shown in Table 11. EXPERIMENTAL
Reagents. All reagents used in this study were of the highest commercially available grade. Radioisotopes (except *l0Bi)were obtained from the Isotopes Division at ORNL. Bismuth-210 was prepared in the Oak Ridge Research Reactor by irradiation of high purity bismuth metal. The radiochemical purity of each isotope was checked by gamma and/or beta-ray spectrometry. Also, where feasible, a decay curve was determined for each isotope. The absolute decay rate for each nuclide was determined using conventional 4 4 counting techniques and multiple aliquots. (7) 0. H. Hogan, P. E. Zigman, and J. L. Mackin, “Beta Spectra,” USNRDL-TR-802, 1964. VOL. 41, NO. 10,AUGUST 1969
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Electron energy (KeV) 275 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000
Nuclide 99Tc lSSW
ac1 2 0 4 ~ 1
170Tm
ZlOBi 90Sr-90Y 2P SOY 3
a
Table I. Cerenkov Photon Yields of Electrons in Water for Selected Spectral Regions Photons/spectral region (nm) ~~
250-300 0 .0032 0. 0041 0.273 0.723 1.37 2.22 3.26 4.45 5.80 7.59 8.94 10.7 12.6 14.6 16.6 18.9 28.5 39.6 51.7 64.8 78.8 93.6 109 125 142 160 178 196 215 235 215
300-350 0.0023 0. 0029 0.194 0.513 0.975 1.58 2.31 3.16 4.12 5.39 6.35 7.59 8.92 10.3 11.8 13.4 20.3 28.1 36.7 46.0 56.0 66.5 77.6 89.1 101 114 126 140 153 167 181
350-400 0.0017 0.0022 0.146 0.385 0.731 1.18 1.73 2.37 3.09 4.04 4.76 5.69 6.69 7.75 8.87 10.0 15.2 21.1 27.5 34.5 42.0 49.8 58.2 66.8 75.8 85.1 94.7 105 115 125 136
400-450 0.0013 0.0017 0.113 0.300 0.569 0.922 1.35 1.85 2.41 3.15 3.71 4.43 5.21 6.04 6.91 7.82 11.8 16.4 21.4 26.9 32.7 38.8 45.3 52.0 59.0 66.3 73.8 81.5 89.3 97.5 106
450-500 0.0011 0.0013 0.091 0.240 0.455 0.737 1.08 1.48 1.92 2.51 2.96 3.54 4.16 4.83 5.52 6.25 9.46 13.1 17.1 21.5 26.1 31 .O 36.2 41.6 47.2 53.0 58.9 65.1 71.4 77.9 84.5
500-550 0.0009 0.0011 0.074 0.196 0.373 0.604 0.884 1.21 1.58 2.06 2.43 2.90 3.41 3.95 4.52 5.12 7.75 10.7 14.0 17.6 21.4 25.4 29.7 34.1 38.7 43.4 48.3 53.3 58.5 63.8 69.3
Table 11. Cerenkov Response of /3 Emitters Detection efficiency 0bserved Observed Calcd theor max. (73 singles coincidence (%) E,,, (MeV) 0.2 MeV) are fully (1) I. M. Koltoff and Philip J. Elving, Eds., “Treatise on Analytical Chemistry,” Part 11, Vol. 9, Interscience Publishers, Inc., New York, N. Y . , 1962.
described in the literature (2). It is the reaction of the uranium-235 in geological samples with thermal neutrons resulting in fission and the production of radioactive isotopes of more than 30 elements which is utilized in the present work. Because the fission yield of each of these products is a reproducible quantity, determination of a fission product is directly related to the original concentration of U235. Furthermore, assuming the isotopic abundance of UZ3j in natural samples is constant, determination of U235is readily extended to the determination of total uranium in these materials. Essential to such an analytical procedure is that the radionuclide determined is not produced in significant yields by any other nuclear reaction. Fission products which have been used in uranium analysis of geological samples include barium-140 (3), xenon-I 33 (4), and tellurium-132 (5). The reported method using suffers from poor sensitivity (50 ppm) and involves the quantitative separation of uranium in the mineral sample prior to irradiation by coprecipitation with ferric hydroxide. An important advantage of determining uranium by activation analysis is that the uranium, or in fact any fission product, need not be quantitatively separated from the sample. Samples which are more than 50 ppm U and from which the uranium is quantitatively separated could probably be determined more conveniently by some other method. None-
’
(2) Murrey D. Goldberg, Said F. Mughabghab, Surendra N. Purohit, Benjamin A. Magurro, and Victoria N. May, “Neutron Cross Sections,” Vol. IIB, Brookhaven National Laboratory, Associated Universities, Inc., Upton, N. Y . , 1966. (3) A. A. Smales, Andyst (London), 77,778 (1952). (4) Larry A. Haskin, Harold W. Fearing, and F. S. Fowland, ANAL. CHEM., 33, 1298 (1961). (5) C. Fisher and J. Beydon, BUN. SOC.C/zim. Fr., 11, C102 (1953). VOL. 41, NO. 10,AUGUST 1969
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