Calculation of Sensitivities in Photon Activation Analysis G . J . Lutz Analytical Chemistry Division, National Bureau of Standards, Washington, D.C. 20234
Estimates have been made of specific activities to be expected from bremsstrahlung produced by an electron accelerator. The photon flux distribution from electrons striking a 0.6-cm tungsten target at different energies and included in the cone described by a 5’ angle from the forward direction is calculated. Flux times cross section for photonuclear reactions of analytical utility was integrated, and disintegration rates of the reaction products for most of the elements under conditions of different electron energies and irradiation times were calculated. Relative values for the specific activities were calculated and compared with the experimental results of Oka and coworkers and found to be in satisfactory agreement.
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ACTIVATION ANALYSIS is now being widely used in a variety of analytical problems where high sensitivity is required. The greater part of this work is being performed with thermal neutrons. The reason for this is the general availability of nuclear reactors and the large cross section of many nuclides for thermal neutron capture. Sensitivities of 10-9 gram are not unusual. There are, however, a number of elements such as carbon, nitrogen, oxygen, iron, and lead which are not highly activated with thermal neutrons. In addition, severe difficulties due to sample self-shielding are encountered when a matrix t o be analyzed contains substantial amounts of elements with large thermal neutron absorption cross sections. High energy photon activation analysis is useful in many of these situations. Several experimental sensitivities have been published for photon activation analysis (1-5). MacGregor (6) has calculated, for bremsstrahlung from 20- and 25-MeV electrons, the expected yields for 84 photonuclear reactions. The purpose of this work is t o calculate the photon flux for a specific target-sample configuration of an electron accelerator and then use this flux to estimate the specific activities to be expected for most of the elements.
When the activation analysis equation where
=
N p a (1 - e-Xt)
GAMMA RAY ENERGY (ARBITRARY UNITS)
Figure 1A. Typical photon intensity IS. energy relationship for bremsstrahlung from high energy electrons
G A M M A RAY ENERGY (ARBITRARY U N I T S )
B. Typical cross-section vs. energy relationship for a photonuclear reaction
CALCULATIONS
A
ELECTRON ENERGY 0
2
(1)
A = activity at end of irradiation (disjsec) N = number of atoms p = flux (particlesjcmz-sec) a = cross section (cmzjatom) X = decay constant (sec-1) t = length of irradiation (sec)
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ANALYTICAL CHEMISTRY
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(1) E. Schweikert and P. Albert, Colloque Sur les Methodes Radio-
chimiques d’analyse, Salzborg, AIEA reprint SM-SS/66 (1964). (2) C. Engelmann, CEA R2559, Commissariat A 1’EnergieAtomique (1 964). ( 3 ) G. H. Anderson, F. M. Graber, V. P. Guinn, H. R. Lukens, and D. M. Settle, Proceedings of the Symposium on Nuclear Activation Techniques in the Life Sciences, Amsterdam, IAEA reprint SM-91/63 (1967). (4) M. Gerrard, Isotopes Radiarion Technol., 3 (4), 334 (1966). (5) Y. Oka, T. Kato, K. Nomura, and T. Saito, Bull. Chem. Sac. Japan, 40, 575 (1967). (6) M. H. MacGregor, Nucleonics, 15 (ll), 176 (1957).
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Table I. Calculated Sensitivities for the Elements Based on 100 HA of Beam Current and Target-Sample Configuration Shown in Figure 3 Disintegrations per second (per microgram of element) 10-Minute irradiation 4-Hour irradiation Element Carbon Nitrogen Oxygen Fluorine Sodium Magnesium Magnesium Silicon Silicon Phosphorus Sulfur Chlorine Argon Potassium Titanium Titanium Chromium Chromium Manganese Iron Cobalt Nickel Copper Copper Zinc Germanium Germanium Arsenic Bromine Bromine Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Molybdenum Ruthenium Ruthenium Rhodium Palladium Silver Cadmium Cadmium Indium Indium Tin Tin Antimony Antimony Iodine Cesium Cerium Praseodymium Neodymium Neodymium Samarium Samarium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Ytterbium Lutetium Tantalum Tungsten
Product half-life 20.5m 10.0m 2.lm 1.87h 2.6~ 15h 60s 2.3m 6.6m 2.5m 2.6s 32.0m 55m 7.7m 3.lh 3.4d 42m 3.77m 303d 8.5m 71d 36h 9.9m 12.9h 38m 82m 40h 18d 6.5m 4.5h 18.7d 64d 108d 78.4h 10.ld 15.5m 66h 99m 40d 206d 17d 24m 3.2h 5.3h 50d 4.4h 35m 125d 5.8d 2.8d 13.2d 6.58d 140d 3.4m 2.5h 1.8h 9m 47h 18h 150y 8.5h 35m 10.4h 86d 18m 4.2d 300d 8.lh 74d
25 MeV 2 x 10' 7 x 10' 1 x 10' 3 9 x 10-4 1 x 10-1 1 x 10' 1 x 10' 3 1 x 102 7 x 10' 2 x 10' 1 x 10' 5 x 10' 5 x 10-1 8 x lo-' 2 8 1 x 10-2 1 x 10' 3 x 10-2 3 x 10-1 2 x 102 2 5 x 10' 7 6 x lo-' 2 x 10-1 5 x 102 3 8 x 7 x 10-3 4 x 10-2 7 x 10-1 6 x 10-1 2 x 10' 2 x 10-1 4 3 x 10-2 3 x 10-2 4 x 10-2 2 x 102 8 x 1 x 10-1 2 x 10-1 2 3 3 x 10-3 6 x lo-' 2 8 x lo-' 1 6 x lo-' 1 x 103 2 x 10' 8 2 x 10'
30 MeV 7 x 10' 2 x 102 3 x 102 8 2 x 10-3 4 x lo-' 3 x 10' 3 x 10' 9 3 x 102 2 x 102 5 x 10' 5 x 10' 1 x 102 1 2 x 10-1 4
2 2 3 7 7 5
7
1 x 10-1 1 3 x 10-1 1 x 10-2 4 x 10' 5 x 10-2
10' 10-2 10' 10-2 x lo-' x 102 5
1 x 102 2 x 10' 1 4 x 10-1 1 x 103 6 2 x 10-1 1 x 10-2 9 x 10-2 2 1 6 x 10' 5 x 10-1 9
6 5 9 4 2 3 4
7
1 3 4 1 5
1
3 2 x 10-4 2 x 10-2 3 x 102
x x x x
3 4 6 1 2 6 3 7 9
x x 10-2 x 10-2 x 102 x 10-1 x lo-' x 10-1 4 6 x 10-3 1 3 2 3 x 10-1 x 103 x 10' x 10' x 10' 2 5 x 10-4 x 10-2 x lo2 x 10' x 10-1 2 x lo-' x 10-2 x 10' x 10-2
35 MeV 1 x 102 4 x 10' 6 x lo2 1 x 10' 4 x 10-3 7 x 10-1 7 x 10' 5 x 10' 2 x 10' 6 x lo2 4 x 102 8 x 10' 1 x 102 2 x 102 2 5 x 10-1 8 4 x 10' 4 x 10-2 5 x 10' 1 x 10-1 1 9 x 102 9 2 x 102 3 x 10' 2 6 x lo-' 2 x 103 1 x 101 3 x 10-1 2 x 10-2 1 x lo-' 3 2 1 x 102 7 x 10-1 2 x 10' 1 x 10-1 9 x 10-2 1 x lo-' 6 x 10' 4 x 10-1 5 x 10-1 6 x lo-' 5 9 1 x 10-2 2 5 3 4 2 x lo-' 4 x 103 6 x 10' 2 x 10' 8 x 10' 3 7 5 x 10-4 7 x 10-2 1 x 103 2 x 101 3 x lo-' 3 9 x lo-' 4 x 10-2 1 x 102 1 x lo-'
25 MeV 6 x 10' 1 x 102 1 x 102 4 x 10' 2 x 10-2 3 1 x 10' 1 x 10' 4 1 x 102 7 x 10' 1 x 102 1 x 102 9 x 10' 8 2 1 x 10' 9 2 x 10-1 2 x 10' 8 x lo-' 7 5 x 102 5 x 10' 3 x 102 7 x 10' 1 x 10' 4 8 x 10' 5 x 10' 2 2 x lo-' 1 2 x 10' 1 x 10' 6 x 10' 5 5 x 10' 7 x lo-' 6 x lo-' 1 7 x 102 1 2 5 4 x 10' 2 x 10' 8 x 1 x 10' 4 x 10' 2 x 10' 3 x 10' 1 2 x 103 3 x 102 1 x 102 5 x 10' 2 x 10' 6 x 10' 4 x 10-3 5 x 10-1 2 x 103 1 x 10' 3 3 8 3 x 10-1 8 x lo2 1
30 MeV 2 x 102 4 x 102 3 x 102 1 x 102 5 x 10-2 9 3 x 10' 3 x 10' 1 x 10' 4 x 102 2 x 102 2 x 102 4 x 102 2 x 102 2 x 10' 6 3 x 10' 2 x 10' 6 x lo-' 5 x 10' 2 2 x 10' 1 x 103 1 x 10' 7 x 102 2 x 10' 3 x 10' 8 2 x 103 1 x 102 4 3 x lo-' 2 4 x 10' 3 x 10' 2 x 102 1 x 10' 1 x 102 2
1 2 1 x 103
7 3 2 3 8 4 6 3 5 2 9 5 1 8 9 4 3
4 5 9 x 10' x 10' x 10-1 x 10' x 10' x 10' x 10' 3 x 103 x 102 x 102 x 10' x 10' x 102 x x lo-' x 103 x 102 5 5
1 x 10' 6 x 10-' 1 x 103 2
35 MeV 5 x 102 8 x lo2 6 x lo2 2 x 102 9 x 10-2 2 x 10' 7 x 10' 5 x 10' 3 x 10' 6 x 10' 4 x 102 4 x 102 9 x 102 4 x 102 4 x 10' 1 x 10' 5 x 10' 4 x 10' 1 9 x 10' 3 3 x 10' 2 x 103 2 x 102 1 x 103 3 x 102 5 x 10' 1 x 10' 3 x 103 2 x 102 7 6 x lo-' 4 7 x 10' 5 x 10' 3 x 102 2 x 10' 2 x 102 3 2 3 2 x 103 6 9 1 x 10' 9 x 10' 5 x 10' 3 x lo-' 4 x 10' 1 x 10' 6 x 10' 1 x 102 4 5 x 103 8 x lo2 3 x 102 1 x 102 7 x 10' 2 x 102 1 x 10-2 1 6 x lo3 4 x 102 8 8 2 x 10' 1 2 x 103 3 (Continued)
VOL. 41, NO. 3, MARCH 1969
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Table I.
Calculated Sensitivities for the Elements Based on 100 p A of Beam Current and Target-Sample Configuration Shown in Figure 3 (continued)
Disintegrations per second (per microgram of element) 10-Minute irradiation 4-Hour irradiation Reaction '*'Re( -r,,n)l86Re 1920s(~,n)1g10s 1911r(y,n)1901r 97A~(-,,n)1 96A~ 198Hg(y,n)197Hg 203Tl(-~,n)20fT1 204Pb(-,,n)203Pb
Element Rhenium Osmium Iridium Gold Mercury Thallium Lead
Product half-life 90h 15d 12d 6.2d 65h 12d 52h
25 MeV 2 3 x lo-'
4 x 10-1 5 x 10-1 3 x lo-' 1 x lo-'
E O = 80/A1/3(MeV)
35 MeV 6 1 1 6 1 9 x lo-' 3 x 10-1
4 6 x lo-' 7 x 10-1 4
2
is applied to thermal neutron activation, discrete values are frequently assigned to q and u. This cannot be done in photon activation analysis. Both flux and cross section are energy dependent. Figure 1A shows the shape of the bremsstrahlung or photon flux spectrum obtained from high energy electrons striking a target. The distribution of photons is continuous from zero energy to the energy of the electron. Figure 1B shows the typical relationship of cross section for a photonuclear reaction as a function of energy. Thus the production rate for a nuclear reaction must be calculated by summing the product of a cross section and the photon flux in a n energy increment over the energy range of interest. The typical cross section curve has the approximate shape of a Lorentzian function. This is characterized by three parameters. They are peak location, peak height and width at half-height. Most of the cross section data utilized in this work were taken from Goryachev's compilation (7) or the National Bureau of Standards Photonuclear Data Index (8). In general, preference was given to cross sections obtained from the radioactivity measurement of the product nucleus. Cross sections have not been measured for (y,n) reactions of some of the heavier nuclides. The parameters of these ( A > 100) were estimated ( 9 , I O ) in the following manner. The location of the cross section peak o n the energy axis was computed from the expression where
30 MeV
9 x 10-1 6 x lo-' 2 x 10-1
25 MeV 5 x 10' 8
9 5 x 10' 1 x 10' 8 2
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2 x 10' 3 x 10' 1 x 102 3 x 10' 2 x 101 6
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Figure 3. Target-sample configuration used as basis for calculations
0 0 35 MeV ELECTRONS
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ANALYTICAL CHEMISTRY
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(7) B. I. Goryachev, A t . Energy Rev., 2, 71-148 (1964). (8) Photonuclear Data Index, National Bureau of Standards Miscellaneous Publication 277, U. s. Government Printing Office (1966). (9) Evans Hayward, "Nuclear Structure and Electromagnetic Interactions,'' (Scottish Univ. Summer School 1964), N. MacDonald, Ed., Oliver and Boyd, London and Edinburgh, 1965, pp 141-204. (10) Evans Hayward, National Bureau of Standards, Washington, D. C., personal communication, 1967. 426
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Widths at half-maximum were interpolated from Figure 2 . The data in Figure 2 are based o n experimentally measured cross sections (9, IO). The integrated cross section was calculated from the expression 0 06NZ S u d E I T = 1 (3) where
30MeV 9 x 10' 1 x 101 2 x 10' 9 x 10' 2 x 10' 1 x 10' 4
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Figure 4. Calculated flux for 3 5 , 30-, and 25-MeV electrons for 100 p A average beam current and a subtended angle of 5'
Photon fluxes were estimated for the sample-target configuration shown in Figure 3. The tungsten target is 0.6 cm or about two radiation lengths in thickness. This is the range of 35-MeV electrons. Although a thickness of 0.2-0.3 radiation length gives a maximum photon yield, it is desirable t o absorb all electrons in a water-cooled target t o prevent them from striking the sample. This is because a large fraction of the energy of the electrons is dissipated as heat when it strikes matter and it would be possible t o melt or vaporize a sample with the electron beam unless very effective cooling was provided. The energy distribution of the photon flux was estimated by the method of Hansen and Fultz (11). It is calculated from the integration of contributions from successive elements of thin target spectra. Each thin target is taken t o attenuate the electron energy a n average of 1 MeV. This is integrated over a n energy range sufficient to bring the initial electron to rest. Photons generated at a certain point in the target are attenuated through the remaining thickness of the target. The angular distribution of the photon flux was calculated by a n equation derived by Schiff (12). The radiation intensity summed over the angle subtended by the sample was divided by the relative intensity over all angles to compute the fraction of bremsstrahlung produced that would strike the sample. Figure 4 shows the calculated flux for electron energies of 25, 30, a n d 35 MeV and for a n average electron beam current of 100 p A for the target sample geometry shown in Figure 3. The production rates for the photonuclear reactions of the elements were calculated by summation of the product of cross section and flux in 1-MeV increments from the threshold energy of the reaction t o the electron energy. Equation 1 was then solved. The values obtained in disintegrations/second for a microgram of element are shown in Table I. They have been calculated o n the basis of the fluxes shown in Figure 4 a n d for two different irradiation times.
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DISCUSSION
The calculations reported here are for a specific and somewhat idealized target-sample configuration. Nevertheless, they can serve as a guide for assessing the potential of photon activation analysis for a specific analytical problem, as is indicated in the comparison discussed below. The shape of the bremsstrahlung spectrum produced in a very thick target is governed almost entirely by electron scattering in the target before radiation. Thus for irradiations utilizing electrons of the energies that are indicated and for tungsten targets of the thickness o n which the above calculations were based, the ratio of yields of the reactions considered should remain fairly constant if electron beam current and sample position are fixed. Oka and coworkers (5) have measured the (y,n) yields for 37 elements from bremsstrahlung produced by 20-MeV electrons falling o n a 2-mm-thick platinum convertor. These yields were normalized to that of the jjMn(y,n) 54Mn reaction for which a value of 2 X 106 reactions/roentgen-mole was used. We have calculated the bremsstrahlung spectral shape for this target thickness and electron energy and have computed production rates for most of these elements. Our results have been normalized to 2 X 106 reactions/mole for the jjMn(y, n) j*Mn reaction. The results are plotted along with those of Oka et al. in Figure 2. (11) N. Hansen and S. Fultz, U. S . At. Energy Comm. Rept. UCRL-
6099 (1960). (12) L. I. Schiff, Phq’s. Rev., 70, 87 (1964).
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Figure 5. Comparison of relative calculated and experimental yields from 20-MeV bremsstrahlung Considering the nature of the calculations, the agreement is quite satisfactory except for the lighter elements. Because the photon end point energy is quite close t o the threshold of their reactions, small errors in computing the high energy region of the flux or in the cross section values used would produce relatively large errors in the calculated yields. Similarly, if the irradiations of Oka et ai. were performed at a n enei gy slightly higher than 20 MeV, the largest discrepancies would be expected in the low Z elements. A rough indication of the degree of precision of these calculations can be obtained by computing the average difference between the normalized calculated yields and those measured by Oka et al. Excluding the values obtained for carbon, oxygen, nitrogen, and fluorine, the average deviation from the calculated values was about 40 %. ACKNOWLEDGMENT
The author thanks Damian DeSoete of the Ghent University in Belgium for many helpful discussions.
RECEIVED for review September 27,1968. Accepted November 27, 1968. VOL. 41, NO. 3, MARCH 1969
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