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E1+α epithermal-isotopic neutron source-spectrum by dual monitor method
Annals of Nuclear Energy 31 (2004) 681–695 www.elsevier.com/locate/anucene
Experimental determination of the a-shape factor in the 1/E1+ epithermal-isotopic neutron source-spectrum by dual monitor method Haluk Yu¨cela,*, Mustafa Karadagb a
Ankara Nuclear Research and Training Center, 06100, Besevler-Ankara, Turkey Gazi University, Gazi Education Faculty, 06500 Teknikokullar-Ankara, Turkey
b
Received 7 April 2003; received in revised form 30 August 2003; accepted 6 October 2003
Abstract The a-shape factor of real, non ideal 1/E1+ epithermal neutron spectrum in an isotropic neutron field of 241Am–Be isotopic neutron sources was determined by dual monitor method using measured cadmium ratios of 197Au(n,g)198Au and 98Mo(n,g)99Mo(b)99mTc reactions. The irradiations of Gold (Au) and Molybdenum (Mo), chosen as suitable monitors, were carried out with and without a 1 mm-Cd shield case. The induced activities in these monitors was measured by high resolution g-ray spectrometry with an n-type HPGe detector. The thermal neutron self-shielding effects in the monitor foils used in irradiations are negligibly small, however, the resonance neutron self-shielding effects were taken into account in the determinations. Thus, the obtained results for the a-shape factors for a real 1/E1+ epithermal-241Am–Be neutron source-spectrum at the four irradiation sites of the neutron irradiator are given and discussed. It is emphasized that the 197Au–98Mo isotopes can be chosen as suitable monitors in a-shape factor determination in real epithermal neutron spectra. # 2003 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, with the development of state of the art modern neutron metrology there has been a need to re-determine thermal neutron and epithermal neutron cross sections for stable or radioactive isotopes in view of some (n,g) reactions. Neutron activation cross section data have become important for nuclear transmutation studies related to waste incineration and for revival of accelerator driven sub-critical reactor * Corresponding author. Tel.: +90-312-212-6230; fax: +90-312-223-4439. E-mail addresses: [email protected] (H. Yu¨cel), [email protected] (M. Karadag). 0306-4549/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2003.10.002
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systems. They are also used in activation analysis and for other studies related to the interaction of neutrons with matter. For cross section measurements, modern neutron metrology necessitates the application of up to date protocols, taking all possible precautions to avoid systematic errors (De Corte and Van Lierde, 2001; Holden, 1996; Mughabghab et al., 1981). Hence, it is important that the characterization of neutron fluence spectra in irradiation sites of reactors or other neutron sources is taken into account for high precise and more accurate determinations. The essential fluence parameters for the characterization of a neutron spectrum are the ratio of thermal fluence rate to epithermal fluence rate, f, and the epithermal neutron fluence shape factor, . For example, in the well thermalized (ideal) neutron spectra with the thermal to epithermal fluence ratio f> 1000 (Lin and Henkelmann, 2002) in the irradiation sites of isotopic neutron sources or reactors, the epithermal neutron fluence is accepted to be inversely proportional to the neutron energy and it is generally called 1/E spectrum (IAEA, 1970). However, the real epithermal neutron spectra in actual irradiation sites may deviate more or less from this ideal 1/E distribution shape (Ahmad, 1983; De Corte et al., 1979a,b; Ryves, 1969; Schumann and Albert, 1965; Fastrup and Olsen, 1963; Ehret, 1961). It was shown that these deviating spectra approximately follow a 1/E1+ neutron fluence distribution (Ryves, 1969; Schumann and Albert, 1965) where is the extent of non-ideality of epithermal fluence shape. The value of can be positive or negative, depending on the configuration of the irradiation system (moderator material, geometry of irradiation site, configuration of neutron source, etc.). In many activation analytical techniques it was shown that epithermal neutrons give rise to an important fraction of the produced activity or even the full produced activity. In these cases when using absolute or single comparator techniques and by the application of resonance integrals, the effect of the non-ideality of the epithermal spectrum should not be underestimated or overlooked (De Corte et al., 1979b). Therefore, the knowledge of the epithermal spectrum shape factor is an essential parameter for the correction of resonance integrals. That is I0-infinite dilution the resonance integral values are only valid in an ideal 1/E epithermal spectrum. In the conversion to non-ideal actual epithermal 1/E1+ neutron spectrum the I0() values are used (De Corte et al., 1981). In an ideal epithermal neutron spectrum, the epithermal neutron fluence rate per unit of energy interval, (E) is inversely proportional to the neutron energy, E: Fepi ðEÞ ¼ F0epi
1 E
ð1Þ
where F0epi the energy independent proportionality constant is the integrated epithermal neutron fluence rate per unit of ln(E) interval for a 1/E epithermal neutron fluence rate. The resonance integral for an isotope in an 1/E epithermal neutron spectrum is defined as: ð1 ðEÞ dE ð2Þ I0 ¼ ECd E
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where I0 is the infinite dilution resonance integral including 1/v tail of thermal neutron spectrum. The s (E) is the cross section as a function of energy E, and ECd is effective cadmium cut-off energy, which is set at 0.55 eV for a detector, having a (v) 1/v cross section for the (n,g) reaction up to 1–2 eV, irradiated in an isotropic neutron fluence rate as a small sample in a cylindrical cadmium box (height/diameter=2) with a wall thickness of 1 mm (Goldstein et al., 1961). In practice, since real epithermal neutron spectrum deviates from the 1/E-law, the resonance integrals defined by Eq. (2) are not valid in the non-ideal, real spectrum. In most cases, the epithermal neutron fluence rate per unit of energy interval for real epithermal neutron spectrum can be expressed by:
Fepi ðEÞ ¼ Fepi
ð1 eVÞ E 1þ
ð3Þ
where epi is the proportionality constant, and is the integrated epithermal fluence rate per unit of E/ interval for a 1/E1+ epithermal spectrum. The can be assumed to be the energy independent epithermal fluence shape factor. Thus, Eq. (2) is replaced by the following definition (Ryves, 1969; Moens et al., 1979; De Corte et al., 1981; El Nimr et al., 1981): ð1 I0 ðÞ ¼
ðEÞð1 eVÞ dE E 1þ ECd
ð4Þ
where I0() is the resonance integral for a 1/E1+, real, non-ideal epithermal neutron spectrum. The resonance integrals defined by Eq. (4) can be used in the calculation of the epithermal activation in a particular irradiation position, characterized by a. For simplicity, the term (1 eV) 1 may be omitted to obtain the relationship between I0 and I0(). If Er and are known, it is possible to convert I0, as tabulated in literature to I0() by the following equation (De Corte et al., 1979b, 1981): "
# ðI0 0:42640 Þ 0:42640 I0 ðÞ ¼ þ
ð1 eVÞ ð2 þ 1ÞECd E
ð5Þ
r
where I0=infinite dilution resonance integral given in the literature (valid for =0, i.e. ideal 1/E neutron spectrum), Er=effective resonance energy (eV), as defined by Ryves (Ryves and Paul, 1968; Ryves, 1969). The term (I00.4264 0) represents the reduced resonance integral (i.e. with the 1/v tail subtracted) and Eq. (5) is only valid for ECd=0.55 eV, since 0.4264=2(E0/ ECd)1/2 with E0=0.025 eV and ECd=0.55 eV. It is clear that the I0() value for any isotope measured in actual site can easily convert to the I0 value tabulated in literature by replacing I0 with I0(a) in Eq. (5).
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For the experimental determination of the a-shape factor of a real epithermal spectrum, there are various simple methods based on bare detector irradiations and Cd covered-detector irradiations as described by De Corte et al. (1979b). For example, the multi resonance-detector method with Cd covered irradiations, as used by Schumann and Albert (1965), has been generalized by subtracting the epithermal 1/v tail contribution and by introducing the effective resonance energy as defined by Ryves. The two detector method of Ryves (1969) has also been modified by using Cd ratio measurements in order to eliminate the introduction of systematic errors due to the inaccuracy of absolute nuclear data (De Corte et al., 1979b). Alternatively, the bare multi-monitor method (Verheijke, 1992; Petri et al., 1992) and the bare dual monitor method involving the 94Zr–96Zr isotopes (De Corte et al., 1993, 1994) for a-epithermal spectrum shape factor determination have been applied by using reactor neutrons, and it was shown that 197Au–94Zr–96Zr monitors would give successful results for a-epithermal spectrum shape factor determination in high neutron fluence rates. However, it seems that the 94Zr(n,g)95Zr and 96Zr(n,g)97Zr reactions used in a-epithermal spectrum shape factor determination are not practical in the low neutron fluence rates of neutron sources compared with high fluence rates of reactors, although these isotopes have high resonance energies far from 1/v region. In irradiation sites having low fluence rates the full activity to be produced will be very low due to the low thermal neutron cross sections and resonance integrals of monitors which are 0=0.052 b and I0=0.3 b for 94Zr, and 0=0.020 b and I0=5 b for 96Zr. On the other hand, in surveying literature, the extent of non-ideality of epithermal neutron fluence shape has not been taken into account for especially old resonance integral cross section measurements carried out by some reactors, accelerator based neutron sources or radioactive neutron sources such as 252Cf(sf), 238Pu–Be, 241Am– Be etc. Therefore, in present work, an attempt was made to experimentally determine a-shape factor in the 1/E1+ epithermal-isotopic neutron source-spectrum by dual monitor method using Cd ratio measurements. It was considered that 197Au and 98Mo-detectors would be suitable monitors for a-determination in the 1/E1+ epithermal-isotopic neutron sources-spectra, because the effective resonance energies, 5.47 eV for 197Au and 211 eV for 98Mo are quite far from the 0.55 eV effective Cd cut-off energy. Thus the requirement for a (v) detector to follow 1/v spectrum shape up to 1–2 eV, is not violated by 197Au and 98Mo monitors.
2. Experimental The foil irradiations have been performed in a useful irradiation facility shown in Fig. 1, which has been constructed at Ankara Nuclear Research and Training Center (ANRTC). It consists of a block of solid paraffin wax surrounding the three 592 GBq 241Am–Be neutron sources and four irradiation tubes. The sources immersed in paraffin moderator are in an equilateral triangle array around a central sample irradiation tube made of stainless steel (No. 4) inserted into the wax. The other three vertical sample irradiation holes numbered by circles 1, 2 and 3, as seen in Fig. 1, are placed in the corners of a larger equilateral triangle. Almost spatially
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685
Fig. 1. Cross sectional view of an irradiation facility of three 592 GBq241Am–Be sources in a solid paraffin wax. Sample irradiation positions are numbered by circles 1–4.
uniform thermal neutron fluence rates of about 1.5 104 n cm2 s1 is obtainable over 3.6 cm cylindrical irradiation holes (Nos. 1, 2 and 3). In the thermal neutron fluence rate in the central sample irradiation tube the value obtained was expected to be higher than those in Nos. 1, 2 and 3, however the result obtained was 1.2 104 n cm2 s1 lower than expected. This was possibly due to the absorption of the thermal neutrons in the stainless steel and in the sources themselves and also the thermalisation distance for neutrons was small between the source and the central irradiation tube. The extent of non-ideality of the epithermal-neutron source-spectrum distribution at the sample irradiation positions numbered by circles 1, 2, 3 and 4 at the present neutron irradiator were determined by using analytical grade Au (0.0005 mm in thickness) and Mo (0.025 mm in thickness) foils with purity of 99.9%, obtained from Good Fellow Cambridge Ltd. Using the bare foils of Au and of Mo, five irradiations for each type foil were carried out individually at the same irradiation position in one of the irradiation holes (No. 4). As well, the experiments were performed by bare foil samples at the same depth and a fixed position in other
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irradiation holes, which are numbered by circles 1, 2, 3 shown in Fig. 1 Then, the irradiations of the Au and Mo foils, which are not irradiated before, were carried out within a cylindrical cadmium shield case of 1 mm thickness, at the same position in all four irradiation holes. The irradiation times for the (n,g) reactions of 98Mo and 197 Au were chosen for a period of 3–6 half lives, yielding enough activity to be measured in a g-ray counting system. The suitable waiting times were employed to minimize dead time losses. Dead times were typically less than 0.1%. The detector used in the measurements was an n-type high pure closed-end coaxial germanium (HpGe) manufactured by Canberra, Inc. The resolution of this n-type Ge detector was 1.80 keV for 1332.5 keV (60Co) and 0.97 keV for 122 keV (57Co) and its relative efficiency was 22.6%. The detector was shielded by a 10 cm thick lead lined with copper sheets on all sides. The counting times which varied between 100,000 and 300,000 s predetermined for each measurement were high enough to ensure good statistical quality of data. The counting system under air conditioning environment of the laboratory was stable during the measuring periods.
3. Data evaluation 3.1. Determination of specific activity from the gamma-ray spectra The specific activities (in cps g1) for 198Au via 411.8 keV gamma ray emission, and for 99Mo via 181.1 keV or via 739.5 keV gamma ray emissions in the collected spectra obtained after a bare and a Cd covered-foil irradiation are determined as follows: Asp ¼
Np =tm wSDC
ð6Þ
where Np is net number of counts under the full-energy peak collected during measuring time, tm.w is the weight of irradiated element. S is saturation factor=1 eltirr , with l=decay constant and tirr=irradiation time. D is decay ltm factor=eltd with td=decay time, and C is measurement factor= 1eltm , correcting for decay during the measuring time, tm. 3.2. The specific activity determination of 99Mo via 140.5 keV gamma ray emission from the 99Mo()99mTc decay The specific activities of 99Mo from the collected gamma ray spectra obtained after a bare and a Cd-covered foil irradiation were also determined via the 140.5 keV gamma ray emission, which is the strongest gamma-ray of its daughter nuclide, 99m Tc. As seen in the simplified decay chain shown in Fig. 2, the mother isotope 99 Mo also contributes to the 140.5 keV gamma ray emission of 99mTc, which is the most intense one after irradiation.
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For deducing only 99Mo specific activity, the total specific activity of 99Mo and Tc can be measured from the mixed 140.5 keV photopeak, as a sum of motherdaughter decay (Simonits et al., 1980, 1981):
99m
Asp
99
NpMoþTc =tm Mo þ 99mTc ¼ l2 K1 l1 K2 1 w þ K1 l2 l 1 2 F12
ð7Þ
where number 1 and 2 denote 99Mo and 99mTc respectively, Asp(99Mo+99mTc) is the sum of specific activities both 99Mo and 99mTc, is net number of counts under the full-energy peak from 99Mo+99mTc gamma ray emissions yielding a peak of 140.5 keV, collected during measuring time, tm. K1 and K2 are factors used for simplification of Eq. (7) defined as: K1 ¼ S1 D1 C1 and K2 ¼ S2 D2 C2 .l is decay constant (=ln 2/T1/2), is absolute gamma ray emission probability, and F12 is the fraction of 99Mo mother isotope decaying to 99mTc daughter isotope. Thus, the specific activity of the 99Mo can be calculated from the measured activity via the 140.5 keV photopeak by the following simple relation: 99 1 Asp Mo ¼ ð8Þ Asp 99 Mo þ 99mTc 2 F12 with
1 0:0452 ¼ 5:992 102 ¼ 0:8906 0:847 2 F12
Fig. 2. Simplified decay chain of
ð9Þ
99
Mo–99mTc.
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Decay data taken from NuDat database (Kinsey, 1996) and the calculated gamma ray self attenuation factors for 197Au and 98Mo, are given in Table 1. It should be noted that gamma ray attenuation factors were used only in absolute measurement of fluence rates by employing gold foil at the irradiation positions. On the contrary, these factors are canceled in Cd ratio measurements. 3.3. Determination of the ratio of thermal fluence rate to epithermal fluence rate and the cadmium ratio In a mixed isotropic thermal and 1/E1+ epithermal neutron field, the ratio of the thermal fluence rate to epithermal fluence rate can be expressed as:
f¼
Fth I0 ðÞ Gepi ¼
ðR 1Þ g0 Gth Fepi
ð10Þ
where th=the thermal neutron fluence rate, epi=epithermal neutron fluence rate, 0=the thermal neutron cross section for the 2200 m/s neutrons, g=Westcott correction factor describing 1/v departure, which can be taken to be unity for 197Au and 98Mo, Gth=thermal neutron self-shielding factor, Gepi=epithermal neutron selfshielding factor, and R=cadmium ratio defined by: R¼
A sp þ Asp =FCd
ð11Þ
þ where A sp , Asp are specific activities obtained after a bare and Cd covered foil irradiation, respectively. FCd is cadmium filter epithermal neutron transmission factor, which is a correction for the absorption of epithermal fluence rate in the cadmium cover. In general, the factor FCd is mostly 41 for elements (El Nimr et al., 1981).
Table 1 Decay data and the calculated gamma ray self attenuation factors for 197Au and 98Mo used in the activity determinations Nuclear reaction
Mo (n,g)99Mo
98
65.94 (1)
98
6.015 (9) 64.684 (5)
Mo(n,g)99Mo(b)99mTc Au(n,g)198Au
197
Detected g-ray
Half-life, T1/2 (h) Gamma ray energy, E (keV)
Gamma ray emission probability, g (%)
Gamma ray self attenuation factora, (Fg)
140.511 (1) 181.068 (8) 739.500 (17) 140.511 (1) 411.8020 (2)
4.52 (24) 5.99 (12) 12.13 (22) 89.06 (24) 95.58 (12)
1.0062 1.0037 1.0008 1.0062 1.0001
a Calculated using mass attenuation coefficients (/ ) taken from XCOM database of Berger et al., (1999) and thickness values of the foils used.
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3.4. Determination of -epithermal fluence shape factor In this study, the dual monitor method with Cd ratios have been used for the determination of a-epithermal fluence shape factor. De Corte et al. (1979b) have modified the dual monitor method of Ryves by introducing effective resonance energies. Additionally, with the introduction of Cd ratios into the dual monitor method, it does not require the knowledge of the detection efficiency curve of a gamma ray detector. Thus, the dual monitor method taking into account neutron self shielding effects in the monitors (Au and Mo) has been applied firstly to an isotopic neutron source spectrum as follows. For the determination of the a- epithermal spectrum shape factor, if, after the measurement of the Cd ratios for 197 Au(n,g)198Au and 98Mo(n,g)99Mo reactions, an equation can be derived from Eqs. 5 and 10, as follows:
ð Q 0:4264 ÞG E þC 0 r;Mo ðR 1ÞAu Mo
F ; xj ¼
¼0 ð12Þ ðR 1ÞMo ðQ 0:4264ÞG E þC 0
r;Au
Au
with C ¼
0:4264 ð2 þ 1ÞECd
ð13Þ
Q0 ¼
I0 g0
ð14Þ
and
where, F(,xj) is an implicit function form of Eq. (12), showing the dependence of a and xj parameters on error analysis. xj are either statistical variables [e.g. the þ measured specific count rates, A sp ; Asp i ] or fixed parameters (e.g. the nuclear data involved in the method). The index, i refers to the 197Au and 98Mo monitors. G is the ratio of the epithermal neutron self shielding factor, Gepi to thermal neutron self shielding factor, Gth given in Table 2 for Au and Mo foils used.
4. Results and discussion The a-epithermal spectrum shape factor has been expressed implicitly as a function of the form, F(a, xj), that is,
þ F ; xj ¼ F ; Asp;i =Asp;i ; Nuclear Data ð15Þ j
þ where x1, x2, x3,. . ., xj=(A sp;i ; Asp;i ,Nuclear Data)j are either statistical variables [e.g. þ the measured specific count rates with and without Cd-cover, A sp;i ; Asp;i ] or a fixed parameter with an associated uncertainty [e.g. the nuclear data involved in Eq. (12)]. The index, i refers to 197Au and 98Mo isotopes used as a-monitor.
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Table 2 Nuclear data used for Detector Form used
197
Au and 98Mo monitors in a-shape factor determination Nuclear reaction
Er (eV)a Fcdb
Mo(n,g)99Mo 0.025 mm-foil Mo(n,g)99Mo(b)99mTc 211 0.0005 mm-foil 197Au(n,g)198Au 5.47
g(20 C) Gthe
Gepi
Q0h
98
Mo Au a b c d e f g h
98
1.0 1.0008c 0.991 1.006d
0.999 0.992f 53.20.9 1.000 0.925g 15.70.1
Moens et al. (1979). El Nimr et al. (1981). Chang (2003). Holden (1999). Calculated by Nisle approximation, including scattering effect, given in Gilat and Gurfinkel (1963). Calculated by approximation given in Beckurts and Wirtz, (1964). IAEA (1970). De Corte et al. (1981).
According to the error propagation law, the overall relative uncertainty on a-epithermal spectrum shape factor is calculated by: " #1=2 X 2 Z; j sj ð16Þ s;T ¼ j
where sj is the relative error on each xj parameter and Z, j is error propagation factor, defined as the multiplier of the relative error on xj parameter to obtain the associated relative error on a-epithermal spectrum shape factor. The error propagation factors, Z, j for each xj parameter is defined by: d dxj xj dF dF ð17Þ ¼
Z;j ¼ xj dxj d The error propagation factors (Z,j) were calculated by using the relative uncertainties (sj) on statistical variables and nuclear data, and they are given in Table 3. Then, the calculated relative uncertainties (s,j) on a-epithermal spectrum shape factor for each parameter (xj) and the resulted overall uncertainties (s,T) on the a-shape factors at the irradiation sites are also given in Table 4. It should be noted that the application of Eq. (16), with the introduction of Z,j factors according to Eq. (17), in principle will only be realistic for moderate sj values or a=F(xj) relations, which do not deviate dramatically from linearity. Nevertheless, in most practical cases the expressions given by Eqs. (16) and (17) can be considered as an acceptable approximation (De Corte et al., 1981). Finally, the a-epithermal spectrum shape factors for the irradiation sites (Nos. 1–4) of the present 241Am–Be neutron source irradiator have been calculated from the graphically solution of Eq. (12), using a microcomputer. Fig. 3 shows a solution of Eq. (12) for a-shape factor when 197Au and 98Mo data are used. The obtained results for a-epithermal spectrum shape factor and the ratio of thermal fluence rate
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Table 3 The relative uncertainties and the calculated error propagation factors on statistical variables and nuclear data used in dual monitor method with Cd-ratios Parameter (xj)
Uncertainty, sj (%)
Error propagation factor, Z,j
197
No. 1 (=0.095)
Au
98
Mo
Q0 Er G FCd ECd a
0.8 0.3 1.4 1.0 0.2 15a
1.1 1.8 22 1.0 –
No. 3 (=0.138)
No. 4 (=0.075)
197
98
197
98
197
98
6.40 3.13 0.26 2.82 6.40 0.03
11.7 2.92 0.27 2.87 11.7
7.37 3.58 0.26 3.22 7.37 0.04
14.0 3.34 0.27 3.29 14.0
4.36 2.16 0.27 1.94 4.36 0.02
7.10 2.01 0.27 1.97 7.10
Au
þ A sp =Asp
No. 2 (=0.083) Mo
Au
Mo
Au
Mo
197
98
12.3 3.96 0.27 3.54 12.3 0.04
27.2 3.70 0.27 3.64 27.2
Au
Mo
De Corte et al. (1981).
Table 4 The relative uncertainties on a-shape factors and the overall uncertainties for each parameter involved in the method Parameter (xj)
Relative uncertainty on a-shape factor, s,j=sjZ,j(%) Irradiation hole No. 1 (=0.095)
Irradiation hole No. 2 (=0.083)
Irradiation hole No. 3 (=0.138)
Irradiation hole No. 4 (=0.075)
197
197
197
197
Au
þ A sp =Asp Q0 Er G FCd ECd
5.12 0.94 0.37 2.82 1.28 0.48
Overall uncertainty on 16.59 a-shape factor, s,T (%)
98
Mo
12.9 5.25 6.00 2.87 –
Au
5.90 1.07 0.37 3.22 1.48 0.55 19.21
98
Mo
15.4 6.01 6.00 3.29 –
Au
3.49 0.65 0.37 1.94 0.87 0.32 11.46
98
Mo
7.81 3.62 6.00 1.98 –
Au
9.87 1.19 0.37 3.57 2.46 0.60
98
Mo
29.9 6.66 6.00 3.64 –
33.25
to epithermal fluence rate for the characterization of the neutron spectrum at each of the irradiation positions are given in Table 5. The a-shape factors at the irradiation positions of 241Am–Be neutron sources in a solid paraffin moderator were found ranging from 0.075 0.025 in the central irradiation hole (No. 4), up to 0.138 0.016 when moving away from the central irradiation hole (No. 4) to the outer regions of the present irradiator. It is unexpectedly that the obtained a-shape factors at the irradiation positions (Nos.1–3) are different from each other although these irradiation holes fixed in an equilateral triangle geometry, shown in Fig. 1 are placed at equal distances. This was possibly due to the non-uniformities of paraffin wax used as a moderator, some voids forming in paraffin during the melting process of the wax, inconvenience alignments of the sources and the irradiation tubes in the present configuration.
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Fig. 3. The graphically solution of Eq. (12) for a-shape factor determination using 197Au–98Mo data.
Table 5 The measured a-spectrum shape factors and the ratios of thermal to epithermal fluence rates at the irradiation holes (Nos. 1–4) of an 241Am–Be irradiation using 197Au–98Mo Irradiation hole
No. 1 No. 2 No. 3 No. 4
f=th/e Au-monitor
Mo-monitor
ðR1ÞAu ðR1ÞMo
Spectrum shape factor, a
10.28 0.30 10.42 0.31 9.77 0.29 5.44 0.24
10.310.90 10.430.92 9.80 0.86 5.45 0.74
2.5230.050 2.6420.052 2.1590.043 2.7170.054
0.0950.015 0.0830.016 0.1380.016 0.0750.025
The overall uncertainties (s,T) on the a-epithermal spectrum shape factors of the irradiation positions (Nos. 1–4) ranged from 11.46 to 33.25%, depending on the magnitudes of the a-factors obtained by using Cd ratios for dual monitor with 197 Au–98Mo. Some methods in literature, for the experimental -determination in the 1/E1+ epithermal reactor-neutron spectrum are critically compared with respect to their accuracy and precision, by employing error propagation theory (De Corte et al., 1981). According to this critical evaluation, the reported a-shape factors were determined by the same dual monitor method, but using Cd ratios of 197Au and 94Zr with reactor neutrons, have been quoted with overall uncertainties (s,T) ranging from 7.05 to 41%. It implies that the range of overall uncertainties estimated on a-shape factors by Cd ratios of the present 197Au–98Mo monitors irradiated in low fluence rates agree reasonably with the range of those by Cd ratios of 197Au–94Zr monitors irradiated in relatively high fluence rates in reactors. In view of the experimental accuracy of the dual monitor method with cadmium ratio it has the important
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advantage that gross errors due to gamma-ray attenuation, detector efficiency, true coincidence effect are cancelled in Cd ratio measurements. However, the main drawback of the dual monitor method with Cd ratio for a-shape factor determination is that four different specific activities, Asp measured for two monitors, have to be introduced in Eq. (12), each of them contributing to the precision of the a-shape factor. This contribution is especially important for the measured Cd-covered foil activities, directly relating to resonance integral cross section of the chosen a-monitor. Hence, the 98Mo monitor having a higher resonance integral cross section of I0=6.6 b, would give more accurate peak results with a good statistical quality than that of 94Zr monitor with I0=0.3 b, when the Cd ratio measurements are carried out in low neutron fluence rates. Further, in case of 98Mo(n,g)99Mo(b)99mTc monitor reaction, the specific activities can be determined in a gamma-ray detector by using one of the gamma ray emissions of 181.1 keV (4.52%) and 739.5 keV (12.13%) from directly emitted from the 99Mo itself, as described in Section 3.1. But, since the gamma ray intensities of both 181.1 and 739.5 keV are relatively low, the statistical errors on the peak area determinations have been found to be in the order of 6–11% in the present measuring system for Cd-covered foil irradiations. Therefore, in this study, the intense 140.5 keV (89.1%) gamma ray emission mixed from mother99 Mo(b)99mTc-daughter decay was used for the more accurate activity determination of 99Mo, as described in Section 3.2. The statistical uncertainties on the 140.5 keV photopeak areas are on average 0.4% for bare Mo-foil irradiations and 0.7% for Cd-covered foil irradiations. The 140.5 keV gamma ray emission of 99 Mo(b)99mTc decay in the activity measurements for Cd- ratio method is a useful analytical peak due to its high gamma emission probability, in order to reduce substantially the counting errors affecting the final result, for example, the value of a-shape factor to be determined. However, it should noted that true coincidence effects in the 140.5 keV gamma ray have to be taken into account in the absolute determinations because of some gamma rays feeding to it especially when the 140.5 keV peak of 99Mo(b)99mTc decay is used in any absolute method. The accuracy of the dual monitor method with Cd ratio applied to the determination of a-shape factor in the real 1/E1+ epithermal-isotopic neutron sourcespectrum is dependant on the choice of suitable resonance detectors, with respect to the dominance of one single resonance peak on a negligible 1/v-tail. In this argument, because of the existing resonance peaks at 12.1 and 467.4 eV of 98Mo in the epithermal region, the use of 98Mo isotope as an a-monitor seems to be questionable at first sight, however, it is interesting to eliminate the need for resonance detectors with one single, dominant resonance peak on a negligible 1/v-tail, with the introduction of the concept of the effective resonance energy of a monitor, by modification of the dual monitor method of Ryves (De Corte et al., 1979b). In addition, when the measured Cd ratios of the chosen monitors introduced into dual monitor method, the effect of systematic errors in the individual absolute nuclear data in a large scattering in the literature can be substantially eliminated for the determination of a-shape factor, and thus the dual monitor method does not necessitate the knowledge of the photopeak efficiency curve for a gamma ray detector.
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5. Conclusions In conclusion, when the Cd ratio measurements of 197Au and 98Mo monitors with the recent nuclear data involved in dual monitor method are used, the a-shape factor in the real, non-ideal 1/E1+ epithermal-isotopic neutron source-spectrum can be determined with a sufficient accuracy. In view of the full activity to be produced in the monitors irradiated in low neutron fluence rates, the 98Mo(n,g)99Mo(b)99mTc monitor reaction as for suitable decay and nuclear data such as half-life, gamma ray and its intensity, cross sections and resonance parameters can be chosen instead of 94 Zr(n,g)95Zr or 96Zr(n,g)97Zr for the purpose of a-shape factor determination. For measuring the 99Mo activity in a gamma ray detector, the mixed 140.5 keV gamma ray emission from mother 99Mo(b)99mTc daughter decay can be preferred as an analytical peak, in especially Cd ratio measurements. However, it should noted that the necessary correction for possible true coincidence effects affecting the 140.5 keV gamma ray emission of 99mTc should be made when this peak is used in absolute measurements requiring gamma ray detection efficiency, especially at a short distance of sample to detector.
References Ahmad, A., 1983. Analysis and evaluation of thermal and resonance neutron activation data. Ann. Nucl. Energy 10, 41–50. Beckurts, K., Wirtz, K., 1964. Neutron Physics. Springer, Berlin. Berger, M.J., Hubbell, J.H., Seltzer, S.M., 1999. XCOM: Photon Cross Sections Database, NIST. Available from . Chang, J., Table of Nuclides, Korea Atomic Energy Research Institute (KAERI). Available from
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Gilat, J., Gurfinkel, Y., 1963. Self-shielding in activation analysis. Nucleonics 21 (8), 143–144. Goldstein, H., Harvey, J.A., Story, J.S., Westcott, C.H., 1961. Recommended Definitions for Resonance Integral Cross Section. Rep. EANDC-12. Holden, N.E., 1996. Neutron Scattering and Absorption Properties. Brookhaven National Laboratory, Upton, New York. Holden, N.E., 1999. Temperature dependence of the Westcott g-factor for neutron reactions in activation analysis. Pure Appl. Chem. 71 (12), 2309–2315. IAEA, Technical Reports, 1970. Series No: 107. Neutron Fluence Measurements. IAEA, Vienna. Kinsey, R.R., 1996, The NuDat Program for Nuclear Data on the Web, (http://www.nndc.bnl.gov/nndc/ nudat/), version 2.5, National Nuclear Data Center, BNL, New York. Lin, X., Henkelmann, R., 2002. Instrumental neutron activation analysis. J. Radioanal. Chem. 251 (2), 197–204. Moens, L., De Corte, F., Simonits, A., De Wispelaere, A., Hoste, J., 1979. The effective resonance energy Er as a parameter for the correction of resonance integrals in the 1/E1+a epithermal neutron spectra. J. Radioanal. Chem. 52 (2), 379–387. Mughabghab, S.F., Divadeenam, M., Holden, N.E., 1981. Neutron Cross Section from Neutron Resonance Parameters and Thermal Cross Sections. Academic Press, New York. Petri, H., Krieger, S., Wolters, D., 1992. Proc. Intern. k0 Users Workshop, Gent. Ryves, T.B., Paul, E.B., 1968. The construction and calibration of a standard thermal neutron flux facility at the National Physical Laboratory. J. Nucl. Energy 22 (12), 759–775. Ryves, T.B., 1969. A new thermal neutron flux convention. Metrologia 5 (4), 119–124. Schumann, P., Albert, D., 1965. Untersuchung epithermischer neutronenspektren mit du¨nnen resonanzsonden. Kernenergie 8, 88. Simonits, A., Moens, L., De Corte, F., De Wispelaere, A., Elek, A., Hoste, J., 1980. k0 Measurements and related nuclear data compilation for (n,g) reactor neutron activation analysis, part-1. J. Radioanal. Chem. 60, 461–516. Simonits, A., Moens, L., De Corte, F., De Wispelaere, A., Hoste, J., 1981. Absolute intensity of the 140.5 keV gamma-ray of 99Mo. J. Radioanal. Chem. 67 (1), 61–74. Verheijke, M. L., 1992. Instrumental Neutron Activation Analysis Developed for Silicon Integrated Circuit Technology. Thesis, Eindhoven.
Experimental determination of the a-shape factor in the 1/E1+ epithermal-isotopic neutron source-spectrum by dual monitor method Haluk Yu¨cela,*, Mustafa Karadagb a
Ankara Nuclear Research and Training Center, 06100, Besevler-Ankara, Turkey Gazi University, Gazi Education Faculty, 06500 Teknikokullar-Ankara, Turkey
b
Received 7 April 2003; received in revised form 30 August 2003; accepted 6 October 2003
Abstract The a-shape factor of real, non ideal 1/E1+ epithermal neutron spectrum in an isotropic neutron field of 241Am–Be isotopic neutron sources was determined by dual monitor method using measured cadmium ratios of 197Au(n,g)198Au and 98Mo(n,g)99Mo(b)99mTc reactions. The irradiations of Gold (Au) and Molybdenum (Mo), chosen as suitable monitors, were carried out with and without a 1 mm-Cd shield case. The induced activities in these monitors was measured by high resolution g-ray spectrometry with an n-type HPGe detector. The thermal neutron self-shielding effects in the monitor foils used in irradiations are negligibly small, however, the resonance neutron self-shielding effects were taken into account in the determinations. Thus, the obtained results for the a-shape factors for a real 1/E1+ epithermal-241Am–Be neutron source-spectrum at the four irradiation sites of the neutron irradiator are given and discussed. It is emphasized that the 197Au–98Mo isotopes can be chosen as suitable monitors in a-shape factor determination in real epithermal neutron spectra. # 2003 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, with the development of state of the art modern neutron metrology there has been a need to re-determine thermal neutron and epithermal neutron cross sections for stable or radioactive isotopes in view of some (n,g) reactions. Neutron activation cross section data have become important for nuclear transmutation studies related to waste incineration and for revival of accelerator driven sub-critical reactor * Corresponding author. Tel.: +90-312-212-6230; fax: +90-312-223-4439. E-mail addresses: [email protected] (H. Yu¨cel), [email protected] (M. Karadag). 0306-4549/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2003.10.002
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systems. They are also used in activation analysis and for other studies related to the interaction of neutrons with matter. For cross section measurements, modern neutron metrology necessitates the application of up to date protocols, taking all possible precautions to avoid systematic errors (De Corte and Van Lierde, 2001; Holden, 1996; Mughabghab et al., 1981). Hence, it is important that the characterization of neutron fluence spectra in irradiation sites of reactors or other neutron sources is taken into account for high precise and more accurate determinations. The essential fluence parameters for the characterization of a neutron spectrum are the ratio of thermal fluence rate to epithermal fluence rate, f, and the epithermal neutron fluence shape factor, . For example, in the well thermalized (ideal) neutron spectra with the thermal to epithermal fluence ratio f> 1000 (Lin and Henkelmann, 2002) in the irradiation sites of isotopic neutron sources or reactors, the epithermal neutron fluence is accepted to be inversely proportional to the neutron energy and it is generally called 1/E spectrum (IAEA, 1970). However, the real epithermal neutron spectra in actual irradiation sites may deviate more or less from this ideal 1/E distribution shape (Ahmad, 1983; De Corte et al., 1979a,b; Ryves, 1969; Schumann and Albert, 1965; Fastrup and Olsen, 1963; Ehret, 1961). It was shown that these deviating spectra approximately follow a 1/E1+ neutron fluence distribution (Ryves, 1969; Schumann and Albert, 1965) where is the extent of non-ideality of epithermal fluence shape. The value of can be positive or negative, depending on the configuration of the irradiation system (moderator material, geometry of irradiation site, configuration of neutron source, etc.). In many activation analytical techniques it was shown that epithermal neutrons give rise to an important fraction of the produced activity or even the full produced activity. In these cases when using absolute or single comparator techniques and by the application of resonance integrals, the effect of the non-ideality of the epithermal spectrum should not be underestimated or overlooked (De Corte et al., 1979b). Therefore, the knowledge of the epithermal spectrum shape factor is an essential parameter for the correction of resonance integrals. That is I0-infinite dilution the resonance integral values are only valid in an ideal 1/E epithermal spectrum. In the conversion to non-ideal actual epithermal 1/E1+ neutron spectrum the I0() values are used (De Corte et al., 1981). In an ideal epithermal neutron spectrum, the epithermal neutron fluence rate per unit of energy interval, (E) is inversely proportional to the neutron energy, E: Fepi ðEÞ ¼ F0epi
1 E
ð1Þ
where F0epi the energy independent proportionality constant is the integrated epithermal neutron fluence rate per unit of ln(E) interval for a 1/E epithermal neutron fluence rate. The resonance integral for an isotope in an 1/E epithermal neutron spectrum is defined as: ð1 ðEÞ dE ð2Þ I0 ¼ ECd E
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where I0 is the infinite dilution resonance integral including 1/v tail of thermal neutron spectrum. The s (E) is the cross section as a function of energy E, and ECd is effective cadmium cut-off energy, which is set at 0.55 eV for a detector, having a (v) 1/v cross section for the (n,g) reaction up to 1–2 eV, irradiated in an isotropic neutron fluence rate as a small sample in a cylindrical cadmium box (height/diameter=2) with a wall thickness of 1 mm (Goldstein et al., 1961). In practice, since real epithermal neutron spectrum deviates from the 1/E-law, the resonance integrals defined by Eq. (2) are not valid in the non-ideal, real spectrum. In most cases, the epithermal neutron fluence rate per unit of energy interval for real epithermal neutron spectrum can be expressed by:
Fepi ðEÞ ¼ Fepi
ð1 eVÞ E 1þ
ð3Þ
where epi is the proportionality constant, and is the integrated epithermal fluence rate per unit of E/ interval for a 1/E1+ epithermal spectrum. The can be assumed to be the energy independent epithermal fluence shape factor. Thus, Eq. (2) is replaced by the following definition (Ryves, 1969; Moens et al., 1979; De Corte et al., 1981; El Nimr et al., 1981): ð1 I0 ðÞ ¼
ðEÞð1 eVÞ dE E 1þ ECd
ð4Þ
where I0() is the resonance integral for a 1/E1+, real, non-ideal epithermal neutron spectrum. The resonance integrals defined by Eq. (4) can be used in the calculation of the epithermal activation in a particular irradiation position, characterized by a. For simplicity, the term (1 eV) 1 may be omitted to obtain the relationship between I0 and I0(). If Er and are known, it is possible to convert I0, as tabulated in literature to I0() by the following equation (De Corte et al., 1979b, 1981): "
# ðI0 0:42640 Þ 0:42640 I0 ðÞ ¼ þ
ð1 eVÞ ð2 þ 1ÞECd E
ð5Þ
r
where I0=infinite dilution resonance integral given in the literature (valid for =0, i.e. ideal 1/E neutron spectrum), Er=effective resonance energy (eV), as defined by Ryves (Ryves and Paul, 1968; Ryves, 1969). The term (I00.4264 0) represents the reduced resonance integral (i.e. with the 1/v tail subtracted) and Eq. (5) is only valid for ECd=0.55 eV, since 0.4264=2(E0/ ECd)1/2 with E0=0.025 eV and ECd=0.55 eV. It is clear that the I0() value for any isotope measured in actual site can easily convert to the I0 value tabulated in literature by replacing I0 with I0(a) in Eq. (5).
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For the experimental determination of the a-shape factor of a real epithermal spectrum, there are various simple methods based on bare detector irradiations and Cd covered-detector irradiations as described by De Corte et al. (1979b). For example, the multi resonance-detector method with Cd covered irradiations, as used by Schumann and Albert (1965), has been generalized by subtracting the epithermal 1/v tail contribution and by introducing the effective resonance energy as defined by Ryves. The two detector method of Ryves (1969) has also been modified by using Cd ratio measurements in order to eliminate the introduction of systematic errors due to the inaccuracy of absolute nuclear data (De Corte et al., 1979b). Alternatively, the bare multi-monitor method (Verheijke, 1992; Petri et al., 1992) and the bare dual monitor method involving the 94Zr–96Zr isotopes (De Corte et al., 1993, 1994) for a-epithermal spectrum shape factor determination have been applied by using reactor neutrons, and it was shown that 197Au–94Zr–96Zr monitors would give successful results for a-epithermal spectrum shape factor determination in high neutron fluence rates. However, it seems that the 94Zr(n,g)95Zr and 96Zr(n,g)97Zr reactions used in a-epithermal spectrum shape factor determination are not practical in the low neutron fluence rates of neutron sources compared with high fluence rates of reactors, although these isotopes have high resonance energies far from 1/v region. In irradiation sites having low fluence rates the full activity to be produced will be very low due to the low thermal neutron cross sections and resonance integrals of monitors which are 0=0.052 b and I0=0.3 b for 94Zr, and 0=0.020 b and I0=5 b for 96Zr. On the other hand, in surveying literature, the extent of non-ideality of epithermal neutron fluence shape has not been taken into account for especially old resonance integral cross section measurements carried out by some reactors, accelerator based neutron sources or radioactive neutron sources such as 252Cf(sf), 238Pu–Be, 241Am– Be etc. Therefore, in present work, an attempt was made to experimentally determine a-shape factor in the 1/E1+ epithermal-isotopic neutron source-spectrum by dual monitor method using Cd ratio measurements. It was considered that 197Au and 98Mo-detectors would be suitable monitors for a-determination in the 1/E1+ epithermal-isotopic neutron sources-spectra, because the effective resonance energies, 5.47 eV for 197Au and 211 eV for 98Mo are quite far from the 0.55 eV effective Cd cut-off energy. Thus the requirement for a (v) detector to follow 1/v spectrum shape up to 1–2 eV, is not violated by 197Au and 98Mo monitors.
2. Experimental The foil irradiations have been performed in a useful irradiation facility shown in Fig. 1, which has been constructed at Ankara Nuclear Research and Training Center (ANRTC). It consists of a block of solid paraffin wax surrounding the three 592 GBq 241Am–Be neutron sources and four irradiation tubes. The sources immersed in paraffin moderator are in an equilateral triangle array around a central sample irradiation tube made of stainless steel (No. 4) inserted into the wax. The other three vertical sample irradiation holes numbered by circles 1, 2 and 3, as seen in Fig. 1, are placed in the corners of a larger equilateral triangle. Almost spatially
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Fig. 1. Cross sectional view of an irradiation facility of three 592 GBq241Am–Be sources in a solid paraffin wax. Sample irradiation positions are numbered by circles 1–4.
uniform thermal neutron fluence rates of about 1.5 104 n cm2 s1 is obtainable over 3.6 cm cylindrical irradiation holes (Nos. 1, 2 and 3). In the thermal neutron fluence rate in the central sample irradiation tube the value obtained was expected to be higher than those in Nos. 1, 2 and 3, however the result obtained was 1.2 104 n cm2 s1 lower than expected. This was possibly due to the absorption of the thermal neutrons in the stainless steel and in the sources themselves and also the thermalisation distance for neutrons was small between the source and the central irradiation tube. The extent of non-ideality of the epithermal-neutron source-spectrum distribution at the sample irradiation positions numbered by circles 1, 2, 3 and 4 at the present neutron irradiator were determined by using analytical grade Au (0.0005 mm in thickness) and Mo (0.025 mm in thickness) foils with purity of 99.9%, obtained from Good Fellow Cambridge Ltd. Using the bare foils of Au and of Mo, five irradiations for each type foil were carried out individually at the same irradiation position in one of the irradiation holes (No. 4). As well, the experiments were performed by bare foil samples at the same depth and a fixed position in other
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irradiation holes, which are numbered by circles 1, 2, 3 shown in Fig. 1 Then, the irradiations of the Au and Mo foils, which are not irradiated before, were carried out within a cylindrical cadmium shield case of 1 mm thickness, at the same position in all four irradiation holes. The irradiation times for the (n,g) reactions of 98Mo and 197 Au were chosen for a period of 3–6 half lives, yielding enough activity to be measured in a g-ray counting system. The suitable waiting times were employed to minimize dead time losses. Dead times were typically less than 0.1%. The detector used in the measurements was an n-type high pure closed-end coaxial germanium (HpGe) manufactured by Canberra, Inc. The resolution of this n-type Ge detector was 1.80 keV for 1332.5 keV (60Co) and 0.97 keV for 122 keV (57Co) and its relative efficiency was 22.6%. The detector was shielded by a 10 cm thick lead lined with copper sheets on all sides. The counting times which varied between 100,000 and 300,000 s predetermined for each measurement were high enough to ensure good statistical quality of data. The counting system under air conditioning environment of the laboratory was stable during the measuring periods.
3. Data evaluation 3.1. Determination of specific activity from the gamma-ray spectra The specific activities (in cps g1) for 198Au via 411.8 keV gamma ray emission, and for 99Mo via 181.1 keV or via 739.5 keV gamma ray emissions in the collected spectra obtained after a bare and a Cd covered-foil irradiation are determined as follows: Asp ¼
Np =tm wSDC
ð6Þ
where Np is net number of counts under the full-energy peak collected during measuring time, tm.w is the weight of irradiated element. S is saturation factor=1 eltirr , with l=decay constant and tirr=irradiation time. D is decay ltm factor=eltd with td=decay time, and C is measurement factor= 1eltm , correcting for decay during the measuring time, tm. 3.2. The specific activity determination of 99Mo via 140.5 keV gamma ray emission from the 99Mo()99mTc decay The specific activities of 99Mo from the collected gamma ray spectra obtained after a bare and a Cd-covered foil irradiation were also determined via the 140.5 keV gamma ray emission, which is the strongest gamma-ray of its daughter nuclide, 99m Tc. As seen in the simplified decay chain shown in Fig. 2, the mother isotope 99 Mo also contributes to the 140.5 keV gamma ray emission of 99mTc, which is the most intense one after irradiation.
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For deducing only 99Mo specific activity, the total specific activity of 99Mo and Tc can be measured from the mixed 140.5 keV photopeak, as a sum of motherdaughter decay (Simonits et al., 1980, 1981):
99m
Asp
99
NpMoþTc =tm Mo þ 99mTc ¼ l2 K1 l1 K2 1 w þ K1 l2 l 1 2 F12
ð7Þ
where number 1 and 2 denote 99Mo and 99mTc respectively, Asp(99Mo+99mTc) is the sum of specific activities both 99Mo and 99mTc, is net number of counts under the full-energy peak from 99Mo+99mTc gamma ray emissions yielding a peak of 140.5 keV, collected during measuring time, tm. K1 and K2 are factors used for simplification of Eq. (7) defined as: K1 ¼ S1 D1 C1 and K2 ¼ S2 D2 C2 .l is decay constant (=ln 2/T1/2), is absolute gamma ray emission probability, and F12 is the fraction of 99Mo mother isotope decaying to 99mTc daughter isotope. Thus, the specific activity of the 99Mo can be calculated from the measured activity via the 140.5 keV photopeak by the following simple relation: 99 1 Asp Mo ¼ ð8Þ Asp 99 Mo þ 99mTc 2 F12 with
1 0:0452 ¼ 5:992 102 ¼ 0:8906 0:847 2 F12
Fig. 2. Simplified decay chain of
ð9Þ
99
Mo–99mTc.
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Decay data taken from NuDat database (Kinsey, 1996) and the calculated gamma ray self attenuation factors for 197Au and 98Mo, are given in Table 1. It should be noted that gamma ray attenuation factors were used only in absolute measurement of fluence rates by employing gold foil at the irradiation positions. On the contrary, these factors are canceled in Cd ratio measurements. 3.3. Determination of the ratio of thermal fluence rate to epithermal fluence rate and the cadmium ratio In a mixed isotropic thermal and 1/E1+ epithermal neutron field, the ratio of the thermal fluence rate to epithermal fluence rate can be expressed as:
f¼
Fth I0 ðÞ Gepi ¼
ðR 1Þ g0 Gth Fepi
ð10Þ
where th=the thermal neutron fluence rate, epi=epithermal neutron fluence rate, 0=the thermal neutron cross section for the 2200 m/s neutrons, g=Westcott correction factor describing 1/v departure, which can be taken to be unity for 197Au and 98Mo, Gth=thermal neutron self-shielding factor, Gepi=epithermal neutron selfshielding factor, and R=cadmium ratio defined by: R¼
A sp þ Asp =FCd
ð11Þ
þ where A sp , Asp are specific activities obtained after a bare and Cd covered foil irradiation, respectively. FCd is cadmium filter epithermal neutron transmission factor, which is a correction for the absorption of epithermal fluence rate in the cadmium cover. In general, the factor FCd is mostly 41 for elements (El Nimr et al., 1981).
Table 1 Decay data and the calculated gamma ray self attenuation factors for 197Au and 98Mo used in the activity determinations Nuclear reaction
Mo (n,g)99Mo
98
65.94 (1)
98
6.015 (9) 64.684 (5)
Mo(n,g)99Mo(b)99mTc Au(n,g)198Au
197
Detected g-ray
Half-life, T1/2 (h) Gamma ray energy, E (keV)
Gamma ray emission probability, g (%)
Gamma ray self attenuation factora, (Fg)
140.511 (1) 181.068 (8) 739.500 (17) 140.511 (1) 411.8020 (2)
4.52 (24) 5.99 (12) 12.13 (22) 89.06 (24) 95.58 (12)
1.0062 1.0037 1.0008 1.0062 1.0001
a Calculated using mass attenuation coefficients (/ ) taken from XCOM database of Berger et al., (1999) and thickness values of the foils used.
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3.4. Determination of -epithermal fluence shape factor In this study, the dual monitor method with Cd ratios have been used for the determination of a-epithermal fluence shape factor. De Corte et al. (1979b) have modified the dual monitor method of Ryves by introducing effective resonance energies. Additionally, with the introduction of Cd ratios into the dual monitor method, it does not require the knowledge of the detection efficiency curve of a gamma ray detector. Thus, the dual monitor method taking into account neutron self shielding effects in the monitors (Au and Mo) has been applied firstly to an isotopic neutron source spectrum as follows. For the determination of the a- epithermal spectrum shape factor, if, after the measurement of the Cd ratios for 197 Au(n,g)198Au and 98Mo(n,g)99Mo reactions, an equation can be derived from Eqs. 5 and 10, as follows:
ð Q 0:4264 ÞG E þC 0 r;Mo ðR 1ÞAu Mo
F ; xj ¼
¼0 ð12Þ ðR 1ÞMo ðQ 0:4264ÞG E þC 0
r;Au
Au
with C ¼
0:4264 ð2 þ 1ÞECd
ð13Þ
Q0 ¼
I0 g0
ð14Þ
and
where, F(,xj) is an implicit function form of Eq. (12), showing the dependence of a and xj parameters on error analysis. xj are either statistical variables [e.g. the þ measured specific count rates, A sp ; Asp i ] or fixed parameters (e.g. the nuclear data involved in the method). The index, i refers to the 197Au and 98Mo monitors. G is the ratio of the epithermal neutron self shielding factor, Gepi to thermal neutron self shielding factor, Gth given in Table 2 for Au and Mo foils used.
4. Results and discussion The a-epithermal spectrum shape factor has been expressed implicitly as a function of the form, F(a, xj), that is,
þ F ; xj ¼ F ; Asp;i =Asp;i ; Nuclear Data ð15Þ j
þ where x1, x2, x3,. . ., xj=(A sp;i ; Asp;i ,Nuclear Data)j are either statistical variables [e.g. þ the measured specific count rates with and without Cd-cover, A sp;i ; Asp;i ] or a fixed parameter with an associated uncertainty [e.g. the nuclear data involved in Eq. (12)]. The index, i refers to 197Au and 98Mo isotopes used as a-monitor.
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Table 2 Nuclear data used for Detector Form used
197
Au and 98Mo monitors in a-shape factor determination Nuclear reaction
Er (eV)a Fcdb
Mo(n,g)99Mo 0.025 mm-foil Mo(n,g)99Mo(b)99mTc 211 0.0005 mm-foil 197Au(n,g)198Au 5.47
g(20 C) Gthe
Gepi
Q0h
98
Mo Au a b c d e f g h
98
1.0 1.0008c 0.991 1.006d
0.999 0.992f 53.20.9 1.000 0.925g 15.70.1
Moens et al. (1979). El Nimr et al. (1981). Chang (2003). Holden (1999). Calculated by Nisle approximation, including scattering effect, given in Gilat and Gurfinkel (1963). Calculated by approximation given in Beckurts and Wirtz, (1964). IAEA (1970). De Corte et al. (1981).
According to the error propagation law, the overall relative uncertainty on a-epithermal spectrum shape factor is calculated by: " #1=2 X 2 Z; j sj ð16Þ s;T ¼ j
where sj is the relative error on each xj parameter and Z, j is error propagation factor, defined as the multiplier of the relative error on xj parameter to obtain the associated relative error on a-epithermal spectrum shape factor. The error propagation factors, Z, j for each xj parameter is defined by: d dxj xj dF dF ð17Þ ¼
Z;j ¼ xj dxj d The error propagation factors (Z,j) were calculated by using the relative uncertainties (sj) on statistical variables and nuclear data, and they are given in Table 3. Then, the calculated relative uncertainties (s,j) on a-epithermal spectrum shape factor for each parameter (xj) and the resulted overall uncertainties (s,T) on the a-shape factors at the irradiation sites are also given in Table 4. It should be noted that the application of Eq. (16), with the introduction of Z,j factors according to Eq. (17), in principle will only be realistic for moderate sj values or a=F(xj) relations, which do not deviate dramatically from linearity. Nevertheless, in most practical cases the expressions given by Eqs. (16) and (17) can be considered as an acceptable approximation (De Corte et al., 1981). Finally, the a-epithermal spectrum shape factors for the irradiation sites (Nos. 1–4) of the present 241Am–Be neutron source irradiator have been calculated from the graphically solution of Eq. (12), using a microcomputer. Fig. 3 shows a solution of Eq. (12) for a-shape factor when 197Au and 98Mo data are used. The obtained results for a-epithermal spectrum shape factor and the ratio of thermal fluence rate
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Table 3 The relative uncertainties and the calculated error propagation factors on statistical variables and nuclear data used in dual monitor method with Cd-ratios Parameter (xj)
Uncertainty, sj (%)
Error propagation factor, Z,j
197
No. 1 (=0.095)
Au
98
Mo
Q0 Er G FCd ECd a
0.8 0.3 1.4 1.0 0.2 15a
1.1 1.8 22 1.0 –
No. 3 (=0.138)
No. 4 (=0.075)
197
98
197
98
197
98
6.40 3.13 0.26 2.82 6.40 0.03
11.7 2.92 0.27 2.87 11.7
7.37 3.58 0.26 3.22 7.37 0.04
14.0 3.34 0.27 3.29 14.0
4.36 2.16 0.27 1.94 4.36 0.02
7.10 2.01 0.27 1.97 7.10
Au
þ A sp =Asp
No. 2 (=0.083) Mo
Au
Mo
Au
Mo
197
98
12.3 3.96 0.27 3.54 12.3 0.04
27.2 3.70 0.27 3.64 27.2
Au
Mo
De Corte et al. (1981).
Table 4 The relative uncertainties on a-shape factors and the overall uncertainties for each parameter involved in the method Parameter (xj)
Relative uncertainty on a-shape factor, s,j=sjZ,j(%) Irradiation hole No. 1 (=0.095)
Irradiation hole No. 2 (=0.083)
Irradiation hole No. 3 (=0.138)
Irradiation hole No. 4 (=0.075)
197
197
197
197
Au
þ A sp =Asp Q0 Er G FCd ECd
5.12 0.94 0.37 2.82 1.28 0.48
Overall uncertainty on 16.59 a-shape factor, s,T (%)
98
Mo
12.9 5.25 6.00 2.87 –
Au
5.90 1.07 0.37 3.22 1.48 0.55 19.21
98
Mo
15.4 6.01 6.00 3.29 –
Au
3.49 0.65 0.37 1.94 0.87 0.32 11.46
98
Mo
7.81 3.62 6.00 1.98 –
Au
9.87 1.19 0.37 3.57 2.46 0.60
98
Mo
29.9 6.66 6.00 3.64 –
33.25
to epithermal fluence rate for the characterization of the neutron spectrum at each of the irradiation positions are given in Table 5. The a-shape factors at the irradiation positions of 241Am–Be neutron sources in a solid paraffin moderator were found ranging from 0.075 0.025 in the central irradiation hole (No. 4), up to 0.138 0.016 when moving away from the central irradiation hole (No. 4) to the outer regions of the present irradiator. It is unexpectedly that the obtained a-shape factors at the irradiation positions (Nos.1–3) are different from each other although these irradiation holes fixed in an equilateral triangle geometry, shown in Fig. 1 are placed at equal distances. This was possibly due to the non-uniformities of paraffin wax used as a moderator, some voids forming in paraffin during the melting process of the wax, inconvenience alignments of the sources and the irradiation tubes in the present configuration.
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Fig. 3. The graphically solution of Eq. (12) for a-shape factor determination using 197Au–98Mo data.
Table 5 The measured a-spectrum shape factors and the ratios of thermal to epithermal fluence rates at the irradiation holes (Nos. 1–4) of an 241Am–Be irradiation using 197Au–98Mo Irradiation hole
No. 1 No. 2 No. 3 No. 4
f=th/e Au-monitor
Mo-monitor
ðR1ÞAu ðR1ÞMo
Spectrum shape factor, a
10.28 0.30 10.42 0.31 9.77 0.29 5.44 0.24
10.310.90 10.430.92 9.80 0.86 5.45 0.74
2.5230.050 2.6420.052 2.1590.043 2.7170.054
0.0950.015 0.0830.016 0.1380.016 0.0750.025
The overall uncertainties (s,T) on the a-epithermal spectrum shape factors of the irradiation positions (Nos. 1–4) ranged from 11.46 to 33.25%, depending on the magnitudes of the a-factors obtained by using Cd ratios for dual monitor with 197 Au–98Mo. Some methods in literature, for the experimental -determination in the 1/E1+ epithermal reactor-neutron spectrum are critically compared with respect to their accuracy and precision, by employing error propagation theory (De Corte et al., 1981). According to this critical evaluation, the reported a-shape factors were determined by the same dual monitor method, but using Cd ratios of 197Au and 94Zr with reactor neutrons, have been quoted with overall uncertainties (s,T) ranging from 7.05 to 41%. It implies that the range of overall uncertainties estimated on a-shape factors by Cd ratios of the present 197Au–98Mo monitors irradiated in low fluence rates agree reasonably with the range of those by Cd ratios of 197Au–94Zr monitors irradiated in relatively high fluence rates in reactors. In view of the experimental accuracy of the dual monitor method with cadmium ratio it has the important
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advantage that gross errors due to gamma-ray attenuation, detector efficiency, true coincidence effect are cancelled in Cd ratio measurements. However, the main drawback of the dual monitor method with Cd ratio for a-shape factor determination is that four different specific activities, Asp measured for two monitors, have to be introduced in Eq. (12), each of them contributing to the precision of the a-shape factor. This contribution is especially important for the measured Cd-covered foil activities, directly relating to resonance integral cross section of the chosen a-monitor. Hence, the 98Mo monitor having a higher resonance integral cross section of I0=6.6 b, would give more accurate peak results with a good statistical quality than that of 94Zr monitor with I0=0.3 b, when the Cd ratio measurements are carried out in low neutron fluence rates. Further, in case of 98Mo(n,g)99Mo(b)99mTc monitor reaction, the specific activities can be determined in a gamma-ray detector by using one of the gamma ray emissions of 181.1 keV (4.52%) and 739.5 keV (12.13%) from directly emitted from the 99Mo itself, as described in Section 3.1. But, since the gamma ray intensities of both 181.1 and 739.5 keV are relatively low, the statistical errors on the peak area determinations have been found to be in the order of 6–11% in the present measuring system for Cd-covered foil irradiations. Therefore, in this study, the intense 140.5 keV (89.1%) gamma ray emission mixed from mother99 Mo(b)99mTc-daughter decay was used for the more accurate activity determination of 99Mo, as described in Section 3.2. The statistical uncertainties on the 140.5 keV photopeak areas are on average 0.4% for bare Mo-foil irradiations and 0.7% for Cd-covered foil irradiations. The 140.5 keV gamma ray emission of 99 Mo(b)99mTc decay in the activity measurements for Cd- ratio method is a useful analytical peak due to its high gamma emission probability, in order to reduce substantially the counting errors affecting the final result, for example, the value of a-shape factor to be determined. However, it should noted that true coincidence effects in the 140.5 keV gamma ray have to be taken into account in the absolute determinations because of some gamma rays feeding to it especially when the 140.5 keV peak of 99Mo(b)99mTc decay is used in any absolute method. The accuracy of the dual monitor method with Cd ratio applied to the determination of a-shape factor in the real 1/E1+ epithermal-isotopic neutron sourcespectrum is dependant on the choice of suitable resonance detectors, with respect to the dominance of one single resonance peak on a negligible 1/v-tail. In this argument, because of the existing resonance peaks at 12.1 and 467.4 eV of 98Mo in the epithermal region, the use of 98Mo isotope as an a-monitor seems to be questionable at first sight, however, it is interesting to eliminate the need for resonance detectors with one single, dominant resonance peak on a negligible 1/v-tail, with the introduction of the concept of the effective resonance energy of a monitor, by modification of the dual monitor method of Ryves (De Corte et al., 1979b). In addition, when the measured Cd ratios of the chosen monitors introduced into dual monitor method, the effect of systematic errors in the individual absolute nuclear data in a large scattering in the literature can be substantially eliminated for the determination of a-shape factor, and thus the dual monitor method does not necessitate the knowledge of the photopeak efficiency curve for a gamma ray detector.
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5. Conclusions In conclusion, when the Cd ratio measurements of 197Au and 98Mo monitors with the recent nuclear data involved in dual monitor method are used, the a-shape factor in the real, non-ideal 1/E1+ epithermal-isotopic neutron source-spectrum can be determined with a sufficient accuracy. In view of the full activity to be produced in the monitors irradiated in low neutron fluence rates, the 98Mo(n,g)99Mo(b)99mTc monitor reaction as for suitable decay and nuclear data such as half-life, gamma ray and its intensity, cross sections and resonance parameters can be chosen instead of 94 Zr(n,g)95Zr or 96Zr(n,g)97Zr for the purpose of a-shape factor determination. For measuring the 99Mo activity in a gamma ray detector, the mixed 140.5 keV gamma ray emission from mother 99Mo(b)99mTc daughter decay can be preferred as an analytical peak, in especially Cd ratio measurements. However, it should noted that the necessary correction for possible true coincidence effects affecting the 140.5 keV gamma ray emission of 99mTc should be made when this peak is used in absolute measurements requiring gamma ray detection efficiency, especially at a short distance of sample to detector.
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