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New neutron long-counter for delayed neutron investigations with the LOHENGRIN fission fragment separator
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P UBLISHED BY IOP P UBLISHING FOR S ISSA M EDIALAB R ECEIVED: April 26, 2012 ACCEPTED: June 26, 2012 P UBLISHED: August 30, 2012
c H. Faust,c O. Litaize,a ¨ L. Mathieu,a,b,1 O. Serot,a T. Materna,c,2 A. Bail,a,3 U. Koster, E. Dupont,d,4 C. Jouanne,e A. Letourneaud and S. Panebiancod a CEA,
DEN, Cadarache, DER/SPRC/LEPh, F-13108 Saint Paul Lez Durance, France b Centre d’Etudes Nucl´ eaires Bordeaux Gradignan, CNRS/IN2P3, Univ. Bordeaux 1, Chemin du Solarium, F-33175 Gradignan, France c Institut Laue-Langevin, 6 rue Jules Horowitz, F-38042 Grenoble, France d CEA, DSM, Saclay, Irfu/SPhN, F-91191 Gif-sur-Yvette, France e CEA, DEN, Saclay, DM2S/SERMA/LLPR, F-91191 Gif-sur-Yvette, France
E-mail:
[email protected] A BSTRACT: Some neutrons are emitted from fission products seconds to minutes after fission occurs. The knowledge of these delayed neutrons is essential in the field of nuclear energy. But the probabilities to emit such delayed neutrons (Pn ) are not always well known. A summary of different databases and compilations of Pn values is presented to show these discrepancies and uncertainties. The usual methods used to determine these nuclear data are then reviewed with an emphasis on biases and systematic errors to be avoided. To measure precise Pn values, a new neutron LOng-counter with ENergy Independant Efficiency (LOENIE) has been built for the LOHENGRIN separator facility installed at Institut Laue Langevin (FRANCE). Its characteristics and first results obtained are presented. K EYWORDS : Neutron detectors (cold, thermal, fast neutrons); Detector modelling and simulations I (interaction of radiation with matter, interaction of photons with matter, interaction of hadrons with matter, etc) 1 Corresponding
author. address CEA Centre de Saclay, Irfu/SPhN, 91191 Gif-sur-Yvette, France. 3 Present address CEA, DAM-Ile de France, F-91290 Arpajon, France. 4 Present address OECD Nuclear Energy Agency, F-92130 Issy-les-Moulineaux, France. 2 Present
c 2012 IOP Publishing Ltd and Sissa Medialab srl
doi:10.1088/1748-0221/7/08/P08029
2012 JINST 7 P08029
New neutron long-counter for delayed neutron investigations with the LOHENGRIN fission fragment separator
Contents Introduction
1
2
Discussion of literature data 2.1 Large discrepancies 2.2 Unknown uncertainties 2.3 Zero-values and theoretical calculations 2.4 Calculation of < νd > with JEFF-3.1.1 data 2.5 Conclusion about available data
2 3 3 4 4 6
3
Measurement methods 3.1 Beta-neutron spectrometry method 3.2 Double gamma spectrometry method 3.3 Gamma-neutron spectrometry method 3.4 Beta-neutron coincidences 3.5 Beta-gamma coincidences
6 8 8 10 10 11
4
Description of LOENIE 4.1 Design of the neutron detector 4.2 Simulations of the detector efficiency 4.3 Experimental calibration of the neutron detector
11 12 13 16
5
Results of the first experiment at the LOHENGRIN separator 5.1 Presentation of the LOHENGRIN 5.2 Experimental results
16 16 18
6
Conclusion
21
A Data tables
22
1
Introduction
Delayed neutron (DN) emission is a process possible in neutron rich nuclei when after a β -decay, the daughter nucleus is left in an excited states with energies higher than the neutron separation energy. Fission produces such neutron-rich nuclei. Historically, DNs are called “delayed” because they are emitted seconds or minutes after fission occurs and can therefore be distinguished from prompt neutrons. They are of relevance for various fields of physics. In nuclear physics the probability of a nucleus to emit a delayed neutron (Pn ) is a probe of the beta-strength function and its dependence on the excitation energy. In astrophysics DNs are of relevance in the r-process [1, 2]. Initially, this rapid neutron capture process follows a path on the chart of nuclides that is determined
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1
< νd >= ∑ Yi × Pni
(1.1)
i
Since the Pn value of a nucleus does not depend on the fissioning system nor on the incident neutron energy, precise measurements of Pn values improve the accuracy of the DN multiplicity for any fissioning system, including the less common ones proposed for new generations of nuclear reactors. Nevertheless, many DN emitters are farther from stability than the majority of nuclei produced by fission. Their fission yields are thus known with large uncertainties, obviously leading to an uncertainty on the < νd > value. A campaign of measurements is in progress to improve our knowledge of isotopic yields for the most important fissioning systems. Light masses were already investigated in the past [4]–[9] and experiments are currently carried out to measure isotopic yields in the heavy mass region using the LOHENGRIN fission fragment separator at the Institut Laue Langevin (ILL) in Grenoble [10]–[12]. In the present article we will focus only on Pn measurements. The first part of this paper gives an overview of the different databases concerning Pn values, and points out the significant differences between them. The DN multiplicity is calculated for various fissioning systems using JEFF-3.1.1 data (for Pn and Yi ) and compared to integral measurements. In the second part, we review the methods involved in the Pn values measurements and we point out the parameters to check and the biases to be avoided in order to improve the measurement accuracy. In the third part, a new neutron long-counter designed to have energy-independent detection efficiency is presented. Lastly, the fourth part presents a first experiment carried out with this neutron long-counter at the LOHENGRIN separator and the first results are given.
2
Discussion of literature data
Pn values have been studied for decades and a large knowledge has been gathered [13]. Nevertheless shell models [14, 15] or quasiparticle-random-phase approximation models [16]–[19] are
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by parameters such as the neutron binding energies, neutron density or temperature. Once the intense astrophysical neutron source disappears (“freeze-out”) the neutron-rich isotopes decay back to stability and produce a characteristic distribution of isotopic abundances that can be compared to observations. As DN emissions during decay towards stability change the mass, high Pn values can alter the isotopic abundances and have to be accounted for when comparing model calculations with observed abundances. DNs are also involved in applied physics such as nuclear energy or non-proliferation control. Nuclear waste or containers with unknown content may be probed with a pulsed neutron or gamma source in order to measure DNs emitted after fission and thus detect fissile matter inside. These DNs also play a key role in the control and in safety aspects of nuclear reactors [3]. Indeed, they enable the power control with a time constant of tens of seconds instead of microseconds with the prompt neutrons. The knowledge of the number of delayed neutrons per fission (DN multiplicity), as well as the properties of the DN precursors are therefore fundamental in the field of nuclear energy. The total DN multiplicity (< νd >) depends on the cumulative isotopic yield of each precursor (Yi ) and on the probability of the precursor to emit a neutron after its β − decay (Pni ). Some exotic precursors may emit more than one neutron, but their contribution to the total DN multiplicity is negligible. < νd > can then be approximated to:
presently not yet able to predict Pn value precisely since only estimates can be made (for example with the Kratz-Hermann formula [20]). A detailed analysis of available data sources is of primary importance before beginning a new campaign of measurements. Table 6 in appendix lists the Pn values of isotopes from Z=28 (Ni) to Z=61 (Pm) for several databases and compilations: – NNDC chart of nuclides: National Nuclear Data Center website managed by the Brookhaven National Laboratory [21] – JEFF-3.1.1: the European database [22, 23]
– ENDF/B-VII.0: the American database [25] – ToI: the Eight Edition of the table of Isotopes book from Firestone [26] – Audi [27], Pfeiffer [20], and Rudstam [28]: compilations of existing data. These databases and compilations are scattered over fifteen years and one can see the evolution from Rudstam et al. (1993) to JEFF-3.1.1 (2009), ENDF/B-VII.0 (2009) or NNDC databases. Results prior to 1993 are included in Rudstam’s compilation (detailed information in [28]). We will discuss here some issues observed from this state-of-the-art analysis. 2.1
Large discrepancies
The investigation of these various data sources shows that the error bars are not always representative of the real uncertainties of the Pn values. A lot of discrepancies exist between these values and the newest values are not necessarily the most accurate/reliable ones. Figure 1 illustrates this point on several examples, whereas figure 2 presents these discrepancies for all delayed neutron precursors. Concerning the Pn values of 85 As, 135 Sb, 147 Cs (examples chosen in figure 1) or 137,138 I, values given by the various data sources are generally said to be quite accurate, with an error of 4%, 14%, 12%, 3% and 4% respectively for these precursors (according to NNDC), while the discrepancies of these values reach respectively 60%, 30%, 30%, 9% and 7% (see appendix for details). Pn values of iodine isotopes are not that uncertain but concern the most important precursors for nuclear energy, and they have to be known with a better accuracy. Moreover as remarked already twenty years ago in ref. [28], a lot of Pn values have still been measured only once, and additional measurements are required to confirm them. 2.2
Unknown uncertainties
A lot of Pn values in modern databases (JEFF-3.1.1, ENDF/B-VII.0 and JENDL/FPD-2000) lack uncertainties. The proportion of Pn values with uncertainties reaches one third of all Pn values for JEFF-3.1.1, 7% for ENDF/B-VII.0 and less than 1% for JENDL/FPD-2000. The majority of these uncertainties are only given for important precursors in term of nuclear energy.
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– JENDL/FPD-2000: the Japanese database [24]
As
147
Cs
135
Sb
94
Rb
102
Sr
136
NNDC
ENDF/B.VII.0 (2009)
JENDL/ FPD-2000 (2001)
JEFF-3.1.1 (2009)
Audi (2003)
Pfeiffer (2002)
Table of Isotope (1998)
Te
Rudstam (1993)
Pn value (%)
85
Figure 1. Example of uncertainties/discrepancies for some chosen delayed neutron precursors. Lines are shown to guide the eye.
2.3
Zero-values and theoretical calculations
The JEFF-3.1.1 database1 contains some unexpected Pn values in comparison with other databases or compilations: there are numerous zero-values for nuclei which were previously considered as DN emitters (about thirty Pn values set to zero in JEFF-3.1.1). These nuclei are often the less exotic neutron emitters of each mass chain. With a low Qβ value, their former Pn values were then often quite low, typically below 2%. One can consider for instance the case of 93 Kr (Pn ∼ 1.95%), 101 Y (P ∼ 1.94%), 129m1 In (P from 2.5 to 3.6%), 136 Te (P ∼ 1.3%, shown in figure 1). But one n n n can also notice the strange case of the very neutron-rich 101 Rb (Pn ∼ 28%). On the contrary the JENDL/FPD-2000 often omits the Pn values of quite exotic nuclei like 94 Br (Pn ∼ 70%), 109 Nb (Pn ∼ 31%) or 136 Sn (Pn ∼ 30%). Nevertheless these modern databases include a lot of Pn values for very neutron-rich nuclei with a tremendous precision (for example 104,105 Y in JEFF-3.1.1 or 125−130 Ag in ENDF/B.VII). These values are obtained by theoretical calculations and their accuracy is highly questionable. 2.4
Calculation of < νd > with JEFF-3.1.1 data
As mentioned before, the sum over all precursors of the product Pn × Yi gives the total number of DN per fission (< νd >). The two neutrons emission is also taken into account but, as previously stated, this contribution to < νd > is extremely weak (lower than 2.10−2 % whatever the fissioning system). This calculation has been performed in thermal neutron induced fission for various nuclei 1 It
also the case for JENDL/FPD-2000 and ENDF/B-VII.0 to a lesser extent.
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80 70 60 50 40 30 20 12 10 8 6 4 2 0
(b)
Figure 2. Partial charts of nuclides showing (a) the uncertainties/discrepancies between databases concerning Pn values, (b) the contribution of the precursors of importance for reactor applications to the DN emission (for 235 U(nth ,f)) and the uncertainties/discrepancies of the most important ones.
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(a)
Table 1. Comparison between < νd > values given in JEFF-3.1.1 (Integral measurement = I, compiled from various authors in [23]) and < νd > values calculated from equation (1.1) (Sum = S) with Pn and Yi from JEFF-3.1.1. 233 U(n ,f) t
235 U(n ,f) th
239 Pu(n ,f) th
241 Pu(n ,f) th
6.73E-03 7.24E-03 +8% 242m Am(n ,f) th 6.50E-03 5.82E-03 -11%
1.62E-02 1.48E-02 -9% 243 Cm(n ,f) th 3.01E-03 2.21E-03 -27%
6.50E-03 6.05E-03 -7% 245 Cm(n ,f) th 6.40E-03 5.26E-03 -18%
1.60E-02 1.23E-02 -23%
and is presented in table 1. We used JEFF-3.1.1 data for both Pn values and cumulative isotopic yields Yi . As the JEFF-3.1.1 database does not include error bars for most of the Pn values, the sum errors cannot be properly calculated. The difference (S-I)/I ranges from around −27% to +8%. One can also notice that a lot of differences are negative. It implies that the sum calculation generally underestimates the total amount of DN, either because of too low Pn and/or Yi values. It is also partly because of the zerovalues included in JEFF-3.1.1 as mentioned in the previous section. Even if Pn values are common for all fissioning systems, some wrong Pn values may have a weak or a strong influence from one fissioning system to another depending on their isotopic yields. 2.5
Conclusion about available data
Databases compiling Pn values are far from being complete (see figure 2). Only a handful of precursors are known with a good accuracy and without discrepancies (lower than 3%). The vast majority of precursors have only approximate Pn values. Nevertheless for nuclear energy, due to large differences in Yi , some isotopes are by far more important than others. The most important precursors are then 85 As, 87−91 Br, 93−95 Rb, 98m,99 Y, 105 Nb, 135 Sb, 137 Te, 137−139 I and 143 Cs. Each one represents more than 1% of the total number of DN (at least, for thermal neutron induced reactions of the main fissioning systems). 137 I itself emits 13% to 40% of the total DN depending on the fissioning system. If we combine such a list with the uncertainties/discrepancies in the data we can define a priority list of nuclei to be measured (see table 2). Thus, experiments aiming at improving the accuracy of < ν d > have to focus on these specific precursors.
3
Measurement methods
Delayed neutrons are emitted after a β decay which populates the daughter nucleus in a very excited state. Figure 3 presents the typical decay scheme of the DN emission from a precursor A X. The lifetime of the intermediate state before neutron emission is very short and the neutron is then considered as emitted at the same time as the beta. There are numerous ways to measure Pn values depending on the particles used to identify the mother nuclei A X and daughter nuclei A−1 Y. The former could be measured via β or γ-ray spectrometry, via the number of incoming ions in
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Fissioning system < νd > (Integral) < νd > (Sum) Diff. (S–I)/I Fissioning system < νd > (Integral) < νd > (Sum) Diff. (S–I)/I
Table 2. Most important nuclei to be measured in the field of nuclear energy. The proportions of DN given by each nucleus vary depending on the fissioning systems presented in table 1. ∆Pn is either the uncertainty or the discrepancy between databases.
Nucleus 137 I 98m Y 94 Rb 138 I 135 Sb 99 Y 105 Nb 91 Br 136 Te 140 I 137 Te 85 As 86 As
Proportion of all DN 13 to 40% 5 to 16% 7 to 12% 4 to 10% 0.3 to 3% 2 to 4% 0.2 to 2% 0.5 to 2% 0.6 to 1.7% 0.1 to 1.3% 0.2 to 1.5% 0.8 to 3% 0.2 to 1%
∆Pn /Pn 8% 30% 5% 2 7% 30% 20% 3 50% 15% 2 100% 4 10% 2 5% 3 60% 12% 2,3
a separated beam [29, 30] or even deduced from the fission yield (although this last old method is quite uncertain). The latter can be obtained via n or γ-rays spectrometry. Any combination of these measurements leads to a different Pn value measurement method. Moreover the two or three neutrons emission probability (P2n, P3n , . . . ) can be determined by measuring neutron-neutron coincidences. Such experiment also enables to measure the angle between the emitted neutrons and give access to information on the nuclear structure. Anyway we discuss in this paper only the β -n, double γ and γ-n spectrometry methods aiming to determine the P1n value, as well as the use of coincidence techniques to these methods. 2 If
we do not take into account a very uncertain value of Pfeiffer et al. [17]. we do not take into account a very uncertain value of table of Isotope [23]. 4 Including the zero-values of JEFF-3.1.1 (otherwise 5% 2,3 ). 3 If
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Figure 3. Typical decay scheme of a delayed neutron emission by a nuclide A X, with: Qβ the mass difference between A X and A Y (the maximum energy for a β -decay), Sn the neutron binding energy and Eβ coinc the energy of a β -decay when a neutron is emitted afterward.
3.1
Beta-neutron spectrometry method
This is the most classical method and has been used extensively for decades [30]–[34]. Its principle is to detect the (β n) branch via neutron counting and to measure the amount of mother nuclei via its β counting. Thus Pn is given by the formula: Pn =
Nn εβ × Nβ εn
(3.1)
3.2
Double gamma spectrometry method
This technique relies on the detection of gamma rays emitted by the different nuclei instead of the detection of neutron or beta particle. It has been rarely used to measure Pn values [36]–[38] but is of renewed interest now that gamma rays of exotic nuclei start to be known with rather good precision. This method has also some systematic errors but these are different from the one of the beta-neutron technique. Figure 3 presents the physics principle of the gamma emission involved in this technique. The Pn value of the nucleus A X is then given by: NA−1Y NA X Nγ BRγ1 εγE1 = 2× × Nγ1 BRγ2 εγE2
Pn =
(3.2)
with: N(A−1)Y the number of nuclei A−1 Y strictly produced by the beta decay of A X, N(A)X the number of beta decaying nuclei A X, Nγ1 and Nγ2 the number of detected γ-rays following the beta decay from A X and A−1 Y respectively, BRγ1 and BRγ2 the branching ratio of γ1 and γ2 respectively, εγ(E1) and εγ(E2) the efficiencies of γ-ray detection at the energy of γ1 and γ2 respectively. One can notice that gamma rays emitted just after the neutron emission are not detected. Indeed, either the nucleus A−1 Y is populated in the ground state or the gamma rays emitted are poorly
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with: Nβ and Nn the number of betas and neutrons detected respectively, εβ and εn the efficiencies for beta and neutron detection respectively. In case where more than one neutron or beta emitter are involved (for instance from the daughter of the A X nucleus), the neutron or beta contribution have to be properly identified via decay analysis. Then instead of equations (3.1), more complex treatment based on Bateman equations have then to be used [35]. The efficiencies of both detectors have to be measured. Or at least their ratio can be measured, via a reference experiment with a well known Pn value. Obviously it only works if this ratio is kept constant between the references experiments and the new measurements. As the efficiencies εβ and εn are completely uncorrelated, both of them have to be kept constant. The beta and neutron detectors have then to be designed according to this principle.
known. This is why the (β n) branch is determined by the number of A−1 Y inferred from its decay into A−1 Z. Equation (3.2) is valid as long as two conditions are fulfilled: –
A−1 Y
must be produced only via the (β n) decay of A X (i.e A X →(β n) A−1 Y). If A W, the mother nucleus of A X, is present and has a significant Pn value, then this nucleus produces A−1 Y via the decay of A−1 X (see the “parasitic A−1 Y production” shown on figure 4).
– Gamma rays from A−1 Y β decay must be produced only by this decay (i.e A−1 Y →β A−1 Z* →A−1 Z). If A Y has a strong (β n) decay and produces A−1 Z in an excited state, this one γ can produce the same γ-rays as the one from A−1 Y β decay (see the “parasitic γ(A−1 Z*) emission” shown on figure 4). As shown in equation (3.2), a good knowledge of the Branching Ratios (BR) is required. Although BRs have been greatly improved during the last decades, their uncertainties sometimes remains quite large. In the well detailed databases, these uncertainties can be divided into two parts: the relative BR for each gamma ray relative to the most intense gamma ray, and the second one for the most intense gamma ray normalized per decay. The first uncertainty may be reduced by using an average of several gamma rays of the same isotope. But the second one characterizes the error on the normalization factor and cannot be reduced. Eventually it induces a similar uncertainty on the Pn value and the database improvements that can be achieved by this technique are limited by the uncertainties on the BRs. Generally, the uncertainties on the A X BRs are larger than those of A−1 Y, because A X is farther from beta stability and thus known with less precision. Eventually, as there is a ratio of efficiencies in the formula, the absolute efficiencies are not needed. Only relative efficiencies are sufficient.
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Figure 4. Complete decay scheme of a delayed neutron emission of a nucleus A X (with parents). One can see that A−1 Y can also be produced via the β n decay of A W, and A−1 Z* via the β n decay of A Y. These two parasitic ways may induce an overestimation of the measured Pn value of A X.
3.3
Gamma-neutron spectrometry method
This technique is a hybrid since it is based partly on both previous methods and is much less used than the first ones. Here the β branch is identified via the gamma rays emission following the beta decay of the A X nucleus (as in the double gamma method), and the (β n) branch is identified via neutron counting (as in the beta-neutron method) [39]. The Pn value is now given by: Nn BR · εγ Pn = × (3.3) Nγ εn
3.4
Beta-neutron coincidences
Coincidence technique is often used to improve the signal-to-background ratio [1, 30, 32]. As delayed neutrons are emitted just after a β decay occurs, it would be possible to detect them simultaneously. In the beta-neutron method, the equation (3.2) would become: εβ Nn−coinc Pn = × (3.4) Nβ εn−coinc where: Nn−coinc is the number of neutrons detected in coincidence with a β , εn−coinc is the efficiency of detecting a neutron in coincidence with a β . If εβ is constant over the whole energy range, then εn−coinc = εn · εβ , and εβ can be discarded: εβ Nn−coinc × Pn = Nβ εn · εβ (3.5) Nn−coinc = Nβ · εn Nevertheless, the beta detection threshold cuts a fraction of the total spectrum which depends on the total beta energy (minor fraction for high energy beta decay, major fraction for low energy beta decay). Table 3 shows the Qβ and Qβ n values for some representative cases: nuclei used for reference measurements (to determine the εβ /εn ratio) or for Pn measurements. Firstly, one can notice that all Qβ are above 5 MeV. Thus, it can be assumed that εβ does not change that much between these two sets of measurements. In fact the essential term is not only Qβ but its effective value (Qβ eff ) taking into account the feedings, as reported in ref. [40]. Secondly, as neutrons are emitted from a highly excited state, they only follow beta decay of low energy and therefore Qβ n is much lower than Qβ . Unless the detection threshold is kept very low, it will cut a different fraction of the spectrum. Then εn−coinc 6= εn · εβ and equation (3.5) is no longer valid. Its use would then induce a significant error on the Pn value. Nevertheless, the use a thin detector (for instance a silicon detector [35, 41]) and/or a digital acquisition system allow to reduce drastically the threshold and to obtain a constant εβ . Under these conditions, εn−coinc = εn · εβ even with very different Qβ values. We have to keep in mind that no thick screen between the beta emission and any part of the beta detector (like the borders of a chamber window or of a collimator) must be present. Indeed, such a screen would introduce a difference between the betas of low and high energy, keeping εβ far from being constant.
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This method has the advantages and drawbacks of both previous methods. As it does not use any beta detector, there is no problem of energy dependant efficiency or threshold. Nevertheless it requires gamma ray BRs of the A X decay scheme which are rarely known with a good accuracy.
Table 3. Example of Qβ values for several precursors of interest [26]. The impact of doing a beta-neutron coincidence is clearly seen on the beta energy (column “Qβ n ”). For the beta-gamma coincidence method, the lower Qβ value of the daughter nuclei is obvious.
Nuclei 88 Br 90 Br 95 Rb 139 I 143 Cs 146 Cs 92 Br 94 Rb
Pn measurements
96 Rb 135 Sb 136 Te 137 I
3.5
Qβ n = Qβ −Sn (MeV) 1.907 4.040 4.903 3.206 2.049 4.320 6.650 3.561 5.860 4.620 1.290 1.854
Daughter nuclei after (β n) 87 Kr 89 Kr 94 Sr 138 Xe 142 Ba 145 Ba 91 Kr 93 Sr 95 Sr 134 Te 135 I 136 Xe
Qβ (MeV) 3.887 4.990 3.511 2.770 2.212 4.120 6.440 4.083 6.080 1.560 2.648 -
Beta-gamma coincidences
The problem here is similar to the one explained for beta-neutron coincidences. In this case, unless the threshold is kept at a very low value, the detection efficiency of A X and A−1 Y via their γrays in coincidence with their β -rays will not be the same. Indeed, in the field of nuclear energy measurement, A X is always relatively far from stability and Z-odd and A−1 Y closer to stability and Z-even. The difference in Qβ is then large as can be seen on the right side of table 3.5 Eventually, the use of coincidence technique in the double gamma method will always underestimate Pn values. Finally, the re-investigation of these methods points out the fact that a beta coincidence should be avoided unless the beta detector can handle a very low threshold. Indeed, without a specific design or detector, a constant εβ cannot be achieved and the use of coincidence technique strongly reduces the relevance and the accuracy of the Pn measurement. As for εβ , εn has to be constant and we will discuss in the following the design of a new neutron detector with such characteristics.
4
Description of LOENIE
The beta-neutron spectrometry is the most commonly used method and therefore Pn value measurements often require a neutron detector. As previously stated, the neutron detection efficiency has to be kept constant in order that equation (3.1) is valid. Therefore, we have developed a new neutron detector designed to fulfil this constraint. Features of this detector will be presented as well as a comparison with the Mainz neutron long counter. 5 Nuclei
of table 3 were chosen for their interest for the explanation of the beta-neutron coincidence method. They are not always interesting or measurable via beta-gamma coincidence.
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Reference measurements
Qβ (MeV) 8.960 10.350 9.296 6.806 6.243 9.380 12.200 10.307 11.756 8.120 5.070 5.880
4.1
Design of the neutron detector
The usual detector used to detect DN is a “long counter”: 3 He tubes embedded in rings into a moderating material (generally polyethylene) as shown in figure 5 [42]–[46]. The 3 He tubes detect neutrons thanks to the 3 He(n,p)t reaction. The cross section of this reaction is quite low in the MeV energy range (1 barn) but reaches high values in the thermal energy range (about 5,000 barns). As the DN energy lies between few keV and few MeV, neutrons have to be thermalized before reaching the 3 He tubes in order to increase their detection efficiency. Because of the thermalization step, the DN initial energy information is nearly lost in this device. It is however possible to derive an average energy via the so-called ring ratio method. Indeed, as the inner and outer rings are more sensitive respectively to neutrons of few keV or few MeV, the ratio between their counting rates provides an indication of the mean neutron energy. In fact, such a method is approximate since the detection efficiency of each ring is strongly non-linear with the energy. The derived mean energy is therefore spectrum-dependent.
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Figure 5. Open and closed side views of LOENIE (upper part) and side and top view of its MCNP scheme (lower part).
0,2 Total
Efficiency
0,15
0,1
Inner Ring
Outer Ring 0,05
0,5
1 1,5 Neutron Energy (MeV)
2
Figure 6. Absolute efficiencies of the LOHENGRIN long-counter “LOENIE” from MCNP simulations as a function of the delayed neutron energy.
The new LOng-counter with ENergy Independant Efficiency (LOENIE) is an octagon (diameter of 42 cm face-to-face) with an axial hole. Eighteen proportional counters filled with 10 bar 3 He are embedded in a polyethylene matrix in two concentric rings. This setup is rather classical in its principle but has been developed to ensure an equilibrium between the inner and the outer rings. Based on Monte Carlo simulations (see following section) the distribution of the 3 He tubes over the rings and the radii of the rings were optimized to minimize the energy dependence of the overall detection efficiency. Thus, the inner ring contains only three 3 He tubes whereas the outer one contains the fifteen remaining tubes. The radius of each ring is 8 cm and 17 cm respectively. The central hole is rectangular-shaped and wide enough (8.5 cm × 11 cm) to contain a vacuum chamber. When using the beta-neutron method, the beta detector (for example a plastic scintillator) has to be placed close to the stopping point of the ions in the central hole. This detector, as well as a HPGe detector, were included in the simulation. A lateral hole was dug to house the tape moving system in order to remove the long-lived activity far from the detectors and to prevent them from increasing the beta and gamma ray background. Around the detector, two layers of neutron shielding are placed: a 5 mm-thick B4 C layer surrounded by a 2.5 cm-thick borated polyethylene layer. This shielding was proven to ensure a neutron background below 1.5 cps over the whole detector. This level is quite small considering the relatively high neutron background in this experimental area. 4.2
Simulations of the detector efficiency
The efficiency εn of the detector has to be known with a good accuracy since this term appears in the Pn determination (equation (3.1)). MCNP [47] simulations were developed to determine the equilibrium between the inner ring and the outer ring. The simulated efficiency shown in figure 6 clearly illustrates the dependence of the detection efficiency on neutron energy: the inner ring is more sensitive to neutrons of few keV while the outer ring is more sensitive to higher energies. As inner and outer rings counter-balance each other almost exactly, the total efficiency is nearly constant (within 1% relative) on a wide energy range [0;1MeV]. In addition above 1MeV the decrease of the efficiency is only −7% per MeV up to 5 MeV.
– 13 –
2012 JINST 7 P08029
0
0,5 Total
Efficiency
0,4 0,3 Inner Ring 0,2 Middle Ring 0,1 Outer Ring 0 0
0,5
1 1,5 Neutron Energy (MeV)
2
Figure 8. Absolute efficiencies of the Mainz long-counter from MCNP simulations as a function of the delayed neutron energy.
Results from MCNP simulations have always to be taken with great care as the final precision (from uncertainties on cross-sections, geometry or materials) is rarely below 5% [48]. MCNP calculations carried out with various hypotheses (thermal treatments, gas pressure,. . . ) show different absolute efficiency but remain in all cases independent of the neutron energy. It can then be assumed that the constancy of the efficiency is reliable. The efficiency of our detector has been compared with some existing neutron long counters in order to assess their detection efficiency in a given neutron spectrum. The Mainz long-counter (figure 7 and detailed in [32, 49]) is a representative example of a neutron detector used to measure Pn values. It is made of three dense rings of 3 He tubes and is surrounded by a thick and efficient neutron shielding. MCNP simulations have been carried out to determine its efficiency as shown in figure 8. The total efficiency is roughly constant from few keV to 500 keV but then decreases at a nearly linear rate (−3.5% per 100 keV up to 3 MeV). This behaviour is due to the paramount role of the inner ring. The Mainz long counter is optimized for best detection efficiency (e.g. to find new exotic isotopes and measure their lifetimes) but not for a very constant detection efficiency. To illustrate this point we have evaluated the efficiency of several long-counters for measured neutron spectra and not only for mono-energetic neutrons. Indeed some delayed neutron spectra
– 14 –
2012 JINST 7 P08029
Figure 7. Mainz long counter (left part) and its MCNP scheme (right part).
88
Br 136
-2
Te 139
-4
I
96
94
Rb
Rb 95
-6
Rb
146
-8
-10 200
"LOENIE" long-counter Mainz long-counter "BELEN-20" long-counter "NERO" long-counter 300
90
Cs
137
Br
I
400 700 600 500 Mean energy of delayed neutrons (keV)
135
Sb
800
900
Figure 9. Evolution in detection efficiency of four detectors for real spectra as a function of average energy. These variations are compared to the efficiency at 248 keV (spectrum from 88 Br).
have been measured [50] and can be associated with the efficiency function to obtain the experimental efficiency. In addition to “LOENIE” and Mainz long-counter, we have added to the evaluation the “BELEN-20” [51] and “NERO” [46] detectors. For these ones, the efficiency function was not simulated but extracted from corresponding publications. Figure 9 shows the evaluated detection efficiencies as a function of the average energy of the delayed neutron spectra and compared to the efficiency in detecting the 88 Br delayed neutron spectrum ( = 248 keV). For instance, the efficiency to detect the 95 Rb delayed neutrons is decreased by 0.7% for the LOHENGRIN long-counter whereas this reduction reaches 4.4% for Mainz long-counter. One can see the strong decrease of the detection efficiency with the average neutron energy on Mainz and NERO long-counters. On the contrary, BELEN-20 and especially LOENIE have a more constant efficiency. Therefore, one can see the impact of the detector design on the efficiency constancy. The 92 Br case (not shown here) is exceptional since = 1,580 keV. The detection efficiency variations reach then −8% for LOENIE or BELEN-20 long-counters and −18% for the Mainz and NERO detectors. This effect is often forgotten or neglected [31, 33] but should be taken into account to measure Pn value for high neutron energy ( > 500 keV). However, the efficiency difference is often applied based on the mean energy obtained by the ring ratio technique [30, 52, 53]. As this technique is very approximate and the mean energy does not infer the mean efficiency, systematic errors may appear at this stage. Apart for precursors of very high energy delayed neutrons, this clearly points out the interest of LOENIE in the field of precise Pn value measurements in a rather large energy range. For other types of measurements or very exotic Pn measurements (where the uncertainty is dominated by other factors like statistic or contaminants), such accuracy becomes pointless and other detectors are more efficient.
– 15 –
2012 JINST 7 P08029
Difference with efficiency at 250 keV (%)
0
Table 4. Delayed neutron average energy for several precurors of interest [50].
4.3
Pn measurement Nuclei (keV) 92 Br 1,580 94 Rb 444 96 Rb 435 135 Sb 811 136 Te 291 137 I 624
Experimental calibration of the neutron detector
The experimental measurement of a long-counter efficiency is not an easy task since one should be able to compare to simulations under very constraining conditions i.e. an isotropic and monoenergetic neutron source. The use of a 252 Cf or Am-Be source provides an isotropic but non monoenergetic neutron spectrum, while using reactions from a light ion beam on a target may produce mono-energetic neutrons (at a given angle) but not an isotropic source. Such sources may nevertheless be used by taking into account the anisotropy of the neutron emission [46]. As reference measurements give the εγ /εn ratio (see section 5.2), it was decided to use a gamma source to measure εγ and thus infer εn . This has been performed with a 60 Co source and the efficiency of the long-counter has been evaluated to be (23.1+/−0.3)%. This result is not in agreement with MCNP simulations which gives an efficiency of 17.3%. This disagreement is either due to a problem during the gamma calibration or due to the MCNP simulations. It can be noticed that in ref. [46], a strong disagreement between MCNP simulations and calibration experiments was also observed and was corrected by using a scaling factor to adjust MCNP results. Nevertheless, in spite of this factor the efficiency evolution was more or less correctly fitted. This discrepancy remains unexplained and may be due to cross section libraries used in the MCNP program and especially for the thermal treatment in the neutron moderation [48]. This part of the calculation is a way to take into account the molecular structure of materials in the neutron moderation at low energy, and is specific for the simulated problem (paraffin, light or heavy water. . . ). Several tests using different databases or S(α, β ) treatments give different efficiencies. For instance without S(α, β ) treatment the simulated efficiency is said to be 21.7%. Most importantly, as already stated, every hypothesis always leads to flat efficiency on the [0;1MeV] energy range. Thus, and according to ref. [46], the description of the efficiency evolution with energy derived by MCNP simulations can be assumed to be correct.
5 5.1
Results of the first experiment at the LOHENGRIN separator Presentation of the LOHENGRIN
The new long-counter LOENIE has been tested on the LOHENGRIN separator [54, 55]. This separator is installed at the high flux reactor of Institut Laue Langevin. An actinide target is placed near the reactor core in a high thermal neutron flux and fission products pass through the spectrometer
– 16 –
2012 JINST 7 P08029
Reference measurement Nuclei (keV) 88 Br 248 90 Br 647 95 Rb 569 139 I 411 143 Cs 251 146 Cs 609
(see figure 10). They are separated thanks to a magnetic field (main magnet) and an electrostatic field (condenser). The combination of both fields selects ions according to their A/q and E/q ratios (A is the ion mass, q its ionic charge and E its kinetic energy). After the ion separation, an additional magnetic field (RED magnet) focuses the fission products in order to increase significantly the ion flux in the spectrometer focal plane. The mass spectrometer then provides not only a mass chain, but different mass chains with the same A/q and E/q ratios. For integer A/q ratios, several masses are separated simultaneously, e.g. for A/q = 100/20, there are also A/q = 95/19 or A/q = 105/21. Usually, one avoids integer ratios in order to reduce possible contaminants by choosing judicious values of A and q (for example A/q = 100/21 or A/q = 100/19). To obtain the maximum ion rate for spectroscopy experiments often relatively large and thick fission targets are used. Hence, the mass resolution of the spectrometer is compromised and even for non-integer A/q ratios tails of other masses may come along with the fission products of interest. Even with relative abundances of few percent these contaminant masses may be problematic, if they emit a lot of gamma rays (for double gamma or gamma-neutron techniques) betas (for beta-neutron technique) or neutrons. As required for the decay analysis, the beam was pulsed thanks to a chopper magnet in order to study the grow-in and specially the disappearance of nuclei. The most problematic contaminants are therefore those with half-life comparable with the half-life of the precursor of interest. It is then useful to repeat experiments for the same nuclei by changing the q value in order to change the contaminant and to validate the results. As presented on figure 5, the experimental setup included a vacuum chamber (where fission products are stopped) placed in the middle of the long-counter. A tape system enables the removing of fission products far from the detection system in order to reduce long-lived background. Since the beta chamber was not ready, we have used the gamma-neutron hybrid method (see section 3.3). Then, the HPGe detector was inserted in the central hole of the long-counter, close to the vacuum chamber. In this first version of LOENIE, only the 5 mm-thick B4 C neutron shielding was present (no 2.5 cm-thick borated polyethylene layer). The purpose of such a thin layer was to stop the already thermalized neutrons in the ambient background in the vicinity of the RED magnet.
– 17 –
2012 JINST 7 P08029
Figure 10. Scheme of the LOHENGRIN separator. LOENIE was installed on the ”bent beam” position.
4×10
3×10
2×10
1×10
5
5
5
5
5
0
0
500
1000 2000 1500 γ-ray energy (keV)
2500
3000
Figure 11. Example of normalized counting rate (including branching ratio correction) of γ-rays of (from 93 Rb β -decay).
5.2
93 Sr
Experimental results
The neutron-gamma method implies to measure gamma rays of the precursors of interest, and to correct the experimental counting rates by the branching ratio data and the γ-rays detection efficiency. This efficiency was determined using reference beams of 96m Y and 93 Sr which have well known transitions over a large energy range. The efficiency evolution as a function of the γ-ray energy has been fitted with a simple function: εγ = a.E−b γ + k. This simplified function is sufficient on a limited energy range (typically from 200 keV to 2200 keV). Figure 11 shows the normalized intensities of the various gamma lines of 93 Rb β -decay. One can see the large discrepancy of some lines but the overall good agreement of the weighted mean value (within its standard deviation) considering the large data uncertainties. From the calibration experiment, the absolute efficiencies were found to be about 2.0% and 1.3% at 662 keV and 1173 keV respectively. Once the energy dependence of γ-rays detection efficiency was determined, several fission products of interest were measured. First, the εγ /εn ratio was deduced from the well known 87,88,90 Br and 94,95,96 Rb P values. Precursors used for that purpose are not strictly those of tan ble 3 since in this method we have to take into account the gamma BR knowledge (which for instance is poor for 139 I and 143,146 Cs). The measured efficiency ratios are shown in figure 12. As in the previous figure, the weighted average and its standard deviation (0.0867+/−0.0025) are represented with lines. According to the MCNP simulation, this ratio is supposed to be constant and valid in the [0;1MeV] energy range. Unfortunately the experimental error bars on figure 12 are yet too large to verify this hypothesis. Three typical examples of Pn measurement are illustrated in figure 13. This figure presents the time evolution of the counting rates during beam ON and beam OFF phases. The upper plot refers
– 18 –
2012 JINST 7 P08029
Normalized counting rate (a.u)
5×10
0,14 0,12
95 87
εγ
662keV
/εn
0,1
96
Br 88
Rb
Rb
(2 meas.)
Br
0,08 94
0,06
Rb
(3 meas.)
90
Br
(4 meas.)
0,04
0 200
300 400 600 500 Mean energy of delayed neutrons (keV)
700
Figure 12. Efficiency ratios εγ662keV /εn measured for reference precursors as a function of the average delayed neutron energy (taken from JEFF-3.1.1). The weighted mean, together with the standard deviation, are also indicated.
to the measurement of the reference 94 Rb Pn value (T1/2 = 2.70 s, NNDC = (10.5+/−0.5)%). Although a high neutron background can be seen on the outer ring, the (β n) decay of 94 Rb clearly appears, fitted with an ‘exponential + background’ function (only N and K were free parameters). Thus, the influence of 94 Kr (T1/2 = 212 ms, low isotopic yield) on the decay curve of 94 Rb is neglected. Knowing the 94 Rb Pn value, this measurement leads to a εγ /εn ratio of 0.0793+/−0.0040. 94 Rb as well as 95 Rb and 90 Br were measured several times with different LOHENGRIN spectrometer settings (see figure 12). The same fit of 99 Y (middle plot, T1/2 = 1.47 s, NNDC = (1.9+/−0.4)%) gives a Pn value of (1.77+/−0.19)%. The case of 136 Te (T1/2 = 17.7 s, = (1.31+/− 0.05)% or 0% in [22, 23]) is more difficult to analyse. A fit of the decay curves with two exponentials was necessary because of the presence of a contaminant. For this case, N, Ncont , λcont and K were free parameters. It appears that the LOHENGRIN spectrometer settings have allowed a non-negligible amount of 85 As (T1/2 = 2.0 s) to pass through. For this first test a very thick fission target with an exceptionally wide energy distribution was used which may lead to the contamination of the beam with masses that are far from the wanted mass but have an identical mass over ionic charge ratio A/q. Under normal operation conditions light and heavy fission fragments cannot occur together. Therefore, the 136 Sb (T1/2 = 0.92 s, = (16.3+/−3.2)%) nucleus of interest, which could have been observed, is completely hidden by 85 As. Moreover, the large neutron background overcomes the delayed neutron signal and increases the uncertainty of the fit result (5% for the inner ring, 20% for the outer ring). The measured Pn value ((1.34+/−0.13)%) is consistent with literature but is provided with a rather large uncertainty. Nevertheless, it still contradicts the zero-value in JEFF3.1.1. This example shows that no accurate measurement of a weak neutron emitter could be made with such a background.
– 19 –
2012 JINST 7 P08029
0,02
94
Rb -λt
total N = 5002(112)
f(t) = λN e
+K
3
Counts
10
outer ring N = 2072(85)
2
10 0
10
5
20
15 Time (s)
total N = 189.3(13.9)
3
10
25 99
Y -λt
f(t) = λN e
30
+K
Counts
outer ring N = 74.0(12.5)
inner ring N = 115.3(6.1) 2
10
0
10
5
15 Time (s)
20
25
total 136 Te N = 10012(800) -λt -λ t f(t) = λN e + λcontNconte cont + K
Counts
136 Te 85 s + A 85 s (cont.) A
3
10
outer ring N = 3846(716) inner ring N = 6179(343)
136
Te
2
10 0
20
40
60
80
100
Time (s) Figure 13. Decay curves measured with LOENIE for 94 Rb (upper part), 99 Y (middle part) and 136 Te (lower part). Numbers in parenthesis represent the statistical uncertainty.
– 20 –
2012 JINST 7 P08029
inner ring N = 2937(72)
Table 5. Pn values measured during the first experiment on LOHENGRIN with LOENIE. Numbers in parenthesis represent the error on the last digits of the Pn value. 99 Y
136 Te
1.9(4)% 1.03(4)% 2.2(5)% 1.9(4)% 1.7(4)% 0.96% 2.5(5)% 1.9(4)% 1.77(19)%
1.30(6)% 1.1(6)% 1.26(2)% 1.31(5)% 0% 1.1% 1.30(6)% 1.31(5)% 1.34(13)%
Table 5 shows the two Pn values measured during this experiment. The 99 Y Pn value is in excellent agreement with previous data and greatly improves its precision. The Pn value obtained for 136 Te is less precise than the previous measurements but constitutes an additional confirmation that the zero-value of JEFF-3.1.1 is actually wrong.
6
Conclusion
A large amount of Pn values are still very uncertain since many discrepancies remain between databases. A large work of compilation has been performed and is summarized in this paper. Pn values important for nuclear energy could still be improved (94 Rb and 137 I for instance). A first experiment has been carried out at the LOHENGRIN separator by using the new LOENIE detector and a hybrid method. The method is based on neutron and gamma-ray detections, and permits to be free from beta detection issues. LOENIE has been built at the Institut Laue Langevin to solve the constraint of constant neutron detection efficiency. In this long-counter a less efficient inner ring counter-balances the outer ring to lead to a constant efficiency. The results of the experiment are rather satisfactory although some of the data have too large uncertainties to be useful. In order to improve this, the neutron background had to be reduced and additional shielding has been added to the detector. Experiments are foreseen with this detector coupled with a beta detector (with a detection efficiency as constant as possible) initially at the LOHENGRIN separator. Later this setup can also be moved to extend the measurement campaign to other facilities.
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2012 JINST 7 P08029
Databases Compilation from Rudstam (1993) Table of Isotope books (1996) Compilation from Pfeiffer (2002) Compilation from Audi (2003) JEFF-3.1.1 Database (2005) JENDL/FPD-2000 Database (2001) ENDF/B-VII.0 Database (2009) Chart of nuclides from NNDC This work
A
Data tables
Table 6. Compilation of Pn values (in %) from different databases. Numbers in parenthesis represent the error on the last digits of the Pn value. Lastly, some Pn values are accompanied by a ’ + ’ symbol, meaning that for these nuclei the β - decay can be followed by the emission of two neutrons. The value given here is the P1n value. Z
29 Cu
30 Zn
31 Ga
32 Ge
33 As
NNDC chart of nuclides
75 76 77 78 73 74 75 76 77 78 79 80 78 79 80 81 82 83 79 80 81 82 83 84 85 86 83 84 85 86 87 88 89 84 85 86 87 88 89 90 91 92
8.43
3.5 (6) 3 (2)
55 (7)
1.3 (4) 1.0 (5) 7.5 (3)
0.089 (19) 0.86 (7) 11.9 (7) 19.8 (10) 37 (7) 70 (15)
10.8 (6) 14 (3)
0.28 (4) 59.4 (24) 33 (4) 15.4 (22)
ENDF/ B-VII.0 (2009) 8.43 4.108 4.859 10.81 0.075 3.5 3 17.5 17.5 55 22.53 1.3 1 7.5 17.17 23.3 0.09 0.86 11.9 19.8 37 70 60.39 60.39 10.8 14 6.044 11.43 17.48 19.09 0.28 59.4 (24) 33 15.4 23.06 29.69 30.83 58.13 40.55
JENDL/ JEFF-3.1.1 FPD-2000 (2001) (2009) 1.6
3.5 3
0.009 1.2 3.37
0.002 4.9 12 13 24
0.085 50 12 42 30
Pfeiffer
(2003) 1.6
(2002)
3.5 3
3.5 (6) 3 (2)
55
55 (7)
0.029 (6) 0.075 (16) 2.6 (5) 2.4 (5) 15 (8) 15 (8) 55 (7)
1.3
1.3 (4) 1.0 (5) 7.5 (3)
1.3 (4) 1.0 (5) 7.5 (3)
7.5
0.1 0.86 12.2 21.9 44 39
Audi
0.089 11.9 21.3 37 70
0.089 (19) 0.89 (6) 11.9 (7) 21.3 (13) 37 (7) 70 (15)
10.8 14
10.8 (6) 14 (3)
10.2 (9) 14 (3)
0.28 22 (3) 33 15.4
0.28 (4) 59.4 (24) 33 (4) 15.4 (22)
0.18 (10) 55 (14) 26 (7) 17.5 (25)
– 22 –
Table of Isotopes (1996)
Rudstam
3.5 (6)
3.5 (6) 3 (2)
(1993)
55 (7)
1.3 (4) 1.0 (5) 7.5 (3)
0.080 (14) 0.098 (14) 0.089 (19) 0.85 (6) 0.79 (7) 0.89 (6) 12.1 (4) 11.4 (8) 11.9 (5) 22.3 (22) 19.8 (10) 22.3 (22) 38.7 (98) 54 (7) 40 (14) 70 (15)
10.8 (6)
0.08 (4) 23 (3) 12 (3) 44 (14)
0.28 (4) 59.4 (24) 33 (4) 15.4 (22)
2012 JINST 7 P08029
28 Ni
A
34 Se
36 Kr
37 Rb
38 Sr
0.2 (4) 0.67 (30) 7.8 (25) 21 (10)
2.6 (4) 6.58 (18) 13.8 (4) 25.2 (9) 20 (3) 33.1 (25) 68 (7) 68 (16)
0.0332 (25) 1.95 (11) 1.11 (7) 2.87 3.8 8.2 7.0 (10) 11 0.0107 (5) 1.39 (7) 10.5 (4) 8.73 (20) 14.0 (7) 25.1 (8) 13.8 (6) 15.9 (20) 6+ (3) 28 (4) < 0.05 0.25 (5) 0.100 (19) 0.78 (13) 2.37 (14) 4.8 (23)
0.2 0.67 7.8 2.991 21 11.77 10.91 13.83 2.52 (7) 6.4 (5) 13.8 (4) 25.2 (9) 20 33.1 68 70 34 27.6 46.8 0.0332 (25) 1.95 (11) 1.26 2.87 3.8 8.2 7 11 16.61 1.39 (7) 10.01 (23) 8.73 14.0 (7) 25.1 (8) 13.8 15.9 6+ 28 18 < 0.05 0.25 (5) 0.100 (19) 0.78 2.37 4.8 9.952 8.34 10.42
0.18 0.94 7.5 7.2 22
2.58 6.35 14.2 24.9 18.3 32 34
0.032 1.93 6.1 12 11
0.01 1.36 10.2 8.59 14.2 26.9 13.4 13.1 6 31 (6) 0.006 0.32 0.33 0.73 2.37 4.8
0.99 7.8
0.20 (4) 0.99 (10) 7.8 (25)
0.36 (8) 0.67 (30) 7.8 (25)
0.18 (5) 0.94 (16) 5.0 (15)
0.36 (8) 0.99 (10) 7.8 (25)
21
21 (10)
21 (10)
21 (10)
21 (10)
2.51(8) 6.7(2) 14.1 24.6(7) 20(2) 33.1 68 70
2.60 (4) 6.58 (18) 13.8 (4) 25.2 (9) 20 (3) 33.1 (25) 68 (7) 70 (15)
2.52 (7) 6.55 (18) 13.7 (4) 24.9 (10) 31.3 (60) 33.7 (12) 65 (8) 68 (16)
2.57 (15) 6.4 (5) 13.0 (11) 24.6 (7) 18.3 (13) 33 (3) 77 30 (10)
2.52 (7) 6.58 (18) 13.8 (4) 25.2 (9) 20 (3) 33.1 (21) 10 (4) 30 (10)
1.11 2.87 3.7 6.7 7 11
0.0332 (25) 1.95 (11) 1.11 (7) 2.87 (18) 3.7 (4) 6.7 (6) 7 (1) 11 (7)
0.033 (3) 1.95 (11) 5.7 (22)
0.033 (3) 0.0332 (25) 2.01 (16) 1.95 (11) 5.7 (22) 5.7 (22)
0.0107 (5) 1.39 (7) 10.01 (23) 8.73 (20) 13.4 (4) 25.7 (8) 13.8 (6) 15.9 (20) 5.6 (12) 28 (4) 18 (8) < 0.05 0.25 (5) 0.100 (19) 0.78 (13) 2.37 (14) 5.5 (15)
0.011 (1) 1.44 (10) 9.1 (11) 8.73 (31) 13.3 (7) 26.0 (19) 14.6 (18) 17.3 (25) 12 (7) 25 (5) 18 (8) 0.02 (1) 0.40 (7) 0.25 (10) 1.11 (34) 2.75 (35) 5.5 (15)
0.0107 (5) 0.0107 (5) 1.35 (7) 1.35 (5) 10.4 (4) 10.01 (23) 8.73 (20) 8.73 (20) 13.8 (9) 13.4 (4) 25.1 (8) 25.7 (8) 13.6+ (5) 13.8 (6) 20.7 (23) 15.9 (20) 6 (3) 5.6 (12) 31 (6) 25 (5) 18 (8) 18 (8) 0.005 (3) < 0.05 0.18 (2) 0.25 (5) 0.095 (6) 0.10 (19) 0.73 (3) 0.98 (23) 2.37 (14) 2.52 (24) 4.8 (23) 5.5 (15)
1.40 (8) 10.1 (2) 8.6 (2) 13.4 (4) 25.1 (8) 13.8+ 15.9 5.6+ 18 0.05
0.78 2.37 5.5
– 23 –
2012 JINST 7 P08029
35 Br
87 88 89 90 91 92 93 94 87 88 89 90 91 92 93 94 95 96 97 92 93 94 95 96 97 98 99 100 92 93 94 95 96 97 98 99 100 101 102 97 98 99 100 101 102 103 104 105
39 Y
41 Nb
42 Mo
43 Tc
0.058 < 0.08 0.331 (24) 3.4 (10) 1.9 (4) 0.92 (8) 1.94 (18) 4.9 (12) 4.9 (12) 8 (3)
0.08 0.331 (24) 3.4 2.5 (5) 0.92 1.5 4 4 8 11.56 20.42 24.01 31.73 25.54
0.061 0.11 0.21 3.1 0.96 0.81 2.3 1.94 6 19
0.02 0.23 1.476 1.727 5.82 3.968 7.114 0.06 (3) 0.05 (3) 1.7 (9) 4.5 (3) 6.2 (5) 31 (5) 40 (8)
0.06 0.05 1.7 4.5 6.0 6.2 31 40 22.06 21.09 55.76
0.01 0.46 0.5 4.5 2.7 9.1
0.07
0.08 (2) 0.04 0.85 (20) 1.5 2.1 (3)
0.313 1.233 1.806 4.255 5.33 0.08 0.04 0.85 1.5 2.1 1.3 13.33 11.74 22.99 17.17
0.055 (4) 0.05 (2) 0.27 (7) 3.44 (95) 1.7 (4) 0.92
4.9 4.9 8 8.7769(880) 19.753(200)
0.058 (7)
0.045 (20) < 0.08 0.295 (33) 3.4 (10) 2.2 (5) 1.16 (32)
0.055 (4) < 0.08 0.24 (1) 3.4 (10) 1.03 (4) 0.81 (4)
0.057 (7) < 0.08 0.331 (24) 3.4 (10) 1.9 (4) 1.02 (7)
1.94 (18) 4.9 (12) 4.9 (12) 8 (3)
2.3 (8) 5.0 (12)
1.94 (18) < 6.0 (17) < 6.0 (17)
2.9 (7) 6.0 (17)
0.06 (3) 0.05 (3) 1.7 (9) 4.5 (3) 6.0 (15) 6.2 (5) 31 (5) 40 (8)
0.06 (3) 0.05 (3) 1.7 (9) 4.5 (3) 6.0 (15) 6.2 (5) 31 (5) 40 (8)
0.08 (2) 0.04 (2) 0.85 (20) 1.5 (2) 2.1 (3)
0.08 (2) 0.04 (2) 0.85 (20) 1.5 (2) 2.1 (3) 1.3 (4)
0.331 (24) 1.9 (4) 0.92 (8)
8.3 (3)
1.40 (14) 1.5242(150) 3.7127(370)
0.06 0.05 1.7 4.5 6 6.2 12.653(130) 40
0.5300 (53) 1.0303(103) 2.0788(210)
0.16 0.37 3.4
0.08 0.04 1.5 7.1864(720) 6.5358(650) 14.337(140) 12.223(120)
– 24 –
0.71
2012 JINST 7 P08029
40 Zr
97 97m 98 98m 99 100 100m 101 102 102m 103 104 105 106 107 108 104 105 106 107 108 109 110 103 104 104m 105 106 107 108 109 110 111 112 113 109 110 111 112 113 114 115 109 110 111 112 113 114 115 116 117 118
44 Ru
45 Rh
47 Ag
48 Cd
49 In
0.2276(23) 1.0811(110) 2.0509(210) 4.1092(410) 4.358(44)
0.053 0.287 1.029 1.712 2.599 0.15 0.24 2.5 3.1 (14) < 5.4
< 2.5
< 0.003 0.080 (13) 0.19 (1) 0.55 (7) > 0.1
1.102 4.196 3.586 11.3 9.057 0.002 0.039 0.224 0.552 0.003
0.741 5.088 3.341 12.21 5.079 11.76 11.76 19.24
2.9167(290) 5.9282(590) 13.568(140) 0.2722 (27)
0.003 0.076 0.186 0.55 0.98 4.2
0.1
< 0.003 0.080 (13) 0.186 (10) 0.55 (5) > 0.1
< 0.003 < 0.003 0.076 (5) 0.080 (13) 0.076 (5) 0.186 (10) 0.186 (10) 0.55 (5) 55 (2) 0.55 (5) > 0.1 > 0.1
3.5 (10) 3.5 (10) 60 (15) < 0.03 0.69 (4) 0.038 (3)
3.6 (10) 3.5 (10) 60 (15) < 0.03 0.69 (4) 0.038 (3)
0.25 (5)
0.23 (7) 3.6 (4) 1.01 (22) 1.65 (18)
0.02 3.5 (10) 3.5 (10) 60 (15) < 0.03 0.69 (4) < 0.05 < 0.05 0.25 (5) 2.5 (5) 0.93 (13) 1.65 (15) 1.65 (15) ¡ 2.0 (3) ¡ 2.0 (3) 0.03 6.3 (9) 85 (10) 65 >0
3.5 3.5 60 0.03 0.69 0.05 0.15 (4) 2.9 (4) 0.93 1.65 2 2 0.03 5.2 85 65 70.89
3.5 3.5 60 0.7 0.06
0.69
0.26 3 1.43
0.93 (12) 1.65 (15) 1.65 (15) 2.2 (3)
1.76 1 4.3 46
2.2 (3)
2 0.028 85 65+
– 25 –
6.2 (11) 85 (10) ≈ 65
5.2 (12) 87 (9) > 17
≈4
< 0.03 0.69 (4) < 0.04 < 0.04 0.25 (5) 2.5 (5) 0.90 (5) < 1.67 < 1.67 ¡ 2.2 (3) ¡ 2.2 (3) ¡ 2.2 (3) 6.2 (11)
< 0.03 0.69 (4) 0.038 (3) 0.23 (7) 3.6 (4) 1.01 (22) 1.65 (18) 2.2 (3)
5.2 (12)
2012 JINST 7 P08029
46 Pd
115 116 117 118 119 120 115 116 117 118 119 120 121 122 121 122 123 124 120 121 122 123 124 125 126 127 128 129 129m 130 129 130 131 132 127 127m 128 128m 129 129m 130 130m 130n 131 131m 131n 132 133 134 135
50 Sn
51 Sb
53 I
54 Xe
55 Cs
6 The
0.08 17 (13) 21 (3) 30 (5) 58 (15) 0.09 22 (3) 16.3 (32) 49 (10)
1.31 (5) 2.99 (16) 6.3 (21)
7.14 (23) 5.56 (22) 10.0 (3) 9.3 (10) 21.2 (30)
0.044 (5) 0.21 1 3 5 6.9
