The consistency of the data for neutron fission averaged cross-sections of threshold reactions: A study on the cross-section of 46Ti(n,p)46Sc, 47Ti(n,p)47Sc, 48Ti(n,p)48Sc and 64Zn(n,p)64Cu reactions

Applied Radiation and Isotopes 77 (2013) 115–129

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The consistency of the data for neutron fission averaged cross-sections of threshold reactions: A study on the cross-section of 46Ti(n,p)46Sc, 47 Ti(n,p)47Sc, 48Ti(n,p)48Sc and 64Zn(n,p)64Cu reactions I.M. Cohen a,b,n, M.C. Fornaciari Iljadica b,c, J.C. Furnari c, M.C. Alí Santoro c a

Universidad Tecnológica Nacional, Facultad Regional Avellaneda, Secretaría de Ciencia, Tecnología y Posgrado, Av. Mitre 750, 1870 Avellaneda, Argentina Universidad Tecnológica Nacional, Facultad Regional Buenos Aires, Departamento de Ingeniería Química, Av. Medrano 951, C1179AAQ Buenos Aires, Argentina c Comisión Nacional de Energía Atómica, Gerencia de Área Aplicaciones Tecnológicas de la Energía Nuclear, Centro Atómico Ezeiza, Presbítero Juan González y Aragón 15, B1802AYA Ezeiza, Argentina b

H I G H L I G H T S







Some published data on cross-sections averaged over a fission spectrum are analyzed. The reactions were 46Ti(n,p)46Sc; 47Ti(n,p)47Sc; 48Ti(n,p)48Sc and 64Zn(n,p)64Cu. Renormalization as a function of five critical parameters was performed. Averages of the renormalized values were calculated and the results discussed.

art ic l e i nf o

a b s t r a c t

Article history: Received 13 June 2012 Received in revised form 1 February 2013 Accepted 5 March 2013 Available online 14 March 2013

The consistency of the published values for fission averaged cross-sections of threshold reactions induced in a nuclear reactor is analyzed. The influence of the literature data involved in the determination of these cross-sections is discussed. Renormalizations based on cross-sections value for the standard reactions, isotopic abundances of the precursors and radiation emission probabilities of the radionuclide under study and the monitor, are applied to the evaluation of the cross-sections for the reactions: 46 Ti(n,p)46Sc; 47Ti(n,p)47Sc; 48Ti(n,p)48Sc; and 64Zn(n,p)64Cu. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Cross-section Threshold reaction Fission spectrum Literature data Renormalization

1. Introduction The scientific activity, connected to both research and routine work, frequently leads to the production of numerical results, the generation of which currently implies a combination of experimental values and some data extracted from the literature. Thus, the quality of the results is directly affected by the quality of these literature data, but the experimenter cannot exert any kind of

n Corresponding author at: Universidad Tecnológica Nacional, Facultad Regional Avellaneda, Secretaría de Ciencia, Tecnología y Posgrado, Av. Mitre 750, 1870 Avellaneda, Buenos Aires, Argentina. Tel.: þ 54 11 4222 1908. E-mail addresses: [email protected], [email protected] (I.M. Cohen).

0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.03.001

control on them; his field of action is confined to the choice of the preferred value, among the published ones. In addition, the often pronounced dispersion of data can create in the user a sensation of disorientation, regarding the “best” value. Furnari and Cohen (1998), based on the analogies between nuclear data and the system of metrological standards, proposed a classification of these constants, consisting of the assignment of hierarchical orders to them. In accordance with this conception, nuclear data can be classified as


First-order data: fundamental constants.
Second-order data: those that can be determined by absolute

methods or by using first-order data; they generally are not renormalized.

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I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129


Third-order data: those determined by relative methods using

first and second-order data, and that can be renormalized. Sometimes these data are obtained using other third order data.

Some implications of this classification, as it was suggested, are as follows: (1) the concept of traceability can be applied to the management of nuclear data; (2) in connection with the third order data, the recognition of their character as data susceptible of renormalization. Since the calculation of a value for a specific third-order datum depends on a group of accepted reference data (which in regard to them is normalized) the process of renormalization is necessary whenever one or more of the values for these reference data change. Therefore, it is a requisite to restore the global consistency. It is worthwhile mentioning the interdependence of the concepts: a traceable datum is, essentially, a renormalizable datum, and the renormalization is only possible when the traceability of the system is assured. In the present work, the factors that influence the consistency of the published values for the 235U fission neutron averaged cross-sections of threshold reactions (third-order data) will be discussed. The results of the analysis of the data referred to the reactions: 46Ti(n,p)46Sc; 47Ti(n,p)47Sc; 48Ti(n,p)48Sc; and 64Zn (n,p)64Cu, will be described.

2. Nuclear reactors and threshold reactions Nuclear reactors are the facilities most used in activation analysis and radioisotope production. The study of reactor-induced reactions refers mainly to those of neutron capture. Thus, thermal crosssections are very well known for most of the capture reactions and, similarly, numerous resonance integrals have been also measured. The situation is dramatically different in connection with the threshold reactions produced by the fast component of the neutron spectrum. For this type of reactions the response, in terms of activity of the products, depends on the actual shape of the spectrum (distribution of neutrons as function of energy). The constants accepted as references are the cross-sections, averaged over the fission spectrum of 235U. The values of these crosssections are inexistent or very scarce for many reactions, whereas a great dispersion of the values is the predominant characteristic for some others. Arribére et al. (2005) have studied the factors that influence the dispersion of the data published for nuclear constants of reactions generated in reactors. Among them, those connected with fission averaged cross-sections are (1) Inadequate characterization of the neutron spectrum. (2) Variety of the nuclear reactions employed for standardization. (3) “Optimistic” evaluation of the uncertainty associated with many determinations, where not all the sources of uncertainty are taken into account. (4) Utilization of non-consistent sets of input data. (5) Differences between values of the input data, both for the reactions investigated and for those used as standard reactions. The first point refers to a mandatory requisite, which is the need to assure that the fast component of the neutron spectrum of the reactor employed for the measurements is similar to an undisturbed fission spectrum. The consideration of the item (2) deserves a particular comment: the inspection of the literature allows recognizing the variety of the reactions used as standards for measurement of fission averaged cross-sections. Thus, some of the reactions that have been indistinguishably employed are: 32S(n,p)32P, specially in the past; 27Al(n,α)24Na; and 58Ni(n,p)58Co. As standards, they are

not exactly equivalent, since their effective threshold energies are different. On the other hand, an ordinary practice to infer that the fast component of the reactor neutron spectrum coincides with a fission spectrum is the determination of the flux with standards of different thresholds and the verification that the results are similar, which implies the indirect use of sets of standard reactions, rather than a specific reaction. Calamand (1974) proposed, as a basis for evaluation and renormalization of fission averaged cross-sections, the following standard set: 24Mg(n,p)24Na; 27Al(n,α)24Na; 32S(n,p)32P; 46Ti(n, p)46Sc; 54Fe(n,p)54Mn; 58Ni(n,p)58Co; 235U(n,f)fp; and 238U(n,f)fp, together with the recommended values for their averaged crosssections. This procedure constituted an adequate attempt in order to reach consistency in the treatment of the published data. Nevertheless, it should be noticed that some of the recommended values were the results of cross determinations, i.e. that one of the standards was used to determine the cross-section for some other standard, which in turn had been employed for measuring the cross-section of the former. This comment, far from being an objection of Calamand's work, tends to point out one of the problems inherent to the search of consistency for these constants. The fact mentioned in (3) often leads to an apparent dispersion of the data, since values that could have some degree of overlapping become different, from the statistical point of view, when some sources of uncertainty are ignored. The values obtained from a non-consistent set of input data for the standard reaction (item 4) are intrinsically incongruent. Therefore, they must not be used, unless a pertinent correction is made. Finally, the problem referred in (5) is particularly relevant when old and modern values for the same constant are compared. In these cases, the renormalization is almost always mandatory. The determination of a fission averaged cross-section entails a sequence of activities that are exclusive responsibility of its generator. The user (or the data compiler) cannot act, for example, on the internal quality control (stability of the equipment, determination and verification of efficiency curves), the characterization of the neutron spectrum or the identification and evaluation of the uncertainty sources. The analysis of the quality of the datum can be carried out only on the basis of the information supplied, this aspect being of fundamental relevance when a collection of published values is compared. The consistency of all the literature values for a third-order constant is associated to the accepted values for the data of first and second order (or other third order data) involved in its calculation. In the next paragraphs, these data will be characterized and their relative importance will be discussed.

3. The renormalization of fission averaged reaction crosssections For a direct nuclear reaction, the cross-section for a specific radionuclide under study (s) is expressed by ss ¼

C s AW s is εs ms N Av θs ϕSDM

where C is the counting rate, i the emission probability of the radiation measured, ε the detector efficiency for the radiation measured, m the mass of the sample, NAv Avogadro's number, AW the relative atomic mass of the element, θ the isotopic abundance of the precursor, s the reaction cross-section (in this case, fission neutron averaged cross-section), ϕ the flux of the particles (fast component of the reactor neutron spectrum), S ¼ ð1−e−λt i Þ produced; ti: the time of irradiation, D ¼ e−λt d the

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129 −λt m

Þ decay factor; td: the decay time, M ¼ ð1−e the measurement λt m factor; tm: the time of measurement. The fast flux is usually determined from irradiation of a suitable monitor (m) and measurement of its activity. Thus, the crosssection under study is determined by

ss ¼

C s AW s im εm mm θm sm Sm Dm M m C m AW m is εs ms θs Ss Ds M s

It can be seen that the only experimental data involved in the determination of the cross-section are masses of sample and monitor, counting rates, efficiency values (which, in turn, were measured using energies and emission probabilities, extracted from the literature) and times of irradiation, decay and measurement (which are indirectly linked with half-lives, other bibliographic data, through the corresponding factors). All the remaining parameters, i.e., cross-section for the standard reaction, emission probabilities, relative atomic masses, isotopic abundances and half-lives, are literature data. The values of the half-lives affect the numerical value of the cross-section through the time-dependent factors. Irradiation, decay and measurement times mentioned in the works are often informative, especially for multiple determinations. Thus, calculations of the corrections that can arise when a half-life value is replaced by other one are very difficult, and in most of the cases impossible. In connection with the reactions evaluated in the present work, Table 1 shows an example of the differences between half-lives of the product, as they were quoted by the authors in their original works, and some modern values extracted from the bibliography (Laboratoire National Henri Becquerel, 2011). As it can be guessed, the incidence of such differences in the time-dependent factors is more pronounced for the shorterlived nuclides. A rough estimation for 64Cu, the radionuclide taken as an example, allows inferring that such differences are the order of the difference in half-life values, i.e. variability of 1% in half-lives imply variations of approximately 1% in the saturation and decay factors. The other constants are directly or inversely proportional to the numerical value of the searched magnitude, the fission averaged cross-section under study. The “best values” for these constants were selected by the experimenter, through his own criterion or following the recommendations of the compilers. Since the best or recommended values can change along the time, it seems reasonable to update, i.e. to renormalize, the data initially calculated.

Table 1 Values of the 64Cu half-life, as quoted in the different determination of the p)64Cu reaction cross-section.

64

Zn(n,

Literature reference

Value (h)

Percentage difference*

(Rochlin, 1959) (Boldeman, 1964) (Shikata, 1964) (Rau, 1967) (Nasyrov and Sciborskij, 1968) (Kimura et al., 1971) (Kobayashi et al., 1976) (Pfrepper and Raitschev, 1976) (Najzer and Rant, 1978) (Grigor‘ev et al., 1989) (Horibe et al., 1989) (Cohen et al., 2005) (Abbasi et al., 2006) (Jonah et al., 2008)

12.8 12.8 12.82** 12.8** 12.8 12.7 12.8 12.9 12.71 12.701 12.70 12.700 12.701 12.7

0.77 0.77 0.93 0.77 0.77 −0.0079 0.77 1.5 0.071 0 −0.0079 −0.0079 0 −0.0079

n With respect to the adopted value of 12.701 h (Laboratoire National Henri Becquerel, 2011). nn Datum given by the author but not quoted in EXFOR.

117

Two drawbacks complicate the accomplishment of successful renormalizations: (1) There are no recommended values, accepted by consensus, for some of the constants involved in the calculation of the numerical values of the fission averaged cross-sections. (2) Frequently, the generators of the data do not indicate the values of all the constants used, thus making a complete renormalization impossible.

The values of relative atomic masses and isotopic abundances (which are not nuclear constants but atomic data associated with the calculations) receive unified treatment by the Union of Pure and Applied Chemistry (IUPAC); other bibliographic sources, like Tulis's tables (Tuli, 2005) are also used. These are data that seldom appear in the original papers. Relative atomic masses rarely record significant historical variations and can be excluded of the process of renormalization in most of the cases, without affecting too much the consistency of a group of published values. The situation is somewhat different with respect to isotopic abundances. Tables 2 and 3 show respectively the evolution of the values of abundances for the isotopes of titanium and zinc, as they were recommended by IUPAC from 1983 to 2011, which correspond to measurements performed during the period 1981–2009. (Holden et al., 1983, 1984; International Union of Pure and Applied Chemistry, 1991; Rosman and Taylor, 1998; De Laeter et al., 2003; Berglund and Wieser, 2011). It can be seen that some isotopes record significant variations, which can reach orders of 1–5%. Therefore, the omission of the pertinent reference when the cross-section values are presented implies a loss of traceability that can affect the overall consistency of the data sets. There are, however, some cases when the author provides such information in the original paper, but afterwards it is not reproduced in the corresponding databases, which sometimes are the preferred or the only literature source consulted by the user. An example of this situation will be commented on the next paragraphs. The accepted values for probability emissions have changed in relevant way for many radionuclides, particularly since the advent of high resolution gamma spectrometry. This fact is of particular importance when old and modern values of the fission averaged cross-sections have to be compared, and can affect to both the radionuclide of interest and to that produced by the standard reaction, in this case in a less extent. There are no bibliographic sources universally adopted. Some examples of the most prestigious tables or data bases are Isotope Explorer (Chu et al.,2011); Nudat (National Nuclear Data Center, 2011) and BIPM, Recommended Data (Laboratoire National Henri Becquerel, 2011). The tables of BIPM are the only ones that give information about the criteria of selection and acceptance of data. Unfortunately, Table 2 Historical and present values of the representative isotopic composition of titanium. Isotope Holden et al. (1983)

Holden et al. (1984)

International Union of Pure and Applied Chemistry (1991)

Rosman and Taylor (1998)

46

8.0 7.3 73.8 5.5 5.4

8.0 7.3 73.8 5.5 5.4

8.25 7.44 73.72 5.41 5.18

Ti Ti Ti 49 Ti 50 Ti 47

48

8.0 7.3 73.8 5.5 5.4

(1) (1) (1) (1) (1)

(1) (1) (1) (1) (1)

(1) (1) (1) (1) (1)

De Laeter et al. (2003)

Berglund and Wieser (2011)

(3) 8.25 (3) 8.25 (3) (2) 7.44 (2) 7.44 (2) (3) 73.72 (3) 73.72 (3) (2) 5.41 (2) 5.41 (2) (2) 5.18 (2) 5.18 (2)

Figures into parentheses correspond to the uncertainty of the recommended values.

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I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

Table 3 Historical and present values of the representative isotopic composition of zinc. Isotope Holden et al. (1983) 64 Zn 48.6 (3) 66 Zn 27.9 (2) 67 Zn 4.1 (1) 68 Zn 18.8 (4) 70 Zn 0.6 (1)

Holden et al. (1984) 48.6 (3) 27.9 (2) 4.1 (1) 18.8 (4) 0.6 (1)

International Union of Pure and Applied Chemistry (1991) 48.6 (3) 27.9 (2) 4.1 (1) 18.8 (4) 0.6 (1)

Rosman and Taylor (1998) 48.63 (60) 27.90 (27) 4.10 (13) 18.75 (51) 0.62 (3)

De Laeter et al. (2003) 48.268 (321) 27.975 (77) 4.102 (21) 19.024 (123) 0.631 (9)

Berglund and Wieser (2011) 49.17 (75) 27.73 (98) 4.04 (16) 18.45 (63) 0.61 (10)

Figures into parentheses correspond to the uncertainty of the recommended values.

Table 4 Bibliographical data used in primary determinations of the cross-section for the Reference

Production of Eγ [keV]

46

Sc

Int. [%]

46

Ti(n,p)46Sc reaction. r, original value, (uncertainty) [mb]

Monitor θ [%]

Reaction

Eγ [keV]

Int. [%]

θ [%]

r [mb]

n/a *

n/a *

n/a n/a

92 60

n/a n/a * n/a n/a * *

n/a n/a * n/a n/a * *

n/a ** n/a n/a n/a n/a n/a

107 0.61 65 1.04 90.6 66 n/a

(Niese et al., 1963) (Boldeman, 1964)

n/a 1120

n/a 100

n/a n/a

58

(Clare et al., 1964) (Fabry and Deworm, 1965)

n/a

n/a

n/a

58

58

Ni(n,p) Co S(n,p)32P

32

17 (3) 12.8 (0.6) 8.0 (0.6) 8 (n/a)

n/a

n/a

n/a

n/a β− 1120 890 n/a 1119 885 1119 890 1120 889 1120

n/a * ** ** n/a 100 100 100 ** ** 100 100

n/a n/a n/a

Ni(n,p)58Co Al(n,α)24Na 32 S(n,p)32P 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 32 S(n,p)32P 32 S(n,p)32P

n/a 7.93

n/a 58 Ni(n,p)58Co

n/a 810

n/a 101

n/a 67.9

n/a 105

9.30 (0.73) 11.4 (0.9)

n/a n/a

27

n/a

n/a

n/a

(Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994)

889.3 n/a 889.25 1120.51

100 n/a 99.984 99.987

n/a n/a Natural

(Fatima et al., 2002)

n/a

n/a

n/a

n/a 100 99 n/a n/a n/a n/a n/a 100 n/a n/a n/a n/a n/an/a n/a n/a

(Jonah et al., 2008)

889.3

**

n/a

** ** n/a n/a n/a ** n/a n/a ** ** ** n/a n/a n/a n/a n/a n/a **

0.695 0.644 102 177 102 0.644 109 190.3 0.705 0.706 0.706 109 80.5 82.5 1.07 113 2.3a 4.28

10.2 (0.4) 11.2 (0.63)

(Mannhart, 1984)

n/a 1370 810 n/a n/a n/a n/a n/a 1368.5 n/a n/a n/a n/a n/a n/a n/a n/a n/a

(Lloret, 1965) (Koehler, 1966) (Deschuyter and Hoste, 1967) (Nasyrov and Sciborskij, 1968) (Son et al., 1968) (Bresesti et al., 1970) (Kimura et al., 1971) (Kobayashi et al., 1976)

27

7.99

Al(n,α)24Na Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n’)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na 27 Al(n,α)24Na 58 Ni(n,p)58Co 54 Fe(n,p)54Mn 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 27 Al(n,p)27Mg 27

n/a

10.40 (0.05) 8.7 (n/a) 12.6 (0.4) 8.6 (1.4)

10.9 (0.59)

11.6 (0.4) 11.6 (0.8) 11.700 (0.695) 11.19 (0.34)

12.87 (1.28)

12.5 (0.7)

n/a: data not available. *: not applicable. **: datum not given by the original authors, but known as equal or practically equal to 100. Italics correspond to data without uncertainty. a

Units (mb) are correctly quoted in the original paper, while in EXFOR appears as barns.

although the list of evaluated nuclides is continuously expanding, they do not contain information about many others. The averaged cross-sections of the standard reactions are the basis of some compilations, although these values have not been adopted by consensus. As an example, the values recommended for some of the standard reaction cross-sections by Calamand (1974) show, in comparison with some later values (Baard et al., 1989), differences relatively significant, taking into account that both are used as reference data.

4. Bibliographic sources of data for cross-sections To the authors' knowledge, Calamand's compilation (1974) is the last published table specifically dedicated to compile and evaluate

primary data related with the determination of fission neutron averaged reaction cross-sections. Despite the obvious usefulness of this compilation as initial reference when a datum of averaged crosssection is required, some of the drawbacks should be pointed out that turn the use of Calamand‘s values unadvisable as the final ones: (1) many modern values for a variety of reactions have appeared in the literature after the publication of his table; (2) the renormalization is only based on the values of the cross-section for the standard reaction, thus neglecting other possible factors of inconsistency between published values; (3) as it is expressed by Calamand, the table includes a recommended value for any single value, even those of doubtful quality. Thus, the assignment of arbitrary or empirical renormalization factors for some cross-sections affects the quality of these values and, consequently, the quality of the recommended values calculated from a weighted average of the individual data.

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

cross-section of the 47Ti(n,p)47Sc reaction: although the input data (in mb) are 13.2±1.0, the figures are transcripted as 1.3200  101±1.0000. This modification implies loss of traceability with respect to the primary information and, in connection with this case, an inconsistency between the number of significant figures (correctly expressed in the original work) for the value and its uncertainty. It is worthwhile mentioning that the consent of the authors about the contents is specifically declared in the more recent EXFOR entries.

While the first of these facts is related with the need of including all the published values in an evaluation, the last ones are connected with the consistency of the overall set of values. The relative relevance of the parameters involved in the calculation of the final data after the experimental determinations has already been discussed. In connection with the policy of “rescuing” values through renormalizations based on not adequately clarified and justified criteria, the authors of the present work are strongly against this practice, because it constitutes a source of errors that cannot be controlled by the user. Nowadays, the databases that are not only the most complete, but also the friendliest source of data, are CINDA (International Atomic Energy Agency, 2011a) and EXFOR (International Atomic Energy Agency, 2011b). CINDA (Computer Index of Neutron Data) contains bibliographical references of neutron cross-section and other microscopic neutron data, in connection with measurements, calculations, reviews and evaluations. EXFOR is dedicated to store experimental data on neutron-induced reaction data, among other reaction data. The EXFOR Basics Manual (Schwerer, 2008) contains a detailed description of the EXFOR format; it includes examples and the use of keywords. The most relevant feature of EXFOR is that most of the pertinent data that can allow a renormalization of the crosssection data are included, provided the authors have supplied this information. Therefore, the user can directly perform the renormalization without consulting the original sources of the published data. However, EXFOR does not usually supply information about atomic weights and isotopic abundances, even in some cases where such information is included in the original work (e.g., Kobayashi et al., 1976, and Rau, 1967). A peculiarity that can lead to confusing interpretations is related to the number of significant figures consigned in the EXFOR database for both the cross-section data and their uncertainties. An example of this situation is the entry about the values published by Koehler (1966) for the average Table 5 Bibliographical data used in primary determinations of the cross-section for the Reference

Production of Eγ [keV]

47

Sc

Int. [%]

47

5. Application of the concepts to some averaged cross-sections A renormalization of the original values is proposed, through the emission probabilities of the measured radiation from both the monitor and the studied product, the isotopic abundance of the precursors and the cross section of the standard reaction. When this information is available in the original works, the renormalization implies the multiplication by a simple factor, which can also be applied to the uncertainties values (this procedure is not a reevaluation of the uncertainties, but a way of preserving the relative uncertainty, as it is quoted in the primary publications). As examples of the application of the concepts, four reactions have been studied in the present work: 46Ti(n,p)46Sc; 47Ti(n,p)47Sc; 48 Ti(n,p)48Sc; and 64Zn(n,p)64Cu, on the basis of the data included in the EXFOR database. The reactions induced on titanium have different threshold energies, which imply that useful information about the characteristics of the fast neutron spectrum of a reactor can be obtained from the irradiation of a single monitor. The 64Zn (n,p)64Cu reaction is interesting because of the possibility of performing an exhaustive analysis, due to the high number of literature values for its cross-section. With respect to this reaction, a previous revision has been published (Cohen et al., 2005).

Ti(n,p)47Sc reaction. r, Original value, (uncertainty) [mb]

Monitor θ [%]

Reaction

Eγ [keV]

int. [%]

θ [%]

r [mb]

58

n/a * * * n/a 810 n/a 1370 810 n/a n/a n/a n/a n/a 1368.5 n/a n/a n/a n/a n/a n/a n/a n/a n/a

n/a * * * n/a 101 n/a 100 99 n/a n/a n/a n/a n/a 100 n/a n/a n/a n/a n/a n/a n/a n/a n/a

n/a n/a n/a n/a n/a 67.9 n/a ** n/a n/a n/a ** n/a n/a ** ** n/a n/a n/a n/a n/a n/a n/a n/a

92 60 66 n/a n/a 105 n/a 0.644 102 177 102 0.644 109 190.3 0.705 0.706 0.706 109 80.5 82.5 1.07 113 2.3a 4.28

(Niese et al., 1963) (Boldeman, 1964) (Koehler, 1966) (Deschuyter and Hoste, 1967) (Nasyrov and Sciborskij, 1968) (Son et al., 1968) (Jenkins and Kam,1971) (Kimura et al., 1971)

n/a 160.8 n/a 159 n/a 155 n/a 160

n/a 66 n/a n/a n/a 70 n/a n/a

n/a n/a n/a n/a n/a 7.28 n/a n/a

(Kobayashi et al., 1976)

160

73

7.32

(Mannhart, 1984)

n/a

n/a

n/a

(Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994)

159.4 n/a 159.38

68.5 n/a 68

n/a n/a Natural

(Fatima et al., 2002)

n/a

n/a

n/a

(Jonah et al., 2008)

159.38

n/a

n/a

58

Ni(n,p) Co S(n,p)32P 32 S(n,p)32P 32 S(n,p)32P n/a 58 Ni(n,p)58Co n/a 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na 27 Al(n,α)24Na 58 Ni(n,p)58Co 54 Fe(n,p)54Mn 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 27 Al(n,p)27Mg 32

n/a: data not available. *: not applicable. **: datum not given by the original authors, but known as equal or practically equal to 100. Italics correspond to data without uncertainty. a

119

Units (mb) are correctly quoted in the original paper, while in EXFOR appears as barns.

18 22.0 13.2 18.2 26.0 19.7 13.6 19.0

(3) (1.5) (1.0) (2.6) (3.1) ( 1.0) ( n/a) (1.2)

18.9 (0.87)

17.7 (0.6) 20.2 (1.4) 18.15 (1.07) 18.25 (0.6)

20.11 (2.02)

16.6 (1.1)

120

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

Table 6 Bibliographical data used in primary determinations of the cross-section for the Reference

(Niese et al., 1963) (Boldeman, 1964) (Koehler, 1966) (Deschuyter and Hoste, 1967)

(Nasyrov and Sciborskij, 1968) (Son et al., 1968)

(Kimura et al., 1971)

(Kobayashi et al., 1976)

(Mannhart, 1984) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994)

(Fatima et al., 2002)

48

Production of

Sc

48

Ti(n,p)48Sc reaction. s, Original value, (uncertainty) [mb]

Monitor

Eγ [keV]

Int. [%]

θ [%]

Reaction

Eγ [keV]

Int. [%]

θ [%]

r [mb]

n/a 1320 n/a 990 1040 1310 n/a 990 1040 1314 980 1040 1314 983 1040 1314 n/a

n/a 100 n/a 100 100 100 n/a 100 100 100 ** n/a ** 100 100 100 n/a

n/a n/a n/a n/a

58

Ni(n,p)58Co S(n,p)32P 32 S(n,p)32P 32 S(n,p)32P

n/a * * *

n/a * * *

n/a n/a n/a n/a

92 60 66 n/a

n/a 73.94

n/a 58 Ni(n,p)58Co

n/a 810

n/a 101

n/a 67.9

n/a 105

0.240 (0.054) 0.28 (0.02)

n/a

27

1370 810

100 99

** n/a

0.644 102

0.294 (0.025)

100 n/a 7.47 100 97.5 n/a

n/a n/a n/a n/a n/a 100 n/a n/a n/a n/a n/a n/a n/a n/a

n/a n/a ** n/a n/a ** ** ** n/a n/a n/a n/a n/a n/a

177 102 0.644 109 190.3 0.705 0.706 0.706 109 80.5 82.5 1.07 113 2.3a

0.256 (0.013)

983.5 n/a 175.35 983.5 1037.5 n/a

n/a n/a n/a n/a n/a 1368.5 n/a n/a n/a n/a n/a n/a n/a n/a

32

Al(n,α)24Na Ni(n,p)58Co

58

73.99

115

In(n,n′)115mIn Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na 27 Al(n,α)24Na 58 Ni(n,p)58Co 54 Fe(n,p)54Mn 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 58

n/a n/a n/a Natural

n/a

0.44 0.21 0.3300 0.11

(0.08) (0.016) (0.0002) (0.01)

0.302 (0.010) 0.305 (0.002) 0.3020 (0.0193) 0.3026 (0.0082)

0.32 (0.04)

n/a: data not available. *: not applicable. **: datum not given by the original authors, but known as equal or practically equal to 100. a

Units (mb) are correctly quoted in the original paper, while in EXFOR appears as barns.

Table 7 Bibliographical data used in primary determinations of the cross-section for the Reference

Production of

64

Cu

Int. [%]

θ [%]

Reaction

(Rochlin, 1959) (Boldeman, 1964 (Shikata, 1964) (Fabry and Deworm, 1966)

n/a 510 n/a 511

n/a 38 n/a n/a

n/a n/a n/a n/a

27

(Rau, 1967)

n/a

n/a

n/a

(Nasyrov and Sciborskij, 1968) (Najzer et al., 1970)

n/a 510

n/a 38

n/a n/a

(Kimura et al., 1971)

n/a

n/a

n/a

(Kobayashi et al., 1976)

1340

0.5

48.89

(Pfrepper and Raitschev, 1976)

511

n/a

n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a

(Najzer, Rant, 1978) (Grigor'ev et al., 1989) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990 (Cohen et al., 2005) (Abbasi et al., 2006)

β 511 1345.6 n/a 1345.77 1345.78 511

19 34.3 0.6 n/a 0.473 0.48 38.6

(Jonah et al., 2008)

1345.8

n/a

Zn(n,p)64Cu reaction. r, Original value, (uncertainty) [mb]

Monitor

Eγ [keV]

þ

64

Eγ [keV]

Al(n,α)24Na S(n,p)32P 58 Ni(n,p)58Co 32 S(n,p)32P 27 Al(n,α)24Na 58 Ni(n,p)58Co 46 Ti(n,p)46Sc n/a 27 Al(n,α)24Na

n/a * n/a * n/a n/a n/a n/a 1368 2750 27 24 Al(n,α) Na 1370 58 Ni(n,p)58Co 810 115 In(n,n’)115mIn n/a 58 Ni(n,p)58Co n/a 27 Al(n,α)24Na n/a 32 S(n,p)32P * 27 24 Al(n,α) Na n/a 27 24 Al(n,α) Na n/a Absolute measurement 27 Al(n,α)24Na 1368.5 27 Al(n,α)24Na n/a 27 Al(n,p)27Mg n/a 54 54 Fe(n,p) Mn n/a 56 Fe(n,p)56Mn n/a 58 58 Ni(n,p) Co n/a 60 Ni(n,p)60Co n/a 27 Al(n,p)27Mg n/a 32

n/a: data not available. *: not applicable. **: datum not given by the original authors, but known as equal or practically equal to 100. Italics correspond to data without the uncertainty. a

Units (mb) are correctly quoted in the original paper, while in EXFOR appears as barns.

Int. [%]

θ [%]

r [mb]

n/a * n/a * n/a n/a n/a n/a 100 100 100 99 n/a n/a n/a * n/a n/a

** n/a n/a n/a ** n/a n/a n/a **

0.6 60 90 63 0.63 95 12.6 n/a 0.61

** n/a n/a n/a ** n/a ** **

0.644 102 177 102 0.644 69 0.725 0.705

100 n/a n/a n/a n/a n/a n/a n/a

** ** ** n/a n/a n/a n/a **

0.705 0.706 3.84 82.5 1.07 113 2.3a 4.28

35 (n/a) 27 (1.6) 26 (n/a) 28.0 (1.5) 26.9 (1.2) 27.0 (4.1) 25.2 (1.3) 35.5 (2.8) 30.9 (2.1)

27.4 (0.8) 28.5 (1.7) 30.1 (0.8) 34.4 (0.8) 29.4 (7.5) 31.680 (1.825) 37.4 (1.4) 34.72 (6.82)

49.7 (2.1)

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

The values for emission probabilities were extracted from the BIPM monographs (Laboratoire National Henri Becquerel, 2011) and, alternatively, from the Nudat database (National Nuclear Data Center, 2011). The literature references for the selected isotopic abundances and standard reactions cross-sections were respectively Berglund and Wieser (2011) (IUPAC recommended values) and Baard et al. (1989).

6. Results and discussion The evaluation performed so far consisted of the analysis of the information and the calculation of renormalized values, on the basis of the proposed criterion. No attempts were made at this stage to update the individual uncertainties (a very difficult, if not

Table 8 Results of renormalization and data analysis for the

46

121

impossible, task). Consequently, the relative uncertainties of the original cross-section values are not modified by this procedure, and the overall renormalization factor would be applied for multiplying the absolute uncertainty. The bibliographical data used in the primary determinations of the cross-section for the studied reactions are indicated in Tables 4–7, preserving the expressions adopted by the original authors. This fact explains the lack of consistency existing in some cases, with respect to the significant figures for cross-sections and uncertainties. It is noticeable the existence of values that cannot be renormalized, because the authors have not indicated the literature values of the constants used at the time of publication of their works, or, in some extreme cases, have not indicated how the values were obtained. The significance of such results is mainly historical; they should not be included in any set of updated

Ti(n,p)46Sc reaction.

Reference

r, Original value [mb]

r, Renormalized value [mb]a

Category

Status

(Niese et al., 1963) (Fabry and Deworm, 1965) (Koehler, 1966b) (Deschuyter and Hoste, 1967) (Nasyrov and Sciborskij, 1968) (Son et al., 1968) (Bresesti et al., 1970) (Kimura et al., 1971) (Kobayashi et al., 1976) (Mannhart, 1984) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994) (Fatima et al., 2002) (Jonah et al., 2008) Arithmetical average Standard deviationc

17 10.40 12.6 8.6 9.30 11.4 10.2 11.2 10.9 11.6 11.6 11.700 11.19 12.87 12.5 11.5 1.9

20.5 11.2 – – – 11.4 10.6 12.4 11.3 11.3 11.8 11.9 11.4 13.0 11.5 11.62 0.64

P.R. P.R. N.R. N.R N.R. T.R. P.R. P.R. P.R. P.R. P.R. P.R. P.R. P.R. P.R.

Rejected Accepted – – – Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted

T.R.: data renormalized for all the parameters involved. P.R.: partially renormalized data. N.R.: not renormalizable data. a b c

No renormalization was performed with respect to the uncertainty of the original data. Data not renormalizable with the methodology applied in the present work. Corresponding to a single determination.

Table 9 Results of renormalization and data analysis for the

47

Ti(n,p)47Sc reaction.

Reference

r, Original value[mb]

r, Renormalized value[mb]a

Category

Status

(Niese et al., 1963) (Boldeman, 1964) (Koehler, 1966)b (Deschuyter and Hoste, 1967) (Nasyrov and Sciborskij, 1968) (Son et al., 1968) (Kimura et al., 1971) (Kobayashi et al., 1976) (Mannhart, 1984) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994) (Fatima et al., 2002) (Jonah et al., 2008) Arithmetical average Standard deviationc

18 22.0 13.2 18.2 26.0 19.7 19.0 18.9 17.7 20.2 18.15 18.25 20.11 16.6 19.0 2.8

21.7 22.9 – – – 20.6 21.0 21.2 17.2 20.7 18.5 18.5 20.3 15.3 19.8 2.2

P.R. P.R. N.R. N.R. N.R. T.R. P.R. P.R. P.R. P.R. P.R. P.R. P.R P.R.

Accepted Accepted – – – Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted

T.R.: data renormalized for all the parameters involved. P.R.: partially renormalized data. N.R.: not renormalizable data. a b c

No renormalization was performed with respect to the uncertainty of the original data. Data not renormalizable with the methodology applied in the present work. Corresponding to a single determination.

122

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

values. In consonance with this criterion, all data informed without uncertainty were not considered for this process of renormalization. Another datum was rejected on different grounds: Boldeman (1964) informed a value of (12.8±0.6) mb for the 46Ti (n,p)46Sc reaction cross-section; such value was then corrected in the same work; a new value (8.0±0.6) mb is consigned, and the author expressed his doubts about the isotopic purity of the samples. Therefore, the value was considered (by the present authors) as intrinsically uncertain and was not accepted for the treatment and not averaged in the set of original values. On the basis of the information collected with respect to the primary determination, the values were classified as: (a) data renormalized for all the parameters involved; (b) partially renormalized data; and (c) not renormalizable data. A fourth category could include the few cases in which the data were not Table 10 Results of renormalization and data analysis for the

48

renormalizable with the methodology applied in the present work. The process of renormalization was applied to all data of categories (a) and (b). When the neutron flux was measured by several monitors or more than one radiation was measured for the same radionuclide, an average renormalization factor was calculated. The renormalized data were analyzed applying the single and double Grubbs' statistical tests (International Organization for Standardization, 1994) for the acceptance or rejection of data. The intermediate category of stragglers corresponds to the data that accepted for one of the criteria but rejected with respect to the stricter one. This kind of situations is always conflictive, since the decision of keeping them or not is not immediate. If the number of the values within a specific set is small it is convenient, in the opinion of the authors, to consider stragglers as valid data, unless their inclusion in the averages leads to an abnormal

Ti(n,p)48Sc reaction.

Reference

r, Original value [mb]

r, Renormalized value [mb]a

Category

Status

(Niese et al., 1963) (Boldeman, 1964) (Koehler, 1966)b (Deschuyter and Hoste, 1967) (Nasyrov and Sciborskij, 1968) (Son et al., 1968) (Kimura et al., 1971) (Kobayashi et al., 1976 (Mannhart, 1984) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994 (Fatima et al., 2002) Arithmetical average Standard deviationc

0.44 0.21 0.3300 0.11 0.240 0.28 0.294 0.256 0.302 0.305 0.3020 0.3026 0.32 0.284 0.075

0.531 0.226 – 0.111 – 0.295 0.325 0.277 0.294 0.311 0.308 0.308 0.323 0.301 0.098

P.R. P.R. N.R. P.R. N.R. T.R. P.R. P.R. P.R. P.R. P.R. P.R. P.R.

Accepted Accepted – Accepted – Accepted Accepted Accepted Accepted Accepted Accepted Accepted Accepted

T.R.: data renormalized for all the parameters involved. P.R.: partially renormalized data. N.R.: not renormalizable data. a b c

No renormalization was performed with respect to the uncertainty of the original data. Data not renormalizable with the methodology applied in the present work. Corresponding to a single determination.

Table 11 Results of renormalization and data analysis for the

64

Zn(n,p)64Cu reaction.

Reference

r, Original value[mb]

r, Renormalized value, [mb]a

Category

Status

(Boldeman, 1964) (Fabry and Deworm, 1966) (Rau, 1967) (Nasyrov and Sciborskij, 1968) (Najzer et al., 1970) (Kimura et al., 1971) (Kobayashi et al., 1976) (Pfrepper and Raitschev, 1976)b

27 28 26.9 27 25.2 35.5 30.9 27.4 28.5 30.1 34.4 29.4 31.68 37.4 34.72 49.7 31.5 6

29 30.4 28.3 – 31.9 39.2 35.4 –

P.R. P.R. P.R. N.R. P.R. P.R. P.R. N.R.

Accepted Accepted Accepted – Accepted Accepted Accepted –

32.7 33.4 37.9 32.3 38.3 36.8 45.9 34.7 4.9

P.R. T.R. P.R. P.R. P.R. P.R. P.R.

Accepted Accepted Accepted Accepted Accepted Accepted Accepted

(Najzer, Rant, 1978) (Grigor'ev et al., 1989) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Cohen et al., 2005) (Abbasi et al., 2006) (Jonah et al., 2008) Arithmetical average Standard deviationc

T.R.: data renormalized for all the parameters involved. P.R.: partially renormalized data. N.R.: not renormalizable data. a b c

No renormalization was performed with respect to the uncertainty of the original data. Data not renormalizable with the methodology applied in the present work. Corresponding to a single determination.

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

increment of the standard deviation. The analysis was straightforward in the present study, because no stragglers were detected. The results of the renormalizations for each of the reactions are shown in Tables 8–11, and a summary of the overall results is indicated in Table 12. The values published by Pfrepper and Raitschev (1976) for the 64Zn(n,p)64Cu reaction represent a special case: they informed two values for this reaction, (27.4±0.8) mb and (28.5±1.7) mb, which were obtained in two different irradiation position applying a methodology that involve the use of cadmium ratios. The data cannot be renormalized by the methodology used in this work, although the procedure is entirely correct. Similar considerations can be formulated with respect to the data published by Koehler (1966). Although the differences

123

between the averages are not high, the statistical deviation tends to be less for those resulting of renormalized values, except for the (n,p) reaction induced on 48Ti. However, it is important to notice that the use of renormalized values, which implies to group the original data in a consistent set, does not necessarily leads to less dispersion. A particular feature of the system is that few values remain in conditions of being totally renormalized, thus making the possibility of carrying out a good statistics difficult. Consequently, the compromise solution was to accept the values resulting from partial renormalization, which were included in the calculation of averages. The problem of the uncertainty of the averages deserves a special consideration: as it was already mentioned, many cross-section data

Table 12 Summary of the results of the renormalization process. Reaction

Number of original values

Number of accepted values for treatment*

Number of not renormalizable values

Number of partially renormalized values

Number of totally renormalized values

46

18

15

3

11 (1)

1

47

15

14

3

10

1

13

13

2

10

1

18

16

3

12

1

Ti(n, p)46Sc Ti(n, p)47Sc 48 Ti(n, p)48Sc 64 Zn(n, p)64Cu

Figures between parentheses indicate the number of rejected values. n

Original values without uncertainty were not considered.

Table 13 Calculation of the systematic uncertainties for the published values of the Reference

Studied reaction

Monitor

Eγ [keV]

Reaction

Relative uncertainty, % Int.

(Fabry and Deworm, 1965)

46

n/a

n/a

Ti(n,p)46Sc reaction cross-section.

Eγ [keV]

θ n/a

27

24

32

Al(n,α) Na S(n,p) P Fe(n,p)56Mn

56

1119 885 1119 890 1120 890 1120

** ** ** ** ** ** **

n/a

58

n/a n/a

27

(Mannhart, 1984)

n/a

n/a

n/a

(Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994)

889.3 n/a 889.25 1120.51

** n/a ** **

n/a n/a n/a

(Fatima et al., 2002)

n/a

n/a

n/a

(Jonah et al., 2008)

889.3

**

n/a

(Son et al., 1968) (Bresesti et al., 1970) (Kimura et al., 1971) (Kobayashi et al., 1976)

n/a

32

Ni(n,p)58Co

Al(n,α)24Na Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na 27 Al(n,α)24Na 58 Ni(n,p)58Co 54 Fe(n,p)54Mn 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 27 Al(n,p)27Mg 27

Relative uncertainty, %

Combined systematic uncertainty of the final result, %a

Overall uncertainty, %b

0.48

int.

θ

r

n/a * n/a 810

n/a * n/a n/a

** n/a n/a n/a

4.9 4.6 4.8 n/a

4 4.9 4 4.6 4 4.8 nc

n/a 1370 810 n/a n/a n/a n/a n/a 1368.5 n/a n/a n/a n/a n/a n/a n/a n/a n/a

n/a ** n/a n/a n/a n/a n/a n/a ** n/a n/a n/a n/a n/a n/a n/a n/a n/a

** ** n/a n/a n/a ** n/a n/a ** ** ** n/a n/a n/a n/a n/a n/a **

2.9 n/a n/a n/a n/a n/a 2.8 3.8 6.2 4 4 2.8 2.9 6.1 7.5 6.2 17 n/a

4 nc nc nc nc nc 4 4 4 4 4 4 4 4 4 4 4 nc

2.9

b

3.9 5.6 5.4

2.8 3.8 6.2 4.0 4.0 2.8 2.9 6.1 7.5 6.2 17

n/a: data not available. *: not applicable. **: datum not given by the original authors, but corresponding to intensity known as equal or practically equal to 100 (null uncertainty). nc: not calculable (all the pertinent data are missing in the original works). a

7.9

Calculated on the basis of the data published by the respective authors; it should be considered as a lower limit when some data are missing. As informed in the original works.

3.4 6.9 5.9 3

9.9

5.6

124

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

Table 14 EXFOR extracts of the considerations formulated by the authors on the uncertainties of their cross-section values for the Reference

46

Ti(n,p)46Sc reaction.

Comments quoted in EXFOR entries

(Fabry and Deworm, 1966) Not given (Bresesti et al., 1970) 2 PC error from curve fitting (statistics þerrors in the position of the samples þ 3 PC systematic errors). Compounded to a total error of 3.5 PC. (Kimura et al., 1971) Statistical error, uncertainty in monitoring the neutron flux, systematic error about 5 percent. Detailed discussion in reference. (Kobayashi et al., 1976) Flux uncertainty, 3%; Ge(Li) efficiency: 2.5%; other systematic errors. All these systematical errors are added up quadratically with systematic error as to give the total error. Systematic error deviation of spectrum for pure fission shape less than 3%. (Mannhart, 1984) The total errors are composed of counting statistics. Error in the scattering correction. Error in the relative photopeak efficiency. (Horibe et al., 1989) Total error, one sigma (Kobayashi and Kobayashi, Deduced by taking into account error correlations between data 1990) (Maidana et al., 1994) Item not included in the entry. (Fatima et al., 2002) The reported uncertainties incorporate both statistical and systematic errors. Main sources of errors associated in cross-section measurements were those associated with determination of fast neutron flux densities (8%) and absolute decay rates (5–10%) Other sources of error were small and were due to uncertainties in the number of target nuclei o 1% and in radiation and cooling times (1%). (Jonah et al., 2008) The given uncertainties incorporate both statistical and systematic uncertainties. The main sources of uncertainties involved in cross section measurements were those associated with the determination of fast neutron flux densities and absolute decay rates.

Table 15 Calculation of the systematic uncertainties for the published values of the Reference

47

Ti(n,p)47Sc reaction cross-section.

Studied reaction

Monitor

Eγ [keV]

Reaction

Relative uncertainty, % Int.

Eγ [keV]

θ

(Niese et al., 1963) (Boldeman, 1964) (Son et al., 1968) (Kimura et al., 1971)

n/a 160.8 155 160

n/a n/a n/a n/a

n/a n/a n/a n/a

(Kobayashi et al., 1976)

160

n/a

n/a

(Mannhart, 1984)

n/a

n/a

n/a

(Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Maidana et al., 1994)

159.4 n/a

n/a n/a

n/a n/a

159.38

n/a

n/a

58

58

n/a

n/a

n/a

(Jonah et al., 2008)

159.38

n/a

n/a

int.

θ

r

Ni(n,p) Co S(n,p)32P 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na

n/a * 810 1370 810 n/a n/a n/a n/a n/a 1368.5 n/a

n/a * n/a ** n/a n/a n/a n/a n/a n/a ** n/a

n/a n/a n/a ** n/a n/a n/a ** n/a n/a ** **

n/a 2 n/a n/a n/a n/a n/a n/a 2.8 3.8 6.2 4

27

n/a n/a n/a n/a n/a n/a n/a n/a

n/a n/a n/a n/a n/a n/a n/a n/a

** n/a n/a n/a n/a n/a n/a **

4 2.8 2.9 6.1 7.5 6.2 17 n/a

32

Al(n,α)24Na Ni(n,p)58Co 54 Fe(n,p)54Mn 54 Fe(n,p)54Mn 56 Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 27 Al(n,p)27Mg 58

(Fatima et al., 2002)

Relative uncertainty, %

Combined systematic uncertainty of the final result, %a

Overall uncertainty, %b

nc 4 2.0 nc nc

17 6.8 5.1 6.3

nc

4.6

4 4 4 4

2.8 3.8 6.2 4.0

3.4

4 4 4 4 4 4 4 nc

4.0 2.8 2.9 6.1 7.5 6.2 17

3.3

6.9 5.9

10

6.6

n/a: data not available. *: not applicable. **: datum not given by the original authors, but corresponding to intensity known as equal or practically equal to 100 (null uncertainty). nc: not calculable (all the pertinent data are missing in the original works). a b

Calculated on the basis of the data published by the respective authors; it should be considered as a lower limit when some data are missing. As informed in the original works.

could not be renormalized for all the parameters involved, because their values were not indicated in the original works. In other cases, information was given about those parameters, but not on their uncertainty. Thus, it is impossible to access the totality of the sources of uncertainties. The situation is additionally complex, since the criteria for evaluation of the overall uncertainty of the final values differ significantly, depending on the different views of the authors. A reasonable expectation is that all the systematic uncertainties, derived from the literature data used in the calculations of the values, should be included in the subsequent calculations of the uncertainties. However, the actual situation is often far from this assumption.

Tables 13, 15, 17 and 19 show the EXFOR information on the constants employed for the determination of the different values for the studied reactions, together with the estimation (calculated by the present authors) of the propagation of their uncertainties over the final uncertainties of the results, whereas Tables 14, 16, 18 and 20 reproduce the EXFOR extracts about the comments drew up by the authors in connection with the uncertainties. The analysis allows formulating the following conclusions: (a) While in some cases the sources of uncertainty are well characterized and evaluated, there are no evidences for the remaining values that all (or any) of the systematic

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

uncertainties have been included in the estimation of the overall uncertainty of the final result. Extreme (and anomalous) situations are represented by the cases when the overall uncertainty assigned by the authors is less than the combined systematic uncertainty. (b) Because of this fact, the cross-section data can only be compared in relation with their absolute values, but not with respect to their uncertainties.

(c) The usual practice of calculating weighted averages to obtain recommended values is not advisable, because it would involve the risk to assign relative less weight to the determinations with uncertainty assessed through the consideration of all the systematic and random sources. As an undesirable consequence, this would imply to punish the authors that follow a thorough and methodologically correct procedure for the expression of their results.

Table 16 EXFOR extracts of the considerations formulated by the authors on the uncertainties of their cross-section values for the Reference

125

47

Ti(n,p)47Sc reaction.

Comments quoted in EXFOR entries

(Niese et al., 1963) (Boldeman, 1964)

Nothing said about uncertainties Uncertainty in branching ratios has not been included in error given. Assumed values of decay parameters are given in J.Nucl.Energy A/B 18,417(1964). (Kimura et al., 1971) Statistical error, uncertainty in monitoring the neutron flux, systematic error about 5 percent. Detailed discussion in reference. (Kobayashi et al., 1976) Flux uncertainty, 3%; Ge(Li) efficiency: 2.5%; other systematic errors. All these systematical errors are added up quadratically with systematic error as to give the total error. Systematic error deviation of spectrum for pure fission shape less than 3%. (Mannhart, 1984) The total errors are composed of counting statistics. Error in the scattering correction. Error in the relative photopeak efficiency. (Horibe et al., 1989) Total error, one sigma (Kobayashi and Kobayashi, Deduced by taking into account error correlations between data 1990) (Maidana et al., 1994) Item not included in the entry. (Fatima et al., 2002) The reported uncertainties incorporate both statistical and systematic errors. Main sources of errors associated in cross-section measurements were those associated with determination of fast neutron flux densities (8%) and absolute decay rates (5–10%) Other sources of error were small and were due to uncertainties in the number of target nuclei o 1% and in radiation and cooling times (1%). (Jonah et al., 2008) The given uncertainties incorporate both statistical and systematic uncertainties. The main sources of uncertainties involved in cross section measurements were those associated with the determination of fast neutron flux densities and absolute decay rates.

Table 17 Calculation of the systematic uncertainties for the published values of the Reference

(Son et al., 1968)

(Kimura et al., 1971)

(Kobayashi et al., 1976)

(Mannhart, 1984)

Ti(n,p)48Sc reaction cross-section.

Studied reaction

n/a 1320 990 1040 1310 990 1040 1314 980 1040 1314 983 1040 1314 n/a

(Horibe et al., 1989) 983.5 (Kobayashi and Kobayashi, 1990) n/a (Maidana et al., 1994) 175.35 983.50 1037.5 (Fatima et al., 2002) n/a

Reaction

Int.

θ

n/a ** ** n/a ** ** n/a ** ** n/a ** ** n/a ** n/a

n/a n/a n/a

58

Ni(n,p)58Co S(n,p)32P 32 S(n,p)32P

n/a

58

n/a

27

** n/a n/a ** n/a n/a

Combined systematic Overall uncertainty, %b uncertainty of the final result, %a

Monitor

Eγ [keV] Relative uncertainty, %

(Niese et al., 1963) (Boldeman, 1964) (Deschuyter and Hoste, 1967)

48

Int.

θ

r

n/a * *

n/a * *

n/a n/a n/a

n/a 2.0 n/a

nc 4 2.0 nc

Ni(n,p)58Co

810

n/a

n/a

n/a

nc

7.2

Al(n,α)24Na

1370

**

**

n/a

nc

8.5

810 n/a n/a n/a n/a n/a 1368.5 n/a n/a n/a n/a n/a n/a n/a n/a

n/a n/a n/a n/a n/a n/a ** n/a n/a n/a n/a n/a n/a n/a n/a

n/a n/a n/a ** n/a n/a ** ** ** n/a n/a n/a n/a n/a n/a

n/a n/a n/a n/a 2.8 3.8 6.2 4.0 4.0 2.8 2.9 6.1 7.5 6.2 17

nc

5.1

32

58

58

Ni(n,p) Co In(n,n′)115mIn 58 Ni(n,p)58Co 27 Al(n,α)24Na 58 Ni(n,p)58Co 115 In(n,n′)115mIn 27 Al(n,α)24Na 27 Al(n,α)24Na 27 Al(n,α)24Na 58 Ni(n,p)58Co 115

n/a n/a n/a n/a n/a n/a

Eγ [keV] Relative uncertainty, %

54

Fe(n,p)54Mn Fe(n,p)56Mn 58 Ni(n,p)58Co 60 Ni(n,p)60Co 56

4 4 4 4 4 4 4 4 4 4 4

2.8 3.8 6.2 4.0 4.0 2.8 2.9 6.1 7.5 6.2 17

n/a: data not available; *: not applicable; **: datum not given by the original authors, but corresponding to intensity known as equal or practically equal to 100 (null uncertainty); nc: not calculable (all the pertinent data are missing in the original works). a b

Calculated on the basis of the data published by the respective authors; it should be considered as a lower limit when some data are missing. As informed in the original works.

18 7.6 9.1

3.3 6.6 6.4 2.7

13

126

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It is apparent that the individual uncertainties, as they were evaluated by the different authors, do not provide any consistent basis for the assessment of the uncertainty of the averages. The approach used in this work consisted of the calculation of an estimate of the uncertainty as the statistical deviation of the average (namely, s N−1) plus the summation of all the estimated systematic uncertainties, according to their present values and following the well-known propagation formula (square root of the summation of the corresponding variances). The relevance of the

latter uncertainties varies significantly, depending on the magnitude considered. On the average, the ranges of uncertainties with respect to the corresponding magnitude are as follows.

6.1. Cross-sections of the monitors They constitute the major source of systematic uncertainties, which go from 2.7% to 5.9%, for the currently used monitors.

Table 18 EXFOR extracts of the considerations formulated by the authors on the uncertainties of their cross-section values for the

48

Ti(n,p)48Sc reaction.

Reference

Comments quoted in EXFOR entries

(Niese et al., 1963) (Boldeman, 1964)

Nothing said about uncertainties Uncertainty in branching ratios has not been included in error given. Assumed values of decay parameters are given in J.Nucl.Energy A/B 18,417(1964). The estimated total error is 15 percent, mainly due to the uncertainty associated with the cross section value of the fast flux monitor.

(Deschuyter and Hoste, 1967) (Kimura et al., 1971) (Kobayashi et al., 1976)

Statistical error, uncertainty in monitoring the neutron flux, systematic error about 5 percent. Detailed discussion in reference. Flux uncertainty, 3%; Ge(Li) efficiency: 2.5%; other systematic errors. All these systematical errors are added up quadratically with systematic error as to give the total error. Systematic error deviation of spectrum for pure fission shape less than 3%. (Mannhart, 1984) The total errors are composed of counting statistics. Error in the scattering correction. Error in the relative photopeak efficiency. (Horibe et al., 1989) Total error, one sigma (Kobayashi and Kobayashi, Deduced by taking into account error correlations between data 1990) (Maidana et al., 1994) Item not included in the entry. (Fatima et al., 2002) The reported uncertainties incorporate both statistical and systematic errors. Main sources of errors associated in cross-section measurements were those associated with determination of fast neutron flux densities (8%) and absolute decay rates (5 to 10%) Other sources of error were small and were due to uncertainties in the number of target nuclei o 1% and in radiation and cooling times (1%).

Table 19 Calculation of the systematic uncertainties for the published values of the Reference

510 511

n/a n/a

n/a n/a

(Rau, 1967)

n/a

n/a

n/a

(Najzer et al., 1970)

510

n/a

n/a

(Kimura et al., 1971)

n/a

n/a

n/a

(Jonah et al., 2008)

βþ 511 1345.6 n/a 1345.77 1345.78 511

1345.8

n/a

Reaction

θ

(Boldeman, 1964) (Fabry and Deworm, 1966)

1340

Overall Combined systematic uncertainty, %b uncertainty of the final result, %a

Monitor

Relative uncertainty, % Int.

(Najzer, Rant, 1978) (Grigor‘ev et al., 1989) (Horibe et al., 1989) (Kobayashi and Kobayashi, 1990) (Cohen et al., 2005) (Abbasi et al., 2006)

Zn(n,p)64Cu reaction cross-section.

Studied reaction

Eγ [keV]

(Kobayashi et al., 1976)

64

n/a

n/a n/a n/a n/a n/a n/a

n/a n/a n/a n/a n/a n/a

n/a

n/a

n/a n/a n/a

Eγ [keV]

Relative uncertainty, % Int.

32

32

S(n,p) P S(n,p)32P 27 Al(n,α)24Na 58 Ni(n,p)58Co 46 Ti(n,p)46Sc 27 Al(n,α)24Na

θ

* * n/a * * n/a ** n/a n/a n/a n/a n/a n/a n/a n/a 1368 ** ** 2750 ** 27 24 Al(n,α) Na 1370 ** ** 58 Ni(n,p)58Co 810 n/a n/a 115 In(n,n′)115mIn n/a n/a n/a 58 Ni(n,p)58Co n/a n/a n/a 27 Al(n,α)24Na n/a n/a ** 27 Al(n,α)24Na n/a n/a ** Absolute measurement 27 24 Al(n,α) Na 1368.5 ** ** 27 Al(n,α)24Na n/a n/a ** 27 Al(n,p)27Mg n/a n/a ** 54 Fe(n,p)54Mn n/a n/a n/a 56 Fe(n,p)56Mn n/a n/a n/a 58 58 Ni(n,p) Co n/a n/a n/a 60 60 Ni(n,p) Co n/a n/a n/a 27 Al(n,p)27Mg n/a n/a ** 32

s 42.0 nc

5.9 5.4

n/a n/a

nc

4.5

n/a n/a

nc

5.2

n/a

nc

7.9

n/a n/a

nc

6.8

nc – 4 6.2 4 4.0 a 4 6.1 4 7.5 4 6.2 4 17 nc

2.7 2.3 26 5.8 3.7 20

2 n/a

n/a n/a n/a 6.2 4 4.7c 6.1 7.5 6.2 17 n/a

n/a: data not available; *: not applicable. **: datum not given by the original authors, but corresponding to intensity known as equal or practically equal to 100 (null uncertainty). nc: not calculable (all the pertinent data are missing in the original works). a: the calculated value is anomalous, because of the aforementioned reason. a b c

Calculated on the basis of the data published by the respective authors; it should be considered as a lower limit when some data are missing. As informed in the original works. Transcribed from the EXFOR entry; the uncertainty informed in the original work is significantly lower.

4.2

I.M. Cohen et al. / Applied Radiation and Isotopes 77 (2013) 115–129

Uncertainty values as high as 12% and 13% are registered for the cross-sections of the 115In(n,n′)115m In and 60Ni(n,p)60Co reactions, used as monitors in isolated cases. In connection with these values, it is pertinent to wonder if such reactions can be considered as standards for determination of other cross-section values. Taking into account the high frequency of utilization of the standard reactions: 54Fe(n,p)54Mn, 58Ni(n,p)58Co and 27Al(n,α)24Na, and the uncertainties of their cross-section values, an average of 3% was consider for their contribution to the overall uncertainty. 6.2. Emission probability of the radiations measured in the monitors This is one of the aspects in which the authors do not provide information, even when the measured radionuclide is a gamma emitter and more than one transition is involved. Assuming that in all the cases the radiation of highest intensity was measured, the uncertainty range would be 0–4.8%. This abnormally high uncertainty, far from what can be considered as reference value, corresponds to the 336.2 keV gamma emission from 115mIn, and opens again the question of the actual usefulness of using 115 In(n,n′)115m In as standard reaction. The range for the remaining monitors is 0–0.07%. Since the 115In(n,n′)115m In reaction was used as standard in very few opportunities, and always together with at least another standard reaction, an average of the uncertainty for the radiations measured in the monitors other than 115mIn, 0.03%, was adopted as estimate of the contribution of these measurements to the total systematic uncertainty. 6.3. Isotopic abundance of the precursors of the standard reactions The uncertainty values of these isotopic abundances are within 0 and 0.6%. An average of 0.3%, which coincides with the uncertainty of the isotopic abundance of one of the most used monitors (58Ni), was adopted. 6.4. Emission probability of the radiations measured in the products In all the cases the uncertainties of the radiations measured at least once, according to the information supplied by the authors, were considered. On this basis, the estimated contributions to the

systematic uncertainty were 0.018% (46Sc); 0.59% (47Sc); 0.95% (48Sc); and 0.79% (64Cu). 6.5. Isotopic abundance of the precursors of the studied reactions The different contributions of the uncertainties of the isotopic abundances are 0.36% (46Ti); 0.27% (47Ti); 0.041 (48Ti); and 1.5% (64Zn). Table 21 sums up the final results with the corresponding estimates of their uncertainties. In connection with their significance, it is worthwhile to discuss some relevant topics: The methodology used for updating the original data is similar to that proposed by Calamand (1974), enhanced in the aspect that more parameters are used for renormalization. As it was explained above, the only criteria for acceptance or rejection of data arose from the application of statistical tests, i.e. the validity of each data is assessed only with respect to the consistency between all the published values. In this sense, the present work does not constitute a data evaluation, as that performed by the International Atomic Energy Agency (2006) in the frame of the International Reactor Dosimetry File (IRDF-2002) project, or those carried out by Zolotarev (2008) and Mannhart (2008). The selection of the values adopted as reference data for renormalization deserves an additional comment: whereas, as it was previously mentioned, the values of isotopic abundances receive unified treatment by the Union of Pure and Applied Chemistry (IUPAC), no sets of universally accepted data exist for emission probabilities and standard cross-sections. In particular, the decision with respect to the latter is more relevant, not only because the individual values configure the major source of systematic uncertainty, but also for the need of assuring the intrinsic consistency between the values of all the reaction cross-sections used as monitors. Although those published by Baard et al. (1989) may appear as relatively old (new values of these cross-sections have been recommended since that time) they were kept as references, due to the fact that the authors experimentally verified the consistency of the set as a whole (Arribére, 1997; Arribére et al., 2005; Cohen et al., 2005). Since all the data required for the renormalizations are explicitly cited, the traceability of the system has been preserved. Thus, it would be possible to repeat each process with new sets of

Table 20 EXFOR extracts of the considerations formulated by the authors on the uncertainties of their cross-section values for the Reference (Boldeman, 1964)

127

64

Zn(n,p)64Cu reaction.

Comments quoted in EXFOR entries

Uncertainty in branching ratios has not been included in error given. Assumed values of decay parameters are given in J.Nucl.Energy A/B 18,417(1964). (Fabry and Deworm, 1966) Not given (Rau, 1967) Statistical errors (Najzer et al., 1970) Nothing said about errors (Kimura et al., 1971) Statistical error, uncertainty in monitoring the neutron flux, systematic error about 5 percent. Detailed discussion in reference. (Kobayashi et al., 1976) Flux uncertainty, 3%; Ge(Li) efficiency: 2.5%; other systematic errors. All these systematical errors are added up quadratically with systematic error as to give the total error. Systematic error deviation of spectrum for pure fission shape less than 3%. (Najzer, Rant, 1978) Uncertainty includes: (ERR-1) The accuracy of gamma intensities with the gamma code (ERR-2) The accuracy of spectrometer efficiency Total uncertainties are not given since only one measurement has been performed. ERR-1 PER-CENT 0.3 ERR-2 PER-CENT 2.0 (Grigor'ev et al., 1989) Error is not specified (Horibe et al., 1989) Total error, one sigma (Kobayashi and Kobayashi, Deduced by taking into account error correlations between data 1990) (Cohen et al., 2005) Total error. The systematic contributions to all cross-section measurements are: *2.8% corresponding to the uncertainty of the reference cross-section value, *2% to 3% to the absolute efficiency (depending on the energy and counting geometry), *1% to sample purity, and *1% to other contributions (sample and monitor concentrations, nickel isotopic abundance, decay constants, self-attenuation correction), amounting to a total systematic uncertainty of 4.3% to 4.8%. (Abbasi et al., 2006) The reported uncertainties incorporate both statistical and systematic errors. Main sources of errors associated in cross-section measurements were those associated with determination of fast neutron flux densities (8%) and absolute decay rates (5–10%) Other sources of error were small and were due to uncertainties in the number of target nuclei o 1% and in radiation and cooling times ( 1%). (Jonah et al., 2008) The given uncertainties incorporate both statistical and systematic uncertainties. The main sources of uncertainties involved in cross section measurements were those associated with the determination of fast neutron flux densities and absolute decay rates.

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Table 21 Final values of the cross-sections and uncertainties for the studied reactions. Reaction Cross section value [mb]

Random Systematic uncertainty [%] uncertainty [%]

Final value [mb]

46

1.7

3.0

11.62±0.40

47

3.4

3.1

19.81±0.90

3.1

0.301±0.031

Ti(n, 11.62 p)46Sc Ti(n, 19.8 p)47Sc 48 Ti(n, 0.301 p)48Sc 64 Zn(n, 34.5 p)64Cu

10 3.7

3.5

34.5±1.7

reference data, depending on the points of view or preferences of the different users. In view of what was discussed in the preceding paragraphs, the answer to the possible question whether the present results are recommended values (with all the implications derived from such assertion) is that they constitute a set of reasonably safe values.

7. Conclusions The present status of the literature values of the fission neutron averaged cross-section for threshold reactions cannot permit a complete updating and evaluation. However, the possibility of improving this situation is open, through a renormalization based on five “critical” parameters: (a) isotopic abundance of the precursor of the reaction of interest; (b) emission probability of the radiation measured for the studied product; (c) isotopic abundance of the precursor of the standard reference reaction; (d) cross section of the reaction used as monitor; (e) emission probability of the radiation measured for the monitor product. These considerations are formulated taking into account the needs of the user; in this respect, the procedure suggested can be a valuable step on the search for a set of consistent values.

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