Introduction

The production of diagnostic and therapeutic radionuclides for medical applications is a very important non-energy related application of nuclear science and technology [1]. Such radionuclides are produced in both neutron and charged-particle induced nuclear reactions, and the list of these reactions used for the generation of diagnostic radioisotopes (gamma-ray emitters for SPECT and β+ emitters for PET imaging) and employed to monitor these preparative procedures is long. Dedicated compilations and evaluations of production cross-section data for such medical radionuclides were started over 20 years ago in a Coordinated Research Project (CRP) initiated and supported by the International Atomic Energy Agency (IAEA) [2]. This first concerted effort was identified with nuclear reactions used to produce widely used diagnostic radionuclides for SPECT and PET imaging (twenty-six reactions to generate 11C, 13N, 15O, 18F, 67Ga, 68Ge/68Ga, 81Rb, 82Sr, 111In, 123I, 123Cs/123Xe/123I and 201Pb/201Tl), and a selection of twenty-two reactions used to monitor beam parameters during the irradiations. All results were published in IAEA-TECDOC-1211 [3], made available within the medical portal of the IAEA Nuclear Data Section [4], and were subsequently updated in 2003 and 2004 [5, 6]. Both methods of presentation contain recommended cross-section data and the corresponding deduced yields. A second IAEA CRP was launched in 2003 to cover the production routes for established (103Pd, 186Re and 192Ir) and emerging therapeutic radionuclides (64Cu, 67Cu, 67Ga, 86Y, 111In, 114mIn, 124I, 125I, 169Yb, 177Lu, 211At and 225Ac) totalling thirty-five reactions [7].

According to citations and the number of data downloads, the IAEA-CRP cross-section databases have been extensively used at radionuclide production facilities worldwide. Furthermore, over recent years, new emerging radioisotopes have appeared and additional experimental data have been published on the previously evaluated reactions for medical applications and beam monitoring, along with studies of new applications of various other emerging radionuclides. Therefore, a third IAEA coordinated research project was launched in 2012, with the following primary aims [8]:

  1. (a)

    Re-evaluate those reactions for which important new data have been reported,

  2. (b)

    Extend the list of potential radionuclides and their recommended excitation functions for medical applications,

  3. (c)

    Determine uncertainties in the recommended cross-section data deduced from Padé fits on statistically consistent and critically selected datasets, and

  4. (d)

    Re-evaluate unreliable relevant decay data.

Sixteen laboratories and institutions from around the world collaborated in the project for which a fair number of specific re-evaluations required additional cross-section and decay-data measurements, and these new experimental datasets were published elsewhere on a regular basis. All cross-section data were also re-assessed and evaluated with the goal of producing recommended data with quantified uncertainties.

The physical yield (instantaneous production rate), activity generated during one hour irradiation with 1 μA beam current, and saturation yield defined in terms of an infinite irradiation were calculated from the recommended cross-section data. Results for direct and cumulative production routes, mono-isotopic and enriched targets, and targets of naturally-occurring isotopic compositions were considered. As agreed at subsequent research coordination meetings [11,12,13,], a set of four papers are in preparation to deal individually with the production routes for γ-emitting diagnostic radionuclides [SPECT imaging, lead author F. T. Tárkányi (this report)], β+ emitters and generators (PET imaging, lead author F. T. Tárkányi), therapeutic radionuclides (lead author J.W. Engle), and re-evaluated decay data (lead author A.L. Nichols). One additional paper on beam monitor reactions (lead author A. Hermanne) had already been published at the time of this submission [9].

The goal of this work is to report new model-independent cross-section evaluations with uncertainties derived by least-squares fits of statistically consistent experimental data. These evaluated data can be used to derive the physical yield for radionuclide production, and also aid in constraining calculations based upon nuclear reaction models.

The excitation functions for twenty-one charged-particle induced reactions have been assessed on the basis of their compilation, evaluation and a well-recognised data fitting procedure. These studies have involved the formation of five specific SPECT radionuclides selected for study in this CRP [8]: 51Cr, 99Mo/99mTc, 111In, 123I and 201Tl. Several other reactions were also considered for the formation of 99Mo induced by photon and neutron beams to assess the production of the extremely important 99Mo/99mTc generator. Our recent studies of various different routes for the selected radioisotopes are each discussed on an individual basis. After a short description of the decay data adopted for radionuclidic quantification and the medical applications for these radionuclides, the individual results for each production route are given, including figures that show (a) all compiled datasets, and (b) selected statistically consistent datasets (with experimental total uncertainties) along with the recommended fitted curve and uncertainty of the fit. Final figures for each dataset compare the integral physical yields for the medically relevant radionuclide that are based on the present recommended data for each route.

All evaluated cross sections and their uncertainties are available online at the IAEA Nuclear Data Section Web site www-nds.iaea.org/medical/gamma_emitters.html and also at the IAEA medical portal www-nds.iaea.org/medportal/. These Web pages include details of the evaluations, and the numerical data considered and adopted for analyses to generate the evaluated cross sections with their uncertainties and the corresponding production yields.

Evaluation, fitting and uncertainty estimates

All available literature sources containing relevant experimental data were used in the compilation process (primary journals, reports, conference abstracts and proceedings, yield compilations, reference databases, nuclear reaction databases such as EXFOR and NSR, PhD theses, etc.). Analyses and selection of the published experimental yields were based on detailed assessments of the measurement procedures including the determination of the particle energy, composition and nature of the target material, intensity of the beam, chemical separation processes, quantifying capabilities of measurement technique, nuclear data adopted, proper definition of the yield, and finally the aims of individual measurements and particularly attempts made to obtain precise values. Whenever needed and possible, known changes were introduced to adopted calibrant values (decay data and/or experimental parameters), as well as correcting conversion and computational errors. The compiled experimental data were also compared with the results of theoretical calculations based on the TALYS code system, and taken from the TENDL-2015 and TENDL-2017 libraries [10].

Corrected experimental data that exhibited large disagreements with the other datasets, unusual shapes, systematic energy shifts, and data significantly below the reaction threshold were rejected from the fitting procedure whereby a fully and statistically consistent dataset was established. Originally reported experimental uncertainties were considered when determining the variable uncertainties in the recommended consistent dataset. However, no proper quantified descriptions of the uncertainties are given in many publications, or the adopted measurements technique(s) imply that the quoted uncertainties had been significantly underestimated and merit correction to avoid excessive weight within the subsequent fitting process. This initiative has involved compilers who possess significant experience in experimental cross-section studies, which allows them to estimate the full functionality and accuracy of the experiments under consideration (i.e., sound subjective judgments can be made with respect to accelerator systems and laboratory facilities, identification of researchers with proven experience, and degree of technical application on production machines).

By and large, most contemporary evaluation procedures are based on various manifestations of the least-squares method (e.g., see review [11] and references therein). The least-squares method is the state-of-art Bayesian approach that combines all available knowledge to derive the evaluated result and corresponding uncertainties. Evaluations undertaken in this paper are in most cases model-independent evaluations free from potential model defects and deficiencies. However, such an approach implies that comprehensive and consistent experimental inputs should be available before the least-square fit is undertaken. When the status of the experimental data is appropriate, a purely statistical fit over the selected data points can be performed.

Often, least-square fits use analytical functions, the most prominent being polynomials or the ratio of two polynomials. An analytical approximation based on the ratio of two polynomials was proposed by Padé over 125 years ago [12], and has become one of the most important interpolation techniques of statistical mathematics [13, 14]. As a rational function, the Padé approximant can be expressed by a set of polynomial coefficients, or by a set of coefficients of the pole expansion

$$ p_{L} (z) = c + \sum\limits_{l} {\tfrac{{a_{l} }}{{z - \eta_{l} }} + \sum\limits_{k} {\frac{{\alpha_{k} (z - \varepsilon_{k} ) + \beta_{k} }}{{(z - \varepsilon_{k} )^{2} + \gamma_{{_{k} }}^{2} }}} } , $$
(1)

where z = x + iy is a complex variable and L is an order of the polynomial presentation of the Padé approximant [15]. This equation is also called the resonance expansion, in which εk and γk are the energy and the total half-width of the k-th resonance, while αk and βk are the partial widths and interference parameters. The first sum corresponds to the real poles, while the second sum relates to the complex poles.

Effective codes for practical applications of the Padé approximation were developed by the Obninsk group [15]. The simplest version of these codes permits analyses of up to 500 experimental points with the number of parameters L ≤ 40 and a ratio limit of analysed experimental data points fj up to max(fj)/min(fj) ≤ 106. A more detailed description of the method can be found in Refs. [15, 16], and some important questions of application are discussed in Refs. [17, 18]. The Padé approximation is also very convenient for calculations of the data uncertainties and the corresponding covariance matrices because the fitting procedure involves minimisation of the least-square deviation functional

$$ \chi^{2} = (N - L)^{ - 1} \sum\limits_{j = 1}^{N} {\left( {p_{L} (x_{j} ) - f_{j} } \right)^{2} /\sigma_{j}^{2} } , $$
(2)

where fj are the available experimental data, σj are their uncertainties and N is the number of analysed points. Such minimisation is carried out by iterations using the discrete optimisation approach. The minimal least-square deviation for a given L is computed using Eq. (2) by looking through a possible choice of L points from the available N points and the construction of corresponding approximants given by Eq. (1). Once this process has been completed, L is changed and the iteration is repeated until an overall minimum is found from all discrete possibilities available. Some additional features of this method of analysis are discussed in our recent paper on evaluated beam-monitor reactions [9].

Along with a consistent consideration of the statistical uncertainties of the experimental data, the Padé method allows (a) determination of some systematic uncertainties in the data that are usually underestimated by their authors and (b) establishment of some implicit correlations of the data. The averaged deviation of the experimental data from the approximating function is regarded as the systematic uncertainty for each reaction, while the deviations of the experimental points from the approximant are regarded as the statistical uncertainties. An optimal description of all data is achieved by the traditional iteration procedure of minimising the mean-squares deviations with respect to these statistical and systematic uncertainties. Whenever required and possible, we have attempted to correct the published experimental data and introduce realistic uncertainties, although the resulting fitting procedures still indicated that the systematic uncertainties of the experimental studies were being underestimated. Often the different experimental datasets for a given reaction show large systematic disagreements, without any obvious explanation. One reason could be that commercially-purchased target thicknesses were not always checked by independent measurement which might result in erroneous estimations of the number of target nuclei. Another explanation is that experimental data are frequently measured relative to beam-monitor reactions, but the monitoring technique is not properly applied: the incident energy is not checked, or possible deviations are not considered; and the complete excitation function of the monitor reactions is not simultaneously re-measured. Another issue is that the recommended cross-section data of the monitor reactions may change over the years, resulting in difficulties in establishing which monitor data were used in older publications. A further problem that cannot be addressed involves outdated decay data that do not linearly contribute to the cross-section dataset (i.e., half-life), because the timescales of the irradiation and the measuring process are not fully documented in the original publication.

Not all of the selected datasets are totally independent, but possess a certain degree of correlation. A significant number of the datasets were obtained by means of the stacked-foil irradiation technique in which the number of particles interacting with each foil is supposed to be constant and can be determined by application of the recommended beam-monitoring data. Several studies involved the generation of datasets obtained from different experiments in which the samples were measured with the same detectors operated at the same efficiency and source-to-detector distances. These correlations and the various correction factors are difficult to take into account in the evaluation, such that components of the systematic uncertainties are only partially considered. Therefore, an additional 4% systematic uncertainty was added to the experimental statistical uncertainties to obtain reasonable and realistic estimates of the evaluated uncertainties on the recommended excitation functions and their production yields.

Summary of the results from previous IAEA evaluations of cross sections for the production of diagnostic gamma emitters

The nuclear reactions for production of SPECT radionuclides evaluated as part of an earlier IAEA coordinated research project are summarised in Table 1. Results of the evaluations were initially presented in Ref. [3], and updated on the IAEA-NDS Web page [4], including plots of all the relevant experimental excitation functions and derived physical yields based upon the approach adopted in Refs. [5, 6]. All recommended cross-section data were based on Padé or spline fitting, as were the integral production yields as a function of beam energy. A full list of references and reasons for their rejection/selection for the fitting procedure were also provided. However, no uncertainties were provided within this first work package of recommended excitation functions.

Table 1 Earlier evaluated nuclear reactions for the production of diagnostic SPECT radionuclides (IAEA-TECDOC-1211 and IAEA nuclear database 2004 [3, 4], with the adopted decay data listed and taken from NuDat [19])—number of quoted digits for each quantity reflects the evaluated uncertainty
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Decay data used in the original cross-section evaluations were updated to the latest recommended values available from NuDat [19], as listed in Table 1.

Further evaluations of cross sections for the production of diagnostic gamma emitters

Overview of reactions studied

The list of SPECT radionuclides studied in this most recent coordinated research project has been extended to consider various production routes for widely used 99mTc and 51Cr. New experimental data measurements since 2004 for production of 123I, 111In and 201Tl have been included in this current series of evaluations based upon the development of suitable lists of possible production reactions. Due to the considerable importance of 99mTc and parent 99Mo in medical applications, consideration has also been given to a number of different production routes including charged-particle irradiations, neutron-induced reactions, and photon beams.

The various production reactions and the decay data of the medical radionuclides as taken from NuDat are listed in Table 2 [19], along with the degree of the adopted Padé polynomial fit.

Table 2 Decay data [19] and production routes of medical radionuclides under investigation—number of quoted digits for each quantity reflects the evaluated uncertainty
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Presentation of results

Every evaluation undertaken and the results for each reaction are illustrated in two figures that display the following: first figure depicts all available experimental data without their uncertainties, followed by a second figure that contains only the selected data with their experimental uncertainties and the Padé fit that defines the recommended cross sections with uncertainties expressed as percentages (uncertainty scale is on the right-hand side of the figure along the y-axis). Predicted cross-section values are also shown for comparison, as taken from the TENDL 2015 and TENDL 2017 libraries that are based on the TALYS code [10]. References for each reaction are reported separately in chronological order but have only been listed once in the reference list. Selection of appropriate and consistent datasets relies on many parameters for which the main reasons for rejection include the following:

  • Systematic energy shift towards lower or higher energy,

  • Significantly higher and lower values, or unusual shape when compared with the main body of data or theory,

  • Cross-section data below the threshold, and

  • Relatively high degree of scattered data.

Almost in all cases, the data points within an individual reference were considered in this manner as a fundamental part of the selection/rejection process. Only in a few cases mainly involving significant outliers close to the threshold were individual data points omitted to improve the possibility of a proper fit. Original proton data published by Levkovskij were all corrected for the erroneous values of the 96mTc beam monitor. The factor used is described in detail with reference to new measurements and earlier discussions within Section II.K of the latest evaluation of monitor reactions [9].

Integral physical yields for the different production reactions of each radionuclide of specific or indirect medical interest are calculated from the recommended data, and are shown in separate figures at the end of each subsection.

Charged-particle induced reactions

Reactions for the production of 51Cr (T 1/2 = 27.701 d)

Applications rather long-lived 51Cr is used to label red blood cells, and quantify gastro-intestinal protein loss and glomerular filtration rate (especially in paediatrics).

Evaluations have been made of the 51V(p,n)51Cr, 51V(d,2n)51Cr, 55Mn(p,x)51Cr, 55Mn(d,x)51Cr, natFe(p,x)51Cr, and natTi(α,x)51Cr reactions.

51V(p,n)51Cr

The thirty-two experimental datasets available in the literature for the generation of 51Cr from 51V targets are shown in Fig. 1 [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] (at 99.75% natural abundance of 51V in natV, irradiations on natural V are considered to express the cross section for interactions on 51V). Refs. [36, 41] contain two datasets each labelled as (a) and (b) in Fig. 1. All of the data in Fig. 1 are also compared with equivalent TENDL-2015 and TENDL-2017 calculations. Ten datasets were rejected (Tanaka and Furukawa [22] (values too low), Albouy et al. [24] (values too high), Hontzeas and Yaffe [28] (energy shift), Chodil et al. [33] (values too high), Mehta et al. (a) [36] (energy shift above 10 MeV), Stück [40] (data in energy range not included in fit), Kailas et al. (b) [41] (energy shift), Michel et al. [42] (data in energy range not included in fit), Bastos et al. [43] (values too high), and Musthafa et al. [47] (values too low)), and the remaining twenty-two sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 2 together with the Padé fit (L = 12, N = 500, χ2 = 1.57) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 1
figure 1

Thirty-two experimental datasets for the 51V(p,n)51Cr reaction available in the literature [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49], and the TENDL calculations. Both Refs. [36, 41] contain two datasets labelled (a) and (b)

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Fig. 2
figure 2

Twenty-two selected experimental datasets for the natV(p,x)51Cr reaction [20, 21, 23, 25,26,27, 29,30,31,32, 34,35,36(b), 37,38,39, 41(a), 44,45,46, 48, 49] with the Padé fit (L = 12, N = 500, χ2 = 1.57) and estimated uncertainties as percentages (dashed line, right-hand scale)

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51V(d,2n)51Cr

Six experimental datasets were found in the literature and all of them were judged as suitable for Padé fitting [44, 50,51,52,53,54]. All data are shown in Fig. 3, and are compared with the TENDL-2015 and TENDL-2017 calculations. These datasets and their experimental uncertainties are shown in Fig. 4 together with the Padé fit (L = 12, N = 151, χ2 = 0.68) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 3
figure 3

Six experimental datasets for the 51V(d,2n)51Cr reaction available in the literature [44, 50,51,52,53,54], and the TENDL calculations

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Fig. 4
figure 4

Six experimental datasets for the 51V(d,2n)51Cr reaction [44, 50,51,52,53,54] with the Padé fit (L = 12, N = 151, χ2 = 0.68) and estimated uncertainties as percentages (dashed line, right-hand scale)

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55Mn(p,x)51Cr

Six experimental datasets were found in the literature for the production of 51Cr by means of a monoisotopic 55Mn target, and all of them were judged as suitable for Padé fitting [38, 40, 45, 55,55,57]. All data are shown in Fig. 5, and are compared with the TENDL-2015 and TENDL-2017 calculations. Direct production occurs by means of the (p,2p3n) reaction (or clustered emission) and decay contributions of simultaneously formed 51Fe and 51Mn short-lived parents. These datasets and their experimental uncertainties are shown in Fig. 6 together with the Padé fit (L = 13, N = 94, χ2 = 1.75) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 5
figure 5

Six experimental datasets for the 55Mn(p,x)51Cr reaction available in the literature [38, 40, 45, 55,55,57], and the TENDL calculations

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Fig. 6
figure 6

Six experimental datasets for the 55Mn(p,x)51Cr reaction [38, 40, 45, 55,55,57] with the Padé fit (L = 13, N = 94, χ2 = 1.75) and estimated uncertainties as percentages (dashed line, right-hand scale)

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55Mn(d,x)51Cr

Only one experimental study was found for the cumulative deuteron-induced formation of 51Cr via a 55Mn target [58] (direct and decay of short-lived parents). This single dataset and experimental uncertainties are shown in Fig. 7 together with TENDL calculations, along with the Padé fit (L = 4, N = 5, χ2 = 0.54) with estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 7
figure 7

Single experimental dataset for the 55Mn(d,x)51Cr reaction [58] with TENDL calculations, and the Padé fit (L = 4, N = 5, χ2 = 0.54) with estimated uncertainties as percentages (dashed line, right-hand scale)

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natFe(p,x)51Cr

Sixteen experimental datasets were found in the literature for the cumulative formation of 51Cr on natural Fe targets [37, 38, 40, 55, 59,60,61,62,63,64,65,66,67,68,69,70]. All data are shown in Fig. 8, and are compared with the TENDL-2015 and TENDL-2017 calculations. Six datasets were rejected [Rayudu [59,60,61,62,63,64,65,66,67,68,69,] (single data point too low), Williams and Fulmer [60] (values too low), Brodzinski et al. [61] (single data point too low), Walton et al. [62] (values too high), Schoen et al. [63] (values too low), and Barchuk et al. [64] (discrepant at low energy)], and the remaining ten sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 9 together with the Padé fit (L = 21, N = 100, χ2 = 0.85) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 8
figure 8

Sixteen experimental datasets for the natFe(p,x)51Cr reaction available in the literature [37, 38, 40, 55, 59,60,61,62,63,64,65,66,67,68,69,70], and the TENDL calculations

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Fig. 9
figure 9

Ten selected experimental datasets for the natFe(p,x)51Cr reaction [37, 38, 40, 55, 65,66,67,68,69,70] with the Padé fit (L = 21, N = 100, χ2 = 0.85) and estimated uncertainties as percentages (dashed line, right-hand scale)

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natTi(α,x)51Cr

Sixteen experimental datasets were found in the literature [45, 50, 71,72,73,74,75,76,77,78,79,80,81,82,83]. Hermanne et al. [78] contained two datasets that have been labelled (a) and (b). All data are shown in Fig. 10, and are compared with the TENDL-2015 and TENDL-2017 calculations. Eight datasets were rejected [Levkovskij [45] (energy shift), Weinreich et al. [50] (energy shift), Iguchi et al. [71] (energy shift), Chang et al. [73] (values too low, and strange shape), Michel et al. [74] (energy shift), Tárkányi et al. [76] (energy shift), Xiufeng Peng et al. [77] (values too low), and Hermanne et al. (b) [78] (values too low)], and the remaining eight sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 11 together with the Padé fit (L = 11, N = 242, χ2 = 1.50) and estimated uncertainties as percentages, including 4% systematic uncertainty (right scale). This reaction is also used as a monitor reaction for α-beams, and is discussed further in Section V.C. of Hermanne et al. [9].

Fig. 10
figure 10

Sixteen experimental data datasets for the natTi(α,x)51Cr reaction available in the literature [45, 50, 71,72,73,74,75,76,77,78,79,80,81,82,83], and the TENDL calculations

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Fig. 11
figure 11

Eight selected experimental data for the natTi(α,x)51Cr reaction [72, 75, 78(a), 79,80,81,82,83] with the Padé fit (L = 11, N = 242, χ2 = 1.50) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Integral yields for 51Cr formation

Integral yields for the six production routes of 51Cr were calculated on the basis of the fits in Figs. 2, 4, 6, 7, 9 and 11, as presented in Fig. 12. Commercially available production accelerators (30-MeV protons) define the (p,n) reaction on natural vanadium targets (containing 99.75% 51V) as the method of choice. The advantages of higher yield through adoption of the (d,2n) reaction above 25-MeV incident particle energy can only be exploited by a limited number of research centres.

Fig. 12
figure 12

Yields calculated from the recommended cross sections for the 51V(p,n), 51V(d,2n)51Cr, 55Mn(p,x)51Cr, 55Mn(d,x)51Cr, natFe(p,x)51Cr and natTi(α,x)51Cr reactions

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Reactions for the production of 99mTc (T1/2 = 6.0072 h)

Applications99mTc is most commonly used to image the skeleton and heart muscle. Also has been applied to the brain, thyroid, lungs (perfusion and ventilation), liver, spleen, kidney (structure and filtration rate), gall bladder, bone marrow, salivary and lachrymal glands, heart blood pool, infection and many other specialised medical studies.

99mTc is the γ-emitting workhorse of diagnostic nuclear medicine (constitutes more than 70% of imaging procedures performed worldwide). Commercially distributed in the form of 99Mo/99mTc generators whereby all 99Mo is obtained from the fission of 235U within thermal research reactors (99Mo T1/2 = 65.924 h). Uncertainty in the sustainability of the supply chain caused by unexpected or progressive shutdown of aged research reactors has triggered a search for alternative reactions to be performed in accelerator systems. Significant attention has been devoted to both charged-particle induced reactions by means of particle accelerators and photon-induced reactions by means of electron linear accelerators (linac).

Production routes under investigation

Various production routes have been fully assessed and evaluated:

  • Indirect production via the 99Mo/99mTc generator based on the 100Mo(p,x)99Mo and 100Mo(d,x)99Mo charged-particle reactions (see below); 100Mo(n,2n)99Mo and 98Mo(n,γ)99Mo radiative neutron capture in reactors, and photon-induced reactions by means of linacs 100Mo(γ,n)99Mo and 238U(γ,f)99Mo (all four of these routes are analysed and discussed in the subsection entitled “99mTc and parent 99Mo: photon-induced and neutron-induced reactions”).

  • Direct production by means of the 100Mo(p,2n)99mTc and 100Mo(d,3n)99mTc reactions (see below).

100Mo(p,x)99Mo

Fourteen experimental datasets were found in the literature [45, 84,85,86,87,88,89,90,91,92,93,94,95,96]. All data are shown in Fig. 13, and are compared with the TENDL-2015 and TENDL-2017 calculations. Five datasets were rejected [Lagunas-Solar et al. [84,85,86,87,88,89,90,91,92,93,94,95,] (values too low), Scholten et al. [85] (values too low), Uddin et al. [87] (values too low), Khandaker et al. [88] (values too low at higher energy), and Alharbi et al. [90] (slight energy shift)], and the remaining nine sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 14 together with the Padé fit (L = 23, N = 153, χ2 = 1.73) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 13
figure 13

Fourteen experimental datasets for the 100Mo(p,x)99Mo reaction available in the literature [45, 84,85,86,87,88,89,90,91,92,93,94,95,96], and the TENDL calculations

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Fig. 14
figure 14

Nine selected experimental datasets for the 100Mo(p,x)99Mo reaction [45, 86, 89, 91,92,93,94,95,96] with the Padé fit (L = 23, N = 153, χ2 = 1.73) and estimated uncertainties as percentages (dashed line, right-hand scale)

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100Mo(d,x)99Mo

Relevant experimental data for the 100Mo(d,x)99Mo reaction are shown in Fig. 15 [91,92,93,94,95,, 97,98,99,100], and are compared with the corresponding TENDL calculations. Only two highly specific datasets exist [97,98,99,, 99] and under such limited circumstances, three other sets of experimental data measured on natMo and normalised to the abundance of 100Mo are also included in Fig. 15 [91, 98, 100]. All normalised data obtained with natMo targets include a significant contribution from the 98Mo(d,p)99Mo reaction at a lower threshold, and therefore the excitation function for these three references are seen to exhibit abnormal behaviour at lower beam energies. Nevertheless, the data measured on natMo support the 100Mo(d,x)99Mo data at energies above 30 MeV whereby the contribution of the 98Mo(d,p)99Mo reaction is small.

Fig. 15
figure 15

Five experimental datasets for the 100Mo(d,x)99Mo reaction available in the literature [91,92,93,94,95,, 97,98,99,100], and the TENDL calculations

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The two datasets obtained with 100Mo targets and their experimental uncertainties are shown in Fig. 16 [97,98,99,, 99] together with the Padé fit (L = 6, N = 70, χ2 = 1.23) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 16
figure 16

Two selected experimental datasets for the 100Mo(d,x)99Mo reaction [97,98,99,, 99] with the Padé fit (L = 6, N = 70, χ2 = 1.23) and estimated uncertainties as percentages (dashed line, right-hand scale)

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100Mo(p,2n)99mTc

Sixteen experimental datasets were found in the literature [45, 84,85,86, 88,89,90, 92,93,94,95,96, 101, 102]. Ref. [92] contains three sets of data labelled (a), (b) and (c). All data are shown in Fig. 17, and are compared with the TENDL-2015 and TENDL-2017 calculations. Ten datasets were rejected [Lagunas-Solar et al. [84] (energy shift, and values too high), Lagunas-Solar et al. [101] (values too high), Scholten et al. [85] (scattered, and values too low), Khandaker et al. [102] (values too low), Khandaker et al. [88] (energy shift, and values too low), Alharbi et al. [90] (values too low), Gagnon et al. (a, b, c) [92] (values too high in all three sets of data), and Manenti et al. [94] (values too high)], while the remaining six sets were used in the statistical fitting procedure. The selected data and their experimental uncertainties are shown in Fig. 18 together with the Padé fit (L = 15, N = 197, χ2 = 2.11) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 17
figure 17

Sixteen experimental datasets for the 100Mo(p,2n)99mTc reaction available in the literature [45, 84,85,86, 88,89,90, 92,93,94,95,96, 101, 102], and the TENDL calculations. Ref. [92] contains three datasets labelled (a), (b) and (c)

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Fig. 18
figure 18

Six selected experimental datasets for the 100Mo(p,2n)99mTc reaction [45, 86, 89, 93, 95, 96] with the Padé fit (L = 15, N = 197, χ2 = 2.11) and estimated uncertainties as percentages (dashed line, right-hand scale)

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100Mo(d,3n)99mTc

Only one experimental dataset has been determined with highly-enriched 100Mo target material [99], and therefore three other sets of normalised data measured on natMo have also been included in Fig. 19 as a guide [98,99,100, 103]. All data are also compared with the equivalent TENDL calculations. While these three additional datasets contain a significant contribution from the 98Mo(d,n)99mTc reaction at low particle-beam energies, such impact is close to being negligible around the maximum of the 100Mo(d,3n)99mTc reaction. All three datasets determined with natMo targets support the single set of data measured with highly-enriched 100Mo. The Padé fit shown in Fig. 20 is based only on the data of Ref. [99] and associated experimental uncertainties (L = 6, N = 33, χ2 = 0.88) with estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 19
figure 19

Four experimental datasets for the 100Mo(d,3n)99mTc reaction available in the literature [98,99,100, 103], and the TENDL calculations

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Fig. 20
figure 20

Single experimental dataset for the 100Mo(d,3n)99mTc reaction [99] with the Padé fit (L = 6, N = 33, χ2 = 0.88) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Integral yields for 99Mo and 99mTc formation using proton/deuteron accelerators

Integral yields for the production routes of 99Mo and 99mTc are shown in Figs. 21 and 22, respectively, as calculated on the basis of the fits in Figs. 14, 16, 18 and 20. Only the direct 100Mo(p,2n)99mTc reaction on highly-enriched 100Mo targets could be an alternative route of production for dedicated and commercially available accelerators (30-MeV protons). Indirect production by means of higher-energy deuteron reactions could increase the yield by a factor of three through adoption of the 100Mo(d,x) 99Mo route, and allow the continued use of parent-based generator systems. However, both direct and indirect charge-particle routes cannot compete economically with fission based 99Mo production as long as heavily subsidised research reactors are available.Footnote 1

Fig. 21
figure 21

Yields calculated from the recommended cross sections for the 100Mo(p,x)99Mo and 100Mo(d,x)99Mo reactions

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Fig. 22
figure 22

Yields calculated from the recommended cross sections for the 100Mo(p,2n)99mTc and 100Mo(d,3n)99mTc reactions

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Reaction for the production of 111In (T1/2 = 2.8047 d)

Applications111In is used for specialist diagnostic studies, such as the brain, colon transit, and infection. Also has been identified as a suitable candidate for radiotherapy.

112Cd(p,2n)111In

Nine experimental datasets were found in the literature for the 112Cd(p,2n)111In reaction [104,105,106,107,108,109,110,111,112]. All data are shown in Fig. 23, and are compared with the TENDL-2015 and TENDL-2017 calculations. Only one dataset was rejected (Nieckarz and Caretto [105] (single data point above the chosen energy range of the fit)), and the remaining eight sets were used in the statistical fitting procedure. These selected datasets and their experimental uncertainties are shown in Fig. 24 together with the Padé fit (L = 9, N = 100, χ2 = 1.46) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 23
figure 23

Nine experimental datasets for the 112Cd(p,2n)111In reaction available in the literature [104,105,106,107,108,109,110,111,112], and the TENDL calculations

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Fig. 24
figure 24

Eight selected experimental datasets for the 112Cd(p,2n)111In reaction [104,105,106,107,108,109,110,111,, 106,107,108,109,110,111,112] with the Padé fit (L = 9, N = 100, χ2 = 1.46) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Integral yield for 111In formation

Integral yield for the 112Cd(p,2n)111In reaction is shown in Fig. 25—used at present as a standard production route for commercially available 30-MeV cyclotrons.

Fig. 25
figure 25

Yields calculated from the recommended cross sections for the 112Cd(p,2n)111In reaction

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Reactions for the production of 123I (T1/2 = 13.2235 h)

Applications123I is a standard radionuclide in the diagnosis of thyroid function and studies of the cardiac and nervous system. Complementary imaging has also been performed in conjunction with the emerging 124I β+ emitter, and for radiotherapy in conjunction with 131I β− emitter.

Production routes for 123I that employ tellurium and 124Xe targets were evaluated as part of an earlier CRP [2, 3]. Following on from these studies, re-evaluations have been made of a selection of nuclear reactions related to the production of 123I precursors by proton-induced reactions on 124Xe targets: 124Xe(p,2n)123Cs, 124Xe(p,pn)123Xe, and 124Xe(p,x)123Xe. Furthermore, an assessment has also been made of the formation of 121I impurity by means of the 124Xe(p,x)121I reaction which limits the shelf-life of 123I.

124Xe(p,2n)123Cs

Three experimental datasets were found in the literature for the 124Xe(p,2n)123Cs reaction [113,114,115] that were all used in the statistical fitting procedure. All data are shown in Fig. 26, and are compared with the TENDL-2015 and TENDL-2017 calculations. These data and their experimental uncertainties are shown in Fig. 27 together with the Padé fit (L = 13, N = 71, χ2 = 0.67) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 26
figure 26

Three experimental datasets for the 124Xe(p,2n)123Cs reaction available in the literature [113,114,115], and the TENDL calculations

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Fig. 27
figure 27

Three experimental datasets for the 124Xe(p,2n)123Cs reaction [113,114,115] with the Padé fit (L = 13, N = 71, χ2 = 0.67) and estimated uncertainties as percentages (dashed line, right-hand scale)

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124Xe(p,pn)123Xe

Three experimental datasets were found in the literature for the direct 124Xe(p,pn)123Xe reaction (Fig. 28) [113,114,115]. All data are shown in Fig. 28, and are compared with TENDL-2015 and TENDL = 2017 calculations. The dataset of Tárkányi et al. [114] was rejected (values too low), and the remaining two sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 29 together with the Padé fit (L = 13, N = 43, χ2 = 1.16) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 28
figure 28

Three experimental datasets for the 124Xe(p,pn)123Xe reaction available in the literature [113,114,115], and the TENDL calculations

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Fig. 29
figure 29

Two selected experimental datasets for the 124Xe(p,pn)123Xe reaction [113,114,, 115] with the Padé fit (L = 13, N = 43, χ2 = 1.16) and estimated uncertainties as percentages (dashed line, right-hand scale)

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124Xe(p,x)123Xe

Three experimental datasets were found in the literature for this means of cumulative formation, including the decay of short-lived 123Xe parent [113,114,115]. All data are shown in Fig. 30, and are compared with the TENDL-2015 and TENDL-2017 calculations. The dataset of Tárkányi et al. [114] was rejected (values too low), and the remaining two sets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 31 together with the Padé fit (L = 16, N = 44, χ2 = 1.00) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 30
figure 30

Three experimental datasets for the 124Xe(p,x)123Xe reaction available in the literature [113,114,115], and the TENDL calculations

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Fig. 31
figure 31

Two selected experimental datasets for the 124Xe(p,x)123Xe reaction [113,114,, 115] with the Padé fit (L = 16, N = 44, χ2 = 1.00) and estimated uncertainties as percentages (dashed line, right-hand scale)

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124Xe(p,x)121I (reaction for generation of 121I impurity)

Unavoidable contamination of 123I by 121I (T1/2 = 2.12 h, daughter product of co-produced 121Cs-121Xe that decays to long-lived 121Te) by means of the reaction processes discussed above limits the shelf-life of batches of 123I [115].

Two datasets were found in the literature [114, 115]. All data are shown in Fig. 32, and are compared with TENDL-2015 and TENDL-2017 calculations. Both sets of data and their experimental uncertainties were used in the statistical fitting procedure as shown in Fig. 33 together with the Padé fit (L = 18, N = 24, χ2 = 1.21) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 32
figure 32

Two experimental datasets for the 124Xe(p,x)121I reaction available in the literature [114, 115], and the TENDL calculations

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Fig. 33
figure 33

Two experimental datasets for the 124Xe(p,x)121I reaction [114, 115] with the Padé fit (L = 18, N = 24, χ2 = 1.21) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Integral yields for 123Cs–123Xe (grandparent and parent of 123I) and 121I impurity formation

Integral yields related to the production of 123I deduced from the fits in Figs. 27, 29, 31 and 33 are shown in Figs. 34, 35 and 36.

Fig. 34
figure 34

Yields calculated from the recommended cross sections for the 124Xe(p,2n)123Cs reaction

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Fig. 35
figure 35

Yields calculated from the recommended cross sections for the 124Xe(p,pn)123Xe and 124Xe(p,x)123Xe reactions

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Fig. 36
figure 36

Yields calculated from the recommended cross sections for the 124Xe(p,x)121I reaction

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Reactions for the production of 201Tl (T1/2 = 3.0421 d)

Applications201Tl has been used for the diagnosis of coronary artery disease, myocardial infarct and heart muscle death, and to locate low-grade lymphomas.

Present commercial production is through the EC/β+ decay of parent 201Pb obtained by means of the 203Tl(p,3n)201Pb reaction (adoption of 95% enriched 203Tl targets) and double Tl–Pb separation chemistry. Quantitative knowledge of the unavoidable and simultaneous production of 200Pb and 202mPb via the 203Tl(p,4n)200Pb and 203Tl(p,2n)202mPb reactions is important from the point of view of radionuclidic purity (limits defined in pharmacopoeia).

203Tl(p,3n)201Pb

Eleven experimental datasets were found in the literature that exhibit contradictory results [116,117,118,119,120,121,122,123,124]. Both Refs. [121, 124] contain two datasets labelled as (a) and (b). All data are shown in Fig. 37, and are compared with the TENDL-2015 and TENDL-2017 calculations. Five datasets were rejected [Sakai et al. [116] (energy shift), Lebowitz et al. [117] (values too low), Blue et al. [119] (values too low), Qaim et al. [120] (values too low), and Bonardi et al. (b) [121] (values too low)], while the remaining six datasets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 38 together with the Padé fit (L = 13, N = 178, χ2 = 1.67) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 37
figure 37

Eleven experimental datasets for the 203Tl(p,3n)201Pb reaction available in the literature [116,117,118,119,120,121,122,123,124], and the TENDL calculations. Both Refs. [121, 124] contain two datasets denoted as (a) and (b)

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Fig. 38
figure 38

Six selected experimental datasets for the 203Tl(p,3n)201Pb reaction [118, 121(a), 122, 123, 124(a) and (b)] with the Padé fit (L = 13, N = 178, χ2 = 1.67) and estimated uncertainties as percentages (dashed line, right-hand scale)

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203Tl(p,4n)200Pb (impurity reaction)

Seven experimental datasets were found in the literature [116, 118,119,120,121,122, 124]. All data are shown in Fig. 39, and are compared with the TENDL-2015 and TENDL-2017 calculations. Only one dataset was rejected [Sakai et al. [116] (discrepant values)], while the remaining six datasets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 40 together with the Padé fit (L = 5, N = 124, χ2 = 2.01) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 39
figure 39

Seven experimental datasets for the 203Tl(p,4n)200Pb reaction available in the literature [116, 118,119,120,121,122, 124], and the TENDL calculations

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Fig. 40
figure 40

Six selected experimental datasets for the 203Tl(p,4n)200Pb reaction [118,119,120,121,122, 124] with the Padé fit (L = 5, N = 124, χ2 = 2.01) and estimated uncertainties as percentages (dashed line, right-hand scale)

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203Tl(p,2n)202mPb (impurity reaction)

Six experimental datasets were found in the literature [118, 120,121,122,123,124]. All data are shown in Fig. 41, and are compared with the TENDL-2015 and TENDL-2017 calculations. Three datasets were rejected [Lagunas-Solar et al. [118], Bonardi et al. [121], and Al-Saleh et al. [123] (all values too low)], and the remaining three datasets were used in the statistical fitting procedure. These selected data and their experimental uncertainties are shown in Fig. 42 together with the Padé fit (L = 9, N = 18, χ2 = 1.87) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 41
figure 41

Six experimental datasets for the 203Tl(p,2n)202mPb reaction available in the literature [118, 120,121,122,123,124], and the TENDL calculations

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Fig. 42
figure 42

Three selected experimental datasets for the 203Tl(p,2n)202mPb reaction [120, 122, 124] with the Padé fit (L = 9, N = 18, χ2 = 1.87) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Integral yields for 201Tl formation

Integral yields of reactions related to the production of 201Tl and deduced from the data fittings in Figs. 38, 40 and 42 are shown in Fig. 43.

Fig. 43
figure 43

Yields calculated from the recommended cross sections for the 203Tl(p,3n)201Pb, 203Tl(p,4n)200Pb and 203Tl(p,2n)202mPb reactions

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99mTc and parent 99Mo: photon-induced and neutron-induced reactions

Consideration was given to various non-charged-particle reactions for the production of parent 99Mo to generate 99mTc, which involved the irradiation of particular molybdenum targets with photons or neutrons as well as the 238U(γ,f) reaction.

100Mo(γ,n)99Mo

Only three experimental datasets were found in the literature, and are shown in Fig. 44 [125,126,127]. These datasets have also been compared with recent evaluations contained within the TENDL-2017 [10] and ENDF/B-VII.1 [128] libraries. Measurements by Ejiri et al. [126] at a gamma-ray energy of approximately 14.5 MeV were performed with bremsstrahlung spectrum, and such conditions differ significantly from the other two studies carried out with monoenergetic gamma rays [125, 127]. Both sets of selected data and their experimental uncertainties are shown in Fig. 45 [125, 127] together with the Padé fit (L = 9, N = 55, χ2 = 1.84) and estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 44
figure 44

Three experimental datasets for the 100Mo(γ,n)99Mo reaction available in the literature [125–127], compared with evaluations in the TENDL-2017 and ENDF/B-VII.1 libraries

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Fig. 45
figure 45

Two selected experimental datasets for the 100Mo(γ,n)99Mo reaction [125, 127] with the Padé fit (L = 9, N = 55, χ2 = 1.84) and estimated uncertainties as percentages (dashed line, right-hand scale)

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98Mo(n,γ)99Mo

Twenty-seven experimental datasets were found in the literature [129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155], and are shown in Fig. 46 together with the TENDL-2017 evaluation. Seven sets of these data relate to cross-section measurements for thermal neutrons [129,130,131,132,133,134,135], and individual data points coincide within their ranges of uncertainties (assigned the same symbol in Fig. 46 because of their overlap). Another group of nine data points at a beam energy of approximately 25 keV relates to measurements in which Po-Be neutron sources were used [132, 136,137,138,139,140,141,142,143], and they are also denoted by a common symbol because of their significant overlap. A set of seven data points measured by Weston et al. [145] over neutron energies from 2 to 100 keV were corrected (corr.) in accord with changes in the monitor reaction cross sections, although only some of them are visible within Fig. 46 owing to the surrounding high density of data.

Fig. 46
figure 46

Experimental datasets for the 98Mo(n,γ)99Mo reaction available in the literature [129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155], and the 75-group evaluation of TENDL-2017 [10]

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Neutron cross sections at low energies possess resonance structure, an example of which is shown in Fig. 46 at an energy of ~ 12 eV as observed in a neutron capture experiment [146]. The number of resonances increases significantly with increasing energy, particularly over the neutron energy interval up to 10 keV as measured by Musgrove et al. [150]. Group representations of overlapping resonances in the form of averaged cross sections are usually adopted in such circumstances, and the TENDL-2017 definition of this particular neutron-capture cross section is shown in Fig. 46 as a 75-group assembly [10]. This TENDL-2017 evaluation below 100 keV coincides closely with the ENDF/B-VII.1 [128], JEFF-3.2 [156], JENDL-4.0 [157], and BROND-3.1 [158] national and international neutron data libraries, whereby the same resonance parameters have often been used [159].

Reference [146] data were only adopted for neutron energies above 3 keV on the basis of their reasonable agreement with the high-resolution data. Eight datasets were rejected because they contradict the main trends of all other data [136,137,138, 140,141,142,143, 148]. A thermal neutron cross section of (130 ± 6) mb was adopted, as recommended by Mughabghab [159] on the basis of a consistent analysis of the experimental data and the resonance parameters. This value is also well supported by epithermal neutron data [155].

All selected datasets are shown in Fig. 47 together with the BROND-3.1 evaluation [158]: BROND-3.1 and TENDL-2017 differ only in the energy region above 100 keV. Both sets of statistical model calculations are important for a consistent description of the abrupt decrease of the capture cross section immediately above the threshold for neutron inelastic scattering (~ 787 keV for 98Mo).

Fig. 47
figure 47

Selected experimental datasets for the 98Mo(n,γ)99Mo reaction compared with BROND-3.1 calculations and evaluation, and estimated uncertainties as percentages (dashed line, right-hand scale)

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Complete consideration of the complex resonance structure of the evaluated data is not required to estimate the uncertainties of the recommended cross sections. Sufficient information can normally be gleaned from the uncertainties of the multi-group cross sections to achieve this objective. Such an approach is described in detail in Ref. [158], and these estimated uncertainties for the 98Mo(n,γ)99Mo reaction are shown in Fig. 47 (right-hand scale).

100Mo(n,2n)99Mo

Twenty-five experimental datasets were found in the literature [160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182]. Ikeda et al. [177] contains three versions of the data measured on the basis of different beam-monitor reactions, and these are labelled (a), (b) and (c). All of these data are shown in Fig. 48 together with TENDL-2017 evaluation except for the two 14-MeV data points of Refs. [160, 161] which exceed essentially all other equivalent data. Results of Ref. [174] have been corrected (corr.) in accord with the current changes in the monitor reaction cross sections, while Ref. [182] constitutes similar adjustments of previous publications performed by the original author. Eight further datasets were rejected [162,163,164, 167, 168, 170, 176, 179] as contradictory to the mean value of all other data around 14 MeV. The remaining fifteen sets were used in the fitting procedure—these selected data and their experimental uncertainties are shown in Fig. 49 together with the Padé fit (L = 19, N = 69, χ2 = 0.84) and estimated percentage uncertainties, including 4% of the systematic uncertainty (right-hand scale).

Fig. 48
figure 48

Twenty-three experimental datasets for the 100Mo(n,2n)99Mo reaction available in the literature [162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182], and the TENDL-2017 evaluation. Ikeda et al. [177] contains three versions of the data measured on the basis of different beam-monitor reactions, and these are labelled (a), (b) and (c)

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Fig. 49
figure 49

Fifteen selected experimental datasets for the 100Mo(n,2n)99Mo reaction with the Padé fit (L = 19, N = 69, χ2 = 0.84) and estimated uncertainties as percentages (dashed line, right-hand scale)

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238U(γ,f)99Mo

While there are no directly measured experimental data for the 238U(γ,f)99Mo reaction, thirteen experimental datasets were found in the literature for the total photofission cross section [183,184,185,186,187,188,189,190,191,192,193,194,195], as shown in Fig. 50. Symbols below a gamma-ray energy of 8 MeV overlap so severely that some data points are rather difficult to resolve. Data were only compiled and assessed for gamma-ray energies below 30 MeV that are important for medical applications. These data are also compared in Fig. 50 with the Varlamov-Peskov (2007) evaluation which is widely considered as optimal for the photofission cross section of 238U [196].

Fig. 50
figure 50

Experimental datasets for the 238U(γ,f) reaction available in the literature [183,184,185,186,187,188,189,190,191,192,193,194,195], and the Varlamov-Peskov (2007) evaluation [196]

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Three datasets were rejected [183, 184, 186] because of their disagreement with all other equivalent data. Data points from both Ref. [191] above 10 MeV and Ref. [192] below 14 MeV were also omitted for the same reason. The Padé fit of all remaining data is shown in Fig. 51 (L = 17, N = 283, χ2 = 3.36) together with the estimated uncertainties as percentages, including 4% systematic uncertainty (right-hand scale).

Fig. 51
figure 51

Selected experimental datasets for the 238U(γ,f) reaction with the Padé fit (L = 17, N = 283, χ2 = 3.36) and estimated uncertainties as percentages (dashed line, right-hand scale)

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Data for the neutron-induced reaction on 238U are most frequently used to estimate the cumulative photofission yield of 99Mo. Such data are available in all of the national and international data libraries, but their accuracy is not high. The following cumulative yields are given for a neutron energy range between 1.0 and 2.0 MeV:

  • (6.17 ± 0.86)% in the ENDF/B-VII.1 library,

  • (5.65 ± 0.73)% in the NEA-OECD JEFF-3.2 library, and

  • 6.12%, without any uncertainties in the Japanese JENDL-4.0 library.

All libraries exhibit some energy dependence of the cumulative yields, but these changes for neutron energies of 14 MeV do not exceed the uncertainties of the yield at lower energies. Under such circumstances, we decided to adopt the ENDF/B-VII.1 value of the cumulative yield for the whole energy region of the 238U(γ,f) reaction. The corresponding cross section for the 238U(γ,f)99Mo reaction as obtained on the basis of the Padé approximant of the total fission cross section is shown in Fig. 52 together with the estimated uncertainties, the main contributor of which is identified with the isotope yield uncertainties.

Fig. 52
figure 52

Evaluated cross section for the 238U(γ,f)99Mo reaction based on the Padé fit of the 238U(γ,f) reaction and the cumulative yield of 99Mo [128]. Estimated uncertainties are shown as percentages (dashed line, right-hand scale)

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Integral yields for production of 99Mo by gamma-ray and neutron-induced reactions

Both the photon and neutron sources that are used for medical radioisotope production generate continuous spectra. These spectra depend on various accelerator-target combinations, the energy of the charged-particle beam, position of the target, etc., such that the production yield depends on the specific experimental arrangements and local circumstances. On the basis of the evaluated cross sections, flux and mass independent production yields can be calculated as a function of the energy of the bombarding particles defined as:

$$ {\text{Activity}}/({\text{incident}}\;{\text{particle}} \times {\text{unit}}\;{\text{mass}}) $$

Derived in the form of a function, this energy is identical in shape to the excitation function. By knowing the energy distribution of the incident particle and the range of energy applied, the integral yield can be readily deduced.

Summary and conclusions

Significant improvements and substantial extensions have been made to the IAEA-NDS recommended cross-section database for the production of specific gamma-emitting radionuclides. Evaluations of production cross sections and their uncertainties were performed on twenty-two reactions for direct, indirect and generator production of 51Cr, 99Mo/99mTc and 99mTc, 111In, 123Cs/123Xe/123I (and 121I impurity), and 201Pb/201Tl (and 200Pb and 202mPb impurities).

Additional production routes for 51Cr, 99mTc and 123I were explored, and some earlier evaluated nuclear reactions to produce 111In and 201Tl were also re-defined. A Padé fitting method was applied to the selected datasets, and uncertainties in all of the recommended cross-section data were deduced following the evaluation methodology described and fully adopted in Ref. [9]. Known experimental data were compared with the theoretical predictions to be found in the TENDL-2015 and 2017 libraries, and significant disagreements in the magnitude and shape of the resulting excitation functions existed in some cases (especially when considering isomeric states or deuteron-induced reactions). No major differences were found in the predictions of these two versions of the TENDL libraries, therefore, improved modelling is required. All of the recommended cross-section data have been used with reasonable confidence to determine integral yields for radionuclide production. Thus, the resulting datasets adopted in the present evaluation are seen as being acceptable for all practical purposes with good confidence. However, in a few cases, the data are more uncertain because of an existing lack of well-measured data.

Selection of the optimal reaction depends on many factors such as available beam particles and their achievable energy range, targetry and possible recovery problems with enriched target materials, production yield, impurities, and necessary chemical separation processes. The recommended cross sections are directly related to production yields and the acceptable levels of radioactive impurities. More specifically, improved radionuclidic purity is an important issue for practical applications in nuclear medicine. Under such circumstances, excitation functions for radionuclidic impurities are required to aid in defining optimum target compositions and the full energy range of the beam within the target in order to avoid or at least minimise their production. Recommendations concerning radioisotopic contaminants have only been made in the present evaluation for the production of 123I with 124Xe targets, and 201Tl with 203Tl targets. Other radionuclidic impurities need to be studied in what remains an important evolutionary programme of work.

Both the recommended excitation functions and production yields are available on the web page of the IAEA NDS at www-nds.iaea.org/medical/gamma_emitters.html and also at the IAEA medical portal www-nds.iaea.org/medportal/. These evaluated experimental data are important for existing and potential nuclear medicine applications, for improvement and validation of the various nuclear reaction models, and may also have useful roles in other fields of non-energy related nuclear studies (e.g., activation analysis and thin layer activation).