Extension of evaluated cross section database for charged particle monitor reactions

Abstract

The evaluation and deduction of recommended cross section values allowing extension of the database to monitor energy and intensity parameters of charged particle beams is presented. Included are 53 charged particle (p, d, ³He, ⁴He) induced reactions on suited C, Al, Ti, Fe, Ni, Cu, Nb and Au targets. The new data allow more systematic simultaneous use of multiple reactions on the same target and promote the backings of electrodeposited and sedimented targets as monitoring aids. Where possible the energy range is extended to above 100 MeV. Integral yield curves over the studied energy range are derived and compared to experimentally measured yields at specific energy points. A comparison with the theoretical excitation curve prediction of the TALYS-code as available in the TENDL 2021–2023 libraries is shown.

Introduction

The development and optimization of radionuclide production routes for industrial and medical applications are of considerable and indisputable interest to the IAEA and to the user community. Cyclotrons and other particle accelerators, available in recent years in an increasing number of countries, often with the support of the IAEA, are being used for the production of radioisotopes for medicinal diagnostic and therapeutic purposes, thin layer activation for industrial wear studies, and nuclear analytics. Besides commercial or in-house medical radionuclide production, reactions with low-energy charged particles are of primary importance for several industrial and scientific applications.

The physical basis for radioisotope production is the nuclear interaction of charged particles, such as protons, deuterons and alphas, with matter atoms. The different contributing processes and reactions have to be well quantitatively understood to obtain useful and high-purity radioisotopes efficiently and safely. For this reason, knowledge of well-evaluated numerical data for excitation functions (cross sections depending on particle energy) and thick target yields over verified energy domains are needed. Both for efficient production of radioisotopes in the different applications and for physics on nuclear reaction characteristics a good control on bombarding beam parameters is essential. A technique applied on-site is the use of monitor reactions. Although cross section data for basic and usefull monitor reactions are available and were evaluated earlier the further development of radionuclide production requires broader and self-controlling possibility of choices for monitors. In this study an extension of the evaluated number of reactions and their critical evaluation is discussed. An overview of basic characteristics and requirements of beam monitoring by charged particle-induced reactions on well-identified and selected targets, followed by measurement of the decay of the activation products is presented in the next sections.

Monitor reactions

The usefulness of monitor reactions for controlling or investigating different beam parameters [1], defined more precisely later, is summarized in Table 1 for three specific types of applications where their importance and requirements are different.

Table 1 Beam parameters

The definitions of the above-listed beam parameters and the methods of determination and measurement are explained here:

Ion species and charge state

• Definition: (Z, N).

• Determination: by parameters of ion source, accelerators, bending magnets.

• Application of monitor reactions: possible.

Current

• Definition: time dependence of the beam current.

• Type: macro pulse, bunch, mean current: DC or AC.

• Determination: Faraday cup, calorimetric measurement, beam current transformers, secondary particles (electrons, ions, neutrons).

• Application of monitor reactions: possible.

Beam profile

• Definition: intensity distribution in transverse directions.

• Determination: Viewing screens (optical, thermographic), profile grids, scanners or harps, residual gas ionization, slits + Faraday cup measurement, monitor reactions.

• Application of monitor reactions: possible.

Beam energy, beam energy spread

• Energy:

• Definition: Nominal energy of a single particle within this beam; in practice the average.

• Energy spread:

• Definition: Energy distribution of the beam particles.

• Determination: Magnetic spectrometers, Telescopes, TOF technique (capacitive pick-ups, coaxial cups, etc.), monitor reactions.

• Application of monitor reactions: yes.

The basic idea for the use of monitor reactions is the activation technique by irradiation of a target sample and measurement of the amount of radioactive reaction products via direct in-beam counting or their nuclear decay. It is based on the use of the general equation:

$${\text{A}}\sim {\text{N}}\sim {\text{s}}({\text{E}},{\text{q}}){\text{F}}\left( {\text{t}} \right){\text{ n}}$$

where A is the activity in Bq, N is the number of produced nuclei,ϕ(t) is the total number of incident particles on the surface of the target (fluence, flux and irradiation time), σ(E, θ) is the energy and angle-dependent reaction cross section, n is the number of irradiated target nuclei (depends on target thickness, density and atomic mass).

Based on this equation the following mean parameters can be determined after activity measurement:

• Number of incident particles (fluence) or irradiation time.

• Number of target nuclei (thickness).

• Incident particle energy.

In most cases, a single unknown parameter can be extracted, in special circumstances several parameters can be obtained simultaneously (e.g. energy, intensity).

A series of general and special conditions have to be respected and maintained for the optimal choice of targets, activation reactions and their cross sections, irradiation conditions to successfully and reliably apply the activation technique.

The target.

• The target material should be of a single element or impurities should not result in the formation of activated contaminating isotopes that significantly disturb the quantitative determination of the reaction products of the primary target. The target material should be obtained without difficulty at a reasonable price.

• The target should be prepared in final form in an easy way to get stable uniform thickness.

• The target material and the prepared target should stand in normal laboratory circumstances without chemical or physical changes (recrystallization, oxidation, etc.).

• The target should be stable during irradiation. Targets having low melting points or chemical instabilities by heating should be avoided.

• The same type of target could be used for broad energy and flux ranges and different bombarding particles.

• The target should have high thermal conductivity to allow higher intensities and effective cooling.

The reaction cross section.

• The absolute cross section for the chosen reaction should be known precisely in a wide range of incident particle energy.

• The activation effect of the secondary particles induced by the primary process should be small (cf. neutron production and activation).

• The cross sections have to be “high” in the investigated energy region.

• For improvement of the energy measurements range the cross sections should change sharply in the investigated energy (preferably around the energy of the maximal cross section) and preferably several reaction channels have to be open with a different slope of the excitation functions.

• For reliable flux measurements, the cross section should be constant or change slowly in the investigated energy range to minimize the uncertainty of energy.

• The reaction products (measurement of activation).

• The emitted radiation should be easily measurable (energy, intensity, type of radiation, form of the reaction products).

• The reaction products (decay) have to remain in the irradiated sample (gas, recoil effects).

• The activity of simultaneously produced “contaminating” reaction products, not used in the monitoring process, should be limited (reduction of background, overloading and increase of dead time).

• The half-life of the reaction products should be not too short to limit important decay during unloading, transport to detector set up and measurement of several targets and not very long as compared to irradiation time to get proper activity. But in the case of using parallel monitor reactions on the same target, the half-life of the products can differ significantly.

• An internationally accepted database for nuclear decay data (half-life, energy and abundance of emitted γ-lines) should be used for deriving cross section from the activity measurements performed at the site. The data as mentioned in Table 4 are the reference values.

The irradiation

• The irradiation parameters (ϕ(t), E) and thickness should be well-known, controlled and fixed during the time of irradiation.

• The monitor should be placed at a known and constant angle with the beam direction and in the energy region of interest if degraders are involved.

Main characteristics of beam monitoring via monitor reactions

Advantages

• Simple and cheap, performed in combination with irradiation of production targets.

• Require small space compared to other methods.

• Local monitor.

• The number of incoming nuclei is controlled.

• Any beam shape can be monitored.

• Both absolute and relative measurements are possible.

• Broad range of energies and intensities can be monitored.

• Good accuracy for determination of the beam fluence.

• The results could be corrected for later changes in nuclear data.

• Nondestructive, the beam passes through, without significant changes.

• The beam could be followed by extended targets inside (by inserting monitor foils through the target to follow the energy degradation and the beam broadening).

Disadvantages

• Moderate accuracy for determination of the energy.

• Highly depend on the quality of the available nuclear decay data.

• The quality of the recent data base is very poor.

• No online information on the measured parameters.

• It is difficult to install at accelerators and beam lines (temporarily installed)??

• Give only average intensity over irradiation time (time variations couldn’t be followed).

• High doses during installation and separation.

• Not independent from the particle species, from energy, their range, etc., compared to other monitor methods.

• The particles have to hit the monitor under well-known conditions.

• Automation, feedback to control during irradiation are impossible.

Main application fields of monitor reactions

• Medical isotope production.

• Parameters of accelerators.

• Nuclear data measurement.

• Irradiation for analytical purposes and thin layer activation technique.

• Research type of works.

Problems when using monitor reactions

• Data base still needs to be extended, especially at higher energies.

• Very few intercomparisons and validations.

• Definition of the used cross sections (direct, cumulative). Problems in case of cumulative having not very significant parent-daughter half-life.

• To place the monitor foil in the proper position (E, geometrically, single monitors in front of the target or series of monitors to follow the beam parameters).

• Uniformity of the monitor targets.

• Irradiation time vs half-lives of product targets.

• Effect of time variation of the fluence (integral).

• Effect of finite thickness (integral).

• Low energy gamma-rays, background lines.

• Effect of energy spread of the beam.

• Comparison of results of monitor reaction and other direct beam current measurement.

• Cumulative effects.

• Correction for recoils.

• Secondary particles.

Evaluation of experimental data and generation of the recommended cross section for standard monitor reactions

At present, the IAEA database [2] contains recommended data for monitor reactions for 4 types of light charged particles: 11 reactions for protons, 11 for deuterons, 6 for ³He, 6 for alpha particles (Table 1) [2,3,4]. It is however to be mentioned that, according to recent publications, the monitor reactions used in new research or production studies continuously change and are often not the recommended standard reactions.

In this work evaluation and proposal for a large number of new recommended cross sections over a wide energy are discussed and an update is presented for 4 earlier evaluated reactions. The new reactions were selected based on reported experimentally determined cross sections, decay properties of the product nuclei and the suitability of target materials as monitors. Attention was paid to discuss similar reactions leading to different activation products on interesting separate isotopes of multi-isotopic targets, allowing direct confirmation in a single experiment (Cu, Ti, Ni, Fe, Mo targets). The different conditions for appropriate target material and irradiation conditions have been summarized in earlier sections. In addition to the 19 new reactions proposed in the IAEA Technical Meeting in 2018 [5], 38 reactions were evaluated/re-evaluated and all are collected in Table 1.

The monitor reactions on C were used extensively earlier up to high energy and they were included in the earlier IAEA compilation [6] but are at present not in the database.

The Nb, Au target materials are new while a reaction on Fe is only present once. The cross sections in Fe are very well measured, the only drawback is the possible corrosion. Nuclear reactions on Au and Nb were used already earlier to monitor charged particle beams. In the case of Nb the low melting point has to be taken into account.

For several of the presently used monitor targets often only two, or even a single, reaction is recommended for a specific incoming particle. Now additional reactions were included for the different incident particles, allowing often comparison and confirmation based on differences in the excitation functions:

• A different energy slope of the excitation functions of different reaction products gives a better possibility to determine the energy of the bombarding particle.

• A nearly constant cross section over a broad energy range gives the possibility to avoid the need for exact energy knowledge for the determination of the number of incident particles.

• The different half-lives of the reaction products give the possibility to separately measure monitor data at optimized times after EOB for each activation product.

• A few reactions on monoisotopic elements or natural targets are common with reactions for the production of medical isotopes. They can be included in both lists of the IAEA database.

4.1 Summary of the method of evaluation

Detailed information on the method of collection and selection of experimental data, followed by Padé fitting methodology and obtaining uncertainties of the fit, can be found in relevant IAEA publications.

We repeat here the main steps and attention points of the compilation and evaluation:

• The experimental cross section data, often without uncertainties, were found in EXFOR [7] and/or in the original publications.

• The EXFOR/published datasets were corrected for up-to-date monitor cross sections or nuclear decay characteristics. Unrealistic low uncertainties in publications were enlarged based on other experimental data and the practice of the compilers.

• The experimental data show in many cases very large disagreements between different publications. This is mainly because they were measured in poor experimental circumstances, without strict rules being agreed upon and information was not always complete (beam current and detector efficiency measurements, nuclear data used,…). It was hence impossible to use the standard evaluation method based on pure statistical methods.

• In practice, the evaluation contains several steps. Collection, if needed correction on the decay data to the values of [8, 9] and of the energy scale, and selection of published experimental data sets by an experimentalist. Fitting of the selected data by an expert on model calculation and data evaluation. During this step often further deselection of a few separate data, outlying more than the uncertainties when compared to the neighboring selected sets, in contradiction to the theoretical predictions and below the reaction thresholds, occurred.

• By investigating the experimental circumstances several corrections can be necessary: rescaling the energy in case of long stacks, normalization of some large sets to ensure data in unmeasured regions, deleting complete data controversy data sets, giving larger weight to data from well-proved authors, detail investigate the used technology (long stacks, coincidence losses, use only one monitor foil, unreliable primary beam energy, measurement of beam intensity with not Faraday cups, detector efficiencies at low energies, etc.)

• Problematic cases occur when only a few (two or three) experimental data sets are available with contradicting results. In this case, to fill the energy range where only one data set was available, selection and correction, and normalization were done based on many facts: on the earlier results of the authors, the used experimental techniques, etc.

• For particle-induced reactions in several cases, the data from some publications are too low by a factor of two. We observed this fact already earlier while evaluating monitor reactions. Our experimental data show that the sets with too low cross sections result from an improper estimation of the number of incident particles (measured by the incoming charge) due to neglecting the double electron charge of the α-particle.

• For the selection of the best monitor reaction by practical users, the most important information is the figures of the excitation function and the yield curves.

• Presently at least two independent data sets are needed before selection and fitting are considered. Reactions for which only a single experimental data set was found in EXFOR or literature are not included or discussed in this article.

• Differential yield data are used only if the yields are given from the threshold on and if the mentioned energy steps are small (depending on the behavior of the excitation function).

• For the selection of data sets earlier evaluations and the results of model calculations were taken into account. An important factor in the selection of sets for contradicting data is the quality of the results and the experience in research of the concerned group.

• Fit of the selected experimental data was done using Padé approach (approximant by rational function) [10,11,12].

• Uncertainties in the fitted results were estimated via a least-squares method with an addition of a 4% systematic uncertainty, an expert estimate of overall unrecognized uncertainties as discussed in earlier evaluations.

• Calculation of so-called physical integral production yields [13] is based on the obtained recommended cross section data.

• We decided to include 2021 and 2023 versions of the TENDL library to show and discuss the change and possible improvement of the theoretical predictions by the evolution of the TALYS code [14].

Some other points on problems encountered during the evaluation process are:

• In a few problematic reactions different Padé fits were done, with the question of which to select: the one based strictly on experimental data or include theory and systematics.

• For practical production the shape of the excitation function and the tabulated yields are important. Hence no covariance calculations were done.

• According to our experience, the pure statistical evaluation methods only work well in cases where a large number of data sets with realistic uncertainties, detailed knowledge of the experiments and the used nuclear data, are available.

• The reason for disagreement of different data sets lies essentially in:

  Estimation of number of incident particles (Faraday cup, beam stop, monitor in single energy point, monitor in all energy range, etc.).

  Quality of targets in case of different target preparation techniques.

  The technique of spectra measurement, distance, dead time, coincidence losses, and corrections.

  Determination of incident energy and control of the energy degradation.

  Properties of the single foil, stacked foil, and rotating wheel irradiation technique.

  Direct measurement vs after chemical separation.

List of evaluated nuclear reactions and the main decay data

An overview of the monitor reactions evaluated earlier is presented in Table 2 [2] while the reactions discussed at present are in Table 3. Table 4 [8] contains the used decay data of the reaction products, Table 5 lists, for each reaction, the number of available experimental data sets, the maximal energy of the available experimental data (fitted only in an energy range useful for practical production), the parameters of the final Padé fit and the number of available experimentally determined yield publications.

Table 2 List of the evaluated monitor reactions with energy range is included presently on the IAEA Web

Table 3 List of the new evaluated monitor reactions (4 reactions are re-evaluated)

Table 4 Decay data of the reaction products

Table 5 Parameters of the evaluated and fitted nuclear reactions

Results and discussion of the studied reactions

All available corrected experimental data in comparison with the TENDL 2021 and 2023 predictions, the selection and the selected data are presented with the obtained recommended data and uncertainties. Integral yield data were deduced from the recommended cross section data and compared with the directly measured experimental integral yield data reported in the literature. In some publications yield data derived from the measured cross section data (so-called DERIV yields) are available. As these data are not independent, they are not included in the comparison.

Evaluated proton-induced nuclear reactions

^natC(p,x)⁷Be reaction

Two reactions contribute to ⁷Be formation: ¹²C(p,3p3n)⁷Be (¹²C abundance is 98.90% in ^natC) and ¹³C(p,3p4n)⁷Be (¹³C abundance is 1.10%). The lowest threshold for the clustered particle emission reaction ¹²C (p,αd)⁷Be is 26.06053 MeV.

A total of 13 cross section data sets, covering the energy range from threshold up to 170 MeV, were found in literature: Dickson [15], Lefort [16], Gauvin [17], Brun [18], Rayudu [19], Vdovin [20], Williams [21], Aleksandrov [22], Bodeman [23], Michel [24], Fassbender [25], Baumer [26], Baecker [27].

As a large disagreement is observed and no TENDL predictions are available for this low Z element, the data of Michel [24] were considered as reference values (Fig. 1). The whole set of Dickdon 1951, the single point of Rayudu 1964 (130 MeV, too low) and of Vdovin 1979 (50 MeV, too low) were deselected. As the sets of Williams 1979 and Aleksandrov 1990 agree well in overall shape with Michel 1997 but show lower values, they were multiplied by, respectively, a factor 1.35 and of 1.2. The data of Lefort 1961 and Brun 1962 were linearly decreased in energy to correspond with the shape of the Michel 1997 excitation curve. The outlying point of Brun 1962 at 42.18 MeV was deselected. As the uncertainties given in the publications of Michel 1997, Gauvin 1962 and Baecker 2019 are well below 10%, for selection they were systematically increased to 12%. The original and corrected datasets of ten publications were selected and fitted (Fig. 2). The calculated yields, based on the recommended values from the Padé fit, are shown in Fig. 9. No experimental yield data were found in the literature. No TENDL predictions are available for this low Z-value target.

Fig. 1

^atC(p,x)⁷Be reaction: all experimental data No TENDL is available, for targets with Z below 9

Fig. 2

^natC(p,x)⁷Be reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natC(p,x)¹¹C reaction

Two reactions contribute to ¹¹C formation in proton bombardment of C targets: ¹²C(p,pn)¹¹C (¹²C abundance is 98.90% in ^natC) and ¹³C(p,p2n)¹¹C (¹³C abundance is 1.10%). The lowest threshold for clustered particle emission reaction is 16362.54 keV.

A total of 26 cross section data sets up to 1000 MeV incident proton energy were found in literature and are presented in Fig. 3: Hintz [28], Aamodt [29], Burcham [30], Crandall [31], Measday [32], Symonds [33], Rosenfeld [34], Whitehead [35], Parikh [36], Goebel [37], Gauvin [17], Brun [18], Cumming [38], Kavanagh [39], Andrews [40], Hogstrom [41], Kostjuchenko [42], Kettern [43], Akagi [44], Matsushita [45], Baumer [26], Baecker [27], Horst [46], Rodriguez-Gonzalez [47].

Fig. 3

^natC(p,x)¹¹C reaction: all experimental data

As some disagreement is observed and as no TENDL predictions are available for this low Z element, the recent data over the whole energy range of interest by Rodriguez-Gonzalez [47] and the sets of Hintz 1962 and Cuming 1963 were accepted as reference values.

Five sets show too low values over a rather extended energy region and were deselected Whitehead 1958 ser1, Gauvin 1962 (also not independent measurements), Akagi 2013, Matsusita 2016, Horst 2019.

Additionally, some data points at energies under 18 MeV are too low and were deleted: Aamodt 1952 ser1 (3 points) Hintz 1952 (4 points), Kettern 2004 (1 point at 12.3 MeV).

As remarked in the previous section for several sets the uncertainties given in the original publication are well below 10% and were systematically increased to 12% for selection. The original and corrected datasets of fourteen publications were selected and fitted (Fig. 4). The integral yields calculated from the recommended cross sections are shown in Fig. 9, together with the experimental yield data of Krasnov [48] and Dmitriev [49].

Fig. 4

^natC(p,x)¹¹C reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

²⁷Al(p,x)⁷Be reaction

As Al is monoisotopic only the ²⁷Al(p,10p11n) reaction can contribute to ⁷Be formation by activation. The lowest threshold for the maximally clustered light particle emission ²⁷Al(p, 5αn)⁷Be reaction is 47.59 MeV. As experimentally formation of ⁷Be is observed at lower energies probably other reaction mechanisms are involved (fission, fragmentation, Be particle emission). The TENDL 2021 and 2023 prediction exists but predict very low cross sections probably because only light particle emission is included in the model (Fig. 5).

Fig. 5

²⁷Al(p,x)⁷Be reaction: all experimental data

A total of 31 cross section data sets, covering the energy range from threshold up to 1000 MeV, were found in literature: Marquez [50], Lavrukhina [51], Neuzil [52], Ligonniere [53], Furukawa [54], Lafleur [55], Williams [21], Cline [56], Bimbot [57], Miyano [58], Bogatin [59], Heydegger [60], Grutter [61], Grutter [62], Aleksandrov [22], Michel [63], Bodemann [23], Scholten [64], Michel [65], Schiekel [66], Sisterson [67], Taddeuci [68], Michel [24], Fassbender [25], Yashima [69], Titarenko [70], Titarenko [71], Szelecsenyi [72], Meigo [73], Baumer [26].

The originally published set by Titarenko 2011 consists of multiple, spreaded, measured data at 9 distinct energy points. Only a single representative value at each energy, corresponding best to the numerous datapoints over the whole energy range of Schiekel 1995 and Michel 1997, was selected. The spread data of Bugatin 1976 and the single outlying point of Michel 1995 at 800 MeV were deselected. Additionally, 8 sets, each containing only a few datapoints that are all outlying, were deselected: Marquez, Lavruskhina, Sisterson, Cline, Heydeggern, Isosimva, Schiekel, Yashima. The original and corrected datasets of the remaining twenty-two publications were selected up to 800 MeV and fitted (Fig. 6). The integral yields calculated from the recommended cross sections are shown in Fig. 9. No experimental yield data were found.

Fig. 6

²⁷Al(p,x)⁷Be reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

^natTi(p,x)⁴³Sc reaction

Reactions of the general shape (p,αxn), with x between 2 and 6, on the five stable isotopes of Ti can contribute to direct ⁴³Sc formation (⁴⁶Ti abundance is 8.25%; ⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The lowest threshold is for the ⁴⁶Ti(p,α2n)⁴³Sc reaction at 3.144 MeV. The contribution of the interaction with the other isotopes occurs at higher energies and results in an excitation function with multiple local maxima. The formation of ⁴³Sc at energies above 32 MeV is always cumulative as it contains the full decay of very short-lived ⁴³Ti (T_1/2 = 0.5 s) produced by (p,pxn) reactions on the different stable Ti isotopes. The threshold for ⁴⁶Ti(p,p3n)⁴³Ti reaction is 31.21 MeV.

A total of 10 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in the literature and are displayed in Fig. 7: Michel [74], Kopecky [75], Zarie [76], Khandaker [77], Garrido [78], Shahid [79, 80], Cervenak [81], Liu [82], Fox [83]. The 4 datapoints of Garrido 2016 were multiplied by a factor of 1.25 to agree with the values of Shahid 2018 and Michel 1978 near the local maximum at 45 MeV. The 4 data points of Azzam 2020 below 8 MeV and the point at 6.7 MeV of Khandaker 2009 were considered as outlying and deselected. The original and corrected datasets of the 10 publications were selected and fitted (Fig. 8).

Fig. 7

^natTi(p,x)⁴³Sc reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 8

^natTi(p,x)⁴³Sc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

While the TENDL 2021 prediction represented in a more pronounced way the multiple contributions of the reactions on the five stable target isotopes the 2023 version is ignoring the dominant local maximum in the 40–50 MeV domain. Both versions seem to overestimate the cross sections above 60 MeV.

The integral yields calculated from the recommended cross sections are shown in Fig. 9. One experimental yield data was found: Abe [84].

Fig. 9

Yield calculated from the recommended cross sections of the ^natC(p,x)⁷Be, ^natC(p,x)¹¹C, ²⁷Al(p,x)⁷Be and ^natTi(p,x)⁴³Sc reactions

^natFe(p,x)⁵⁵Co reaction

Three (p,xn) reactions on the stable target isotopes ⁵⁶Fe( abundance 91.754% in ^natFe), ⁵⁷Fe (2.119%) and ⁵⁸Fe (0.282%) contribute to the formation of ⁵⁵Co. Due to the predominance of the ⁵⁶Fe isotope, the (p,2n) reaction with a threshold of 15.71 MeV will in practice be the single contribution.

A total of 23 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 10: Lavrukhina [85], Williams [86], Brodzinski [87], Barrandon [88], Orth [89], Michel [90], Lagunas-Solar [91], Daum [92], Aleksandrov [93], Fassbender [94], Aleksandrov [95], Schiekel [66], Zhao Wenrong [96], Michel [65], Michel [24], Gloris [97], Neumann [98], Ditroi [99], Al Abyad [100], Kim [101], Graves [102], Voyles [103].

Fig. 10

^natFe(p,x)⁵⁵Co reaction: all experimental data and the TENDL theoretical excitation functions

The four sets by Orth 1976, Aleksandrov 1989, Schiekel 1990, and Neumann 1999 only contain data above the 200 MeV energy limit considered as being appropriate for practical use and are hence not presented in the figure.

The data sets of Williams 1967 and Kim 2014 are too low over the whole energy domain and are deselected. The two datapoints of Voyles below 12 MeV are deleted. We accepted the value at 12.11 MeV of Voyles and 13.43 MeV of Michel, both below the threshold mentioned earlier, as indications of the presence of contribution of the ⁵⁴Fe(p, γ)⁵⁵Co reaction.

The errors of all Laguna-Solar data were increased to 8% and the error of Michel 1979 point was corrected to 10%. The first two low-energy points were omitted.

The original and corrected datasets of 14 publications were selected up to 180 MeV and fitted (Fig. 11). The two TENDL predictions enhance the predominance of the ⁵⁶Fe(p,2n)⁵⁵Co reaction. While the TENDL 2021 slightly overestimates the maximal value the TENDL 2023 predictions are systematically lower over the whole energy range. The integral yields calculated from the recommended cross sections are shown in Fig. 18. One experimental yield data was found by Talebi 2013 [104].

Fig. 11

^natFe(p,x)⁵⁵Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natFe(p,x)⁵⁶Co reaction

Three (p,xn) reactions on the stable target isotope ⁵⁶Fe( abundance 91.754% in ^natFe), ⁵⁷Fe (2.119%) and ⁵⁸Fe (0.282%) contribute to the formation of ⁵⁵Co. Due to the predominance of the ⁵⁶Fe isotope the (p,n) reaction with a threshold of 5.44 MeV will in practice be the single contribution.

A total of 43 cross section data sets, covering the energy range from threshold up to 100 MeV, were found in literature and are displayed in Fig. 12: Remsberg [105], Tanaka [106], Read [107], Lavrukhina [85], Lavrukhina [108], Rayudu [109], Williams [86], Rayudu [19], Jenkins [110], Cline [56], Brodzinski [87], Gadioli [111], Barrandon [88], Orth [89], Lagunas Solar [91], Michel [90], Schoen [112], Michel [113], Michel [114], Antropov [115], Michel [63], Aleksandrov [93], Neumann [98, 116], Levkovskii [117], Jung [118], Zhao Wenrong [96], Takacs [119], Sudar [120], Michel [65], Schiekel [66], Michel [24], Daum [92], Gloris [97], Ditroi [99], Sisterson [121], Al Abyad [100], Titarenko [71], Kim [101], Graves [102], Zherebchevsky [122], Uddin [123], Lawriniang [124], Voyles [103].

Fig. 12

^natFe(p,x)⁵⁶Co reaction: all experimental data and the TENDL theoretical excitation functions

The too low set of Williams 1967 was deselected and all datapoints of several publications below the threshold mentioned earlier were deleted.

The original and corrected datasets were selected up to 50 MeV, the energy limit for interesting practical applications, and fitted (Fig. 13).

Fig. 13

^natFe(p,x)⁵⁶Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are enhancing the predominance of the ⁵⁶Fe(p,n)⁵⁶Co reaction and are well estimating the maximal value and shape.

The integral yields calculated from the recommended cross sections are shown in Fig. 18. Three experimental yield data were found: Acerbi [125], Dmitriev [126], Isshiki [127], Abe [84]. Acerbi data are differential yields, and not presented in the figure.

^natFe(p,x)⁵⁷Co reaction

Two reactions ⁵⁷Fe(p,n) reaction (abundance 2.119%, threshold of 1.647 MeV) and ⁵⁸Fe(p,2n) (lower abundance 0.282%, threshold 11.87 MeV) contribute to the formation of ⁵⁷Co when irradiating ^natFe targets.

A total of 17 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in the literature and are displayed in Fig. 14:

Fig. 14

^natFe(p,x)⁵⁷Co reaction: all experimental data and the TENDL theoretical excitation functions

Tanaka [106], Brodzinski [87], Michel [90], Shoen [112], Michel [113], Zhao [96], Michel [114], Jung [118], Sudar [120], Michel [24], Gloris [97], Ditroi [99], Al-Abyad [100], Kim [101], Uddin [123], Lawriniang [124], Voyles [103].

Two outlying points were deleted: Shoen 1979 at 5.8 MeV (too low) and Lawriniang 2018 at 9.73 MeV.

The data of up to 50 MeV, from 17 publications were selected and fitted (Fig. 15). Both TENDL predictions are in good agreement with the experimental data over the entire energy domain and slightly overestimate the maximal experimental values of the ⁵⁷Fe(p,n)⁵⁷Co reaction. Only TENDL 2021 shows the small contribution of the ⁵⁸Fe(p,2n) reaction above 15 MeV.

Fig. 15

^natFe(p,x)⁵⁷Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The integral yields calculated from the recommended cross sections are shown in Fig. 18. One experimental yield data was found by Dmitriev [128].

^natFe(p,x)⁵⁸Co reaction

Only the ⁵⁸Fe(p,n) reaction, with a threshold of 3.144 MeV, on low abundance ⁵⁸Fe (0.282%) contributes to the formation of ⁵⁷Co when irradiating ^natFe targets.

A total of 16 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 16: Michel [90], Michel [113], Antropov [115], Zarubin [129], Jung [118], Levkovskii [130], Tims [131], Sudar [120], Michel [24], Daum [92], Gloris [97], Al-Abyad [100], Uddin [123], Ghosh [132], Voyles [103].

Fig. 16

^natFe(p,x)⁵⁸Co reaction: all experimental data and the TENDL theoretical excitation functions

Outlying data points of Antropov 1985 (at 6.24 MeV), Tims 1993 (at 3.895 MeV), Ghosh 2017 (at 3.38 MeV) and Voyles 2021 (at 4. 1 MeV) were deleted. As the two data points at 2.9 and 2.4 MeV of Uddin 2017 are below the reaction threshold they were removed.

The data up to 85 MeV, the energy limit for interesting practical applications, of 14 publications were selected and fitted (Fig. 17). The two TENDL predictions are in very good agreement with the experimental data over the entire energy domain. The integral yields calculated from the recommended cross sections are shown in Fig. 18. One experimental yield data was found by Nickles [133], which is saturation yield on ⁵⁸Fe, so it is not shown in Fig. 18.

Fig. 17

^natFe(p,x)⁵⁸Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 18

Yield calculated from the recommended cross sections of the ^natFe(p,x)⁵⁵Co, ^natFe(p,x)⁵⁶Co, ^natFe(p,x)⁵⁷Co and ^natFe(p,x)⁵⁸Co reactions

^natNi(p,x)⁵⁵Co reaction

In principle five (p,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 2), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁵Co if high energy proton bombardment is performed.

The threshold for reactions where at least 4 separate particles are emitted will be around 25 MeV but by clustering the (p,αyn) reaction is favored with 28 MeV lower thresholds.

A total of 27 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 19.

Fig. 19

^natNi(p,x)⁵⁵Co reaction: all experimental data and the TENDL theoretical excitation functions

The publications are: Kaufman [134], Ewart [135], Cline [56], Tanaka [136], Barrandon [88], Michel [74], Michel [113], Michel [114], Aleksandrov [137], Neumann [98], Tarkanyi [138], Levkovskii [117], Sonck [139], Michel [65], Michel [24], Reimer [140], Porras [141], Al Saleh [142], Titarenko [71], Khandaker [143], Jost [144], Amjed [145], Hermanne [146], Uddin [147], Garrido [78].

All datasets were selected and fitted up to 200 MeV (Fig. 20). The two TENDL predictions represent well the overall behavior of the multiple contributing reactions but are systematically shifted to lower energy and overestimate the experimental data in the 30–80 MeV energy range.

Fig. 20

^natNi(p,x)⁵⁵Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The integral yields calculated from the recommended cross sections are shown in Fig. 31. Three experimental yield data were found: Abe [84], Sadeghi [148], Le Van So [149].

^natNi(p,x)⁵⁶Ni reaction

In principle five (p,pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 2), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁵Ni if high energy proton bombardment is performed. The threshold for the ⁵⁸Ni(p,p2n)⁵⁶Ni reaction with emission of 3 separate particles is 22.85 MeV but by clustering the ⁵⁸Ni(p,dn)⁵⁶Co reaction is favored with 20.59 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 23 cross section data sets, covering the energy range fom threshold up to 400 MeV, were found in literature and are displayed in Fig. 21: Ewart [135], Tanaka [136], Michel [150], Michel [114], Aleksandrov [151], Furukawa [152], Michel [63], Levkovskii [117], Michel [153], Neumann [98], Schiekel [66], Michel [24], Reimer [140], Sisterson [121], Bringas [154], Al Saleh [142], Titarenko [71], Khandaker [143], Jost [144], Amjed [145], Hermanne [146], Hermanne [155], Garrido [78].

Fig. 21

^natNi(p,x)⁵⁶Ni reaction: all experimental data and the TENDL theoretical excitation functions. TENDL stops here at 200 MeV

The values of Michel 1978 are outlying and too low in the energy region of the maximum and were deselected. All other original datasets of 22 publications were selected up to 150 MeV and fitted (Fig. 22).

Fig. 22

^natNi(p,x)⁵⁶Ni reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are in good agreement with the overall shape of the excitation function, but overestimate the experimental data in the 50–150 MeV energy range. The integral yields calculated from the recommended cross sections are shown in Fig. 31. No experimental yield data was found.

^natNi(p,x)⁵⁶Co reaction

In principle five (p,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 1), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁶Co if high energy proton bombardment is performed. The threshold for the ⁵⁸Ni(p,2pn)⁵⁶Co reaction with emission of 3 separate particles is 19.89 MeV but by clustering the ⁵⁸Ni(p,dp)⁵⁵Co reaction is favored with 17.62 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 15 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 23: Ewart [135], Tanaka [136], Aleksandrov [151], Levkovskii [117], Jung [118], Tarkanyi [138], Reimer [140], Michel [24], Sisterson [121], Al Saleh [142], Titarenko [156], Khandaker [143], Amjed [145], Hermanne [146], Garrido [78].

Fig. 23

^natNi(p,x)⁵⁶Co reaction: all experimental data and the TENDL theoretical excitation functions

An additional set, only containing datapoints above 200 MeV is available but was not included further in the evaluation: Schiekel [66].

The total set of Ewart 1964 with too low values was deselected. The set of Hermanne 2015 consists of two series of data obtained in two irradiations with respectively 34 and 65 MeV incident proton beam energy. As results for the 65 MeV experiment are too low they were multiplied by a factor of 3 to be in good agreement with the values of Garrido 2016 and Michel 1997. Additionally, the 6 data points below the practical 18 MeV threshold were deleted. The set of Reimer 1998 was energy-shifted and the two points at 26 and 24.5 MeV were deleted. Some outlying data points at energies below 30 MeV of Tanaka 1972, Aleksandrov 1987, Levkovski 1991 and Al Saleh 2007 were deleted.

The original and corrected datasets of 13 publications were selected up to 130 MeV and fitted (Fig. 24). The two TENDL predictions overestimate the experimental excitation functions above 40 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 31. Two experimental yield data were found Dmitriev [126] and Le Van So [149].

Fig. 24

^natNi(p,x)⁵⁶Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(p,x)⁵⁷Ni reaction

In principle five (p,pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 1), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁷Ni if high energy proton bombardment is performed.

The threshold for the ⁵⁸Ni(p,pn)⁵⁷Ni reaction with the emission of 2 separate particles is 12.43 MeV but by clustering the ⁵⁸Ni(p,d)⁵⁷Co reaction is favored with 10.16 MeV threshold. The same observation is valid for the reactions on other Ni isotopes. A total of 43 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in the literature and are displayed in Fig. 25:

Fig. 25

^natNi(p,x)⁵⁷Ni reaction: all experimental data and the TENDL theoretical excitation functions

Cohen [157], Kaufman [134], Ewart [135], Cline [56], Tanaka [136], Barrandon [88], Weigel [158], Haasbroek [159], Brinkman [160], Piel [161], Brinkmann [162], Michel [113], Stück [163], Zhuravlev [164], Michel [114], Aleksandrov [151], Michel [63], Furukawa [152], Aleksandrov [151], Tarkanyi [165], Levkovskii [117], Bodemann [166], Michel [65], Schiekel [66], Steyn [167], Michel [24], Sonck [168], Neumann [98], Porras [141], Szelecsenyi [169], Takacs [170], Garrido [78], Sisterson [121], Al Saleh [142], Titarenko [156], Alharbi [171], Khandaker [143], Amjed [145], Hermanne [155], Uddin [147], Adel [172].

Datapoints above 200 MeV were not included further in the evaluation. The outlying datasets of Cohen 1955, Kaufmann 1960, Ewart 1964, Tanaka 1972, Haasbroek 1977, Brinkmann 1977, Zhuravlev 1984 and Steyn 1996 data were deselected. The data of Aleksandrov 1987 are too high and the set was deselected. Additionally, the points with too low cross section values below 20 MeV of Barandon 1975, Szelecsenyi 2001 and Garrido 2016 were deleted. The remaining data from 31 publications were selected up to 200 MeV and fitted (Fig. 26). The two TENDL predictions estimated the maximal value around 26 MeV but overestimated the contribution of the reactions where multiple separate particles are emitted in the 30–60 MeV domain.

Fig. 26

^natNi(p,x)⁵⁷Ni reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

The integral yields calculated from the recommended cross sections are shown in Fig. 31. Four experimental yield data were found: Dmitriev [126], Abe [84], Sadeghi [148], Le Van So [149].

^natNi(p,x)⁵⁷Co reaction

In principle five (p,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 0), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 2), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁵⁷Co (T_1/2 = 271.74 d) if high energy proton bombardment is performed. Depending on the cooling time before measurement contribution of the shorter-lived ⁵⁷Ni (T_1/2 = 35.60 h) can contribute. The threshold for the ⁵⁸Ni(p,2p)⁵⁷Co reaction is 8.31 MeV, for the ⁶⁰Ni(p,α)⁵⁷Co reaction (clustering) a low threshold of 0.268 MeV is seen and for ⁶¹Ni(p,αn) it is 8.22 MeV. The possible contribution of parent ⁵⁷Ni can only start at 10.16 MeV, the threshold of the ⁵⁸Ni(p,d)⁵⁷Ni reaction.

A total of 15 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in the literature and are displayed in Fig. 27:

Fig. 27

^natNi(p,x)⁵⁷Co reaction: all experimental data and the TENDL theoretical excitation functions

Cline [56], Michel [150], Michel [113], Aleksandrov [151], Tarkanyi [165], Jung [118], Schiekel [66], Michel [24], Al Saleh [142], Khandaker [143], Amjed [145], Hermanne [146], Garrido [78], Uddin [147], Adel [172].

As far as can be deduced from the information in the original publications, full cumulative cross sections, after decay of ⁵⁷Ni, were reported. TENDL predictions allow us to calculate a contribution starting at 2% at 14 MeV, rising continuously to 85% at 35 MeV and decreasing to a value around 65% from 55 MeV on.

The outlying dataset of Aleksandrov 1987 was deleted. The whole set of Michel 1978 has a good shape but is too low and was multiplied with a factor of 1.3 to correspond to the data of Michel 1997, Garrido 2016 and Amjed 2014 in the 30–45 MeV region. Additionally, the too high values point at the lowest energies in Hermanne 2015 and Adel 2020 were deleted, while at higher energies all points Khandaker 2011 above 35 MeV and two values of Michel 1997 (at 24.4 and 23.8 MeV) were considered outlying.

The original and corrected datasets of 14 publications were selected up to 150 MeV and fitted (Fig. 28).

Fig. 28

^natNi(p,x)⁵⁷Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are well estimating the maximal value around 26 MeV but are overestimating the contribution of the ⁵⁷Ni decay in the 35–55 MeV domain. The integral yields calculated from the recommended cross sections are shown in Fig. 31. Four experimental yield data were found Gruverman [173], Dmitriev [126]. Le Van So [149], Sadeghi [148].

^natNi(p,x)⁵⁸Co reaction

In principle four (p,2pxn) reactions on the stable target isotopes ⁶⁰Ni (abundance 26.223% in ^natNi, n = 1), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁸Co if high energy proton bombardment is performed.

The threshold for the ⁶⁰Ni(p,2pn)⁵⁸Co reaction with the emission of 3 separate particles is around 12.47 MeV but by clustering the ⁶¹Ni(p,α)⁵⁸Co reaction with a positive Q-value of 0.489 MeV can contribute.

A total of 13 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 29: Michel [113], Michel [114], Jung [118], Schiekel [66], Michel [24]Targeted radionuclide therapy, Sisterson [121], Al Saleh [142], Khandaker [143], Amjed [145], Hermanne [146], Garrido [78], Uddin [147], Adel [172].

Fig. 29

^natNi(p,x)⁵⁸Co reaction: all experimental data and the TENDL theoretical excitation functions

An additional set, only containing datapoints above 200 MeV is available but was not included further in the evaluation], Sisterson [121].

All sets were in acceptable agreement but some outlying datapoints were deleted: Hermanne 2015 (7 points below 20 MeV), Garrido 2016 (3 points below 18 MeV), Amjed 2014 (7 too high points between 13 and 7.5 MeV). The original and corrected datasets of 13 publications were selected up to 180 MeV and fitted (Fig. 30). The two TENDL predictions represent well the overall shape of the excitation function with an underestimation of the maximal value.

Fig. 30

^natNi(p,x)⁵⁸Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

The integral yields calculated from the recommended cross sections are shown in Fig. 31. 3 experimental yield data was found: Dmitriev [126], Le Van So [149] and Sadeghi [148].

Fig. 31

Yield calculated from the recommended cross sections of the ^natNi(p,x)⁵⁵Co, ^natNi(p,x)⁵⁶Ni, ^natNi(p,x)⁵⁶Co, ^natNi(p,x)⁵⁷Ni, ^natNi(p,x)⁵⁷Co and ^natNi(p,x)⁵⁸Co reactions

^natCu(p,x)⁶¹Cu reaction

As in 2020 updated abundances for the different γ-lines emitted in the decay of ⁶¹Cu were adopted in NUDAT3.0 (see Table 2) nearly all data sets published before 2020 had to be attentively checked and corrections for used absolute abundances or ratios made. Moreover, new relative intensity values for the 656.008 keV line were found in a well-documented study published by Bleuel 2021 [174]. However, the ratio of the 656.008 keV (10.4%) to 282.956 keV (12.7%) intensities used in the present evaluation (ratio 0.820 (140), see Table 3) only differs by 3% from the proposed Bleuel 2021 data (ratio 0.793 (10)). On the other side practically in all compiled work, the cross section data were corrected by using the 282.956 keV line. Possible additional corrections for a new update of ENSDF accepted absolute abundance will hence be well within the 10–12% uncertainties on the used experimental data and the change in fit and recommended values will be small.

Two (p,pxn) reactions on the stable target isotopes ⁶³Cu (abundance 69.15% in ^natCu, n = 2), ⁶⁵Cu (abundance 30.85% in ^natCu, n = 4), can contribute to the formation of ⁶¹Cu if high energy proton bombardment is performed.

The threshold for the ⁶³Cu(p,p2n)⁶¹Cu reaction with the emission of 3 separate particles is 20.054 MeV while the ⁶⁵Cu(p,p4n)⁶¹Cu reaction has a 38.15 MeV threshold. Above 30 MeV incident proton energy decay of short-lived ⁶¹Zn (T_1/2 = 89.1 s), formed in the ⁶³Cu(p,3n)⁶¹Zn reaction, will start cumulative formation.

A total of 20 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 32: Meadows [175], McCormick [176], Williams [86], Orth [177], Grutter [61], Greenwood [178], Aleksandrov [151], Aleksandrov [137], Levkovskii [130], Mills [179], Titarenko [180], Michel [24], Yashima [69], Al Saleh [181], Shahid [182], Graves [102], Garrido [78], Voyles [183], Cervenak [81], Voyles [103], Fox [83].

Fig. 32

^natCu(p,x)⁶¹Cu reaction: all experimental data and the TENDL theoretical excitation functions

An additional set, only containing datapoints above 200 MeV is available but is not included further in the evaluation: Alksandrov [95].

Five sets with outlying points were deselected: Williams 1967, Greenwood 1984, Aleksandrov 1987, Titerenko 1996, Yashima 2002. The two points at 20 and 23 MeV, too high values, of Meadows 1953 were deleted.

The original and corrected datasets of 15 publications were selected up to 200 MeV and fitted (Fig. 33).

Fig. 33

^natCu(p,x)⁶¹Cu reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL 2021 prediction underestimates the maximal value at a slightly energy-shifted position but the 2023 version more correctly describes the experimental values. The integral yields calculated from the recommended cross sections are shown in Fig. 42. A single experimental yield data was found: Le Van So [149].

⁹³Nb(p,4n)⁹⁰Mo reaction

As Nb is monoisotopic only the ⁹³Nb(p,4n) reaction with the threshold of 32.384 MeV contributes to the formation of ⁹⁰Mo. A total of 6 cross section data sets, covering the energy range from threshold up to 200 MeV, were found in literature and are displayed in Fig. 34: Ditroi [184], Ditroi [185], Titarenko [156], Voyles [183], Kim [186], Fox [83]. The values of Ditroi 2008 are too low but the excitation function has a good overall shape and hence the set was multiplied by a factor of 2.5 to agree with the maximal values of 120 mb near 51.5 MeV given by Fox 2021 and Voyles 2018. As for several sets the uncertainties given in the original publication are well below 10% they were systematically increased to 12% for selection.

Fig. 34

⁹³Nb(p,x)⁹⁰Mo reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 6 publications were selected up to 100 MeV and fitted (Fig. 35). While TENDL 2021 prediction underestimates the maximal value by a factor of 2.5–3, the new 2023 version is even a factor of two lower. Although the overall shape of the excitation curve is well represented, a 4 MeV energy shift is noted. The integral yields calculated from the recommended cross sections are shown in Fig. 42. No experimental yield data were found.

Fig. 35

⁹³Nb(p,x)⁹⁰Mo reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natMo(p,x)^95mTc reaction

In principle five (p,xn) reactions on the stable target isotopes ⁹⁵Mo (abundance 15.84% in ^natMo, n = 1), ⁹⁶Mo (abundance 16.67% in ^natMo, n = 2), ⁹⁷Mo (abundance 9.60% in ^natMo), ⁹⁸Mo (abundance 24.39% in ^natMo), ¹⁰⁰Mo (abundance 9.82% in ^natMo, n = 6) can contribute to formation of ^95mTc if a high energy proton bombardment is performed.

The threshold for the ⁹⁵Mo(p,n)^95mTc reaction is 2.499 MeV and it rises to 41.727 MeV for the ¹⁰⁰Mo(p,n)^95mTc reaction.

A total of 12 cross section data sets, covering the energy range from threshold up to 70 MeV, were found in literature and are displayed in Fig. 36: Zhao Wenrong [187], Bonardi [188], Uddin [189], Khandaker [190], Khandaker [191], Lebeda [192], Tarkanyi [193], Takacs [194], Cervenak [195], Ahmed [196], Elbinawi [197], Ahmed [198]. The values of Uddin 2004 are low compared to other sets above 30 MeV and were multiplied by a factor of 1.2 to be in better agreement. Outlying datapoints at separate energies were deleted: Bonardi 2002 (at 4.9 and 7.5 MeV), Khandaker 2007 (at 2.5 and 21 MeV), Tarkanyi 2012 (at 2.78 MeV) (Fig. 37).

Fig. 36

^natMo(p,x)^95mTc reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 37

^natMo(p,x)^95mTc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

The original and corrected datasets of the 12 publications were selected up to 70 MeV and fitted (Fig. 13).

The TENDL predictions enhance better the separate contributions of the different stable target isotopes than the experimental results where only a secondary maximum near 40 MeV (probably (p,4n) on more abundant ⁹⁸Mo) can be seen. All maximum values are underestimated in the two versions.

The integral yields calculated from the recommended cross sections are shown in Fig. 42. Four experimental yield data were found: Dmitriev [199], Dmitriev [126], Lagunas-Solar [200], Bonardi (differential yield, not in figure) [188].

¹⁹⁷Au(p,x)¹⁹⁴Au reaction

As Au is monoisotopic only the ¹⁹⁷Au(p,p3n) reaction, with threshold for emission of single particles at 23.26 MeV, contributes to direct formation of ¹⁹⁴Au. As the threshold for the (p,³H n) reaction is 14.73 MeV also small cross sections in the 15–24 MeV domain can be expected. Although the ¹⁹⁷Au(p,4n) reaction will result in formation of very long-lived parent ¹⁹⁴Hg (T_1/2 = 367 y) it will in practice not contribute to cumulative formation of ¹⁹⁴Au.

A total of 5 cross section data sets, covering the energy range from threshold up to 250 MeV, were found in literature and are displayed in Fig. 38: Kavanagh [201], Michel [24], Szelecsenyi [202], Ditroi [203], Cervenak [204]. All datasets of the 5 publications were selected up to 170 MeV and fitted (Fig. 39).

Fig. 38

¹⁹⁷Au(p,x)¹⁹⁴Au reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 39

¹⁹⁷Au(p,x)¹⁹⁴Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions agree well in overall shape but slightly overestimate the maximum value of the experimental points. The integral yields calculated from the recommended cross sections are shown in Fig. 42. Only 1 experimental yield data was found: Birattari [205] (differential yield, not in figure).

¹⁹⁷Au(p,x)^196gAu reaction

As Au is monoisotopic only the ¹⁹⁷Au(p,pn) reaction, with the threshold for emission of single particles at 8.114 MeV, contributes. As the threshold for (p,d) is 5.878 MeV also small cross section in the 6–9 MeV domain can be expected. The parallel formation of the two excited states, with respective half-lives of 9.7 h and 8.2 s, both decaying for 100% by IT to ^196gAu, will result in cumulative formation when using ^196gAu in practice for monitoring.

A total of 8 cross section data sets, covering the energy range from threshold up to 175 MeV, were found in literature and are displayed in Fig. 40: Yule [206], Gusakow [207], Kavanagh [201], Nagame [208], Michel [24], Szelecsenyi [209], Szelecsenyi [202], Ditroi [203].

Fig. 40

¹⁹⁷Au(p,x)^196gAu reaction: all experimental data and the TENDL theoretical excitation functions

The disagreeing set of Gusakov 1960 was deleted. The original sets of the remaining 7 publications were selected up to 150 MeV and fitted (Fig. 40). The two TENDL predictions agree well in overall shape but slightly overestimate the maximal value of the experimental points. The integral yields calculated from the recommended cross sections are shown in Fig. 41. Two experimental yield data point were found, Dmitriev [126], Abe [84] and Birattari (differential yield, not in figure) [205] (Fig. 42).

Fig. 41

¹⁹⁷Au(p,x)^196gAu reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

Fig. 42

Yield calculated from the recommended cross sections of the ^natCu(p,x)⁶¹Cu,⁹³Nb(p,x)⁹⁰Mo, ^natMo(p,x)^95mTc, ¹⁹⁷Au(p,x)¹⁹⁴Au and ¹⁹⁷Au(p,x)^196gAu reactions

Evaluated deuteron-induced nuclear reactions

^natTi(d,x)⁴³Sc reaction

Reactions of the general shape (d,αxn), with x between 1 and 5, on the five stable isotopes of Ti can contribute to direct ⁴³Sc formation (⁴⁶Ti abundance is 8.25% in natural Ti; ⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The lowest threshold is for the ⁴⁶Ti(d,αn)⁴³Sc reaction at 5.526 MeV while the ⁴⁷Ti(d,α²n)⁴³Sc reaction has a 14.772 MeV threshold. If only separate particles are emitted, for instance, the ⁴⁶Ti(d,2p3n)⁴³Sc reaction, the threshold is 35.029 MeV. Formation by partly clustered emission will occur at intermediate energies and the contribution of the interactions with the other isotopes at different energies will result in an excitation function with multiple local maxima. The formation of ⁴³Sc at energies above 43 MeV is always cumulative as it contains the full decay of very short-lived ⁴³Ti (T_1/2 = 0.5 s) produced by (d,pxn) reactions on the different stable Ti isotopes. The threshold for the ⁴⁶Ti(d,p4n)⁴³Ti reaction is 43.011 MeV.

As only 4 cross section data sets, covering the energy range from threshold up to 24 MeV, were found in the literature, only the direct formation by ⁴⁶Ti(d,αn)⁴³Sc, with low contribution of the ⁴⁷Ti(d,α₂n)⁴³Sc reaction, is available as displayed in Fig. 43: Takacs [210], Khandaker [211], Khandaker [212], Lebeda [213].

Fig. 43

^natTi(d,x)⁴³Sc reaction: all experimental data and the TENDL theoretical excitation functions

All sets were selected and fitted up to 25 MeV (Fig. 44). While the TENDL 2021 prediction does not show multiple reaction contributions in the 2023 version a pronounced local maximum of around 19 MeV is seen. The maximum value is nearly double that of the experiments. The integral yields calculated from the recommended cross sections are shown in Fig. 47. As the Khandaker 2013 data are derived from cross section they are not presented in Fig. 47 [211].

Fig. 44

^natTi(d,x)⁴³Sc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

^natTi(d,x)⁴⁷Sc reaction

Reactions of the general shape (d,2pxn), with x between 0 and 3, on four stable isotopes of Ti can contribute to direct ⁴⁷Sc formation (⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The threshold for the ⁴⁷Ti(d,2p)⁴⁷Sc reaction is 5.526 MeV while for the ⁴⁹Ti(d,α)⁴⁷Sc reaction a positive Q-value of 6.483 MeV is noted and the ⁵⁰Ti(d,2p3n) reaction with emission of not clustered particles would have a 34.033 MeV threshold. Formation by partly clustered emission on the different target isotopes will occur at intermediate energies and should result in an excitation function with multiple local maxima. The parallel formation of parent, somewhat longer-lived, ⁴⁷Ca (T_1/2 = 4.536 d, 100% β⁻ decay) by the ⁵⁰Ti(d,αp)⁴⁷Ca reaction with 5.887 MeV threshold or ⁴⁹Ti(d,3pn) with 23.942 MeV threshold could influence and disturb the practical use of this reaction for monitoring (Fig. 45).

Fig. 45

^natTi(d,x)⁴⁷Sc reaction: all experimental data and the TENDL theoretical excitation functions

All original datasets of the 8 publications were selected up to 50 MeV and fitted (Fig. 46): Takacs [210], Takacs [214], Hermanne [215], Gagnon [216], Khandaker [211], Khandaker [212], Duchemin [217], Lebeda [213].

Fig. 46

^natTi(d,x)⁴⁷Sc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

The two TENDL predictions do not show multiple reaction contributions but above 15 MeV a steeper rise than the experimental values, increasing further above 45 MeV, is seen. The integral yields calculated from the recommended cross sections are shown in Fig. 47. A single experimental yield data point was found: Dmitriev [218].

Fig. 47

Yield calculated from the recommended cross sections of the ^natTi(d,x)⁴³Sc and ^natTi(d,x)⁴⁷Sc reactions

^natFe(d,x)⁵⁵Co reaction

Four (d,xn) reactions on the stable target isotopes ⁵⁴Fe (abundance 5.845% in ^natFe) ⁵⁶Fe (abundance 91.754% in ^natFe), ⁵⁷Fe (2.119%) and ⁵⁸Fe (0.282%) contribute to the formation of ⁵⁵Co. At energies below 20 MeV the ⁵⁴Fe(d,n)⁵⁵Co reaction with a positive Q-value of 2.839 MeV will contribute while, due to the predominance of the ⁵⁶Fe isotope, the (d,3n) reaction, with the threshold of 18.270 MeV, will in practice be more important.

A total of 7 cross section data sets, covering the energy range from threshold up to 48 MeV, were found in literature and are displayed in Fig. 48: Clark [219], Zhao Wenrong [220], Hermanne [215], Nakao [221], Kiraly [222], Khandaker [211]. Avrigeanu [223]. As the overall shape of the excitation function published in Clark 1969 is acceptable but too high, all data points were multiplied by a factor of 0.5 to agree with the two local maxima found in the other publications. In the lower energy domain, the outlying data points of Zhao Wenrong 1995 at 3.669 MeV and Hermanne 2000 (at 0.2, 1.4, 6.2, 7.1, 9.1 and 9.8 MeV) were deleted. The original and corrected datasets of the 7 publications were selected and fitted up to 50 MeV (Fig. 49).

Fig. 48

^natFe(d,x)⁵⁵Co reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 49

^natFe(d,x)⁵⁵Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL predictions represent well the overall shape of the combined reactions' excitation function but are energy-shifted above 20 MeV. The TENDL 2023 version is significantly lower in the 20–50 MeV domain. The integral yields calculated from the recommended cross sections are shown in Fig. 56. A single experimental yield data was found: Dmitriev [218].

^natFe(d,x)⁵⁶Co reaction

Three (d,xn) reactions on the stable target isotopes ⁵⁶Fe( abundance 91.754% in ^natFe), ⁵⁷Fe (2.119%) and ⁵⁸Fe (0.282%) contribute to the formation of ⁵⁵Co. Due to the prominence of the ⁵⁶Fe isotope the ⁵⁶Fe(d,2n)⁵⁶Co reaction, with the threshold of 7.837 MeV, will be dominant.

A total of 13 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 50: Irwine [224], Burgus [225], Clark [219], Tao Zhenlan [226], Jung [227], Sudar [120], Zhao Wenrong [220], Takacs [228], Takacs [229], Ochiai [230], Kiraly [222], Khandaker [231], Zavorka [232], Avrigeanu [223]. As the Zavorka 2011 data (reported in a conference) are identical to the data of Avregianu 2014, only this last set is represented. The data of Irwine 1949 are outlying above 10 MeV and were deselected. The too high values of Clark 1969 data were normalized by a factor of 0.72 to bring them in agreement with the average value of the other publications near the maximum around 18 MeV. The original and corrected datasets of the 12 publications were selected up to 50 MeV and fitted (Fig. 51).

Fig. 50

^natFe(d,x)⁵⁶Co reaction: all experimental data and the TENDL theoretical excitation function

Fig. 51

^natFe(d,x)⁵⁶Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL predictions are well representing the shape of the experimental excitation function, with 10% lower maximum in the 2023 version, but are slightly energy-shifted. The integral yields calculated from the recommended cross sections are shown in Fig. 56. A single experimental yield data point was found: Dmitriev [218] (Fig. 52).

Fig. 52

^natFe(d,x)⁵⁷Co reaction: all experimental data and the TENDL theoretical excitation functions

^natFe(d,x)⁵⁷Co reaction

Three (d,xn) reactions on the stable target isotopes ⁵⁶Fe (abundance 91.754% in ^natFe), ⁵⁷Fe (2.119%) and ⁵⁸Fe (0.282%) contribute to the formation of ⁵⁵Co. Due to the prominence of the ⁵⁶Fe isotope the ⁵⁶Fe(d,n)⁵⁷Co reaction, with a positive Q-value of 3.802 MeV, will be dominant.

A total of 10 cross section data sets, covering the energy range from threshold up to 49 MeV, were found in literature and are displayed in Fig. 52: Clark [219], Tao Zhenlan [226], Jung [227], Zhao Wenrong [220], Takacs [228], Hermanne [215], Ochai [230], Kiraly [222], Khandaker [231], Avrigeanu [223]. The too high and energy-shifted set of Clark 1969 was deselected. The outlying sets of Zhao Wenrong 1995 and Ochai 2007 were normalized, respectively by a factor of 1.45 and by a factor of 0.8, to bring them in agreement with an average value of the other publications near a maximum of 300 mb around 7 MeV. Four wrongly rising points of Tao Zhenlan 1995 above 14 MeV were deleted. The too low dataset of Zhao Wenrong is deselected.

The original and corrected datasets of 8 publications were selected up to 49 MeV and fitted (Fig. 53).

Fig. 53

^natFe(d,x)⁵⁷Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are well representing the shape of the experimental excitation function but are slightly energy-shifted and a 10% overestimation of the maximum cross section is seen. The integral yields calculated from the recommended cross sections are shown in Fig. 56.

Two experimental yield data was found: Dmitriev [218] and Gruverman [173].

^natFe(d,x)⁵⁸Co reaction

Only two (d,xn) reactions on the low abundance stable target isotopes, ⁵⁷Fe (2.119% abundance in ^natFe) and ⁵⁸Fe (0.282%), contribute to the formation of ⁵⁸Co. Due to the prominence of the ⁵⁷Fe isotope the ⁵⁷Fe(d,n)⁵⁸Co reaction, with a positive Q-value of 4.729 MeV, will be dominant.

A total of 7 cross section data sets, covering the energy range from threshold up to 30 MeV, were found in literature and are displayed in Fig. 54: Clark [219], Jung [227], Sudar [120], Zhao Wenrong [220], Kiraly [222], Khandaker [231], Avrigeanu [223].

Fig. 54

^natFe(d,x)⁵⁸Co reaction: all experimental data and the TENDL theoretical excitation functions

The too high and energy-shifted set of Clark 1969 was deselected. The outlying point of Zhao Wenrong 1995 at 3.67 MeV was deleted. The original and corrected datasets of 6 publications were selected and fitted up to 25 MeV (Fig. 55).

Fig. 55

^natFe(d,x)⁵⁸Co reaction:  selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions represent the shape of the experimental excitation function but are slightly energy-shifted. The integral yields calculated from the recommended cross sections are shown in Fig. 56. A single experimental yield data was found: Dmitriev [218].

Fig. 56

Yield calculated from the recommended cross sections of the ^natFe(d,x)⁵⁵Co, ^natFe(d,x)⁵⁶Co, ^natFe(d,x)⁵⁷Co and ^natFe(d,x)⁵⁸Co reactions

^natNi(d,x)⁵⁵Co reaction

In principle five (d,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁵Co if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,2p3n)⁵⁵Co reaction with the emission of 5 separate particles is 32.924 MeV but by clustering the ⁵⁸Ni(d,αn)⁵⁵Co reaction is favored with 3.678 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 11 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 57: Zweit [233], Takacs [234], Takacs [235], Ochiai [230], Hermanne ser.I-4[236], Amjed [237], Usman [238], Avrigeanu [239]. The data of Takacs 1997 are too high in the rising part of the excitation function and were multiplied by a factor of 0.8 before selection. Additionally, too high outlying points of Zweit 1991 at 17.6 and 18.9 MeV and the series of Ochai 2007 between 21 and 30 MeV were deleted. The original and corrected datasets of the 11 publications were selected up to 50 MeV and fitted (Fig. 58).

Fig. 57

^natNi(d,x)⁵⁵Co reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 58

^natNi(d,x)⁵⁵Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions strongly underestimate the maximal value observed around 24 MeV but represent well the rising excitation function above 42 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 69. Two experimental yield data were found: Zweit [233] Amjed [237].

Fig. 59

^natNi(d,x)⁵⁶Ni reaction: all experimental data and the TENDL theoretical excitation functions

^natNi(d,x)⁵⁶Ni reaction

In principle five (d,pxn) reactions on the stable target isotopes isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁶Ni if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,p3n)⁵⁶Ni reaction with emission of 4 separate particles is 25.517 MeV while clustering allows the ⁵⁸Ni(d,³Hn)⁵⁶Ni reaction with 16.750 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 7 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in the literature and are displayed in Fig. 59: Cline 1971 (⁵⁸Ni norm) [240], Zhu Fuying [241], Takacs [235], Hermanne [236], Amjed [237].

The data of Cline 1971 are given for the ⁵⁸Ni(d,x)⁵⁶Ni reaction and were normalized for the ⁵⁸Ni abundance in ^natNi.

All 7 datasets were selected up to 50 MeV and fitted (Fig. 60). The TENDL predictions are overestimating, with observable differences between the two versions the excitation function over the entire energy domain. The integral yields calculated from the recommended cross sections are shown in Fig. 69. No experimental yield data are available.

Fig. 60

^natNi(d,x)⁵⁶Ni reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(d,x)⁵⁶Co reaction

In principle five (d,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁶Co if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,2p2n)⁵⁶Co reaction with the emission of 4 separate particles is 22.504 MeV but by clustering the ⁵⁸Ni(d,α)⁵⁶Co reaction is favored with a positive Q value of 6.522 MeV. The same observation is valid for the reactions on other Ni isotopes and hence a double-peaked excitation function, starting at low energies, can be expected. Taking into account that the threshold for the ⁸⁰Ni(d,α2n)⁵⁶Co reaction is 14 MeV, the data sets of the publications reporting cross sections for the ⁵⁸Ni(d,α) reaction, using ⁵⁸Ni or ^natNi targets, were considered only up to 14 MeV.

A total of 14 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 61: Cline [240], Zhu Fuying [241], Jung [227], Takacs [234], Zweit [233], Takacs [235], Ochiai [230], Hermanne [236], Amjed [237], Avrigeanu [239].

Fig. 61

^natNi(d,x)⁵⁶Co reaction: all experimental data and the TENDL theoretical excitation functions

All datasets were selected up to 50 MeV and fitted (Fig. 62). The TENDL predictions represent well the shape of the double peaked excitation function, but values differ significantly between the two versions. The integral yields calculated from the recommended cross sections are shown in Fig. 69. Two experimental yield data points are available: Dmitriev [218] and Amjed [237].

Fig. 62

^natNi(d,x)⁵⁶Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(d,x)⁵⁷Ni reaction

In principle five (d,pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁷Ni if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,p2n)⁵⁷Ni reaction with the emission of 3 separate particles is 14.925 MeV while clustering allows the ⁵⁸Ni(d,t)⁵⁷Ni reaction with a 6.159 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 11 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 63: Zweit [233], Takacs [234], Takacs [235], Hermanne [236], Amjed [237], Usman [238], Avrigeanu [239]. Some outlying data points were deleted: Zweit 1991 at 13 MeV, Amjed 2013 (at 3.7 MeV, 6.3 MeV and 8.5 MeV), Hermanne 2013 (at 5.3 MeV, 15.8 and 15.9 MeV).

Fig. 63

^natNi(d,x)⁵⁷Ni reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected 11 published datasets were selected up to 50 MeV and fitted (Fig. 64).

Fig. 64

^natNi(d,x)⁵⁷Ni reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

While the TENDL 2021 prediction is low near the threshold, it is in good agreement with the experimental excitation function up to 40 MeV. The TENDL 2023 version better predicts the low energy part but significantly overestimates the experimental data from 25 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 69. Two experimental yield data points are available: Dmitriev [218] and Amjed [237].

^natNi(d,x)⁵⁷Co reaction

In principle five (d,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to formation of ⁵⁵Co if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,2pn)⁵⁷Co reaction with the emission of 3 separate particles is 10.745 MeV but by clustering the ⁵⁸Ni(d,dp)⁵⁷Co reaction is possible with 8.446 MeV threshold. The same observation is valid for the reactions on other Ni isotopes.

A total of 12 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 65: Zweit [233], Jung [227], Takacs [234], Ochiai [230], Takacs [235], Hermanne [236], Amjed [237], Usman [238], Avrigeanu [239]. All data from the 9 publications were selected up to 50 MeV and fitted (Fig. 66).

Fig. 65

^natNi(d,x)⁵⁷Co reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 66

^natNi(d,x)⁵⁷Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL 2021 predictions are shifted above 18 MeV and are overestimating the maximal value by 15%. Good agreement can be found up to 30 MeV for the TENDL 2023, but the prediction does not follow the expected decreasing behavior as shown in the experimental data. The integral yields calculated from the recommended cross sections are shown in Fig. 69. Two experimental yield data points are available: Dmitriev [218] and Amjed [237].

^natNi(d,x)⁵⁸Co reaction

In principle five (d,2pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 3), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 5), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6349% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to the formation of ⁵⁸Co if high energy deuteron bombardment is performed.

The threshold for the ⁵⁸Ni(d,2p)⁵⁸Co reaction is 1.885 MeV but by clustering the ⁶⁰Ni(d,α)⁵⁸Co reaction is possible with a positive Q-value of 6.084 MeV. The same observation is valid for the reactions on other Ni isotopes.

A total of 8 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 67: Jung [227], Zweit [233], Jung [118], Takacs [234], Takacs [235], Hermanne [236], Amjed [237], Usman [238], Avrigeanu [239].

Fig. 67

^natNi(d,x)⁵⁸Co reaction: all experimental data and the TENDL theoretical excitation functions

As Jung 1987 data are identical with Jung 1991 only the most recent version is displayed and considered for evaluation. The values in Zweit 1991 are too low and do not show a good maximum structure, the set was hence deselected. The whole, too high, set of Takacs 1997 data was multiplied by a factor of 0.7 to be in acceptable agreement with the average value of 220 mb near the maximum at 19 MeV found in the other publications. The original and corrected datasets of 7 publications were selected up to 50 MeV and fitted (Fig. 68).

Fig. 68

^natNi(d,x)⁵⁸Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The overall shape of the excitation function predicted by TENDL 2021 is in good agreement with the experimental results but overestimates the maximal value around 19 MeV. The predictions of TENDL 2023 are lower by a factor of 2 near the maximum and do not represent well the expected shape of the excitation curve. The integral yields calculated from the recommended cross sections are shown in Fig. 69. Two experimental yield data points are available: Dmitriev [218] and Amjed [237].

Fig. 69

Yield calculated from the recommended cross sections of the ^natNi(d,x)⁵⁵Co ^natNi(d,x)⁵⁶Ni, ^natNi(d,x)⁵⁶Co, ^natNi(d,x)⁵⁷Ni, ^natNi(d,x)⁵⁷Co and ^natNi(d,x)⁵⁸Co reactions

⁹³Nb(d,2n)^93mMo reaction

As the element Nb is monoisotopic only the ⁹³Nb(d,2n)^93mMo reaction with an effective threshold of 5.907 MeV (taking into account the excitation energy of 2.425 MeV of the metastable state) is possible. A total of 5 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in the literature and are displayed in Fig. 70: Ditroi [242], Tarkanyi [243], Avrigeanu [244], Ditroi [245], Aikawa [246].

Fig. 70

⁹³Nb(d,x)^93mMo reaction: all experimental data and the TENDL theoretical excitation functions

The data points below the threshold value of 6 MeV of Tarkanyi 2007, Avrigeanu 2013 and Aikawa 2018 were deleted. The original and corrected datasets of the 5 publications were selected up to 50 MeV (Fig. 71).

Fig. 71

⁹³Nb(d,x)^93mMo reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL 2021 prediction does not well represent the peak near 18 MeV and is largely underestimating the maximal value. For the TENDL 2023 version the peaked shape agreement is better and the maximum value is overestimated by 20%. The integral yields calculated from the recommended cross sections are shown in Fig. 80. One experimental yield data point is available: Dmitriev [218].

^natMo(d,x)⁹⁶Tc reaction

In principle five (p,xn) reactions on the stable target isotopes ⁹⁵Mo (abundance 15.84% in ^natMo, n = 1), ⁹⁶Mo (abundance 16.67% in ^natMo, n = 2), ⁹⁷Mo (abundance 9.60% in ^natMo), ⁹⁸Mo (abundance 24.39% in ^natMo), ¹⁰⁰Mo (abundance 9.82% in ^natMo, n = 6) can contribute to formation of ⁹⁶Tc if high energy deuteron bombardment is performed. The ⁹⁵Mo(d,n)⁹⁶Tc reaction has a positive Q-value of 3.174 MeV and the threshold rises to 36.340 MeV for the ¹⁰⁰Mo(d,6n)⁹⁶Tc reaction.

A total of 6 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 72: Randa [247], Wu Sheng [248], Zhao Wenrong [249], Lebeda [192], Tarkanyi [250], Elbinawi [251]. Outlying data points of Randa 1976 (at 12.7 MeV), Tarkanyi 2012 (at 7.57, 7.94, 8.44, 8.9, 11.16 and 11.55 MeV) and Elbinawi 2021 (at 3.62 MeV) were deleted.

Fig. 72

^natMo(d,x)⁹⁶Tc reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 6 publications were selected up to 50 MeV and fitted (Fig. 73). While the TENDL 2021 predictions represent well the shape and amplitude of the multiple reaction excitation functions in the TENDL 2023 version the disagreements become significant above 25 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 80. Two experimental yield data points are available: Svoboda [252], Dmitriev [218].

Fig. 73

^natMo(d,x)⁹⁶Tc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

¹⁹⁷Au(d,x)¹⁹⁴Au reaction

As Au is monoisotopic only the ¹⁹⁷Au(d,p4n) reaction, with the threshold for emission of single particles at 25.595 MeV, contributes to direct formation of ¹⁹⁴Au. As the threshold for (p,³H2n) is 17.037 MeV also low cross sections in the 18–26 MeV domain can be expected. Although the ¹⁹⁷Au(d,5n) reaction, with a threshold of 26.413 MeV, will result in the formation of very long-lived ¹⁹⁴Hg (T_1/2 = 367 y) it will in practice not contribute to the cumulative formation of ¹⁹⁴Au.

A total of 4 cross section data sets, covering the energy range from threshold up to 86 MeV, were found in the literature and are displayed in Fig. 74: Jahn [253], Ochiai [230], Tarkanyi [254], Tarkanyi [255]. Above 40 MeV the status of the experimental database is poor: the two available sets by Jahn 1973 and Tarkanyi 2015 show systematic disagreement. To get selected data they were normalized to each other taking into account acceptance of the Ochai 2007 and Tarkanyi 2011 cross section values at energies between 30 and 40 MeV.

Fig. 74

¹⁹⁷Au(d,x)¹⁹⁴Au reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 4 publications were selected up to 86 MeV and fitted (Fig. 75). The two TENDL predictions show a more pronounced and higher maximum of around 80 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 80. No experimental yield data is available.

Fig. 75

¹⁹⁷Au(d,x)¹⁹⁴Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

¹⁹⁷Au(d,x)¹⁹⁶Au reaction

As Au is monoisotopic only the ¹⁹⁷Au(d,p2n) reaction, with the threshold for emission of single particles at 10.390 MeV, contributes to the formation of ¹⁹⁶Au. As the threshold for (d,³H) is only 1.832 MeV also low cross sections in the 3–12 MeV domain can be expected.

A total of 9 cross section data sets, covering the energy range from threshold up to 80 MeV, were found in the literature and are displayed in Fig. 76: Baron [256], Chevarier [257], Khrisanfov [258], Jahn [253], Long [259], Zhao Wenrong [260], Tarkanyi [254], Tarkanyi [255], Lebeda [261]. As all data points of Tarkanyi 2015 are too high, the whole set was multiplied by a factor of 0.8 for selection.

Fig. 76

¹⁹⁷Au(d,x)¹⁹⁶Au reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 9 publications were selected up to 80 MeV and fitted (Fig. 77). The small local maximum suggested by the experimental data around 15–16 MeV is probably due to more than expected contribution of the clustered emission in the (d,³H) and (d,dn) reactions. The two TENDL predictions do not show the contribution of clustered emission below 20 MeV and are overestimating the maximal value around 40 MeV by more than 40%. The integral yields calculated from the recommended cross sections are shown in Fig. 80. One experimental yield data is available: Dmitriev [218].

Fig. 77

¹⁹⁷Au(d,x)¹⁹⁶Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

¹⁹⁷Au(d,x)^198gAu reaction

As Au is monoisotopic only the ¹⁹⁷Au(d,p) reaction, with a positive Q-value of 4.287 MeV contributes to the formation of ^198gAu. A total of 12 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 78: Baron [256], Sandoval [262], Nassiff [263], Chevarier [257], Khrisanfov [258], Jahn [253], Long [259], Zhao Wenrong [260], Tarkanyi [254], Tarkanyi [255], Ditroi [264], Lebeda [261].

Fig. 78

¹⁹⁷Au(d,x)¹⁹⁸Au reaction: all experimental data and the TENDL theoretical excitation functions

As the cross sections for co-producing the metastable state parent with similar half-life, ^198mAu (T_1/2 = 2.876 d, IT 100%), is very low (less than 1 mb up to 20 MeV in Tarkanyi 2011 and Lebeda 2019) the contribution in the formation of the ground state is negligible and not further considered.

The two datasets with too low values at energies below 12 MeV (Nasiff 1966 and Khrisanfov 1972) were deselected. Also, the too low values of Chevarier 1971 at 9.51 MeV and four points of Tarkanyi 2015 (at 5.1, 7.8, 10 and 12 MeV) were deleted. The clearly outlying and too high sets of Tarkanyi 2015 and Lebeda 2019 were reduced by a factor of 0.8 while the really low set of Ditroi 2017 was multiplied by a factor of 10. The original and corrected datasets of 10 publications were selected up to 80 MeV and fitted (Fig. 79).

Fig. 79

¹⁹⁷Au(d,x)¹⁹⁸Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are energy-shifted and strongly underestimate the maximal value. This is because a ratio for formation of metastable state to ground state of around 2.5–5 10^–1 is predicted in the 5–20 MeV range while values derived from experimental results are 3–4 10^–3. The integral yields calculated from the recommended cross sections are shown in Fig. 80. One experimental yield data point is available: Dmitriev [218].

Fig. 80

¹⁹⁷Au(d,x)¹⁹⁸Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

7. Evaluated ³He-induced nuclear reactions

^natC(³He,x)¹¹C reaction

Two reactions contribute to ¹¹C formation after ³He bombardment of ^natC: ¹²C(³He,α)¹¹C (¹²C abundance is 98.90%, positive Q-value of 1.856 MeV) and ¹³C(³He,αn)¹¹C (¹³C abundance is 1.10%, threshold 3.791 MeV). A total of 6 cross section data sets, covering the energy range from threshold up to 37 MeV, were found in the literature and are displayed in Fig. 81: Crandall [31], Brill [265], Hahn [266], Cirilov [267], Liebler s1-2 [268]. The too low point of Brill 1965 at 5.09 MeV was deleted. The original and corrected datasets of the 6 publications were selected and fitted up to 40 MeV (Fig. 82). No TENDL predictions are available for these low Z-value targets. The integral yields calculated from the recommended cross sections are shown in Fig. 93.

Fig. 81

^natC(³He,x)¹¹C reaction: all experimental data

Fig. 82

^natC(³He,x)¹¹C reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right hand scale)

Two experimental yield data available: Krasnov [48], which is independent and Nozaki [269], which is derived saturation yield, that’s why it was not presented in Fig. 93.

^natTi(³He,x)^44mSc reaction

Reactions of the general shape (³He,αpxn), with x between 0 and 3, on the five stable isotopes of Ti can contribute to direct ^44mSc formation (⁴⁶Ti abundance is 8.22% in natural Ti, ⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The threshold for the ⁴⁶Ti(³He,αp)^44gSc reaction is 1.163 MeV while for the ⁵⁰Ti(³He,αp4n) ^44gSc reaction a threshold of 43.09 MeV is reached. A value of 0.2710 MeV, the excitation energy of the metastable state, should be added to these threshold values. More clustering with the emission of Li isotopes could also occur, the ⁴⁷Ti(³He,⁶Li)^44gSc reaction has a threshold of 6.663 MeV.

A total of 4 cross section data sets, covering the energy range from threshold up to 135 MeV, were found in literature and are displayed in Fig. 83: Weinreich [270], Ditroi [271], Szelecsenyi [272], Khandaker [273]. The two lowest points of Weinreich 1980 at 4.9 and 9 MeV are deleted. The pronounced local maximum around 55 MeV is due to the most contributing reaction on dominant ⁴⁸Ti.

Fig. 83

^natTi(³He,x)^44mSc reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 4 publications were selected up to 135 MeV and fitted (Fig. 84). The two versions of the TENDL predictions reproduce the overall shape of the experimental data and show the local maxima of the contributing reactions on the different stable Ti isotopes but with an energy shift of 50 MeV for the dominant ⁴⁸Ti(3He,x)^44mSc reaction. A difference by a factor of two between the two versions is noted. The integral yields calculated from the recommended cross sections are shown in Fig. 93. No experimental yield data are available.

Fig. 84

^natTi(³He,x)^44mSc reaction: all experimental data and the TENDL theoretical excitation functions

^natTi(³He,x)⁴⁶Sc reaction

Reactions of the general shape (³He,3pxn), with x between 1 and 5, on the five stable isotopes of Ti can contribute to direct ⁴⁶Sc formation (⁴⁶Ti abundance is 8.22% in natural Ti, ⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The threshold for the ⁴⁶Ti(³He,3p)⁴⁶Sc reaction is 9.887 MeV while for the maximal clustered emission ⁴⁸Ti(³He,αp)⁴⁶Sc reaction a threshold of 1.605 MeV is reached. More clustering with the emission of Li isotopes could also occur, the ⁴⁹Ti(³He,⁶Li)⁴⁶Sc reaction has a threshold of 6.308 MeV.

A total of 4 cross section data sets, covering the energy range from threshold up to 135 MeV, were found in the literature and are displayed in Fig. 85: Weinreich [270], Ditroi [271], Szelecsenyi [272], Khandaker [274]. All sets were selected up to 100 MeV and fitted (Fig. 86).

Fig. 85

^natTi(³He,x)⁴⁶Sc reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 86

^natTi(³He,x)⁴⁶Sc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions are well representing the overall shape but the values are a factor 3–7 too low. The integral yields calculated from the recommended cross sections are shown in Fig. 93. No experimental yield data are available.

^natTi(³He,x)⁴⁷Sc reaction

Reactions of the general shape (³He,αpxn), with x between 0 and 3, on four stable isotopes of Ti can contribute to direct ⁴⁷Sc formation (⁴⁷Ti abundance is 7.44% in natural Ti, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The threshold for the ⁴⁷Ti(³He,3p)⁴⁷Sc reaction is 8.000 MeV while for the ⁴⁹Ti(³He,αp)⁴⁷Sc reaction a positive Q-value of 990 keV is obtained.

A total of 4 cross section data sets, covering the energy range from threshold up to 135 MeV, were found in literature and are displayed in Fig. 87. Weinreich [270], Ditroi [271], Szelecsenyi [272], Khandaker [274]. The excitation function obtained from the data set of Weinreich [270] was energy corrected.

Fig. 87

^natTi(³He,x)⁴⁷Sc reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of the 4 publications were selected up to 140 MeV and fitted (Fig. 88). The two TENDL predictions represent well the overall shape up to 60 MeV but the values are a factor of 3–5 too low. The integral yields calculated from the recommended cross sections are shown in Fig. 93. No experimental yield data are available.

Fig. 88

^natTi(³He,x)⁴⁷Sc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natTi(³He,x)⁴⁸Cr reaction

Reactions of the general shape (³He, xn), with x between 1 and 5, on the five stable isotopes of Ti can contribute to direct ⁴⁸Cr formation (⁴⁶Ti abundance is 8.22%, ⁴⁷Ti abundance is 7.44%, ⁴⁸Ti abundance is 73.72%, ⁴⁹Ti abundance is 5.41%, ⁵⁰Ti abundance is 5.18%). The ⁴⁶Ti(³He,n)⁴⁸Cr reaction has a positive Q-value of 5.553 MeV while for the ⁵⁰Ti(³He,5n) ⁴⁸Cr reaction a threshold of 35.998 MeV is reached.

A total of 5 cross section data sets, covering the energy range from threshold up to 135 MeV, were found in literature and are displayed in Fig. 89: Weinreich [270], Ditroi [271], Szelecsenyi [272], Khandaker [274], Lebeda [275].

Fig. 89

^natTi(³He,x)⁴⁸Cr reaction: all experimental data and the TENDL theoretical excitation functions

The excitation function obtained from the data set of Weinreich is energy-shifted in the lower energy domain and has too low cross section values near the maximum. A negative, linearly decreasing towards accepted energy of 134.7 MeV correction was applied (− 1.2 MeV at 9.4 MeV original) and all values were multiplied by a factor of 1.2. The original and corrected datasets of the 5 publications were selected up to 135 MeV, and fitted up to 100 MeV (Fig. 90).

Fig. 90

^natTi(³He,x)⁴⁸Cr reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions have a more pronounced dip in the 14–19 MeV region before the dominant contribution of the ⁴⁸Ti(³He,3n)⁴⁸Cr reaction with a 15.854 MeV threshold is starting. The excitation curve is however shifted to lower energy and underestimates the maximal value by 40%. The integral yields calculated from the recommended cross sections are shown in Fig. 93. No experimental yield data are available.

^natTi(³He,x)⁵¹Cr reaction

Reactions of the general shape (³He,xn), with x is 1 or 2, on two stable isotopes of Ti, can contribute to direct ⁴¹Cr formation (⁴⁹Ti abundance is 5.41% in natural Ti, ⁵⁰Ti abundance is 5.18%). The ⁴⁹Ti(³He,n)⁸¹Cr reaction has a positive Q-value of 9.746 MeV while for the ⁵⁰Ti(³He, 2n) ⁵¹Cr reaction a threshold of 1.261 MeV is reached.

A total of 3 cross section data sets, covering the energy range from threshold up to 135 MeV, were found in the literature and are displayed in Fig. 91: Weinreich [270], Ditroi [271], Solieman [276].

Fig. 91

^natTi(³He,x)⁵¹Cr reaction: all experimental data and the TENDL theoretical excitation functions

The excitation function obtained from the data set of Weinreich is energy-shifted in the lower energy domain. A negative, linearly decreasing towards accepted energy of 134.7 MeV), the correction was applied (− 1.9 MeV at 9.4 MeV original,—0.7 at 90 MeV).

The original and corrected datasets of the 3 publications were selected and fitted up to 135 MeV, the energy limit for interesting practical application (Fig. 92). The TENDL predictions are in good agreement with the available experimental results in the maximum, confirm a practical threshold of 6 MeV, but above the maximum are shifted to low energies. The integral yields calculated from the recommended cross sections are shown in Fig. 93. No experimental yield data are available.

Fig. 92

^natTi(³He,x)⁵¹Cr reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 93

Yield calculated from the recommended cross sections of the ^natTi(³He,x)^44mSc ^natTi(³He,x)⁴⁶Sc ^natTi(³He,x)⁴⁷Sc ^natTi(³He,x)⁴⁸Cr and ^natTi(³He,x)⁵¹Cr reactions

Evaluated alpha-induced nuclear reactions

²⁷Al(α,x)²⁸Mg reaction

As Al is monoisotopic only the ²⁷Al(a,3p) reaction with a threshold of 24.665 MeV contributes to ²⁸Mg formation.

A total of 13 cross section data sets, covering the energy range from threshold up to 170 MeV, were found in literature and are displayed in Fig. 94: Hudis [277], Nethaway [278], Martens [279], Nozaki [280], Probst [281], Rattan [282], Rattan [283], Vysotskiy [284], Rattan [285], Karamyan [286], Kirov [287], Lange [288], Paul [289].

Fig. 94

²⁷Al(α,x)²⁸Mg reaction: all experimental data and the TENDL theoretical excitation functions

The energy scale of Probst 1976 was positively, linearly decreasing with the accepted original value at 155 MeV, corrected. The single points of Hudis 1957 and Kirov 1992 were deleted while the too low data point of Vysotskiy 1989 at 52 MeV was deselected.

The original and corrected datasets of 11 publications were selected up to 160 MeV and fitted (Fig. 95). The maximum cross section in both versions of the TENDL predictions is more than a factor 6 lower than the experimental maximum. The integral yields calculated from the recommended cross sections are shown in Fig. 96. Three experimental yield data are available: Dmitriev [290], Paul [289] and Probst [281].

Fig. 95

²⁷Al(α,x)²⁸Mg reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 96

Yield calculated from the recommended cross sections of the ²⁷Al(α,x)²⁸Mg reaction

^natNi(α,x)⁵⁷Ni reaction

In principle five (α,αxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 1), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁵⁷Ni if high energy α-particle bombardment is performed. The threshold of the ⁵⁸Ni(α,αn)⁵⁷Ni reaction is 12.967 MeV while the reaction with un-clustered particle emission ⁵⁸Ni(α,2p3n)⁵⁷Ni can start at 43.104 MeV.

A total of 10 cross section data sets, covering the energy range from threshold up to 170 MeV, were found in literature and are displayed in Fig. 97: Tanaka [291], Houck [292], Blann [293], Muramatsu [294], Michel [153], Levkovskii [130], Takacs [295], Singh [296], Uddin [297], Takacs [298]. Two datasets in the rising part of the excitation function (Blann 1964 and Levkovskii 1991) are too low and were multiplied by a factor of 2. The set of Singh 2005 is considered to be too high near the maximum and is deleted as is the too low point of Muramatsu 1978 (at 36.8 MeV).

Fig. 97

^natNi(α,x)⁵⁷Ni reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of 9 publications were selected and fitted up to 150 MeV (Fig. 98). The increase of the excitation function above 50 MeV is due to the start of reactions with single particle emissions. The two TENDL predictions confirm the double region excitation function but are energy-shifted and oppositely describe the relative importance of clustered and single particle emissions.

Fig. 98

^natNi(α,x)⁵⁷Ni reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The integral yields calculated from the recommended cross sections are shown in Fig. 111. A single experimental yield data point is available: Paul [289].

^natNi(α,x)⁵⁷Co reaction

In principle five (α,αpxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 0), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 2), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁵⁷Co (T_1/2 = 271.74 d) if high energy α-particle bombardment is performed. The threshold for the ⁵⁸Ni(α,αp)⁵⁷Co reaction is 8.172 MeV. Depending on the cooling time before measurement contribution of the shorter-lived ⁵⁷Ni (T_1/2 = 35.60 h), formed by (α,xn) reactions with as lowest threshold 12.967 MeV, can contribute (see previous section).

A total of 10 cross section data sets, covering the energy range from threshold up to 145 MeV, were found in literature and are displayed in Fig. 99: Tanaka [291], Houck [292], Blann [293], Muramatsu [294], Michel [153], Capurro [299], Levkovskii [130], Paul [289], Takacs [295], Uddin [297].

Fig. 99

^natNi(α,x)⁵⁷Co reaction: all experimental data and the TENDL theoretical excitation functions

The two outlying data sets of Muramatsu 1978 and Paul 1995 were deselected. To be in acceptable agreement with the other data the set of Levkovskii 1991 was multiplied by a factor of two while the set of Blann 1964 was energy shifted. The too high data points at 17 MeV of Michel 1983 and Capurro 1990 were deleted.

The original and corrected datasets of 8 publications were selected and fitted up to 150 MeV (Fig. 100). The increase of the excitation function above 50 MeV is due to the reactions with single particle emissions.

Fig. 100

^natNi(α,x)⁵⁷Co reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

As already remarked in the previous section the two TENDL predictions confirm the double region excitation function but are energy-shifted and oppositely describe the relative importance of clustered and single particle emissions. The integral yields calculated from the recommended cross sections are shown in Fig. 111. A single experimental yield data point is available: Paul [289].

^natNi(α,x)⁶⁰Cu reaction

In principle five (α,pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 1), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 3), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁶⁰Cu if high energy α-particle bombardment is performed. The threshold of the ⁵⁸Ni(α,pn)⁶⁰Cu reaction is 15.730 MeV while the reaction with clustered particle emission ⁵⁸Ni(α,d)⁶⁰cu can start at 13.369 MeV. Depending on the cooling time before measurement contribution of the shorter-lived ⁶⁰Zn (T_1/2 = 2.38 min), formed by ^natNi(α,xn) reactions with as lowest threshold 20.988 MeV, can contribute.

A total of 8 cross section data sets, covering the energy range from threshold up to 50 MeV, were found in literature and are displayed in Fig. 101: Tanaka ser 1–2 [291], Muramatsu [294], Levkovskii [130], Takacs [295], Yadav [300], Uddin [301], Takacs [298]. The three outlying and energy-shifted sets of Tanaka 1960 ser1, Levkovskii 1991 and.Yadav 2008 (all obtained on ⁵⁸Ni targets but published results normalized to ^natNi) were deselected. The values in Uddin 2018 are too low and were multiplied by a factor of 1.3. The original and corrected datasets of 4 publications were selected up to 50 MeV and fitted (Fig. 102). Both TENDL predictions are representing well the overall excitation function. The integral yields calculated from the recommended cross sections are shown in Fig. 111. A single experimental yield data is available: Muramatsu [294].

Fig. 101

^natNi(α,x)⁶⁰Cu reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 102

^natNi(α,x)⁶⁰Cu reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(α,x)⁶¹Cu reaction

As in 2020 updated abundances for the different γ-lines emitted in the decay of ⁶¹Cu were adopted in NUDAT3.0 (see Table 2) nearly all data sets published before 2020 had to be attentively checked and corrections for used absolute abundances or ratios made. Moreover, new relative intensity values for the 656.008 keV line were found in a well-documented study published by Bleuel [174]. However, the ratio of the 656.008 keV (10.4%) to 282.956 keV (12.7%) intensities used in the present evaluation (ratio 0.820 (140), see Table 3) only differs by 3% from the proposed Bleuel 2021 data (ratio 0.793 (10)). On the other side practically in all compiled work, the cross section data were corrected by using the 282.956 keV line, when it was possible. Possible additional corrections for a new update of ENSDF accepted absolute abundance will hence be well within the 10–12% uncertainties on the used experimental data and the change in fit and recommended values will be small.

In principle five (α,pxn) reactions on the stable target isotopes ⁵⁸Ni (abundance 68.077% in ^natNi, x = 0), ⁶⁰Ni (abundance 26.223% in ^natNi, n = 2), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁵⁷Ni if high energy α-particle bombardment is performed. The threshold of the ⁵⁸Ni(α,p)⁶¹Cu reaction is 3.300 MeV while the reaction with clustered particle emission ⁶⁰Ni(α,³H)⁶¹Cu can start at 15.903 MeV. As the half-life of the parent ⁶¹Zn (T_1/2 = 89.1 s) is very short and is formed by the ⁵⁸Ni(α,n)⁶¹Cu reaction with a positive Q-value of 3.364 MeV, probably always cumulative formation of ⁶¹Cu will be measured. All measured cross sections have hence to be assumed as for ⁶¹Cu(cum).

A total of 13 cross section data sets, covering the energy range from threshold up to 170 MeV, were found in the literature and are displayed in Fig. 103:

Fig. 103

^natNi(α,x)⁶¹Cu reaction: all experimental data and the TENDL theoretical excitation functions

Cumming [302], McGowan [303], Vlieks [304], Rios [305], Muramatsu [294], Michel [153], Levkovskii [130], Antropov [115], Takacs [295], Singh [296], Yadav [300], Uddin [301], Takacs [298].

The outlying data sets of Cumming 1959, Muramatsu 1978, Antropov 1985, Levkovskii 1991, and Singh 2005 were deselected. The original datasets of the remaining 8 publications were selected and fitted up to 100 MeV (Fig. 104).

Fig. 104

^natNi(α,x)⁶¹Cu reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The two TENDL predictions describe well the overall shape of the excitation function but are energy-shifted and give too low maximal values. The integral yields calculated from the recommended cross sections are shown in Fig. 111. Three experimental yield data are available: Muramatsu [294], Abe [84] and Paul [289].

^natNi(α,x)⁶²Zn reaction

In principle four (α,xn) reactions on the stable target isotopes⁶⁰Ni (abundance 26.223% in ^natNi, n = 2), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of ⁶²Zn if high energy α-particle bombardment is performed. The threshold of the ⁶⁰Ni(α,2n)⁶²Zn reaction is 18.031 MeV.

A total of 12 cross section data sets, covering the energy range from threshold up to 122 MeV, were found in the literature and are displayed in Fig. 105: Ghoshal [306], Tanaka [291], Neirinckx [307], Muramatsu [294], Michel [153], Levkovskii [130], Paul [289], Takacs [295], Singh [296], Yadav [300], Uddin [297], Takacs [298]. The outlying sets of Ghoshal 1950, Muramatsu 1978 and Singh 2005 were deleted.

Fig. 105

^natNi(α,x)⁶²Zn reaction: all experimental data and the TENDL theoretical excitation functions

As the data of Neirinckx 1977 follow the shape of the excitation function but are energy shifted a linearly decreasing positive correction was applied (highest energy point at 31.9 MeV maintained). Data points at specific energies were deleted in two sets: Michel 1983 (at 16.96 and 29.02 MeV) and Takács 2020 (at 50.5 MeV). The original and corrected datasets of the remaining 9 publications were selected and fitted up to 120 MeV (Fig. 106). The TENDL predictions describe well the overall shape of the excitation function but are energy-shifted and give a too low maximum value. The integral yields calculated from the recommended cross sections are shown in Fig. 111. Two experimental yield data are available: Neirinckx [307], Paul [289].

Fig. 106

^natNi(α,x)⁶²Zn reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(α,x)⁶³Zn reaction

In principle four (α,xn) reactions on the stable targets ⁶⁰Ni (abundance 26.223% in ^natNi, n = 1), ⁶¹Ni (abundance 1.1399% in ^natNi), ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to direct formation of short-lived ⁶³Zn if high energy α-particle bombardment is performed. The threshold of the ⁶⁰Ni(α,n)⁶³Zn reaction is 8.374 MeV.

A total of 9 cross section data sets, covering the energy range from threshold up to 51 MeV, were found in the literature and are displayed in Fig. 107: Ghoshal [306], Cumming [302], Tanaka [291], Stelson [308], Muramatsu [294], Levkovskii [130], Takacs [295], Uddin [297], Takacs [298].

Fig. 107

^natNi(α,x)⁶³Zn reaction: all experimental data and the TENDL theoretical excitation functions

As the overall shape of the excitation function is acceptable but the cross section values near the maximum at 18 MeV are too low for three sets a correction was performed before selection: Muramatsu 1978 (is multiplied by a factor of 1.3), Levkovskii 1991 (multiplied by a factor of 2) and Uddin 2017 (multiplied by a factor of 1.3). Additionally, some outlying data points at specific energies were deleted: Goshal 1950 (at 12.6 and 15.4 MeV) and Levkovskii 1991 (at 7.4, 8.9 and 10.4 MeV). The original and corrected datasets of the 9 publications were selected up to 51 MeV and fitted (Fig. 108). The two TENDL predictions describe properly the overall shape of the excitation function but are energy-shifted and give too low maximal values. The integral yields calculated from the recommended cross sections are shown in Fig. 111. No experimental yield data are available.

Fig. 108

^natNi(α,x)⁶³Zn reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natNi(α,x)⁶⁵Zn reaction

Only two (α,xn) reactions on the stable target isotopes ⁶²Ni (abundance 3.6346% in ^natNi), ⁶⁴Ni (abundance 0.9255% in ^natNi) can contribute to the direct formation of long-lived ⁶⁵Zn if α-particle bombardment is performed. The threshold of the ⁶²Ni(α,n)⁶⁵Zn reaction is 6.850 MeV while the reaction on very low abundance ⁶⁴Ni can start at 24.240 MeV.

A total of 8 cross section data sets, covering the energy range from threshold up to 88 MeV, were found in the literature and are displayed in Fig. 109: Tanaka [291], Stelson [308], Muramatsu [294], Zyskind [309], Michel [153], Levkovskii [130], Takacs [295], Uddin [297].

Fig. 109

^natNi(α,x)⁶⁵Zn reaction: all experimental data and the TENDL theoretical excitation functions

The energy shifted and too low set of Levkovskii 1991 was deselected. The 5 data points of Muramatsu 1978 between 9 and 22.5 MeV were deleted. The original and corrected datasets of 7 publications, showing the contribution of the two reactions in separate energy domains, were selected up to 88 MeV and fitted (Fig. 110). The TENDL 2023 predictions agree well with the overall shape and values. The TENDL 2021 description is acceptable up to 25 MeV, but the prediction of the higher energy part is too sharp and overestimated. The integral yields calculated from the recommended cross sections are shown in Fig. 111. No experimental yield data are available.

Fig. 110

^natNi(α,x)⁶⁵Zn reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 111

Yield calculated from the recommended cross sections of the ^natNi(α,x)⁵⁷Ni, ^natNi(α,x)⁵⁷Co, ^natNi(α,x)⁶⁰Cu, ^natNi(α,x)⁶¹Cu, ^natNi(α,x)⁶²Zn, ^natNi(α,x)⁶³Zn and ^natNi(α,x)⁶⁵Zn reactions

^natMo(α,xn)⁹⁵Ru reaction

In principle seven (α,xn) reactions on the stable target isotopes ⁹²Mo (abundance 14.53% in ^natMo, n = 1), ⁹⁴Mo (abundance 9.15% in ^natMo, n = 3), ⁹⁵Mo (abundance 15.84% in ^natMo, n = 4), ⁹⁶Mo (abundance 16.67% in ^nat Mo, n = 5), ⁹⁷Mo (abundance 9.60% in ^nat Mo), ⁹⁸Mo (abundance 24.39% in ^nat Mo), ¹⁰⁰Mo (abundance 9.82% in ^nat Mo, n = 9) can contribute to formation of ⁹⁵Ru if high energy α-particle bombardment is performed.

The threshold for the ⁹²Mo(α,n)⁹⁵Ru reaction is 9.321 MeV, for the ⁹⁴Mo(α,3n)⁹⁵Ru reaction it is 27.682 MeV and it rises to 75.321 MeV for the ¹⁰⁰Mo(α,9n)⁹⁵Ru reaction.

A total of 8 cross section data sets, covering the energy range from threshold up to 40 MeV, were found in literature and are displayed in Fig. 112: Esterlund [310], Graf [311], Levkovskii [130], Denzler [312], Rapp [313], Ditroi [314], Tarkanyi [315], Choudhary [316]. All datasets were selected, showing the single contribution of the ⁹²Mo(α,n)⁹⁵Ru reaction up to 28 MeV, and fitted (Fig. 113). The TENDL predictions agree well with the shape and cross sections values of the experimental excitation function. The integral yields calculated from the recommended cross sections are shown in Fig. 118. A single experimental yield data point is available: Abe [84].

Fig. 112

^natMo(α,xn)⁹⁵Ru reaction: all experimental data and the TENDL theoretical excitation function

Fig. 113

^natMo(α,xn)⁹⁵Ru reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

^natMo(α,xn)^96gTc (m +) reaction

In principle six (α,pxn) reactions on the stable target isotopes ⁹⁴Mo (abundance 9.15% in ^natMo, n = 1), ⁹⁵Mo (abundance 15.84% in ^natMo, n = 2), ⁹⁶Mo (abundance 16.67% in ^nat Mo, n = 3), ⁹⁷Mo (abundance 9.60% in ^nat Mo), ⁹⁸Mo (abundance 24.39% in ^nat Mo), ¹⁰⁰Mo (abundance 9.82% in ^nat Mo, n = 7) can contribute to the formation of ⁹⁶Tc if high energy α-particle bombardment is performed. The formation of ⁹⁶Tc will always be a cumulative ground state as the short-lived metastable state (T_1/2 = 51.5 min) decays for 98% by IT to ^96gTc.

The threshold for the ⁹⁴Mo(α,pn)⁹⁶Tc reaction is 16.072 MeV, for the ⁹⁵Mo(α,p2n)⁹⁶Tc reaction it is 23.689 MeV (reduced to 14.914 MeV for the clustered emission ⁹⁵Mo(α,³H) reaction) and it rises to 63.739 MeV for the ¹⁰⁰Mo(α,p7n)⁹⁶Tc reaction.

A total of 4 cross section data sets, covering the energy range from threshold up to 67 MeV, were found in literature and are displayed in Fig. 114: Ditroi [314], Tarkanyi [315], Sitarz [317], Choudhary [316]. The outlying datapoint at 20 MeV of Tarkanyi 2017 was deleted. The original and corrected datasets of the 4 publications were selected and fitted up to 70 MeV (Fig. 115).

Fig. 114

^natMo(α,xn)^96gTc m + reaction: all experimental data and the TENDL theoretical excitation functions

Fig. 115

^natMo(α,xn)⁹⁶Tc reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

The TENDL 2023 predictions are higher than the experimental values up to 40 MeV but agree well at higher energies. In the case of TENDL 2021 the values of the ^96gTc m + are surprisingly higher compared to ⁹⁶Tc total, due to the overestimation of the production of the meta state (Fig. 114). The integral yields calculated from the recommended cross sections are shown in Fig. 118. A single experimental yield data point is available: Dmitriev [199].

^natMo(α,xn)⁹⁷Ru reaction

In principle seven (α,xn) reactions on the stable target isotopes ⁹⁴Mo (abundance 9.15% in ^natMo, n = 1), ⁹⁵Mo (abundance 15.84% in ^natMo, n = 2), ⁹⁶Mo (abundance 16.67% in ^nat Mo, n = 3), ⁹⁷Mo (abundance 9.60% in ^nat Mo), ⁹⁸Mo (abundance 24.39% in ^nat Mo), ¹⁰⁰Mo (abundance 9.82% in ^nat Mo, n = 7) can contribute to formation of ⁹⁷Ru if high energy α-particle bombardment is performed.

The threshold for the ⁹⁴Mo(α,n)⁹⁷Ru reaction is 8.218 MeV and it rises to 55.905 MeV for the ¹⁰⁰Mo(α,7n)⁹⁷Ru reaction.

A total of 6 cross section data sets, covering the energy range from threshold up to 67 MeV, were found in the literature and are displayed in Fig. 116: Graf [311], Levkovskii [130], Rapp [313], Ditroi [314], Tarkanyi [315], Sitarz [317], Choudhary [316]. The set of Graf 1974 with too low values was deselected. The two outlying data points of Chaudhary 2022 at 10 and 16 MeV were deleted.

Fig. 116

^natMo(α,xn)⁹⁷Ru reaction: all experimental data and the TENDL theoretical excitation functions

The original and corrected datasets of 6 publications were selected up to 67 MeV and fitted (Fig. 117). The two TENDL predictions show more explicitly the contributions of the reactions on the different stable target isotopes but are from 20 MeV on underestimating the cross section values. The integral yields calculated from the recommended cross sections are shown in Fig. 118. A single experimental yield data point is available: Abe [84].

Fig. 117

^natMo(α,xn)⁹⁷Ru reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 118

Yield calculated from the recommended cross sections of the ^natMo(α,xn)⁹⁵Ru, ^natMo(α,x)⁹⁶Tc and ^natMo(α,xn)⁹⁷Ru reactions

¹⁹⁷Au(α,x)¹⁹⁶Au reaction

Only the ¹⁹⁷Au(α,αn) reaction with a threshold of 8.175 MeV, or the reaction with not clustered emission ¹⁹⁷Au(α,2p3n) with a threshold of 36.83 MeV, contributes to the formation of ¹⁹⁶Au. A total of 11 cross section data sets, covering the energy range from threshold up to 99 MeV, were found in the literature and are displayed in Fig. 119:

Fig. 119

¹⁹⁷Au(α,x)¹⁹⁶Au reaction: all experimental data and the TENDL theoretical excitation functions

Vinciguerra [318], Mukherjee [319], Lanzafame [320], Singh [321], Nagame [208], Chakravarty s1-2 [322], Shah [323], Necheva [324], Kulko [325], Bonesso [326].

The sets of Mukherjee 1995 and Singh 1988 with too low values were deselected. Although the double-peaked set of Bonesso 2017 can be explained by the separate contribution of clustered and not clustered emission, this fact is not confirmed by all the other available data sets. A practical threshold of around 25 MeV is indicated by 10 publications and hence the set of Bonesso 2017 was deselected. The too low data points of Vinciguerra 1966 (last 6 points) and Shah 1995 (last point) were deleted. The original and corrected datasets of 8 publications were selected up to 99 MeV, the energy, and fitted (Fig. 120). The two TENDL predictions show a single peak near 38 MeV and do not correspond to the shape of the experimental excitation function. The integral yields calculated from the recommended cross sections are shown in Fig. 125. No experimental yield data are available.

Fig. 120

¹⁹⁷Au(α,x)¹⁹⁶Au reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

¹⁹⁷Au(α,x)¹⁹⁹Tl reaction

Only the ¹⁹⁷Au(α,2n) reaction with a threshold of 17.01 MeV contributes to the formation of ¹⁹⁹Tl.

A total of 18 cross section data sets, covering the energy range from threshold up to 115 MeV, were found in literature and are displayed in Fig. 121: Van de Vijver [327], Vinciguerra [318], Lanzafame [320], Kurz [328], Nagame [208], Calboreanu [329], Hashimoto [330], Capurro [331], Bhardwaj [332], Singh [321], Mukherjee [319], Shah [323], Necheva [324], Chakravarty [333], Ismail [334], Basunia [335], Kulko [325], Szucs [336].

Fig. 121

¹⁹⁷Au(α,x)¹⁹⁹Tl reaction: all experimental data and the TENDL theoretical excitation functions

The 4 sets with too low values, especially in the rising part of the excitation function, of Van de Vijver 1963, Capurro 1985, Shah 1995 and Necheva 1997 were deselected. The set of Kurz 1971 was energy corrected while the data of Chakravarty 1998 were multiplied by a factor of 2.

The original and corrected datasets of 14 publications were selected and fitted up to 80 MeV (Fig. 122). The TENDL 2021 prediction is in very good agreement with the experimental excitation function while the 2023 version is too low above 30 MeV. The integral yields calculated from the recommended cross sections are shown in Fig. 125. No experimental yield data are available.

Fig. 122

¹⁹⁷Au(α,x)¹⁹⁹Tl reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

¹⁹⁷Au(α,n)²⁰⁰Tl reaction

Only the ¹⁹⁷Au(α,n) reaction with a threshold of 9.86 MeV contributes to the formation of ²⁰⁰Tl. A total of 18 cross section data sets, covering the energy range from threshold up to 80 MeV, were found in the literature and are displayed in Fig. 123: Van de Vijver [327], Vinciguerra [318], Lanzafame [320], Kurz [328], Nagame [208], Calboreanu [329], Capurro [331], Bhardwaj [332]. Singh [321], Mukherjee [319], Shah [323], Necheva [324], Chakravarty [333], Ismail [334], Basunia [335], Kulko [325], Sharma [337], Szucs [336].

Fig. 123

¹⁹⁷Au(α,x)²⁰⁰Tl reaction: all experimental data and the TENDL theoretical excitation functions

The 8 sets giving maximal cross section values under 25 mb were deselected: Van de Vijver 1963, Vinciguerra 1966, Kurz 1971, Capurro 1985, Singh 1988, Ismai 1988, Shah 1995, Necheva 1997.

All data points in the remaining 10 publications were selected up to 80 MeV and fitted (Fig. 124). The two TENDL predictions represent well the overall shape of the excitation function but TENDL 2021 gives significantly higher cross sections. The integral yields calculated from the recommended cross sections are shown in Fig. 125. No experimental yield data are available.

Fig. 124

¹⁹⁷Au(α,x)²⁰⁰Tl reaction: selected experimental works and Padé fit (solid line) with total derived uncertainties, including 4% systematic uncertainty (dashed line, right-hand scale)

Fig. 125

Yield calculated from the recommended cross sections of the ¹⁹⁷Au(α,x)¹⁹⁶Au, ¹⁹⁷Au(α,x)¹⁹⁹Tl and ¹⁹⁷Au(α,x)²⁰⁰Tl reactions

Summary and conclusions

Evaluations of production cross sections and their uncertainties were performed on sixty reactions for charged particle beam monitor reactions on C, Al, Ti, Fe, Ni, Cu, Nb, Mo and Au targets. The experimental data in some cases show large disagreements and were selected based on many factors, not only statistically. In such a way the reliability of the recommended data is different for different reactions and the obtained uncertainties refer only to the selected data. Despite this, the deduced recommended data will be useful for different applications. Validation of the recommended data with properly made integral measurements would be very useful. The collected experimental data were compared with the theoretical predictions found in the TENDL-2021 and 2023 libraries, but still, in some cases, significant disagreements in the magnitude and shape of the resulting excitation functions exist (especially when considering isomeric states or deuteron-induced reactions).

A Padé fitting method was applied to the selected datasets, and uncertainties for all recommended cross-section data were deduced. The recommended cross-section data have been used to determine integral yields for practical radionuclide production. In the literature, only very few experimental data and intercomparison exist to validate the recommended cross section data. The recommended cross section data and the deduced integral yields may also be useful in other fields of non-energy related nuclear studies (e.g., accelerator technology, activation analysis and thin layer activation) and further development of the theory of nuclear reactions.