^natPd(n,x)¹¹¹Ag reaction

Natural palladium was irradiated in a nuclear reactor [21, 22]. The ¹¹¹Ag activity concentration in the irradiated target was determined using Eq. (1): $A=\frac{N_{\text{net}}}{I_{\gamma } t}$ (1) where A is the activity concentration of ¹¹¹Ag by Becquerel (disintegration per second), N_net is the net area under the peak of 695 keV, while ε the absolute efficiency of the detector at the given gamma energy, I_γ is the branching ratio (7.1%) of the given gamma energy, and t is the measurement time. The quantity of produced stable ¹⁰⁹Ag isotope (μg) may be calculated by using the Avogadro number to estimate the number of radionuclides (N) in ¹⁰⁹Pd by knowing its activity (A) measured by Eq. (1) at a gamma energy peak of 88 keV, which has a branching ratio (I_γ) of 3.6%. Because both activity A and the half-life of ¹⁰⁹Pd (13.7 h) are known, equation (2) can be used to determine the number of radionuclides for ¹⁰⁹Pd. $N=\frac{A}{\lambda }$ (2) where λ is the decay constant. The mass of 109Ag (g) was calculated using Eq.(3). $m \left(\text{g}\right)=\frac{109}{N_{\text{A}}}\times N,$ (3) where N_A is the Avogadro's number.

^natPd(d,x)¹¹¹Ag reaction

Excitation functions were accomplished by stacked-foil activation on natural palladium by deutron-induced reactions in medium-energy cyclotron [23-25] using a small beam current, after which the irradiated targets were measured by high-resolution gamma-ray spectroscopy. The cross-sections of ^{103, 104, 105, 106m, 110m, 111}Ag were calculated using the standard activation Eq. (4). $\sigma =\frac{T_{\gamma }}{{\epsilon }_d{\epsilon }_{\gamma }{\epsilon }_t{N}_t{N}_b\left(1-e^{-t_b}\right)e^{-t_c}\left(1-e^{-t_m}\right)}$ (4) where N_t is the surface density of the target atoms, N_b is the number of bombarding particles per unit time, T_γ is the photo-peak number count, ε_d is the efficiency of the detector, ε_γ is the gamma-ray intensity, ε_t is the dead time of measurement, which is the ratio of live time to real time, λ is the decay constant, t_b is the time of irradiation, t_c is the time of cooling, and t_m is the time of acquisition.

The data obtained from cross-section reactions play a very important role in the production of radionuclides by cyclotrons, as described earlier [38, 39]. In order to be able to determine the yield with a good accuracy, one needs to know the full excitation functions. Therefore, the estimated yield of a product within a certain energy range, that is, the target thickness, may be determined using Eq. (5): $Y=\frac{N_{\text{A}}H}{M}I(1-e^{-\lambda t}){{\displaystyle {\int }_{E1}^{E2}\left[\frac{\text{d}E}{\text{d}(\rho x)}\right]}}^{\text{'}-1}\sigma (E)\text{d}E$ (5) where Y is the yield of the activity concentration of the product by Becquerel, H is the enrichment (or isotopic abundance) of the target nuclide, M is the mass number of the target element, σ(E) is the cross section within a certain energy range, ρ is the density of the target material, and x is the projectile distance travelled through the target material.

Photonuclear reactions

Experimental photonuclear reaction data are typically collected by directly recording the number of particles released or by measuring the residual nuclear activity. In the case of energies that exceed the multi-particle emission threshold, more than one combination of emitted light particles may associate the same number of neutrons produced or may contribute to the same residual nucleus. The experimental data collection recorded for the (γ, n) cross-section may contain charged particles released at the same time as a single neutron emission, that is, (γ, 1n)+(γ, 1np)+(γ, n2p)….etc., which depend on the incident photon energy. Continuous bremsstrahlung spectra are generated by impacting the target with an electron beam from the accelerator (initially betatrons and synchrotrons, and now, linear accelerators). The photon energy spectrum is continuous, and the yield of the reaction Y(E_o) can be measured as in equation (6): [28] $Y\left(E_{\text{o}}\right)=N_R{\displaystyle {\int }_{E_{\text{th}}}^{E_0}\frac{\sigma \left(E_{\gamma }\right)}{E_{\gamma }}W\left(E_0{E}_{\gamma }\right)\text{d}{E}_{\gamma }},$ (6) where E_γ is the photon energy, σ(E_γ) is the reaction cross-section, W is the bremsstrahlung energy-dependent photon flux, E₀ is the endpoint energy of the bremsstrahlung spectrum relative to the electron beam energy, is the threshold energy, and N_R is the standardized coefficient. Adjusting the E₀ by simple changes allows the measurement of the yield curve, and then the use of the "unfolding" technique achieves a cross section for the photonuclear reaction. The benefit of bremsstrahlung measurements is the high photon beam intensity, which introduces the possibility of achieving sufficient statistics even with very limited cross-section reactions. However, this technique has many challenges [28]. It is necessary to know more regarding the bremsstrahlung spectrum for all electron energies. Then, γ- analysis of the residual nucleus is performed after irradiation of the target by bremsstrahlung  at varying endpoint energies [28-30]. From the γ-lines, the photo nuclear reaction cross-sections were calculated. The photon charged particle reaction cross sections, σ(γ, p) and σ(γ, α), respectively, are insufficient and limited in the literature, and do not contain photon fission reactions.

2.3.1

natCd(γ,x)111Ag reaction

The RM-55 microtron (55 MeV) was used for the irradiation experiments, as illustrated in Fig. 1. A tungsten braking converter (2.2 mm tungsten thickness) was used to generate bremsstrahlung radiation. The CdO target powder occupied an area of 6.3 cm² [28]. The cadmium target was placed directly behind the braking target. The gamma radiation dose was monitored with the aid of a Faraday cylinder. The target is irradiated for a known duration and then transported for gamma-ray spectrum measurement by the Hp-Ge detector. The reaction yield (Y) was calculated using the following Eq. (7): $Y=\frac{S_{\gamma }}{{\epsilon }_{\gamma }{I}_{\gamma }\left(1-e^{-t_1}\right)e^{-t_2}\left(1-e^{-t_3}\right)}$ (7) where S_γ is the count rate of gamma rays under the peak, ε_γ is the efficiency of the gamma-ray detector at the specific energy, λ is the decay constant of a radionuclide produced, I_γ is the branching ratio of gamma rays for the radionuclide produced by that specific energy, t₁, t₂, t₃ are the irradiation, cooling, and the measurement times, respectivley.

Fig. 1Full-screen View

Photodisintegration of natural cadmium [28]

2.3.2

natIn(γ,x)111Ag reaction

The following equation governs the activity A(t) of a produced radioisotope when a target is irradiated in a nuclear radiation flux: [40]: $A\left(t\right)=R\left(1-e^{-\lambda t}\right),$ (8) where R is the rate of nuclear interaction and can be expressed by Eq. (9), where λ is the decay constant of the radionuclide formed. $R=N{\text{ σ}}_{\text{eff}} \varphi ,$ (9) N is the number of atoms in the target for a given nuclide, as calculated by equation (10), σ_eff denotes the effective cross section of the reaction, and φ represents the radiation flux. $N=\frac{a m N_{\text{A}}}{M}$ (10) where $a$ and $M$ are the abundance and atomic mass of the nuclide, $m$ is the mass of the element in the target.

The analysis assumes that a natural indium target is exposed to a bremsstrahlung radiation beam produced by an electron accelerator at the energy distributions provided in Ref. [41], particularly at the endpoint energy of 24 MeV for the production of ¹¹¹Ag through the (γ, α) reaction. Indium has two naturally occurring stable isotopes, ¹¹³In and ¹¹⁵In, with natural abundances of 0.0429 and 0.9571, respectively. As a consequence of the (γ, α) reaction, the undesirable stable ¹⁰⁹Ag is produced alongside the radioisotope ¹¹¹Ag. The ¹⁰⁹Ag production is based on the abundance of ¹¹³In on the natural indium target. Figure 2 illustrates the (γ, α) reaction cross-sections of the two isotopes, and the threshold energy for both nuclides is approximately 10 MeV. The effective cross section can be calculated as follows: ${\sigma }_{\text{eff}}=\frac{{{\displaystyle \int }}_{10 \text{MeV}}^{24 \text{MeV}}\sigma \left(E\right) \varphi \left(E\right)\text{d}E}{{{\displaystyle \int }}_{10 \text{MeV}}^{24 \text{MeV}}\varphi \left(E\right)\text{d}E}$ (11) where σ(E) represents the reaction cross-section of energy E, and φ(E) represents the energy-dependent flux. In this case, the bremsstrahlung radiation was calculated using the following equation: $\varphi ={\displaystyle {\int }_{10 \text{MeV}}^{24 \text{MeV}}\varphi \left(E\right)\text{d}E.}$ (12)

Fig. 2Full-screen View

(γ,α) reaction cross sections of In-113 and In-115 ［www-nds.iaea.org］.

Production of ¹¹¹Ag by ^natPd(n,x) reactions

Palladium involves six stable isotopes of natural abundance; therefore, different radionuclides are produced by their activation using thermal neutrons in the nuclear reactor, as shown in Scheme 1. Activation of natural palladium targets by thermal neutrons produced ^111,111mPd as an intermediate radionuclide, as shown in the first nuclear reaction pathway. Nuclear data were obtained from literature data [42-46]. Scheme 1 shows that ¹¹¹Ag can be produced by pathway (1) accompanied by ¹⁰³Pd and ¹⁰⁹Pd. In the case of ¹⁰³Pd, which decayed to ¹⁰³Rh by electron capture and could easily be separated by chemical methods. However, the parallel reaction for the production of ¹¹¹Ag using natural palladium is the neutron capture of ¹⁰⁸Pd to form ¹⁰⁹Pd, which eventually decays by β^- emission into stable ¹⁰⁹Ag.  This reaction also limits the final specific activity of ¹¹¹Ag due to the high concentration of ¹⁰⁹Ag. Therefore, ¹¹¹Ag is produced as a carrier, according to the data provided in Table 3 [21, 47]. An increase in the irradiation time from 24h to 960h contributes to a decrease in the specific activity of ¹¹¹Ag from 90 to 24 GBq/mg due to an increase in ¹⁰⁹Ag resulting from the decay of the high ¹⁰⁹Pd activity level based on a high natural abundance of ¹⁰⁸Pd (26.46%) and a high neutron cross-section reaction (8.68 b). According to Alberto et al., 1992 [21], the average yield of ¹⁰⁹Pd is 1630 MBq at 3×10¹³ n cm^-2 s^-1 of neutron flux for 26 h of irradiation time, followed by 72 h of cooling to produce 100 MBq of ¹¹¹Ag (1μg of Ag). The specific activity of ¹¹¹Ag was enhanced by decreasing the amount of ¹⁰⁹Ag, which could be accomplished by decreasing the cooling time and rapid chemical separation of ¹¹¹Ag from ¹⁰⁹Pd after EOB. However, the enriched ¹¹⁰Pd could be used instead of the natural palladium to achieve a high specific activity for the production of ¹¹¹Ag carrier-free. However, this type of nuclear reaction is not preferred because of the high target price.

Scheme 1Full-screen View

Irradiation scheme of natural palladium target by thermal neutrons for the production of ¹¹¹Ag radionuclide

Production of ¹¹¹Ag by ^natPd(d, x) reactions

There are two long-lived states of the ¹¹¹Ag radioisotope: the ground state (t_1/2 = 7.45 d) and the excited state of ^111mAg (t_1/2 = 64.8 s), which decays to ^111gAg by IT (99.3%). Excitation studies have been performed to determine the potential to produce ¹¹¹ Ag (theranostic applications) using deuteron-induced reactions on ^natPd [23, 25, 48-51]. The meta-stable and ground-state of ¹¹¹Ag is occupied by the beta-decay of meta-stable and ground-state of ¹¹¹Pd (t_1/2= 5.5 h and 23.4 min, respectively. Experimental excitation functions have been studied using deuteron-induced reactions on natural palladium [23, 25], which have encountered difficulties in ¹¹¹Ag production with high purity due to a variety of nuclear reactions that are synchronized with the main reaction (d,n), as shown in Table 4. Side nuclear reactions depend on the projectile energy (deuteron energy) to reach the reaction threshold energy and the abundance of each isotope. Table 4 reveals that ¹¹¹Ag production uses a ^natPd(d,x) reaction based on a ¹¹⁰Pd(d,n) reaction as a direct nuclear reaction. However, there are parallel reactions to ^{106m,105,104,103}Ag production that also consume the products of the ¹⁰⁵Pd(d,n), ¹⁰⁴Pd(d,n), ¹⁰³Pd(d,n), and ¹⁰²Pd(d,n) reactions, respectively. ^104,103Ag does not pose a problem because of their short half-lives and decay by electron capture and positron emission to yield stable ¹⁰⁴Pd and ¹⁰³Rh isotopes, which can be easily separated by chemical methods. The experimental cross-section data for ^{105,106m,110m,111}Ag indicated the presence of their cross sections with high values within the deuteron energy range of 5–25 MeV [25, 51]. Half-lives of ^110mAg, ^106mAg and ¹⁰⁵Ag are longer than the ¹¹¹Ag half-life and are thus difficult to separate chemically. In the literature, experimental data for integral physical yields are rare and have only been found in Ditroi et al., 2012 [23], as shown in Fig. 3.

Fig. 3Full-screen View

Integral yields for the ^nat.Pd(d,xn)^{111,110m,106m,105,104,103}Ag reactions [23]

Furthermore, as shown in Table 5, ¹¹¹Ag can be produced indirectly via ^natPd(d, x) on the basis of a ¹¹⁰Pd(d, p) reaction to produce ¹¹¹Pd, which decays by beta-emission to ¹¹¹Ag. The deutreon-induced reaction for ¹⁰⁸Pd via (d, p) produces ¹⁰⁹Pd, which decays by beta emission to stable ¹⁰⁹Ag, reducing the specific activity of ¹¹¹Ag. Although the cross-section values for the production of ¹⁰⁹Pd via ^natPd (d, p) are high [23], there is no documented existence of ¹⁰⁹Ag in the literature.

Production of ¹¹¹Ag based on ^natCd(γ,x) reactions

Figure 4 indicates that the maximum cross sections of (γ, n) and (γ, p) reactions on natural cadmium within the gamma energy range of 15–20 MeV are 200–250 mb [52]. Table 6 provides the threshold energies for various photon reactions to cadmium isotopes, which clarified that both (γ, n) and (γ, p) reactions begin within the energy range of 7–11 MeV, whereas the photon energy produced and required for the reaction to occur is within the range of 15–20 MeV, which is greater than the threshold energies for these reactions. Therefore, the generated γ-ray energy was able to produce all the radionuclides established in Table 6 [28, 30, 53-54], as verified by the relative yield measurements for these radionuclides [28]. ¹¹¹Ag is difficult to produce through ^natCd(γ, x) reactions because of simultaneous nuclear reactions that produce ^{105, 107, 109, 110m, 112, 113, 115}Ag based on the direct reactions (γ, p) cadmium isotopes at the same γ-energy used. In contrast, there are parallel reactions based on indirect reactions such as ¹⁰⁸Cd(γ, n) and ¹¹⁰Cd(γ, n) which produce ¹⁰⁷Cd and ¹⁰⁹Cd. These two isotopes which decay by electron capture to ¹⁰⁷Ag and ¹⁰⁹Ag stable isotopes. These two Ag isotopes decrease the specific activity of ¹¹¹Ag. The literature has not definitively indicated the presence of silver isotopes, whether long-lived radioactive, such as ¹⁰⁵Ag, ^110mAg, or stable silver isotopes such as ¹⁰⁷Ag and ¹⁰⁹Ag, and concentrations can influence the specific activity of ¹¹¹Ag.

Fig. 4Full-screen View

Bremsstrahlung gamma-ray spectrum as in the solid curve and cross-section ［σ(γ, x)= σ(γ, n)+ σ(γ, p) +...］ (the dashed curve) for the reaction of the natural cadmium target according to data obtained from [40]

Production of ¹¹¹Ag based on ^natIn(γ,x) reactions

Table 7 indicates that ¹¹¹Ag may be produced by the ^natIn(γ, x) based on the ¹¹⁵In(γ, α) reaction when the photon energy is greater than the sum of the two energies of the threshold and the Coulomb barrier (14.1 MeV). Other channels, such as the (γ, n) and (γ, p) reactions, are opened at threshold energies of 9 and 6.8 MeV, respectively, less than that required for the (γ, α) reaction, to produce ^114mIn (t_1/2= 49.51 d) and the stable ¹¹⁴Cd isotope, which can be easily separated by chemical methods. Parallel nuclear reactions produce a stable isotope of ¹⁰⁹Ag, a radionuclide of ^112mIn (t_1/2= 20.56 min) and a stable isotope of ¹¹²Cd, based on the reactions of ¹¹³In(γ, α), (γ, n), and (γ, p), respectively. Fortunately, ¹¹³In has a small abundance (4.3%) compared to ¹¹⁵In (95.7%), so the ¹⁰⁹Ag concentration produced will not be a concern, as in other nuclear reactions.

Figure 5 shows the energy distributions of bremsstrahlung radiation, as quoted in the energy range of interest. The integrations in Eq. (5) for the effective cross section of ¹¹³In and ¹¹⁵In were calculated using the data in Figs. 4 and 5 (0.00532 and 0.00432 barns, respectively). In addition, the bremsstrahlung radiation flux in the range of concern was assessed, producing 10.37% of the overall bremsstrahlung radiation, as summarized in Table 8.

Fig. 5Full-screen View

Distributions of bremsstrahlung radiation in the range from 10 to 24 MeV

The bremsstrahlung photon flux in the range of interest will be 5.7 × 10¹³ cm^-2 s^-1 if the electron accelerator is set to 10 μA [40, 41]. Substituting the evaluated results in equation (2), the interaction rates for both nuclides per gram of target (6.94 × 10⁷ and 1.24 × 10⁹ s^-1, respectively) are calculated, as shown in Table 8. Since the (γ,α) reactions of ¹¹³In and ¹¹⁵In produce 109Ag and ¹¹¹Ag, respectively, the rate of ¹⁰⁹Ag production to the rate of ¹¹¹Ag production is approximately 1:18. The generated activity of ¹¹¹Ag was calculated as a function of irradiation time by substituting the interaction rate of ¹¹⁵In in equation (1), as shown in Fig. 6.

Fig. 6Full-screen View

The generated activity of Ag-111 as a result of irradiating 1 g of natural indium metal in electron accelerator operated at 10 μA