Influence of enriched 100Mo on Mo reaction yields

In accelerator-driven 99Mo/99mTc production, the 100Mo enrichment level should be chosen carefully as it greatly affects the yields of the involved Mo reactions. To facilitate selecting the 100Mo enrichment level, we defined a figure of merit called density change coefficient and developed its calculation program. Density change coefficients calculated for nine commercial enriched 100Mo products are presented and their use in selecting the 100Mo enrichment level is discussed.


Introduction
Technetium-99 m ( 99m Tc), arguably the most widely used gamma emitter in nuclear medicine, is obtained via the negatron decay of its precursor, molybdenum-99 ( 99 Mo). Most of this precursor nuclide is produced via the fission reaction 235 U(n,f) 99 Mo in research reactors. All but one of the major reactors, however, have only about 10 years left until the end of operation (figure 1), resulting in an increasingly unstable 99 Mo supply chain; there have been a number of 99 Mo supply shortages attributed to the aging of the reactors in the past few decades [1][2][3]. In response to the unstable 99 Mo supply chain, accelerator-based alternative methods of 99 Mo/ 99m Tc production have been explored extensively, including (figure 2): • Production of 99 Mo via the 100 Mo(γ,n) 99 Mo reaction using electron linear accelerators [4][5][6][7][8][9].
In all of the accelerator methods mentioned above, use of enriched 100 Mo is necessary: in the 100 Mo(γ,n) 99 Mo and 100 Mo(n,2n) 99 Mo reaction routes, the use of 99%-enriched 100 Mo can provide approximately tenfold increases in the yield and specific yield of 99 Mo. In the 100 Mo(p,2n) 99m Tc reaction route, the use of >99%-enriched 100 Mo is required to minimize the production of Tc isotopes other than 99m Tc. Such a need for enriched 100 Mo has been known for years, and the minimum required 100 Mo enrichment levels have been reported by a number of researchers [15,18,23,27]. The required 100 Mo enrichment level can be determined by considering (i) the yields of 99 Mo/ 99m Tc, (ii) the yields of impurity nuclides, and (iii) the influence of individual impurity nuclides on the radiation dose and image quality. In order to facilitate selecting the 100 Mo enrichment level, we defined a figure of merit that can be used to evaluate (i) and (ii) above. The theoretical basis, calculation results, and use of the figure of merit are presented.
are used in accelerator production of 99 Mo [2,6,9,11], and the former of which is used in cyclotron production of 99m Tc [2,16,18,21,[23][24][25]27]. We hereafter refer to Mo metal as Mo met to distinguish it from the Mo element. Based on this hierarchy, we examine how the physical quantities of Mo materials and Mo elements are affected by their 100 Mo content.      increased mass fraction of a Mo element means an increase in its mass density, which further increases the 100 Mo mass density and in turn contributes to improving the 100 Mo reaction yields. These cascading effects will be explained in the next subsection.

Density change coefficient
The mass density of 100 Mo can be written as leading to an underestimation. Note, also, that (5) is actually the product of (2) and (6) in which the role of (1) is clearly shown. Under the same conditions, the 100 Mo mass density increment of Mo met will be 0.990 0 0.101 5 0.990 0 1.000 0 10.28 g cm 0.101 5 1.000 0 10.28 g cm 9.754.

Mo 100
Mo 100 The dependence of mass densities of Mo element and 100 Mo on the 100 Mo mass fraction are summarized in   (7) shows that the 100 Mo reaction yields of Mo met are greater than those of MoO 3 regardless of the 100 Mo enrichment level. Next, we examine how the number densities of the hierarchical Mo entities are affected by the 100 Mo mass fraction. The number density of a substance i is related to its mass density by where N A is the Avogadro constant. Inserting (4) into (8), the number density of 100 Mo is written as Mo 100 Mo 100 Mo 100 Mo Mo 100 Mo mat Mo 100 which, in terms of the 100 Mo amount fraction, is equivalent to provided that the Mo material is Mo met or MoO 3 , either of which has x 1 Mo = .

enrimo: A DCC calculation program
Despite the concise forms of the DCC, its calculation can be error-prone and time-consuming. To automate DCC calculations and to facilitate data exchange, we developed a Perl program called enrimo.
The DCC calculation algorithm of enrimo is described in figure 8. As of v1.05, the following conditions can be customized via the command-line options: (i) Mo materials of interest, (ii) the Mo isotope to be enriched (in addition to enriched 100 Mo, enriched 98 Mo can be examined for the 98 Mo(n,γ) 99 Mo reaction route), (iii) the fraction type to refer to the enrichment level, (iv) the range of enrichment levels, (v) the minimum depletion level applied to all of the associated nuclides, and (vi) the order of nuclide depletion in the process of isotopic enrichment. Also, an input file can be used to specify the minimum depletion levels of individual nuclides and the calculation precision.
Once the calculation conditions are specified, enrimo prepares the data necessary for DCC calculations and enters the main module. The core task of the main module is to redistribute the fraction quantities of the Mo isotopes according to the given 100 Mo enrichment level. Based on the redistributed fraction quantities, the molar mass of the Mo material under investigation is recalculated, which in turn is used for the DCC calculation via (13). If the mass fraction has been set to represent the enrichment level, (12) is used instead. Finally, the precision of calculation results are adjusted according to the user specifications, and the product nuclides of photon, neutron, and proton reactions on 92,94-98,100 Mo are associated with the calculated DCCs.
Data files are generated each time a series of calculations for a Mo material is completed. The supported output formats are plain text (.dat); LaTeX tabular environment (.tex); comma-separated values (.csv); More detailed descriptions of enrimo are documented in its source code, which is available in [32].

DCC calculation conditions
Two enriched isotope vendors use gas centrifuges for 100 Mo enrichment [33,34]. When

Results and discussion
The overall dependence of 92,94-98,100 Mo DCCs on the 100 Mo enrichment level is shown in figure 9. In its most basic sense, the DCC of a Mo isotope is the factor by which the amount of the Mo isotope concerned is modified by a change in the 100 Mo enrichment level. Because the amount of a Mo isotope is directly proportional to the yields of the involved Mo reactions, a DCC can be deemed as a scale factor for reaction yields. In other words, a DCC greater than 1.0 means that the yields of the involved reactions will increase, and a DCC less than 1.0 means that the yields of the involved reactions will decrease. DCCs calculated for the nine commercial enriched 100 Mo products are presented in table 2, some of which are also plotted in figure 10 for showing their relative magnitudes. As expected from (1), the 100 Mo DCCs were greater in MoO 3 than in Mo met , meaning that the 100 Mo increment ratio is higher in MoO 3 than in Mo met . As shown in (7), however, it should be noted that the absolute 100 Mo mass density is always greater in Mo met than in MoO 3 by a factor of about 3. On the other hand, the 92,94-98 Mo DCCs were almost the same in the two target materials.
The importance of 92,94-98,100 Mo DCCs differs by the 99 Mo/ 99m Tc production methods. In both the 100 Mo(γ,n) 99 Mo and 100 Mo(n,2n) 99 Mo reaction routes, the major impurity radionuclides are niobium (Nb) radioisotopes produced from 92,94-98 Mo [5,6,9,11]. Because Nb isotopes can be separated from 99 Mo and 99m Tc by chemical means [6,35], the practical importance of 100 Mo enrichment is its influence on the yield and specific yield of 99 (table 3). These Tc impurities, which cannot be chemically separated from 99m Tc, increase radiation dose [15] and result in image quality degradation [20]. Therefore, an enriched 100 Mo product having low 92,94-98 Mo DCCs as well as a high 100 Mo DCC is necessary in the 100 Mo(p,2n) 99m Tc reaction route.
In their studies [15] and [20], Hou et al reported that at proton beam energies below 20 MeV, the contents of [94][95][96][97] Mo contribute more than the content of 98 Mo to the dose increase and image quality degradation. Recent studies by [24,25] figure 10.
The 98 Mo DCC should also be considered if the proton beam energies are greater than 20 MeV, which is the threshold for the 98 Mo(p,3n) 96 Tc and 98 Mo(p,3n) 96m Tc reactions [14,36]. 96m Tc deexcites to 96 Tc with 98% probability [37], and 96 Tc is reported to be one of the major impurities affecting the radiation dose and image quality [15,20,24,25]. Therefore, the 99.815% and 99.86% enriched 100 Mo products, whose 98 Mo DCCs as well Table 3. Product radionuclides (PRNs) associated with proton reactions on 92,94-98,100 Mo. Listed are PRNs whose half-lives are longer than 10 min and shorter than one year, and reactions whose TENDL-2017 [36] peak cross sections below 25 MeV a are greater than 0.1 mb. The decay data were retrieved from NuDat 2.7 [37]. Detailed studies of proton reactions on Mo isotopes can be found in [14,[17][18][19].

Principal decay mode Proton reaction
Half-life Decay product 92 Mo 94 as 92,94-97 Mo DCCs are significantly lower than the other enriched 100 Mo products, are preferable for proton beams of >20 MeV.

Conclusion
A figure of merit called the DCC can quantify the influence of enriched 100 Mo on Mo reaction yields. DCCs can be calculated for various 100 Mo enrichment levels using the dedicated program enrimo.
The main advantage of using DCCs is that the changes in Mo reaction yields resulting from a change in the 100 Mo enrichment level can be easily estimated. For example, the 100 Mo DCC of 99.01% enriched 100 Mo in the form of Mo met is 9.765 8, meaning that 9.765 8 times greater 100 Mo reaction yields can be obtained. Likewise, the [94][95][96][97] Mo DCCs of 97.39% enriched 100 Mo in the form of Mo met , or 0.000 3-0.001, suggest that the 94-97 Mo reaction yields can be reduced by factors of 1000-3333.
In determining the required 100 Mo enrichment level, the 100 Mo DCC alone can be useful in the 100 Mo(γ,n) 99 Mo and 100 Mo(n,2n) 99 Mo reaction routes, where the yield and specific yield of 99 Mo are the primary concerns. In contrast, the 92,94-98 Mo DCCs as well as the 100 Mo DCC need to be considered in the 100 Mo(p,2n) 99m Tc reaction route, where the production of chemically inseparable Tc impurities must be minimized.
Complete DCC data are available as supplementary materials online at stacks.iop.org/JPCO/3/055015/ mmedia. The source code of the DCC calculation program enrimo is available in an open-source repository [32].