Estimation of ⁹⁹Mo production rates from natural molybdenum in research reactors

Molybdenum-99 and its daughter nuclide ^99mTc are of paramount importance in medical diagnostics: the NRG 2014 annual report of the High Flux Reactor in Petten states that there, about 1/4 of the world’s supply is being produced, and that 1000 people per hour are subjected to diagnostics using Petten-produced ⁹⁹Mo, every hour, every day of the year. At the same time, the ⁹⁹Mo supply is at risk because it is being produced at only a few locations, and mostly as a ²³⁵U fission product. This has the advantage of very high ⁹⁹Mo specific activity after the chemical separation from the other fission products, but also the disadvantage of generating large amounts of radioactive waste. Recently, the producers are also hampered by the restricted use of highly-enriched uranium targets as an initial material.

The International Atomic Energy Agency (IAEA) [1, 2] and others [3, 4] propose or consider a more distributed network of ⁹⁹Mo production sites, where it would then be produced through the ⁹⁸Mo(n,γ)⁹⁹Mo reaction. The achievable specific activities are less favourable that way, but the absolute amounts can be amply sufficient for local needs. Subsequently, this would also improve the utilization of national research reactors and would ease the issues associated with international imports [5]. Hot-atom chemistry methods have been developed to separate ⁹⁹Mo from the targeted ⁹⁸Mo atoms to improve the specific activity of the product [6].

In 2012, a feasibility study was perfomed at the Atominstitut in Vienna, involving small samples of MoO₃ [7]. Ryabchikov et al. [8] reported on the complex relationship between the ⁹⁹Mo production rate, the neutron spectrum and neutron self-shielding effects at various resonance energies in natural and enriched Mo, concluding that the use of enriched Mo has a minor effect of the activation rate through the self-shielding of epithermal neutrons by the other Mo isotopes. Both papers stress the dominance of the epithermal contribution to the activation rate. Wolterbeek et al. point out that the epithermal contribution is sometimes overlooked when this production route is compared to others [9].

In Japan, ⁹⁹Mo production from ⁹⁸Mo appears to be well on its way, both solid and dissolved Mo having been investigated as targets [10].

El Abd reports on measurements of the \(^{ 9 8} {\text{Mo}}({\text{n}},\gamma )^{ 9 9} {\text{Mo}}\) cross section and resonance integral, performed on metal foils (0.15 mm thick for natural Mo), confirming the generally accepted values [11].

In order to allow the various research reactors in the world to assess their ⁹⁹Mo production capabilities, the IAEA organised a round-robin in 2015 where 16 reactor institutes from all over the globe irradiated sizeable natural molybdenum samples, measured the induced radioactivity and attempted to predict the experimental results quantitatively by performing model calculations. In this paper, the lessons learned are presented, as well as the approximate production capacity of the reactors involved.

In the following, often-used existing methods of modelling the neutron activation rate are related to each other. This should make it easy to estimate \(^{ 9 8} {\text{Mo}}({\text{n}},\gamma )^{ 9 9} {\text{Mo}}\) production rates, no matter what set of neutron spectrum parameters is available. It is a useful exercise to perform because various definitions of thermal neutron flux (also known as “thermal neutron fluence rate”) and epithermal flux are in use in different places and contexts, and the confusion that might ensue can lead to erroneous production capacity estimates. More in-depth information on the subject and the basic equations given here can be found in [12, 13].

If a nuclear reactor is used as the neutron source, it is helpful to distinguish three energy regions: the thermal region (where the neutrons are in thermal equilibrium with the moderator, their velocities are represented by the Maxwell–Boltzmann distribution and the (n,γ) neutron capture cross sections are mostly inversely proportional to the neutron velocity), the epithermal region (where the neutrons are slowing down, the neutron flux is roughly inversely proportional to the neutron energy and the (n,γ) capture cross sections exhibit resonances), and the fast region (where the neutrons have the energy distribution as dictated by the emission of fast neutrons during the ²³⁵U fission process and the (n,γ) capture cross sections are very small).

The IAEA sent 3 molybdenum samples to each participant in the exercise: approx. 1 g of Mo₂O₃ in a polyethylene capsule (9 mm internal diameter × 9 mm height), and two rectangular pieces of Mo metal of 10 × 10 × 1 and 50 × 10 × 1 mm, weighing about 1 and 5 g, respectively.

From the neutron spectrum parameters of the irradiation facility used, as reported by the participants, the capture rates and the specific saturation activities for a very small natural molybdenum sample (i.e. with negligible neutron self-shielding) were calculated, as well as for the actual bulky molybdenum samples. Both epithermal self-shielding correction approaches were applied.

Most participants experimentally activated the three molybdenum samples and measured the induced activities using a (HP)Ge detector.

The irradiation, decay and measurement times were to be chosen so that the precision of the irradiation time would be better than 1 %, the decay time would be long enough to allow the counting of the samples at dead time below 10 %, and the measurement would provide a Poisson uncertainty in the observed peak area of less than 1 %.

From the observed peak areas, the capture rates during activation were calculated (in the process correcting for dead time, coincidence summing effects and counting geometry differences), using

The resulting specific Eq. (15). Finally, the measured specific saturation activities were compared to the calculated ones to assess the quality of the various methods used.

Even though many experimental over calculated ratios as reported in Table 7 are close to unity, as they should be, the entire set of results indicates that the calculation and/or measurement of specific saturation activities for a reaction like ⁹⁸Mo(n,γ) is challenging. The contribution of epithermal neutrons to the total activation rate is high—up to 80 % of the total rate in an in-core facility like the BigBeBe in the Netherlands. This, in turn, necessitates accurate epithermal neutron self-shielding corrections.

Disregarding the epithermal contribution entirely leads to gross underestimation of the saturation activity, as occurred in the case of Kazakhstan. In the neutron trap position in the Vietnam Dalat reactor, the epithermal flux was not disregarded but perhaps underestimated in the characterization process.

Not all participants achieved the desired overall precision of 1 % or better in the measured activation rates. In view of the standard deviations of the resulting ratios between measured and predicted activation rates of about 20 % (Kazakhstan excluded), all reported results were still deemed relevant.

In the cases of Malaysia, Peru, Romania and Vietnam (beam position), it appears that confusion may have occurred between the thermal fluxes Φ ₀, Φ _T and the corresponding capture cross sections. It is indeed unfortunate that both Φ ₀ and Φ _T are known by the same name, i.e. “thermal flux”, when the definitions are different by a factor of √π/2 = 0.886—a value that appears to occur a number of times as the experimental-over-theoretical ratio in Table 7.

Various participants reported measured specific saturation activities quite close to the theoretical values, like Hungary and Egypt. The Hungarian results strongly suggest that Chilian’s method for epithermal neutron self-shielding correction performs better than Trkov’s. The Egyptian results were obtained with a very thermalized neutron spectrum and do not offer conclusive evidence in this respect. The results from Slovenia and especially The Netherlands, where the least thermal spectrum was employed, suggest that Trkov’s method may overestimate the severity of the epithermal self-shielding, where Chilian’s may underestimate it to a smaller extent.

For neutron spectrum characterization, the Monte Carlo methods used by various participants appear to perform equally well as the experimental methods.

To assist the reader in quickly estimating the ⁹⁹Mo production capability in a given irradiation facility, Fig. 1 shows the specific saturation activities to be expected in an irradiation facility with a neutron flux of 10¹³ cm⁻² s⁻¹, as a function of thermal/epithermal flux ratio, for typical values of α, molybdenum oxide and 1 mm thick molybdenum metal, as calculated with the procedures and equations (i.e. Eqs. 14, 15) given in this paper, where Chilian’s epithermal neutron self-shielding correction method was used.

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The results presented in this paper demonstrate that the specific saturation activity for the ⁹⁸Mo(n,γ)⁹⁹Mo reaction in natural molybdenum can be estimated with good accuracy, i.e. better than 10 %, if the epithermal activation contribution is taken into account properly and the epithermal neutron self-shielding is corrected for. Both Trkov’s and Chilian’s method give satisfactory results.

In-core irradiation facilities where the epithermal neutrons are strongly present are to be favoured over more thermalized facilities when the goal is to produce as much ⁹⁹Mo as possible.

Metallic molybdenum exhibits more neutron self-shielding than molybdenum oxide, leading to a higher specific saturation activity in the molybdenum itself. On the other hand, due to the lower density, less material can be introduced to the irradiation facility. Finally, post-irradiation processing capabilities available at a given site will determine which material is to be favoured in practice.