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Journal of Radioanalytical and Nuclear Chemistry

, Volume 311, Issue 1, pp 409–418 | Cite as

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

  • M. Blaauw
  • D. Ridikas
  • S. Baytelesov
  • P. S. Bedregal Salas
  • Y. Chakrova
  • Cho Eun-Ha
  • R. Dahalan
  • A. H. Fortunato
  • R. Jacimovic
  • A. Kling
  • L. Muñoz
  • N. M. A. Mohamed
  • D. Párkányi
  • T. Singh
  • Van Dong Duong
Open Access
Article

Abstract

Molybdenum-99 is one of the most important radionuclides for medical diagnostics. In 2015, the International Atomic Energy Agency organized a round-robin exercise where the participants measured and calculated specific saturation activities achievable for the 98Mo(n,γ)99Mo reaction. This reaction is of interest as a means to locally, and on a small scale, produce 99Mo from natural molybdenum. The current paper summarises a set of experimental results and reviews the methodology for calculating the corresponding saturation activities. Activation by epithermal neutrons and also epithermal neutron self-shielding are found to be of high importance in this case.

Keywords

Mo-99 Tc-99 m production Research reactor utilization Epithermal neutron self-shielding 

Introduction

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.

Theory

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, in a neutron activation experiments, the neutron flux can be considered homogeneous in the sample, then the activation rate R (s−1) per atom is given by.
$$R = \int\limits_{0}^{\infty } {\varPhi \left( v \right)\sigma \left( v \right){\text{d}}v} = \int\limits_{0}^{\infty } {\varPhi \left( E \right)\sigma \left( E \right){\text{d}}E} ,$$
(1)
where v is the neutron velocity (ms−1), (v) is the neutron capture cross-section (m−2) for neutrons with velocity v and \(\varPhi \left( v \right)dv\) is the neutron flux (m−2s−1) of neutrons with velocities between v and \(v \, + \, dv\), E is the neutron energy (eV), σ(E) is the neutron capture cross-section (m−2) for neutrons with energy E, and (E)dE is the neutron flux (m−2s−1) of neutrons with energies between E and E + dE.

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 thermal region is taken here to range from 0 to 0.55 eV, where 0.55 eV is the “Cd cut-off energy” and the corresponding neutron flux is then called the “subcadmium flux”, the epithermal region from 0.55 eV to 100 keV as the “epicadmium flux”, and the fast region from 100 keV to several MeV. Equation (1) can then be written as
$$R = \int\limits_{0}^{0.55} {\varPhi \left( E \right)\sigma \left( E \right){\text{d}}E} + \int\limits_{0.55}^{{10^{5} }} {\varPhi \left( E \right)\sigma \left( E \right){\text{d}}E} + \int\limits_{{10^{5} }}^{\infty } {\varPhi \left( E \right)\sigma \left( E \right){\text{d}}E} ,$$
(2)
Next, it is assumed that the neutron capture cross section in the thermal region can be written as
$$\sigma \left( v \right) = \frac{{\sigma_{0} v_{0} }}{v} ,$$
(3)
where v 0 is 2200 m/s and σ 0 the neutron capture cross section (m2) for neutrons of that velocity, and that
$$\varPhi_{\text{e}} \left( E \right) = \frac{{\varPhi_{\text{e}} }}{E} ,$$
(4)
where Φ e is the epithermal flux (m−2 s−1) at 1 eV. Also, the contribution of the fast neutrons is considered negligible because the (n,γ) capture cross sections are very small for such neutrons. Equation (1) then transforms to
$$R = \int\limits_{0}^{10251} {\varPhi \left( v \right)\frac{{\sigma_{0} v_{0} }}{v}{\text{d}}v} + \int\limits_{0.55}^{{10^{5} }} {\frac{{\varPhi_{e} \sigma \left( E \right)}}{E}{\text{d}}E} ,$$
(5)
where 10,251 m/s is the neutron velocity corresponding to 0.55 eV. Now, it can be observed that
$$n = \int\limits_{0}^{10251} {\frac{\varPhi \left( v \right)}{v}{\text{d}}v},$$
(6)
where n is the neutron density (m−3) in the thermal region, and the conventional thermal neutron flux Φ 0 is defined by
$$\varPhi_{0} = nv_{0} .$$
(7)
The resonance integral I 0 (m2) is defined as
$$I_{0} = \int\limits_{0.55}^{{10^{5} }} {\frac{\sigma \left( E \right)}{E}{\text{d}}E} .$$
(8)
So that Eq. (1) transforms to the Høgdahl [14] convention:
$$R = \sigma_{0} \varPhi_{0} + I_{0} \varPhi_{e} .$$
(9)
Values for σ 0 and I 0 are tabulated and widely available in the literature [15] as well as in on-line databases.

Refinements for non-1/v thermal reactions, epithermal activation and self-shielding

In this section, a few refinements often encountered in activation rate modelling are discussed.

If the nucleus that will result from the capture of a thermal neutron has a resonance energy close to the excited state it will be produced in, the capture cross section will not be inversely proportional to the neutron velocity in the thermal range. Then the thermal capture rate R t is approximated by
$$R_{\text{t}} = g\left( T \right)\sigma_{0} \varPhi_{0} ,$$
(10)
where g(T) is the Westcott factor, for which tabulated values as a function of the temperature T of the Maxwell–Boltzmann neutron velocity distribution are available [16]. Only a few (n,γ)-reactions show this effect to a context-relevant degree in research-reactor conditions. In the neutron activation analysis community, where the highest possible accuracy is of interest, is has been established that the epithermal neutron spectrum shape is better described by
$$\varPhi_{\text{e}} \left( E \right) = \frac{{\varPhi_{\text{e}} \left( {E_{1} } \right)}}{{\left( {\frac{E}{{E_{1} }}} \right)^{1 + \alpha } }} ,$$
(11)
where E 1 is 1 eV and α characterizes the deviation from the perfect epithermal spectrum [12]. Accordingly, the definition of the resonance integral changes to
$$I_{0} \left( \alpha \right) = \int\limits_{0.55}^{{10^{5} }} {\frac{\sigma \left( E \right)}{{\left( {\frac{E}{{E_{1} }}} \right)^{1 + \alpha } }}dE} ,$$
(12)
which leads to an additional parameter to characterize the dependence of I 0 on α, i.e. the effective resonance energy E r. This relation can then be expressed as
$$I_{ 0} \left( \alpha \right) = \frac{{I_{ 0} - 0.429}}{{E_{\text{r}}^{\alpha } }} + \frac{0.429}{{(2\alpha + 1)0.55^{\alpha } }} .$$
(13)
When objects are irradiated that are not transparent to neutrons due to scattering or absorption, the neutron flux inside the material will be affected. This phenomenon is called neutron self-shielding and depends on sample composition, size, and shape as well as on incident neutron energy.
With all these refinements, the sample-volume averaged capture rate is then given by
$$R = g\left( T \right)G_{\text{t}} \sigma_{0} \varPhi_{0} + G_{\text{e}} I_{0} \left( \alpha \right)\varPhi_{\text{e}} ,$$
(14)
where Gt and Ge are the thermal and epithermal neutron self-shielding correction factors.
The specific saturation activity A s (Bq g−1) can then be calculated with
$$A_{\text{s}} = \frac{{R\theta N_{\text{A}} }}{M} ,$$
(15)
where θ is the isotopic abundance, N A is Avogadro’s number and M is the molar mass of the element.

Other conventions and neutron spectrum parameters

Alternative definitions for thermal or subcadmium flux

In other conventions, similar expressions are derived, but the thermal neutron flux may be defined differently. Beckurts and Wirtz [13], for example, define a thermal flux Φ T as
$$\varPhi_{T} = n\left\langle v \right\rangle = n\frac{2}{\sqrt \pi }\sqrt {\frac{T}{{T_{0} }}} v_{0},$$
(16)
and a corresponding Maxwell–Boltzmann flux-averaged thermal cross-section
$$\sigma_{T} = \left\langle \sigma \right\rangle = \frac{{\int\limits_{0}^{\infty } {\varPhi \left( v \right)\sigma \left( v \right)dv} }}{{\int\limits_{0}^{\infty } {\varPhi \left( v \right)dv} }}\frac{\sqrt \pi }{2}\sqrt {\frac{{T_{0} }}{T}} \sigma_{0},$$
(17)
where T is the temperature associated with the Maxwell–Boltzmann velocity distribution, and T 0 is 293.6 K. In each convention, the definitions of the thermal cross section and the thermal neutron flux match, so the product R = Φσ always turns out the same. The choice of convention is therefore arbitrary, as long as the corresponding matching pairs of σ and Φ definitions are used.
Because of the easy availability of literature values for σ 0 and I 0, Eq. (14) with its parameters is taken as the convention to relate the other models to in this paper, in this case by writing
$$\varPhi_{0} = \frac{\sqrt \pi }{2}\sqrt {\frac{{T_{0} }}{T}} \varPhi_{\text{T}}.$$
(18)

Alternative definition for epithermal or epicadmium neutron flux

In the reactor physics community, the epithermal or epicadmium neutron flux is often defined as
$$\varPhi_{\text{e}}^{*} = \int\limits_{{E_{\hbox{min} } }}^{{E_{\hbox{max} } }} {\varPhi \left( E \right){\text{d}}E} ,$$
(19)
where E min and E max are the energy limits chosen for the integration—various values are used to this end. Using Eq. (4), the two epithermal fluxes are related by
$$\varPhi_{\text{e}}^{*} = \int\limits_{{E_{\hbox{min} } }}^{{E_{\hbox{max} } }} {\frac{{\varPhi_{\text{e}} }}{E}{\text{d}}E} = \varPhi_{\text{e}} \left[ {\ln \left( {E_{ \hbox{max} } } \right) - \ln \left( {E_{\hbox{min} } } \right)} \right] ,$$
(20)
or
$$\begin{aligned} \varPhi_{\text{e}} = \frac{{\varPhi_{\text{e}}^{*} }}{{\ln \left( {\frac{{E_{\hbox{max} } }}{{E_{\hbox{min} } }}} \right)}} \hfill \\ \hfill \\ \end{aligned} .$$
(21)

Alternative spectrum parameters: cadmium ratio, thermal/epithermal ratio

The neutron spectrum shape can be characterized with the parameter f, i.e. the thermal-to-epithermal flux ratio, defined as
$$f = \frac{{\varPhi_{0} }}{{\varPhi_{\text{e}} }},$$
(22)
So that
$$\varPhi_{\text{e}} = \frac{{\varPhi_{0} }}{f},$$
(23)
and often also with the cadmium ratio R Cd, i.e., the ratio of the activation rate without and with cadmium cover, defined by
$$R_{\text{Cd}} = \frac{{\left( {\sigma_{0} \varPhi_{0} + I_{0} \left( \alpha \right)\varPhi_{\text{e}} } \right)}}{{I_{0} \left( \alpha \right)\varPhi_{\text{e}} }}$$
(24)
So that
$$\varPhi_{\text{e}} = \varPhi_{0} \frac{{\sigma_{0} }}{{I_{0} \left( \alpha \right)}}\frac{1}{{\left( {R_{\text{Cd}} - 1} \right)}} .$$
(25)
Typically, gold is used as the flux monitor and the tabulated values for σ 0 and I 0 for the 197Au(n,γ)198Au reaction are to be used as a consequence. Imperfect shielding of subcadmium neutrons by the cadmium cover as well as neutron self-shielding in the flux monitor have been disregarded here.

Determination of neutron spectrum parameters

The neutron spectrum parameters (Φ 0, Φ e, f, α etc.) can be determined in a variety of ways, ranging from theoretical Monte Carlo calculations, where the reactor and the irradiation facility are modelled in their entirety, to experimental irradiation and measurement of appropriate combinations of elements (such as Zr+Au, or Cr+Mo+Au), possibly with and without cadmium cover.

Neutron self-shielding calculation

Both the thermal and the epithermal neutron flux tend not to be homogeneous throughout the sample. The ratio of the volume-averaged flux within the sample and the flux in the same location in the absence of the sample is the self-shielding correction factor.

In the thermal region, equations to calculate these factors are readily available for various sample shapes. A good overview is given by De Corte [12].

In the epithermal region, the situation is more complex because of the presence of resonance energies where neutron absorption may be extremely high. Two approaches were employed in this work: the MATSSF software developed by Trkov [17] and the method of Martinho [18] and Chilian [19].

Experimental

The participating countries and reactors are presented in Table 1.
Table 1

Participant countries, reactors and their maximum thermal powers

Participant country

Reactor

Power (MW)

Chile

RECH-1

5

Egypt

ETRR-2

22

Hungary

BRR

10

India

DHRUVA

100

Kazakhstan

WWR-K

6

Korea

HANARO

30

Malaysia

RTP

1

Mexico

Triga Mark III

1

Morocco

MA-R1

2

Netherlands

HOR

2

Peru

RP-10

10

Portugal

RPI

1

Romania

Triga II Pitesti

12

Slovenia

Triga Mark II

0.25

Ukraine

WWR-M

8

Uzbekistan

WWR-SM

11

Vietnam

Dalat RR

0.5

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 %.

The characteristics of the Ge detectors used are shown in Table 2. Full-energy detection efficiency curves were determined with mixed-radionuclide sources emitting multiple gamma-ray energies or combinations of calibrated point sources in all cases, at the same distances used for sample measurements. Each participant used their own, unspecified nuclear data source to this end. All participants used the same gamma-ray yields for the 99Mo gamma rays.
Table 2

Detector characteristics

Country

Diameter (mm)

Height (mm)

Distance (mm)

Peak efficiency

Remarks(keV)

Egypt

80

100

100

7.81 × 10−3

740

7.60 × 10−3

778

Morocco

58.5

76.3

100

1.93 × 10−3

 

Malaysia

50

20

223

1.54 × 10−4

 

Vietnam

69.4

67.1

50

1.08 × 10−2

140

Hungary

64.9

89.6

300

5.88 × 10−4

 

Kazachstan

59

50

60

4.94 × 10−3

 

Netherlands

55

60

150

1.12 × 10−3

 

Portugal

51

48

295

5.41 × 10−4

366

3.30 × 10−4

740

3.18 × 10−4

778

3.05 × 10−4

822

Romania

50

65.4

100

1.74 × 10−3

 

150

9.24 × 10−3

200

5.75 × 10−3

250

3.90 × 10−3

Slovenia

35.5

50

160

1.88 × 10−3

 

Ukraine

74

53

1510

3.63 × 10−5

778

Chile

49

36

55

2.50 × 10−3

 

Mexico

42

43.5

57

1.29 × 10−2

 

107

3.60 × 10−3

Peru

80.3

54

240

1.58 × 10−3

 

The detection efficiencies shown apply to the 99Mo main energy of 740 keV, if not stated otherwise

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

$$R = \frac{{\lambda N_{\text{p}} }}{{\left( {1 - e^{{ - \lambda t_{\text{ir}} }} } \right)e^{{ - \lambda t_{\text{d}} }} \left( {1 - e^{{ - \lambda t_{\text{m}} }} } \right)\gamma \varepsilon }}\frac{M}{{wN_{\text{Av}} \theta }},$$
(26)
where N p is the net peak area after correction for dead time during measurement, t ir, t d and t m are irradiation time, decay time and counting time (s), λ is the decay rate (s−1), γ is the gamma mission probability, ε is the full-energy detection efficiency and w is the sample mass (g).
The detection efficiency for the molybdenum samples differed from the detection efficiencies as measured with small calibration sources, necessitating corrections for gamma-ray self-absorption and geometrical effects. The participants who estimated these corrections used solid angle approaches, where a numerical integration is carried out over the sample volume, taking the pathlength through the sample towards the detector, as well as the distance from the detector, into account at the same time. The result is a single correction factor, rather than two separate ones for geometry and self-absorption. Also, 99Mo often emits the 740 keV photon in coincidence with the 181 keV, so that true-coincidence summing corrections must be applied. These correction factors and the dead-time correction factors or methods, if made available by the participant, are shown in Table 3.
Table 3

Correction factors as used

Country

 

Dead time

Gamma self-absorption and geometry

TCC

Egypt

MoO3

1.0015

1.0840

1.0000

 

1 g

1.0079

1.0720

1.0000

 

5 g

1.0020

1.0850

1.0000

Morocco

MoO3

1.015

 

1.007

 

1 g

1.022

 

1.006

 

5 g

1.105

 

1.002

Malaysia

MoO3

1

1

1

 

1 g

1

1

1

 

5 g

1

1

1

Vietnam

MoO3

 

1.28 (140 keV)

 
 

1 g

 

1.36 (140 keV)

 
 

5 g

 

1.36 (140 keV)

 

Hungary

MoO3

ZDT

1.0406

1

 

1 g

ZDT

1.0020

1

 

5 g

ZDT

1.0050

1

Kazachstan

MoO3

1.0042

1

 
 

1 g

1.0063

1.014

 
 

5 g

1.0383

1.015

 

Netherlands

MoO3

1.0846

1.0638

1.0050

 

1 g

1.0050

1.0395

1.0050

 

5 g

1.0299

1.0428

1.0050

Portugal

MoO3

LT preset

1.0860

 
 

1 g

LT preset

1.0360

 
 

5 g

LT preset

1.0360

 

Romania

MoO3

Genie

1

1

 

1 g

Genie

1

1

 

5 g

Genie

1

1

Slovenia

MoO3

ZDT

1.1125

1.0078

 

1 g

ZDT

1.0262

1.0087

 

5 g

ZDT

1.0208

1.0089

Ukraine

MoO3

1.0215

1.031

 
 

1 g

1.0194

1.031

 
 

5 g

1.0846

1.031

 

Chile

MoO3

1.0000

1.0000

1.0000

 

1 g

1.0000

0.8438

1.0000

 

5 g

1.0000

0.9694

1.0000

Mexico

MoO3

1.0054

  
 

1 g

1.0359

  
 

5 g

1.0460

  

Peru

MoO3

 

1.0130

1.0000

 

1 g

 

1.0380

1.0000

 

5 g

 

1.0380

1.0000

All factors are stated so that an uncorrected measured activation rate has to be multiplied with these to obtain the activation rate in a very small sample

TCC stands for true coincidence summing, ZDT denotes zero-dead time counting

Unity values indicate that the participant deemed the correction negligible, blank values that no data were provided by the participant

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.

During a follow up workshop at the IAEA in Vienna, in December 2015, the participants compared notes, corrected their results for a number of issues found, and decided on the best nuclear data and methods to be used for 99Mo production rate estimation. Not all discrepancies were resolved during this meeting—however all results presented in this paper are the ones obtained from the participant-supplied information during or after this meeting, using the agreed-upon methods and nuclear data. The equations used are the ones given above in this paper. The nuclear data used, all taken from De Corte et al. [15], are as shown in Table 4.
Table 4

Nuclear data used in this work (1 b = 10−28 m2)

Reaction

σ 0 (b)

I 0 (b)

E r (eV)

M

θ

197Au(n,γ)198Au

98.7

1549.6

5.7

196.97

1

98Mo(n,γ)99Mo

0.131

6.96

241

95.96

0.2413

For the 740 keV gamma-ray of Mo-99, a yield of 12.1 % was used. All data were obtained from [15]

Results

Neutron spectrum characterization

In Table 5, the neutron spectrum parameters as reported by the participants are shown (the participants were not instructed on which parameters to supply in the round-robin process). From these parameters, the parameters needed as input for Eq. 14 were calculated using the equations given above as needed. The resulting values are also shown in Table 5. The Westcott factor g(T) was assumed to be unity in all cases for the 98Mo(n,γ)99Mo reaction. In case of unspecified values for the α parameter, a value of 0 was assumed.
Table 5

Neutron spectrum parameters and characterization methods as provided by the participants for the various irradiation facilities used

Participant country, facility

Neutron spectrum characterization method

Φ 0 (cm−2s−1)

Φ e (1 eV) (cm−2s−1)

Φ e (integral) (cm−2s−1)

E min (eV)

E max (eV)

α

F

R Cd

Saturation activity (Ci/g)

Chile

Not specified

4.76E+12

4.15E+10

      

3.72E02

Egypt

Au+Zr

2.80E+11

1.12E+09

   

0.180

250

 

1.62E−03

Hungary

Au+Zr

9.37E+13

3.86E+12

   

−0.038

  

1.84E+00

India

Monte Carlo

3.60E+13

4.26E+11

6.00E+12

0.625

8.21E+05

   

3.13E−01

Kazakhstan

Estimated

6.50E+13

0.00E+00

      

3.47E−01

Korea

Monte Carlo

6.78E+13

1.21E+11

1.45E+12

0.625

1.00E+05

   

3.97E−01

Malaysia

Au, Cd-cover

7.99E+12

1.54E+11

     

4.30

8.64E−02

Mexico

Not specified

2.78E+13

1.56E+11

1.87E+12

     

1.93E−01

Morocco

Au+Zr, Au+Cr+Mo

6.40E+12

2.85E+11

   

−0.020

22.5

 

1.15E−01

Netherlands BigBeBe

Au+Cr+Mo

2.40E+13

1.73E+12

   

0.000

13.9

 

6.18E−01

Netherlands BP3

Au+Cr+Mo

5.55E+12

6.97E+10

   

0.040

79.65

 

4.57E−02

Peru

Au+Mo+Co+Lu

6.76E+12

1.62E+11

   

0.071

40

 

6.94E−02

Portugal

Au, Cd-cover

1.90E+12

1.80E+10

   

0.061

42

 

1.53E−02

Romania

Monte Carlo

1.20E+13

2.88E+11

   

0.012

41.65

3.61

1.41E−01

Slovenia

Au+Zr, Cd-cover

1.04E+12

3.85E+10

   

−0.004

27.11

 

1.67E−02

Ukraine

Monte Carlo

1.84E+14

9.85E+11

     

12.9

1.26E+00

Uzbekistan

Not specified

3.70E+13

4.65E+11

    

79.65

 

3.29E−01

Vietnam beam

Au+Mo+W, Cd-cover

1.60E+06

2.43E+02

     

420

8.62E−09

Vietnam trap

Au+Mo+W, Cd-cover

1.46E+13

1.28E+11

   

−0.083

114.3

7.29

1.34E−01

Values in bold italics were calculated from the other data in the table with the equations given in this paper

Also in Table 5, the specific saturation activities for a very small Mo target are shown, as calculated from the neutron spectrum parameters and the nuclear data for the 98Mo(n,γ) reaction, assuming absence of neutron self-shielding, using Eqs. 13, 14 and 15.

Table 6 shows the thermal and epithermal neutron self-shielding factors, the latter as calculated using Trkov’s and Chilian’s methods, for the three sample types.
Table 6

Thermal and epithermal neutron self-shielding factors G th and G epi for the three sample types

 

1 g of Mo2O3 powder

Mo slab 1 × 1 cm

Mo slab 1 × 5 cm

Method

G th

G epi

G th

G epi

G th

G epi

 

0.982

 

0.954

 

0.954

 

Chilian

 

0.857

 

0.742

 

0.742

Trkov

 

0.804

 

0.599

 

0.574

Two methods were used for the epithermal self-shielding calculation

In Table 7, the measured specific saturation activities are shown, as well as the ratios of these over the values that were calculated with the two epithermal neutron self-shielding methods.
Table 7

Measured specific saturation activities as compared to the calculated values obtained with the two methods for epithermal neutron self shielding correction

 

Measured saturation activities

Measured over calculated sat.act. Ratios

Participant country

      

Trkov

Chilian

 

Mo2O3

Unc

Slab 1 × 1 cm

Unc

Slab 1 × 5 cm

Unc

Mo2O3

Slab 1 × 1 cm

Slab 1 × 5 cm

Mo2O3

Slab 1 × 1 cm

Slab 1 × 5 cm

 

Ci/g

%

Ci/g

%

Ci/g

%

Ci/g

Ci/g

Ci/g

Ci/g

Ci/g

Ci/g

Chile

3.21E−02

4.0

3.24E−02

4.0

3.21E−02

4.0

0.931

1.034

1.034

0.915

0.982

0.973

Egypt

1.59E−03

0.3

1.47E−03

0.4

1.49E−03

1.3

1.011

0.977

0.992

1.008

0.966

0.979

Hungary

1.63E+00

0.4

1.45E+00

0.4

1.46E+00

0.4

1.040

1.133

1.172

0.995

0.986

0.993

Kazachstan

6.25E−01

3.0

5.62E−01

2.0

5.79E−01

2.0

1.831

1.695

1.746

1.833

1.697

1.748

Malaysia

6.85E−02

15.0

7.49E−02

5.5

8.27E−02

9.0

0.888

1.118

1.255

0.862

1.023

1.130

Morocco

5.75E−02

0.9

5.32e−02

1.0

4.75E−02

1.0

1.003

1.131

1.034

0.961

0.990

0.883

NL BBB

  

4.49E−01

2.0

4.42E−01

2.0

 

1.079

1.094

 

0.923

0.909

NL BP3

4.27E−02

1.4

    

1.015

  

0.996

  

Peru

5.46E−02

3.0

5.38E−02

3.0

5.26E−02

3.0

0.877

0.989

0.982

0.853

0.910

0.889

Portugal

1.72E−02

8.0

1.21E−02

8.0

1.32E−02

8.0

1.221

0.949

1.046

1.199

0.898

0.980

Romania

1.04E−01

1.5

1.02E−01

6.0

9.60E−02

1.5

0.833

0.950

0.911

0.807

0.863

0.812

Slovenia

1.45E−02

0.7

1.19E−02

0.6

1.28E−02

0.5

1.004

0.992

1.092

0.965

0.876

0.942

Ukraine

1.55E+00

3.0

1.44E+00

3.0

1.38E+00

3.0

1.305

1.298

1.251

1.290

1.254

1.201

Vietnam beam

7.50E−09

2.0

8.40E−09

2.0

7.30E−09

2.0

0.887

1.024

0.890

0.887

1.024

0.890

Vietnam trap

1.89E−01

2.1

1.85E−01

2.0

1.88E−01

2.1

1.550

1.709

1.760

1.514

1.592

1.618

The 1 s.d. uncertainties were calculated from the Poisson uncertainties in the measured peak areas

Discussion

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.
Fig. 1

Specific saturation activities to be expected in an irradiation facility with a thermal neutron flux of 1 × 1013 cm−2s−1, as a function of the thermal/epithermal flux ratio, for various values of α and for the two sample types, as calculated with Eqs. 14 and 15 in this paper

Conclusions

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.

Notes

Acknowledgments

The authors would like to thank the IAEA for the initiative in organizing this round robin exercise and financial support provided is supplying the samples and organizing the follow-up workshop.

Authors contribution

The authors also acknowledge the contributions of the following individuals to the success of the round robin study: M. Soliman (Egypt), L. Szentmiklósi, R. Baranyai, F. Gajdos (Hungary), K. Embarch, H. Amsil, I. Aarab, B. Moussa (Morocco), M. Sarilar (Netherlands), Manuel Zegarra, Pablo Mendoza (Peru), J. Santos (Portugal) and Pham Ngoc Son (Vietnam).

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • M. Blaauw
    • 1
  • D. Ridikas
    • 2
  • S. Baytelesov
    • 3
  • P. S. Bedregal Salas
    • 4
  • Y. Chakrova
    • 5
  • Cho Eun-Ha
    • 6
  • R. Dahalan
    • 7
  • A. H. Fortunato
    • 8
  • R. Jacimovic
    • 9
  • A. Kling
    • 10
  • L. Muñoz
    • 11
  • N. M. A. Mohamed
    • 12
  • D. Párkányi
    • 13
  • T. Singh
    • 14
  • Van Dong Duong
    • 15
  1. 1.Reactor Institute DelftDelft University of TechnologyDelftThe Netherlands
  2. 2.Division of Physical and Chemical Sciences, Department of Nuclear Sciences and ApplicationsInternational Atomic Energy AgencyViennaAustria
  3. 3.Institute of Nuclear PhysicsAcademy of Sciences of UzbekistanTashkentUzbekistan
  4. 4.Instituto Peruano de Energia NuclearLimaPeru
  5. 5.Institute of Nuclear Physics of Ministry of Energy of the Republic of KazakhstanAlmatyKazakhstan
  6. 6.RI Research DivisionKorea Atomic Energy Research InstituteYuseong-guKorea
  7. 7.Medical Technology DivisionMalaysian Nuclear AgencyKajangMalaysia
  8. 8.Instituto Nacionale de Investigciones NuclearesOcoyoacacMexico
  9. 9.Jozef Stefan InstituteLjubljanaSlovenia
  10. 10.Centro de Ciências e Tecnologias Nucleares and Laboratório de Engenharia Nuclear, Instituto Superior TécnicoUniversidade de LisboaBobadela LRSPortugal
  11. 11.Comisión Chilena de Energía Nuclear (CCHEN)SantiagoChile
  12. 12.Egypt Second Research Reactor (ETRR-2)Atomic Energy Authority (AEA)Abou Zabal, CairoEgypt
  13. 13.Centre for Energy ResearchHungarian Academy of SciencesBudapestHungary
  14. 14.Department of Atomic Energy (DAE)Bhabha Atomic Research Centre (BARC)MumbaiIndia
  15. 15.Vietnam Atomic Energy InstituteDalatVietnam

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