The use of self-induced X-ray fluorescence in gamma-ray spectroscopy of uranium ore samples

currently based on total counting with Geiger Müller gas detectors or NaI (TI) scintillators. However, the total count rate interpretation in terms of uranium concentration may be impaired in case of roll fronts, when the radioactive equilibrium of the natural 238U radioactive chain is modified by differential leaching of uranium and its daughter radioisotopes of thorium, radium, radon, etc. Indeed, in case of secular equilibrium, more than 95 % of gamma rays emitted by uranium ores come from 214Pb and 214Bi isotopes, which are in the back-end of 238U chain. Consequently, these last might produce an intense gamma signal even when uranium is not present, or with a much smaller activity, in the ore. Therefore, gamma spectroscopy measurements of core samples are performed in surface with high-resolution hyper-pure germanium HPGe detectors to directly characterize uranium activity from the 1001 keV gamma ray of 234mPa, which is in the beginning of 238U chain. However, due to the low intensity of this gamma ray, i.e. 0.84 %, acquisitions of several hours are needed. In view to characterize uranium concentration within a few minutes, we propose here a method using both the 92 keV gamma ray of 234Th and the 98.4 keV uranium X-ray. This last is due to uranium self-induced fluorescence caused by gamma radiations of 214Pb and 214Bi, which create a significant Compton scattering continuum acting as a fluorescence source and resulting in the emission of uranium fluorescence X-rays. The comparison of the uranium activity obtained with the 92 keV and 98.4 keV lines allows detecting a uranium heterogeneity in the ore. Indeed, in case of uranium nugget, the 92 keV line leads to underestimated uranium concentration due to gamma self-absorption, but on the contrary the 98.4 keV line leads to an overestimation because of increased fluorescence. In order to test this new approach, several tens of uranium ore samples have been measured with a handheld HPGe FALCON 5000 detector.


I. INTRODUCTION
urrent gamma measurements used to characterize the uranium content of ore samples are mainly based on two estimators. The first one is the total gamma count rate, which is approximately 90 % due to gamma radiations of 214 Pb and 214 Bi daughters (see further Fig. 1), in the back-end of 238 U chain. It allows short acquisition times but it is subject to potential imbalances in this decay chain. The second one is the 1001 keV gamma ray of 234m Pa daughter in the beginning of 238 U chain, which is therefore not subject to a potential disequilibrium of the decay chain. Moreover, the sample mineralogy has little impact on attenuation of this radiation with a relatively high energy. However, its emission intensity is very small (0.847%) and its detection requires acquisition times of several hours, see Fig. 1. The objective of this study is to measure uranium content using more intense lines at lower energy, i.e. the 92 keV gamma ray of 234 Th and 235 U, and the 98 keV line due to uranium self-induced fluorescence (and to a lesser extend to a 234m Pa gamma ray). This study is performed with samples of crushed ore filling a PVC holder. The gamma spectra are measured with a Falcon 5000 [1] handheld spectrometer from Mirion-Canberra, equipped with a HPGe planar detector (BEGE 2830 model). The method is studied by MCNP6 Monte Carlo calculation by the Nuclear Measurement Laboratory of CEA, DEN, Cadarache, and validated with experimental data obtained by ORANO Mining during a measurement campaign intended to characterize uranium content and imbalance of the samples [2]. The two rays at 92 keV and 98 keV are systematically present with a high intensity on uranium ore spectra (see example of a small concentration sample in Fig. 1), which makes it possible to envisage a significant measurement time reduction with respect to 1001 keV line.

II. ANALYSIS OF THE GAMMA SPECTRUM
A. Typical gamma spectrum of a uranium ore sample Fig. 1 shows a typical HPGe high-resolution gamma spectrum of a real ore sample with a 419 ppm uranium concentration. The experimental setup is described further in Section II. In this section, we develop the theoretical formulae used to determine the uranium concentration from the net area of 1001 keV, 92 keV and 98 keV peaks, respectively. The concentration obtained with the 1001 keV gamma ray is considered in this work as the reference because it is less sensitive to attenuation effects compared to the two other low-energy radiations.
The use of self-induced X-ray fluorescence in gamma-ray spectroscopy of uranium ore samples T. Marchais , B. Pérot , C. Carasco , J-L. Ma , P-G. Allinei , H. Toubon , R. Goupillou , J. Collot C Fig. 1. Experimental spectrum of a 479 g ore sample with an uranium concentration of 419 ppmU and a density of 1.46 g.cm -3 with for 7503 seconds of acquisition B. Radioactive gamma emission at 1001 keV Equation (1) allows converting the net area of the 1001 keV peak into uranium mass concentration in ppm (i.e. in mg of uranium per kg of ore, dimensionless unit). This equation has been already used and validated during a measurement campaign in Bessines (France) calibration facility [3].

C. Radioactive gamma and X-ray emissions at 92 keV
The "92 keV" peak is already used in ORANO Mining laboratories for fast uranium characterization. It is composed of close-in-energy lines mainly due to 235 U and 234 Th:  the α-decay of 235 U towards 231 Th is followed by the emission of a thorium X-ray at 93.35 keV, after internal conversion of the excited 231 Th daughter. This X-ray contributes to the signal at 92 keV due to the finite resolution of the detector, with a tabulated emission intensity ����� ( �� ��� ) = 5.75 % [5],  234 Th (in the beginning of the 238 U decay chain) emits two gamma rays at 92.38 keV and 92.80 keV following its βradioactive decay into 234 Pa. We use here the total intensity ����� ( ℎ �� ��� ) = 4.33% [5], As 235 U and 234 Th are located at the top of the uranium decay chains, the net area of the 92 keV peak is not subject to potential imbalances and correctly reflects the uranium concentration.
Equation (2) allows converting the net area of the 92 keV peak into uranium mass concentration. Where:

D. Radioactive emission at 98 keV
The 98 keV peak is dominated by four contributions:  the X-Kα1 fluorescence line of uranium at 98.44 keV. The net area of this peak does not follow linearly uranium concentration, contrary to the above radioactive-decay emissions, but it rises in a quadratic way because of the combined increase of fluorescence source intensity (gamma emitters of the uranium chain) and uranium quantity itself (which undergoes fluorescence).  the same 98.44 keV X-ray but emitted after the βdisintegration of 234m Pa (at the beginning of the 238 U decay chain) into 234 U, followed by internal conversion. The tabulated emission intensity is ����� ( �� ���� ) = 0.316 %,  two close 97.53 keV and 97.85 keV X-rays linked to 223 Ra ( 235 U decay chain) α-decay into 219 Rn, followed by internal conversion of the excited daughter 219 Rn. The tabulated total intensity for these two X-rays is ����� ( �� ��� ) = 2.72 % [5],  the same 97.53 keV and 97.85 keV X-rays but linked to 226 Ra ( 238 U decay chain) α-decay towards 222 Rn, again followed by internal conversion. The tabulated total intensity is here ����� ( �� ��� ) = 0.036% [5].
Concerning the first contribution, each gamma ray emitted by the uranium decay chain can cause the fluorescence of uranium after undergoing Compton scattering and photoelectric absorption in the sample. In order to quantify the ability of a photon of energy E to induce uranium fluorescence, the ƞ ���� ( ) yield defined in equation (3) is calculated by MCNP (in g -1 units). This fluorescence yield is specific to the geometry of the sample: uranium content, filling height, density, mineralogy.  The fluorescence yield and the three radioactive decay emissions listed above allow us to convert the net area of the 98 keV peak into a uranium mass concentration using equation (4). It is important to notice that, in order to limit the number of simulations, only the six more intense gamma rays were taken into account to calculate the fluorescence yield: 185 keV ( 214 Pb), 242 keV ( 214 Pb), 298 keV ( 214 Pb), 352 keV ( 214 Pb), 609 keV ( 214 Bi) and 1120 keV ( 214 Bi). As they represent 78 % of the total fluorescence signal, a correction factor F equal to 0.78 is used in equation (4). -F: correction factor to take into account the limited number the lack of gamma rays modeled in the fluorescence source (here F = 0.78).

III. EXPERIMENTAL QUALIFICATION
In order to validate the new approach described above, we use 76 gamma spectra of uranium ore samples recorded by ORANO Mining (such as the spectrum of Fig. 1) to study radioactive disequilibrium in Dulann Uul and Zoovch Ovoo deposits, Mongolia [2]. The samples have different densities and filling heights. The uranium ore was coarsely crushed with a hammer and placed in a flask, as shown in Fig. 3. The crushed samples have an average density of 1.4 g.cm -3 . The average filling height is 6 cm and the sample holder diameter is 11 cm. The sample is placed on PVC shims of variable height to ensure the contact between the detector cover and the ore sample. In addition, a copper shielding was used to absorb fluorescence X-rays of the lead shielding (Fig. 3). The BEGE 2830 planar HPGe crystal of the FALCON 5000 handheld detector (from MIRION-CANBERRA) has a 60 mm diameter and a 30 mm length. In order to calculate the fluorescence yield, the measurement geometry was modeled with MCNP6 Monte-Carlo transport code [4], see Fig. 3. Efficiencies at 92 keV, 98 keV and 1001 keV are those calculated with ISOCS software [6] for a typical FALCON 5000 geometry. The uncertainty associated to calculated efficiencies is 10 % for 92 keV and 98 keV peaks and 5 % for 1001 keV peak.
The following graph represents the � (92 ) and � (98 ) concentrations calculated with the net area of the 92 keV and 98 keV peaks, respectively, as a function of the concentration calculated with the 1001 keV peak, which is considered as the reference.  The uncertainty calculated for each sample (considered as homogeneous) includes: -detector calibration and detection efficiency calculation by ISOCS [6], -the statistical uncertainty on the net area of the 1001 keV, 92 keV and 98 keV peaks, -the relative uncertainties on the intensities of the gamma or X-rays of interest are given in the nuclear databases [5]: 0.94 % for the 1001 keV gamma ray; for the 92 keV peak it is 6.21% for the 234  ). The uncertainty on � (1001 ) is mainly due to the poor counting statistics, leading to large uncertainties in both the Gaussian adjustment of the gamma ray (broadened by the detector resolution) and in the estimation of the Compton continuum under the peak. Concerning � (92 ) and � (98 ) the relative uncertainty on the efficiency calculated with ISOCS software dominates (10 %). It could be reduced by using a MCNP refined detector model based on a fine geometrical characterization with collimated calibration sources, which will be reported in a future article. For most of the 76 samples, � (92 ) and � (98 ) are consistent with the reference � (1001 ), but for seven samples (in red on Fig. 4 and Fig. 5), discrepancies are observed that might be due to heterogeneities. Indeed, for all these samples, we observe the following inequality: � (98 ) > � (1001 ) ≥ � (92 ) As explained above, in case of uranium nuggets in the sample, X and gamma emissions following radioactive decays are more self-absorbed than with a uniform distribution, while on the contrary, X-ray fluorescence is enhanced. This phenomenon was demonstrated by simulating with MCNP a uranium nugget of 0.343 gU in a homogeneous matrix of uranium of 0.455 gU. This simulation, equivalent of a homogeneous sample of 1000 ppmU, gives � (92 ) = 690 ppmU and � (98 ) = 3645 ppmU. Beyond detection of possible heterogeneities, the advantage of the method is to reduce measurement time. The gain in measurement time was calculated for each sample by comparing the statistical uncertainty of the 1001 keV with that of 92 keV and 98 keV peaks, taking in account the estimation and subtraction of the Compton continuum under the peaks. Than the gain in measurement time is estimated with the aim to have the same relative uncertainty in the 92 and 98 keV lines, during a short acquisition, as in the 1001 keV line during the long acquisition. In other words, based on Poisson law, the ratio of the 1001 keV relative uncertainty to that of 92 or 98 keV lines is squared to be converted in time gain. The average gain

IV. CONCLUSION AND PROSPECTS
In this work, we have shown the possibility to measure the uranium concentration of uranium ore samples by gamma-ray spectroscopy using the 92 keV and 98 keV lines, which lead to a large measurement time gain (minutes vs. hours) compared to the reference 1001 keV peak. The total relative uncertainty on � (92 ) and � (98 ) mass concentrations measured in a short acquisition remains lower than 13 %, while it was about 10 % for the long measurement of � (1001 ). In addition, a difference in the uranium concentrations assessed with the 92 and 98 keV peaks, respectively, alerts the operator of a possible heterogeneity of the sample. In next studies, the geometric MCNP model of the Falcon 5000 detector will be optimized to reduce the uncertainty on � (92 ) and � (98 ), which is so far dominated by modeling uncertainty. This detector is equipped with a planar HPGe crystal, which will be finely characterized with a multi-energy highly collimated 152 Eu gamma source. This narrow photon beam will allow precisely estimating the dead layers vs. active area of the germanium crystal [3]. We will also measure 38 additional ore samples provided by ORANO Mining, on a wider range of uranium concentrations, to fully qualify the method in the Nuclear Measurement Laboratory of CEA, DEN, Cadarache. In parallel, we also study a low-resolution spectroscopy approach with easy-to-use room temperature NaI(Tl) or LaBr3(Ce) detectors, reducing again measurement time, and system cost as well.