Matias Rodrigues
email: matias.rodrigues@cea.fr

Martin Loidl

Sylvie Pierre

Determination of absolute Np L X-ray emission intensities from Am-241 decay using a metallic magnetic calorimeter

Keywords: Photon emission intensity, radionuclide metrology, metallic magnetic calorimeter

Photon emission intensities of radionuclides, i.e. the number of emitted photons per decay, are the single most important decay data when the photon spectrometry technique is employed in ionizing radiation metrology. However, their precise measurement is problematic because they are usually determined by photon spectrometry with spectrometers having a detection efficiency calibrated with X-ray and -ray emission intensities from other radionuclides. Therefore, these intensities are ultimately interdependent and correlated to some extent. A novel method was applied to determine the photon intensities of -emitting radionuclides by measuring the ratio between the rate of photons in the full energy peaks and the rate of detected -particles with the same detection set-up. Thus, there is no need to calibrate the detection efficiency and to standardize calibration sources by primary methods. The main condition to reach low uncertainties is to have a spectrometer with an intrinsic detection efficiency close to unity for the measured photons and -particles. This condition was fulfilled by a metallic magnetic calorimeter (MMC) with an intrinsic efficiency of around 99% between 5 and 25 keV. In addition, the MMC provides an ultra-high energy resolution of 28 eV (full width at half maximum), facilitating the processing of the spectrum. The method was applied to determine L X-ray emission intensities from the decay of 241 Am() → 237 Np emitted between 11.9 keV and 22.4 keV. A total L X-ray emission intensity of 37.90 (12) per 100 disintegrations was obtained; the value agrees well with previous measurements and has a lower uncertainty. The uncertainties of the L X-ray groups L, L and L were improved by a factor of two. Moreover, due to the high-energy resolution of 28 eV, a detailed set of 33 L X-ray emission intensities are provided.

Introduction

During the decay of a radionuclide, the atom or the nucleus of the daughter is excited, leading to the emission of X-rays or rays with characteristic energies E and photon emission intensities 𝐼 𝐸 (PEI). The PEIs are expressed as the number of photons emitted per decay. It is the most important decay parameter for quantitative analysis of a radioactive material by means of photon spectrometry [START_REF] Debertin | Gamma-and xray spectrometry with semiconductor detectors[END_REF]. Indeed, in ionizing radiation metrology, the activity 𝐴 of a radionuclide in a source at the measurement date t is determined from the energy spectrum obtained with an energy dispersive spectrometer. In stationary conditions, i.e. when the measurement live time ∆𝑡 is much smaller than the radionuclide half-life, the activity is given by the equation [START_REF] Debertin | Gamma-and xray spectrometry with semiconductor detectors[END_REF]:

𝐴 𝑡 • •∆ • (1)
where 𝑁 𝐸 and 𝑛 𝐸 are respectively the number of counts and the count rate in the full-energy peak (FEP) at the characteristic energy E, 𝜀 is the FEP detection efficiency, i.e. the probability for a photon emitted by the source to deposit all of its energy in the detector.

The FEP detection efficiency is usually obtained using standard radioactive sources with calibrated activity and wellknown PEIs in the appropriate energy range [START_REF] Bé | Recommended standards for gamma ray intensities[END_REF][START_REF] Herman | International Atomic Energy Agency[END_REF] and following:

𝜀 𝐸 • •∆ • . ( 2
)
Therefore, the activity measurement of a radionuclide by photon spectrometry is a relative method that strongly relies on the PEIs from other radionuclides, both to quantify the radionuclides in activity (equation [START_REF] Debertin | Gamma-and xray spectrometry with semiconductor detectors[END_REF]) and to establish the detection efficiency curves (equation ( 2)). In addition, the uncertainty of the PEIs is one of the major contributions to the uncertainty budget of the activity measured with photon spectrometry. At best, their relative uncertainties are about 0.5%, but generally 1-2%, in particular in the problematic low energy range below 100 keV [START_REF] Bé | Recommended standards for gamma ray intensities[END_REF][START_REF] Campbell | State-of-theart efficiency determination for a Si(Li) X-ray detector in the 3-40 keV energy range[END_REF][START_REF] Lépy | Consistency of photon emission intensities for efficiency calibration of gamma-ray spectrometers in the energy range from 20 keV to 80 keV[END_REF].

PEIs of a radionuclide are measured by semiconductor spectrometers generally with the same methodology as for the activity measurement (equation ( 1)), in this case using:

𝐼 𝐸 • •∆ • • (3)
i.e. they are determined by measuring the photon energy spectrum of a source with a precisely determined activity A and with a spectrometer with a well-established detection efficiency curve.

Therefore, the need to decrease the uncertainty of PEIs is part of a vicious circle; it requires a detection efficiency with a lower uncertainty, itself limited by PEIs from radionuclides.

Several studies have proposed to determine PEIs by a spectrometer with an efficiency established independently of the PEIs. The FEP detection efficiency, 𝜀 , can be expressed as the product of the geometry factor 𝑓 and the intrinsic detector efficiency 𝜀 . The factor, 𝑓 , refers to the probability that an emitted photon to go in the direction of the detector (or the collimator aperture) and the efficiency 𝜀 refers to the probability that a photon in the direction of the detector will deposit all its energy in the detector. A third factor, 𝑡 , can be introduced, related to the probability the photons will be transmitted through the windows between the source and the detector (vacuum or entrance window). The factor 𝑓 can be accurately calculated by measuring precisely the dimensions of the detection geometry (source and collimator diameters, and source-collimator distance) as it is the case for defined solid angle (DSA) -particle counting [START_REF] Pommé | Typical uncertainties in alphaparticle spectrometry[END_REF][START_REF] Pommé | The uncertainty of counting at a defined solid angle[END_REF]. Bambynek proposed to apply the DSA technique for the measurement of activity by photon counting [START_REF] Bambynek | Precise solid-angle counting Proc. Int. Symp. on Standardization of Radionuclides[END_REF]. Later, DSA photon spectrometry with proportional counters or scintillators was developed for measuring emission intensities of radionuclides [START_REF] Denecke | Measurement of the 59.5-keV gamma-ray emission probability in the decay of 241Am with a 4π-CsI(T1) -sandwich spectrometer[END_REF][START_REF] Elvira | Absolute determination of low-energy X-ray emission rates with a proportional counter[END_REF]. The advantage of these detectors is their well-defined and simple detection geometry to determine the geometrical efficiency, 𝑓 , associated with an intrinsic efficiency close to 100% that helps to minimize its correction. However, they have a poor energy resolution for spectrometry; proportional counters have an intrinsic efficiency of 100% only achievable below about 10 keV, hence, measurements of emission intensities did not reach accuracies better than 1% below 10 keV [START_REF] Pommé | The uncertainty of counting at a defined solid angle[END_REF], and scintillators were applied to some specific cases [START_REF] Denecke | Measurement of the 59.5-keV gamma-ray emission probability in the decay of 241Am with a 4π-CsI(T1) -sandwich spectrometer[END_REF].

DSA photon spectrometry was then studied by Martin and Burns to measure PEIs with a HPGe spectrometer independently of other radionuclides [START_REF] Martin | The HPGe as a defined-solid-angle detector for low-energy photons[END_REF]. In this case, the intrinsic efficiency has to be calculated analytically using atomic fundamental parameters or more frequently numerically with Monte Carlo (MC) simulations of particle transport through matter. Nevertheless, the intrinsic efficiency 𝜀 of semiconductor spectrometers is difficult to calculate accurately due to the contributions of many energy-dependent interacting processes:

-the transmission of photons through the detector absorber and the escape of secondary particles, -the incomplete collection of electron-hole pairs in the dead layers, -scattering photons around the detector environment overlapping with the FEPs [START_REF] Gysel | Description of Compton peaks in energydispersive x-ray fluorescence spectra X[END_REF][START_REF] Plagnard | Study of scattering effects in low-energy gamma-ray spectrometry[END_REF]. In addition, when MC simulations are performed, a precise knowledge of the dimensions of the detector is needed which is not guaranteed by the manufacturers and difficult to access. Consequently, the critical dimensions, in particular the dead A c c e p t e d M a n u s c r i p t layers [START_REF] Boson | A detailed investigation of HPGe detector response for improved Monte Carlo efficiency calculations[END_REF][START_REF] Elanique | Dead layer thickness characterization of an HPGe detector by measurements and Monte Carlo simulations[END_REF], have to be fitted to find the best agreement between simulations and experimental data from standard sources, and ultimately these methods rely on PEIs [START_REF] Vidmar | Automated construction of detector models for efficiency interpolation in gamma-ray spectrometry[END_REF][START_REF] Helmer | The use of Monte Carlo calculations in the determination of a Ge detector efficiency curve[END_REF]. Instead of calculating the intrinsic efficiency, Lépy and coworkers precisely characterized it for one of their semiconductor spectrometers with a monochromatic photon source; in addition, the geometrical efficiency was calibrated by a 55 Fe source with a calibrated emission rate [START_REF] Lépy | Measurement of 241Am L X-ray emission probabilities[END_REF]. They were able to measure the total L X-ray emission intensities from the decay of 241 Am independently of other radionuclide PEIs with a relative uncertainty of 0.7%.

In the present work, we propose a new method for measuring the photon emission intensities of 100% -emitting radionuclides independently of any efficiency calibration based on PEIs, and without the need to measure a source with a calibrated activity. In a simplified way, the method consists in measuring, with the same detection set-up, the ratio between the photon rate and the -particle rate from the source; the photon intensity 𝐼 𝐸 emitted at energy E is a given by:

𝐼 𝐸 • • (4)
where 𝑛 and 𝑛 are respectively the count rates of detected photons in the full energy peaks and detected-particles, each rate 𝑛 𝑁 ∆𝑡 ⁄ , where 𝑁 is the number of counts and ∆𝑡 is the measurement live time.

𝜀

and 𝜀 are respectively the detection efficiencies for the photons of energy E and the -particles.

For radionuclides decaying only by -particle emission, this method can be very precise without any calibration on the condition that 𝜀 𝜀 𝑓 ; which means that the detector must be able to measure both -particles and photons, with the same geometrical efficiency and with intrinsic efficiencies for photons and -particles as close as possible to unity. For -particles, since their energy is absorbed in a few µm, an intrinsic efficiency close to 100% is readily achieved. The LNE-LNHB has developed a detection set-up for photon spectrometry called SMX3 that fulfills these requirements. SMX3 is a metallic magnetic calorimeter (MMC) with a special absorber conceived to provide an intrinsic efficiency of 99% between 5 keV and 25 keV [START_REF] Rodrigues | A metallic magnetic calorimeter dedicated to the spectrometry of L X-rays emitted by actinides[END_REF]. Although it is not optimized for this purpose, it is able to measure -particles with the same detection geometry only by removing a beryllium window that stops -particles for most other measurements. Moreover, MMCs are a type of thermal cryogenic detector with the main advantage of having an excellent energy resolution, about one order of magnitude better than semiconductor detectors [START_REF] Fleischmann | Metallic Magnetic Calorimeters Cryogenic Particle Detection[END_REF].

The method was applied to the measurement of the L-X ray emission intensities from 241 Am α-decay. Americium-241 was chosen because it is one of the best known -emitting radionuclides, commonly used as a calibration source below 100 keV in the metrology of ionizing radiation and in many other applications [START_REF] Bé | Recommended standards for gamma ray intensities[END_REF]. On the one hand, this allows the present results to be compared with the most precise measurements of PEIs below 100 keV [START_REF] Chechev | Decay data evaluation project (DDEP): Updated evaluations of the 233Th and 241Am decay characteristics[END_REF], and on the other hand, this allows disseminating accurate and reliable PEIs to end users for the efficiency calibration of their spectrometers with 241 Am sources. Furthermore, the resolution of SMX3 is a very important asset in this case because it can separate the tens of X-ray lines, and provide as many PEIs, which is not possible with semiconductor detectors.

The experimental detection set-up

General principle of MMCs

MMCs are thermal cryogenic detectors, i.e. the absorbed energy E from an incoming particle is measured as a temperature rise:

∆𝑇 ( 5
)
where C is the detector heat capacity.

An MMC detector for photon spectrometry is often composed of a metallic absorber where the particle interacts and deposits partially or fully its energy, leading to a temperature elevation ∆𝑇. The absorber is tightly thermally coupled to a paramagnetic sensor made of gold (or silver) doped with a few hundred ppm of Er [START_REF] Fleischmann | Metallic Magnetic Calorimeters Cryogenic Particle Detection[END_REF]. The sensor is magnetized by a magnetic field of a few mT, and acts as a thermometer by converting the change of temperature in a variation of magnetization. The latter can be precisely measured by a DC SQUID sensor. The paramagnetic sensor is weakly thermally coupled to a heat bath, at a temperature 𝑇 , through a weak thermal link with a thermal conductance G. Therefore, each deposit of energy E in the detector is measured as a pulse with a height proportional to E and with a decay time constant (1/e) of d = C/G. The energy resolution of MMCs is not limited by the statistical uncertainty on the number of excited states created by the absorbed energy, as it is the case e.g. for the creation of electron-hole pairs in a semiconductor. For thermal cryogenic detectors, the energy resolution is given by the signal-to-noise ratio. The intrinsic noise limit is set by the so-called thermodynamic fluctuation noise (TFN), i.e. the statistical fluctuations of the detector internal energy with the thermal bath through the weak thermal link; the TFN causes a standard deviation on the energy resolution of:

𝜎 4 • 𝑘 • 𝑇 • 𝐶 ( 6
)
where 𝑘 is the Boltzmann constant.

Knowing that the heat capacity of non-superconducting metal absorbers decreases proportionally with the temperature, and considering equations ( 5) and ( 6): both the signal amplitude increases and the noise decreases toward very low temperature. Around 20 mK, very high-energy resolutions are achieved, up to more than one order of magnitude better than semiconductor spectrometers [START_REF] Kempf | Physics and Applications of Metallic Magnetic Calorimeters[END_REF][START_REF] Boyd | Metallic Magnetic Calorimeters for High-Accuracy Nuclear Decay Data[END_REF].

The dedicated MMC SMX3

In this work, the SMX3 MMC detector was used (figure 1). It was specially conceived for photon spectrometry below 25 keV, it has [START_REF] Rodrigues | A metallic magnetic calorimeter dedicated to the spectrometry of L X-rays emitted by actinides[END_REF]:

-a confirmed full width at half maximum (FWHM) energy resolution of about 30 eV up to 166 keV, -an intrinsic detection efficiency of about 99% between 5 and 25 keV, -an maximum acceptable count rate up to about 10 s -1 , -a total absorber area of 4 mm². The SMX3 absorber is divided into 4 pixels of 1 mm² each. By sharing the total absorber heat capacity between pixels, the signal-to-noise ratio and the energy resolution are improved. Each absorber is attached to a magnetic Au:Er sensor with about 300 ppm of erbium and each sensor is read by a meander shaped superconducting pick-up coil [START_REF] Burck | Microstructured Magnetic Calorimeter with Meander-Shaped Pickup Coil[END_REF]. Two pick-up coils are connected in parallel with a DC SQUID input coil thereby forming a superconducting magnetic flux transformer; the pulses of the two different sensors of one MMC chip cause signals with opposite polarities in the SQUID. Two SQUID channels allow reading the four pixels (figure 1). The weak 1 MMC chips were optimized, designed and produced by C. Enss' group at Kirchhoff-Institute for Physics, Heidelberg University [START_REF] Kempf | Physics and Applications of Metallic Magnetic Calorimeters[END_REF]. magnetic field of a few mT, required to magnetize the sensor, is created by a permanent current I0 circulating in double meander pick-up coils.

The absorbers of SMX3 are composed of a Au-Ag bi-layer in order to achieve an intrinsic efficiency as close as possible to unity below 25 keV. Indeed, the efficiency of a single gold layer absorber calculated by MC simulations, with the code PENELOPE [START_REF]A code system for Monte Carlo simulation of electron and photon transport[END_REF], shows a curve with three discontinuities around 13 keV (figure 2). These discontinuities are difficult to characterize. They are, firstly, due to the discontinuities of the photoelectric cross section of gold at the L3, L2 and L1 subshell binding energies, respectively 11.9 keV, 13.7 keV and, 14.4 keV, and secondly due to the escape of photons from the absorber surface facing the source. For the latter reason, the discontinuities are present regardless of the thickness of the absorber. Therefore, an additional layer of silver was added on top of the gold layer to reabsorb the escape photons, thus forming a Au-Ag bi-layer absorber. MC simulations have shown that it is possible to reach an efficiency close to 100% below 25 keV with thicknesses of at least 54 µm of gold and 16 µm of silver (figure 2) [START_REF] Rodrigues | A metallic magnetic calorimeter dedicated to the spectrometry of L X-rays emitted by actinides[END_REF][START_REF] Rodrigues | A Novel Type of Absorber Presenting a Constant Detection Efficiency for up to 25 keV X-Ray Photons[END_REF]. The intrinsic efficiency of the bi-layer has a small discontinuity at 3.4 keV and a large discontinuity at 25.5 keV (not shown), they correspond respectively to the L1-and Kbinding energies of silver. In the Np L-X ray energy range between 11.8 keV and 22.4 keV2 , the mean intrinsic efficiency is 99.03% and varies by less than 0.59%. In comparison the detection efficiencies of Si(Li) and HPGe detectors vary by more than 10% [START_REF] Lépy | Measurement of 241Am L X-ray emission probabilities[END_REF]. The absorbers were fabricated with the minimum required thicknesses of 54 µm of gold and 16 µm of silver in order to minimize their heat capacity and maximize the signal-to-noise ratio.

Figure 3 shows the overall detection assembly comprising: the SQUID (not shown) and the MMC chips, the source, the A c c e p t e d M a n u s c r i p t tungsten collimator and the beryllium window. The latter is necessary to absorb the -particles and the electrons emitted during the 241 Am decay when measuring the photon spectrum only. Indeed, the 5.5 MeV -particles could saturate the signal output and make the SQUID electronics unstable, while the Auger and internal conversion electrons will unnecessarily pollute the spectrum and increase the dead time of the measurement. The dimensions of the detection geometry are detailed in section 3.3.

The 241 Am sources

The need for two sources

Americium-241 has a half-life of 432.6 (6) a and decays by-particle emission to 237 Np, the latter having a half-life of 2.144 (7)×10 6 a. There are two main -particle energies that subsequently populate the 59.54 keV and the 102.959 keV levels with a probability of 13.23% and 84.45% respectively. Among the-transitions, four of these are below 60 keV: 26.34 keV, 33.20 keV, 43.42 keV and 59.54 keV. They are intense and strongly converted and are responsible for 98% of the emitted L X-rays by the 237 Np daughter. The recommended value of the total L-X-ray emission intensity is 37.66 (17) per 100 decays [START_REF] Chechev | Decay data evaluation project (DDEP): Updated evaluations of the 233Th and 241Am decay characteristics[END_REF].

Ideally the count rates 𝑛

and 𝑛 should be obtained from one spectrum, i.e. from one measurement with the same source, in order to consider the same live time, the same activity and the same source geometry (equation ( 4)). However, in practice, measuring both the X-rays and the particles at the same time would be very penalizing for the Xray spectrum measurement. Firstly, it is not possible to achieve the best energy resolution in the photon spectrum whilst also measuring the -particles. Indeed, with the optimal operating conditions for X-ray spectrometry, the SMX3 detector is too sensitive to measure the energies of -particles: an -particle of 5.5 MeV will produce a pulse of about 18 0 in the SQUID3 with a permanent current of I0 = 70 mA in the meander pick-up coil and at a temperature of 14 mK. Such a pulse is impossible to measure without signal instabilities given the rise time of a few µs and a slew rate of the SQUID electronics of about 1 0/µs. Therefore, to measure particles, the detector sensitivity has to be reduced, by reducing the sensor magnetization using a smaller permanent current, thus degrading the energy resolution. In addition, the measurement of the count rate 𝑛 must be performed without any window between the source and the absorbers, meaning that all the emitted particles (-particles, nuclear recoils, Auger and internal conversion electrons, X and -ray photons) emitted during the decay are detectable. As there are ten times as many emitted particles per decay as there are X-rays, most of the counting statistics would be useless, interfering in the X-ray region of interest. This is all the more penalizing since the maximum acceptable count rate of SMX3 is about 10 s -1 . For these reasons, two different sources of 241 Am with activities suited to the detector count rate were measured successively (table 1): an 241 Am source (called "X-ray source") dedicated to the measurement of the X-ray rate 𝑛 and an 241 Am source (called "-particle source") with lower activity for the rate 𝑛4 . Therefore, two correction factors must be introduced in equation ( 4):

A c c e p t e d M a n u s c r i p t

𝐼 𝐸 • • ∆ ∆ • • • , , (7)
where ∆𝑡 and ∆𝑡 are respectively the live times of the photon spectrum acquisition and the -particle counting acquisition,

𝐹 is the ratio of the relative activities of the -particle and the X-ray sources, 𝜀 , 𝐸 is the intrinsic efficiency for the X-rays with an energy 𝐸, 𝜀 , is the intrinsic efficiency for the -particles, lower than unity due to partial energy deposition in the absorber edges, 𝑡 is the transmission of photons through the beryllium window, and 𝐹 is a correction factor determined by MC simulations taking into account the differences between the geometries and the surface activity distributions of the sources.

The 241 Am source activities and the factor 𝐹

To determine the factor 𝐹 , the activities of the two 241 Am sources were measured by DSA -particle counting5 [START_REF] Pommé | The uncertainty of counting at a defined solid angle[END_REF]. The activity is given by the -particle count rate divided by the geometrical efficiency of the DSA system; the latter has been calibrated by the characterization of the detection geometry dimensions.

Knowing that the activity factor 𝐹 is the ratio between these activities determined with the same experimental system and the same spectrum processing technique, some of the uncertainty components are common, thus cancel each other.

The activities of the -particle source and the X-ray source are respectively 1816.4 [START_REF] Martin | The HPGe as a defined-solid-angle detector for low-energy photons[END_REF] Bq and 32169 (34) Bq at the A c c e p t e d M a n u s c r i p t measurement dates by the MMC (table 1). Only the uncertainties of the counting statistics, the extrapolation down to zero, the surface activity distribution and the reproducibility are considered. The activity distributions of the sources were measured by a source imager (figure 4). It results in 𝐹 0.05646 [START_REF] Pommé | The uncertainty of counting at a defined solid angle[END_REF].

Calculation of the correction factor 𝐹

The necessity to use two sources implies introducing the second correction factor 𝐹 that takes into account the different geometrical efficiencies due to the different surface activity distributions (active diameters and inhomogeneity of the distributions) and the different source-collimator distances 𝑍 (table 1). Given the detection geometry of the SMX3 set-up (figure 3), i.e. a large source diameter close to the collimator with a smaller hole diameter, the detection efficiency decreases with the source diameter. This dependence is amplified by the relatively large collimator thickness that acts as a double diaphragm for particles emitted at a distance from the center of the source larger than the radius of the collimator. Moreover, as shown in figure 4, the sources are inhomogeneous, so the count rate for a given source diameter will not only depend on the activity and the solid angle but also on the activity distribution of the source. To take into account the activity distributions, 𝐹 can be expressed as:

𝐹 ∑ ∑ , , , , ∑ ∑ , , , , (8) with
and where 𝑥, 𝑦, 𝑧 is the position coordinate of an elementary surface with an area of 100×100 µm 2 ; the activity distribution has 𝑛 𝑛 elementary surfaces, 𝑓 , 𝑥, 𝑦, 𝑧 is the geometrical efficiency for an elementary surface of 100×100 µm 2 at the position 𝑥, 𝑦, 𝑧 , and 𝑎 , and 𝑎 , are the normalized source activity distributions respectively for the -particle and X-ray sources obtained from the source imager (figure 4), such that:

∑ ∑ 𝑎 , 𝑥, 𝑦 ∑ ∑ 𝑎 , 𝑥, 𝑦 1 (11)
The elementary geometrical efficiencies 𝑓 𝑥, 𝑦, 𝑧 were calculated by MC simulations using the code PENELOPE. To model the detection geometry in the code, its dimensions involved in the solid angle were precisely determined using mainly two dimensional metrology systems: a Mitutoyo Quick vision measuring system for areas and a precision measuring column (Roch) for the distances and the thicknesses respectively. These dimensions are:

-the distances between the planes of the source disk, the collimator and the absorbers, -the area of the collimator hole 𝐴 , -the absorber area of the four pixels visible through the collimator 𝐴 . The collimator aperture is smaller than the area formed by the four absorbers (figure 3), therefore, 𝐴 𝐴 𝐴 , where 𝐴 is the gap area between the absorbers visible through the collimator. The total absorber area though the collimator aperture is 𝐴 = 2.410 (13) mm², the collimator hole area is 𝐴 = 2.592 [START_REF] Gysel | Description of Compton peaks in energydispersive x-ray fluorescence spectra X[END_REF] mm² and the gap area is 𝐴 = 0.182 (6) mm², the absorber covering area is 93.1%. The collimator has a circular hole with a radius of 𝑟 = 0.9083 (20) mm derived from its measured area. The area uncertainties are given by the uncertainty from the calibration of the vision measuring system and by the uncertainty for the detection of the surface edges by this system.

The distance between the plane of the source and the plane of the four absorbers facing the source is the sum of the three distances:

1-the distance between the plane of the rear of the collimator and the top plane of the absorbers 𝑍 = 0.491 (37) mm. To have access to 𝑍 , a lasermeter was used through the collimator hole, 2-the collimator thickness 𝑒 = 1.0066 (28) mm, 3-the distance between the source plane and the plane of the collimator front side 𝑍 , 12) mm respectively for the X-ray and the particle sources (table 1). Therefore, among the dimensions only 𝑍 contributes to the uncertainty of 𝐹 . The geometry modeled in the MC simulation is shown in figure 3. Figure 5 shows the simulated map of the geometrical efficiency 𝑓 𝑥, 𝑦, 𝑧 . One can notice that the geometrical efficiency varies significantly over the source area. It drops by 41% between the center and 5 mm from the center.

The uncertainty of the factor 𝐹 was investigated through the uncertainties of the sums 𝑆 and 𝑆 (equations ( 9) and ( 10)). For each sum, several contributions were taken into account:

-the background in the source distribution images (figure 4), -the position of the source center relative to the collimator center, -the distance between the source and the collimator, -the spatial resolution of the source distribution.

The background in the source activity distributions has very little impact on the sums, considering it will change the sums by less than 0.01%.

The spatial resolution is mainly due to the distance between the source and the radiographic film. The profile has a half-width at half maximum (HWHM) between 0.2 mm and 0.3 mm (figure 4). To estimate the effect of the spatial resolution, the sums 𝑆 and 𝑆 were calculated as a function of the HWHM for the simplified case of a homogenous source. Figure 6 shows that the values of the sums 𝑆 and 𝑆 decrease with the spatial resolution HWHM because a larger HWHM virtually spreads the activity outside the source where the 𝑓 efficiency decreases. This effect is cancelled for the most part, because 𝐹 is the ratio between 𝑆 and 𝑆 . As seen in figure 6, 𝐹 is slightly increased by a factor 1.00031 (7) due to the different source diameters. The uncertainty of the eccentricity between the source centers and the z-axis is about 0.2 mm and the source orientations with respect to the absorbers are unknown. These two uncertainties contribute 0.033% for both 𝑆 and 𝑆 . The uncertainties on the 𝑍 and 𝑍 distances contribute by 0.010% and 0.15% respectively for 𝑆 and 𝑆 . Nevertheless, in the factor 𝐹 , the uncertainties of 𝑍 and 𝑍 are correlated, therefore, the factor 𝐹 is 0.9783 [START_REF] Plagnard | Study of scattering effects in low-energy gamma-ray spectrometry[END_REF] with an uncertainty dominated by the one of the difference between the source-collimator distances i.e. 0.494 (9) mm.

The intrinsic detection efficiencies

3.4.1 The intrinsic alpha efficiency 𝜀 , . The absorbers are thick enough to fully absorb the -particle energy but due to the detection geometry, some -particles can reach the absorbers with an angle of up to 21° from the surface normal (figure 3); and hence some of -particles can cross the absorber edges without depositing all their energy. In the spectrum, these events contribute to the background leading to a lower detection efficiency in the -peaks. They could be taken into account by summing this background, however, other events contribute to the background, such as -particles partially losing their energy in the collimator edges and interacting in the absorbers. Therefore, it was preferable to calculate the reduction in the intrinsic efficiency 𝜀 , by MC simulations using the code AlfaMC [START_REF] Peralta | AlfaMC: A fast alpha particle transport Monte Carlo code[END_REF]. The simulated geometry takes into account the source diameter, the collimator and the four absorbers. In this case, absorbers are rectangular cuboids with perfectly sharp edges, but 𝜀 , depends on the sharpness of the edges, which is unknown. MC simulation gives an intrinsic efficiency of 0.9958; 𝜀 , lies between this latter value and unity (case of round edges), 𝜀 , and its uncertainty were calculated considering a uniform distribution between these two values: 𝜀 , = 0.9979 [START_REF] Gysel | Description of Compton peaks in energydispersive x-ray fluorescence spectra X[END_REF].

3.4.2

The intrinsic photon efficiency, 𝜀 , . As shown in figure 2, although the intrinsic efficiency 𝜀 , of photons between 5 keV and 25 keV is close to unity, there is about a 1% loss due to:

the escape of photons or electrons from the top surface of the absorbers, -the photons transmitted through the edge of the absorbers. Indeed, given the detection geometry, some photons arrive with an angle close to 19° from the normal of the absorber surface. The intrinsic efficiency, 𝜀 , , was calculated by MC simulations and its uncertainty depends only on the interaction cross sections and on the transport of the photons and secondary electrons. The PENELOPE database of the attenuation coefficients relies on the data generated by the XCOM database and on the Dirac-Hartree-Fock-Slater model of Scofield [START_REF] Sabbatucci | Theory and calculation of the atomic photoeffect[END_REF][START_REF] Seltzer | XCOM-Photon Cross Sections Database[END_REF][START_REF] Scofield | Theoretical photoionization cross sections from 1 to 1500 keV[END_REF]. For the photons, the uncertainties come from the cross sections, they are not well known and depend strongly on the energy range and on the absorption edge energies [START_REF] Chantler | Theoretical Form Factor, Attenuation, and Scattering Tabulation for Z =1-92 from E =1-10 eV to E =0[END_REF]. Fortunately, Islam and co-workers precisely measured, in the energy range of interest, the attenuation coefficients of silver and gold, the materials composing our absorber [START_REF] Scofield | Theoretical photoionization cross sections from 1 to 1500 keV[END_REF][START_REF] Chantler | Theoretical Form Factor, Attenuation, and Scattering Tabulation for Z =1-92 from E =1-10 eV to E =0[END_REF]. They observed a percentage difference of about 3% with the values from XCOM; this has been taken as a conservative relative uncertainty on the attenuation coefficients. For electrons, the uncertainty comes from their transport; since they are produced in a very large amount, the calculation of their transport has to distinguish between hard interactions (individually tracked) and soft interactions (statistical approximation calculation). The two types of calculation are set in the code PENELOPE by choosing cut-off energy parameters to get either precise or fast MC calculations.

To estimate these uncertainties, the intrinsic efficiency was simulated by varying many parameters:

1-the densities of gold and silver were changed by 3% to take into account the differences between measured and XCOM photon attenuation coefficients, 2-the cut-off values for the calculations of hard and soft interactions were changed to determine the impact of the more or less precise transport calculation of electrons, 3-the atomic numbers of the absorber materials were changed by ±1, keeping the same density of gold and silver in order to estimate the contribution of the cross section interactions as suggested in [START_REF] Bochud F O, Laedermann | Uncertainty associated with Monte Carlo radiation transport in radionuclide metrology[END_REF]. The results from all these MC simulations at 16 keV give an intrinsic detection efficiency of 𝜀 , = 0.9901 [START_REF] Martin | The HPGe as a defined-solid-angle detector for low-energy photons[END_REF]. The intrinsic efficiency varying little between 11 keV and 25 keV, a constant relative uncertainty of 0.11% was considered for this energy range.

Transmission of the beryllium window

For the measurement of the X-ray spectrum, a 37.4 (23) µm thick beryllium window was used to absorb the -particles and most of the electrons emitted during the decay of 241 Am.

The transmission of the beryllium window is shown in figure 2 and given by:

𝑡 𝑒 • ⁄ ( 12
)
where 𝜇 is the mass attenuation coefficient of beryllium, 𝑚 is the window mass, weighed with a microbalance, and 𝐴 is the area of the window determined with the vision measuring system. The ratio 𝑚 𝐴 ⁄ is 0.006681 (20) g/cm².

The attenuation coefficient 𝜇 is the dominant source of uncertainty for 𝑡 . Gerward measured and compared the photoelectric cross sections of beryllium between 5 keV and 18 keV and noticed a deviation of the order of 5% from the data from the Dirac-Hartree-Fock-Slater model [START_REF] Gerward | Theoretical upper and lower limits to experimental X-ray attenuation coefficients[END_REF]. By taking this discrepancy as a conservative relative uncertainty on the mass attenuation coefficient, and by combining it with the uncertainty of the ratio 𝑚 𝑆 ⁄ , a constant relative uncertainty of 0.03% was considered for the energy range 11 keV to 25 keV. The transmission at 16 keV is 𝑡 0.99831 [START_REF] Scofield | Theoretical photoionization cross sections from 1 to 1500 keV[END_REF].

The -particle counting

The -particle source of 241 Am was measured to determine the count rate such as:

𝑛 ∑ ∑ 𝑛 , , = ∑ ∑ 𝑁 , , ∆𝑡 , ⁄ (13)
where 𝑁 , , are the numbers of -particle counts in each pixel, the index i designates one of the two SQUID channels and the index j one of the two pixels of a given channel. The pixels of the same channel have the same live time ∆𝑡 , .

The output voltages of the two SQUID channels were digitized and recorded continuously using a 16-bit resolution acquisition card at a sampling frequency of 100 kHz. The data were recorded during 9.6 days on a hard disk and the data analysis to obtain the spectrum was performed and optimized offline.

A c c e p t e d M a n u s c r i p t

Figure 8. Pulse heights as a function of the pulse shape parameter Qpulse/template obtained after the least squares fit with the truncated templates. The two top subplots present the results using the regular pulse template (figure 7). The two bottom subplots show the results using the template of flux jump pulses. The two right subplots are a zoom around the selected pulses.

As explained in section 3.1, the SMX3 detector is too sensitive for measuring -particle energies when it is in its normal operating conditions; its sensitivity was reduced by choosing a smaller permanent current I0, in the pick-up coils, lower than 1 mA. However, one channel showed too high sensitivity for which some pulses had a flux jump6 of 1 0 3 (figure 7). These flux jumps are due to detected -particles and have to be taken into account in the count rate 𝑛 .

Each channel shows positive and negative pulses according to which of the two absorbers has absorbed a particle. Once the off-line trigger has detected the pulses in the continuous streams, the pulse heights are determined by scaling the height of a truncated pulse template of W = 2.56 ms on each triggered pulse with a least squares fit (figure 7). This pulse height analysis degrades the energy resolution by about 20% compared with an optimal filtering analysis, but it has the advantage to strongly reduce the pile-up probability and the dead time; indeed optimal filtering requires longer templates, typically about 16 ms [START_REF] Szymkowiak | Signal processing for microcalorimeters[END_REF]. More details of the data processing are given in [START_REF] Mariam | Determination of L-X ray absolute emission intensities of 238Pu, 244Cm, 237Np and 233Pa radionuclides using a metallic magnetic calorimeter[END_REF].

For the channel having some flux jumps, two pulse templates were applied: one template representative of regular pulses and the other one representative of the flux jump pulses (figure 7). Each of the two types of pulses can easily be selected by comparing the pulse shape parameter Qpulse/template calculated as the mean squared error of the fits between the pulses and the two templates (figure 8).

The live times ∆𝑡 , were determined by two methods. The first method applies an extendable dead time. However, with this method, the live time must be corrected by the pileup rejection. Indeed, when a pulse is triggered, a second pulse can arrive within the time window 𝑊 required to estimate the pulse energy (figure 7); the resulting pulse energy is not properly determined and can be out of the region of interest in the energy spectrum, leading to a missing count. These pulse pile-ups were rejected based on a selection criterion of the parameter Qpulse/template. However, regarding the live time, these pile-ups are valid pulses and hence the live time must be corrected by the probability 𝑃 of not having a pulse during the time 𝑊:

𝑃 𝑒𝑥𝑝 • ( 14
)
where 𝜏 is the count rate of each channel, Given the recorded count rates, 𝑃 was calculated to be 99.73% and 99.65% respectively for the two channels with a truncated template. The second method is the pulser method. It consists in adding pulses in the continuously digitized raw stream data with a unique height and with random times of arrival. The rate of the pulser pulses 𝑛 being known, the live time ∆𝑡 is given by the count number 𝑁 in the pulser peak of the spectrum divided by 𝑛 . The main advantage is that the determination of the live time is independent of pile-up jump to another working point. This appears on the electronics output as a voltage jump equivalent to an integer number of 0.

A c c e p t e d M a n u s c r i p t rejection. However, a large pulser count is required to reach a small statistical uncertainty, which tends to increase also the dead time. By comparing the results of the two methods, we can ensure that no potentially hidden dead time is missed, in particular from saturations.

The count numbers 𝑁 , , were determined by summing all the counts in a region of interest (ROI) between 4.0 MeV and 5.6 MeV in order to take into account: most of the counts in the left tail due to the straggling of α-particles in the source and all the -emissions of 241 Am lying between 4.76 MeV and 5.54 MeV (figure 9). A nearly constant background is present between 1 MeV and 4 MeV with a level much higher than the one in the DSA -particle spectrum obtained in section 3.2. Part of this background is due to straggling in the source and must be taken into account in 𝑁 . While from the DSA spectrum the source straggling is expected to be 0.1 count per keV around 3 MeV, the observed level is 1.1 counts per keV. We attributed the excess of background to scattering of particles in the detector surrounding and to straggling in the edges of the collimator and the absorbers, the detection set-up being not configured to minimize these effects. Therefore, the count number 𝑁 , , was subtracted of the background by an extrapolation from the range 1 MeV -4 MeV to 4 MeV -5.6 MeV. The total alpha rate 𝑛 is 1.0408 ( 14) counts per second, with a relative uncertainty dominated by the counting statistics (relative contribution of 0.13%).

L X-ray spectrum of 237 Np from the decay of 241 Am

Signal and data processing

The X-ray source of 241 Am was measured during 15 days at 13 mK, the SQUID electronics output voltage, digitized with a resolution of 16-bits and a sampling frequency of 500 kHz, was recorded continuously on a hard disk.

Here, two methods were applied to determine the pulse heights. The first one determines them by fitting a truncated pulse template to the detected pulses with a time window W = 2.05 ms. This method was preferable for the determination of the L, L, and L group PEIs and the total PEI: although it is not the best pulse height estimator, it minimizes the pile-up probability and therefore gives a more reliable live time with lower uncertainty. The second method estimates the pulse energy after applying an optimal filter [START_REF] Szymkowiak | Signal processing for microcalorimeters[END_REF]; it gives the best amplitude estimation and the best energy resolution (15% better than with the truncated template method) to separate as many lines as possible. However, this optimal filtering required a long pulse time window W = 16.4 ms with a larger pile-up probability of 5.8% versus 0.73% with the truncated template method. This method was preferred to determine the PEIs of the individual LX-ray transitions; they were renormalized with respect to the total PEI obtained from the first truncated template method. The live time was determined after applying an extendable dead time, and it was checked using the pulser method as described in section 4. Each pixel provides a spectrum with its own energy resolution and energy non-linearity which are slightly different from each other. In order to obtain a total energy spectrum by summing the individual spectra without degrading the energy resolution nor distorting the energy peak shape, the energy scales² were linearized and their energy resolutions were homogenized to match the poorest resolution among the four spectra [START_REF] Mariam | Determination of L-X ray absolute emission intensities of 238Pu, 244Cm, 237Np and 233Pa radionuclides using a metallic magnetic calorimeter[END_REF]. For each pixel, the deviation from the linear response was determined as the difference between A c c e p t e d M a n u s c r i p t a number of measured energies and their corresponding tabulated data from [START_REF] Deslattes | X-ray transition energies: new approach to a comprehensive evaluation[END_REF]. The deviation was fitted with a second order polynomial to allow the non-linearity to be corrected (figure 10). Afterward, the individual corrected spectra were summed after being weighted by their respective live times (equation ( 13)).

Spectrum processing of L X-rays.

In order to extract the count rate in the FEP, 𝑛 , the L X-ray spectrum was processed with the software Colegram in a ROI between 10.4 keV and 24.5 keV and around 4.8 keV to determine the PEI of the L1-L3 transition [START_REF] Ménesguen | COLEGRAM, a flexible user-friendly software for processing of ionizing radiation spectra[END_REF]. Due to the high statistical precision (6×10 6 counts) and the energy resolution (between 28.0 eV and 33.8 eV FWHM), the spectrum is highly detailed and many lines and structures have to be taken into account during the spectrum processing (figures 11 and 12): -the X-ray diagram lines of Np correspond to X-ray transitions occurring when the atoms are singly ionized; the corresponding peaks were fitted with a single Voigt function, i.e. the convolution of a Lorentzian function and a Gaussian function. The Lorentzian function represents the natural line width of the transition given by the sum of the initial and the final atomic level widths. The Gaussian function is the contribution from the detector energy resolution. For the most intense and well-separated lines, one of the two widths is a free parameter, while for the other lines the two widths are fixed. The Lorentzian fixed widths were set according to the values from [START_REF] Hoszowska | Linewidths of photoinduced L x rays of uranium[END_REF][START_REF] Campbell | WIDTHS OF THE ATOMIC K-N7 LEVELS At[END_REF]. The fixed Gaussian widths were set according to the least good energy resolution among the four pixels (figure 10) 7 . The energies and the heights of the Voigt functions are free parameters.

-the satellite X-ray structures come from X-ray transitions of multiply ionized atoms: these structures are present for the L3 X-rays. Indeed most of the L3 vacancies are created following a Coster-Kronig transition with an initial vacancy in L2 or L1. The resulting atom is multi-ionized with at least two vacancies, one in L3 and a second vacancy (spectator vacancy) in an outer shell. When the L3 vacancy is filled by an outer electron, the emitted X-rays have a higher energy than that of the diagram transition, due to the different electronic configurations. X-ray satellites have a complex shape due to the tens of possible transitions, depending on the quantum numbers of the electronic configuration [START_REF] Parente | L x-ray satellite energies At[END_REF]. The shape cannot be fitted with a single Voigt; instead, each satellite structure was fitted using two or three Voigt functions with the same width as the diagram lines, and with free energies and free heights (figure 11). 7 For the main X-ray lines, the Lorentzian width could have been a free parameter, however the shape of a Lorentzian function has extended « wings » compared to the Gaussian -the background between 10.4 keV and 24.5 keV was fitted with a constant function and three step functions. The constant function represents the Compton background from the -rays. The three step functions represent the background produced by the main L X-ray groups: L, L and L. The step functions are centered on each group energy (figure 12).

-the left tailed components appearing on the left side of each main X-ray peak were fitted with exponential functions (figure 12). The origin of these tails is not clear; they are also present on the -ray peaks of 26.3 keV and 59.5 keV. While for Xrays, left tails could come from physical processes of the atomic rearrangement, such as radiative Auger emission (RAE) [START_REF] Åberg | Theory of the Radiative Auger Effect[END_REF][START_REF] Campbell | and radiative Auger photon intensities in K x-ray spectra from atoms in the 20≤Z≤40 region[END_REF], the -ray line profile is expected to be emitted with a perfect Lorentzian shape with a very narrow natural line width. Therefore, left tails must be caused either by Compton scattering of photons in the surrounding materials between the source and the absorber, e.g. the beryllium window, or by a detector response distortion [START_REF] Gysel | Description of Compton peaks in energydispersive x-ray fluorescence spectra X[END_REF]. The contribution from Compton scattering has been excluded by MC simulations, the response distortion is therefore assumed to be responsible for these tails. The hypothesis to explain this distortion is that many 59.5 keV -rays pass through the absorbers and interact in the MMC chip nearby the sensor leading to a strong change in the temperature of the chip. Therefore, thermodynamic quantities of materials thermally coupled with the MMC are modified, affecting the pulse shape and the measured energy.

In figure 13, the -ray peaks are well fitted with a Gaussian and two exponential functions representing a short and a long tail. The area of the long component is constant with the energy and represents 0.5% of the peak area while the area of the short exponential components decreases from 2.0% to 1.3% at 59.5 keV and 26.3 keV, respectively. In the L Xray spectrum, the long exponential components are clearly present with the same ratio tail area over peak area for -rays as well as for the most intense L X-rays, i.e. ~ 0.5%; this component was fitted for the most intense L X-ray peaks (figure 12). Concerning the short left tail components, they are hardly noticeable for L X-rays due to the complexity of the spectrum and due to the shape of the Voigt functions. Thus, the short components were ignored assuming that they are included in the Voigt functions. Indeed, figure 13 shows that for a Gaussian and a Voigt with equal area, a Voigt function strongly overlaps with the tails, in contrast with the Gaussian function. Moreover, for the most intense peaks, one of the two widths (Gaussian or Lorentzian) is a free parameter in order to include the short tails in the Voigt.

shape, so the wings tend to alter the peaks depending on certain background features and increase the peak area.

A c c e p t e d M a n u s c r i p t

After applying this fitting procedure, the residuals between the fit and the experimental spectrum did not show any particular trend adjacent to the peaks (figure 12). There are only a few lines interfering in the ROI coming from the fluorescence of gold, silver and tungsten; they are easily distinguished in the spectrum (figure 11). 237 Np from the decay of 241 Am

L X-ray emission intensities of

Emission intensities of the Siegbahn L X-ray groups

For the following Siegbahn lines and groups, L, Ls, Lt, L, L, L and Lthe absolute PEIs were determined with equation ( 7), the rate 𝑛 of each group being the sum of the rates in the Voigt functions (diagram lines and satellite structures) and the exponential functions in the respective energy range. The present absolute total L X-ray emission, i.e. the sum of these group intensities, is 37.90 [START_REF] Gysel | Description of Compton peaks in energydispersive x-ray fluorescence spectra X[END_REF] per 100 decays 8 . Figure 14 shows the comparison of the present value with the published data and with the recommended value from Chechev [START_REF] Chechev | Decay data evaluation project (DDEP): Updated evaluations of the 233Th and 241Am decay characteristics[END_REF]. A good agreement with all the data is observed and the present uncertainty is about a factor 2 lower than the most precise previous measurement (table 2).

Table 2 and figure 15 show and compare the absolute PEIs of L, L, Land L, obtained in this work and the ones published in the literature from various measurements with semiconductor detectors. The present PEIs are in good agreement with the published data, with uncertainties about two times lower than the best measurements [START_REF] Lépy | Measurement of 241Am L X-ray emission probabilities[END_REF][START_REF] Lépy | Comparison of experimental and theoretical L X -ray emission probabilities of 241Am, 239Pu and 240[END_REF]. The only intensity group which is not consistent with the recommended value and with most of the measurements is the L intensity, while all the published values agree. Theoretical calculations do not seem to support our value, the deviation 𝐷 𝜄/𝛼 between the theoretical intensity ratio L/L and the present results is 𝐷 𝜄/𝛼 = 9.2%, while the data in the literature are in agreement with the theoretical emission rate ratio of L/L. Nevertheless, nothing can explain such A c c e p t e d M a n u s c r i p t a discrepancy in the present experiment; the efficiency cannot vary by about 9% within a few keV while there is no possible edge discontinuity; in addition, the L and L peaks are well separated, allowing for a safe spectrum processing, and no other peaks from fluorescence or from escape photons can overlap with L.

In a past measurement with MMCs, a discrepancy was also observed for the L/L ratio of Bi X-rays emitted from the decay of 210 Pb (𝐷 𝜄/𝛼 = 16.4%) while we observed a good agreement with the calculated ratio of U X-rays emitted by the decay of 238 Pu L/L (𝐷 𝜄/𝛼 = 1.2%) [START_REF] Mariam | Determination of L-X ray absolute emission intensities of 238Pu, 244Cm, 237Np and 233Pa radionuclides using a metallic magnetic calorimeter[END_REF][START_REF] Rodrigues | Determination of absolute photon emission intensities of 210 Pb[END_REF]. In fact, the ratio L/L depends strongly on the satellite intensity of the L3 transitions. Indeed, the observable satellites represent a few tens of percent of the L3 transition intensity for 210 Pb and 241 Am, while it is only a few percent for 238 Pu 9 . For 210 Pb and 241 Am, respectively 99% and 61% of L3 vacancies are produced consecutively to Coster-Kronig transitions from L1 and L2 vacancies, versus only 15% for 238 Pu. After the Coster-Kronig transition, the spectator vacancies are mostly located in M4 or M5 subshells, the creation of an M1 vacancy being energetically not possible. Therefore the decay channel of an M4,5 electron filling the L3 (i.e. an L transition) vacancy is reduced in favor of the L3-M1 (L transition) because there is one electron missing in the M4,5 subshells [START_REF] Larkins | Dependence of fluorescence yield on atomic configuration[END_REF][START_REF] Campbell | Measurement of the L1 subshell fluorescence and Coster-Kronig yields of bismuth[END_REF]. Finally, the disagreement with the calculated L/L ratio is not surprising because calculated data assume single vacancy states [START_REF] Scofield | Hartree-Fock values of L x-ray emission rates[END_REF]. Thus, we are confident in the present measurement of the L intensity even if we cannot explain why the other measurements have lower L PEIs.

Emission intensities of L X-ray transitions

Owing to the excellent resolution of the MMC SMX3 and the large counting statistics, it was possible to measure the intensities of 32 L X-rays of 237 Np from the decay of 241 Am in the energy range 10.4 keV -24.5 keV, and the L1-L3 PEI at 4.8 keV 8 .

For each L X-ray transition, its PEI is the sum of the diagram line, with the satellites structure and left tail component when they are present. Table 3 shows the results of PEI for the 33 X-ray transitions. Some closely spaced transitions cannot be well separated, these transitions are either X-ray satellites (see L3-N4,5, L3-N6,7, L3-O4,5 in figure 11) that spread over several tens of eV and/or X-rays involving electrons from outer shells with closely spaced binding energies (L3-O1,2,3, L3-P1,4,5, L1-O4,5 in figure 11). In these cases, the PEIs are the sum of the overlapped transitions.

While the spectrum processing had little impact on the uncertainty of the Siegbahn groups (table 3), some PEIs vary 9 Satellites are observable only if their energy shift is significantly higher than the width of the diagram peaks and the resolution of the detectors. For L3-M transitions, it is the greatly depending on the fitting procedure applied, especially the X-rays sitting on the left tail of an intense peak, for example for L3-M3, L2N3 or L3-O4,5. Often simply ignored, systematic errors related to the fitting procedure are difficult to estimate. In the present work, the systematic errors were calculated from different results derived of different assumptions (how the left tail areas are shared between the peak areas) and different procedures (with and without left tails). The partial relative uncertainties for each transition are detailed in table 3.

Uncertainty budget

The uncertainties involved in equation ( 7) to measure the PEIs, and detailed throughout the article, are summarized in table 4. One can distinguish three types of uncertainty:

-the counting statistics uncertainties, which appears in the correction factor 𝐹 , the count numbers 𝑁 and 𝑁 , they contribute with a relative uncertainty of 0.17%, -the uncertainty of the corrections related to the interaction of particles (intrinsic efficiencies 𝜀 , and 𝜀 , , beryllium window transmission 𝑡 ) with a relative contribution of 0.20%, -the uncertainty related to the geometry (source positioning, and source activity inhomogeneities) with a relative contribution of 0.18%. The weights of these contributions are comparable and, together, they represent 93% of the total combined uncertainty. For future measurements, it is interesting to see how these contributions could be reduced. The counting uncertainty could be reduced to 0.1% whilst maintaining reasonable measurement times.

The geometry uncertainty can be reduced to 0.06% with more appropriate source holder and source geometries. It remains much more challenging to reduce the uncertainty on the intrinsic efficiencies. For now, it is not clear how to reduce the uncertainty of the photon intrinsic efficiency, 𝜀 , . Potentially, the uncertainty of the -particle intrinsic efficiency, 𝜀 , , could be suppressed by using a nonpixelated absorber to get rid of the pixel edge effects. However, this will obviously be at the detriment of the resolution and the count rate capabilities. Taking into account all these reductions, a total relative uncertainty closer to 0.2% could be achieved. case when the spectator vacancy is in an M subshell: the shift is in the order of a few tens of eV, while when the spectator vacancy is in an N shell the shift is the order of a few eV.

Conclusion

Measurements have been made of the total L X-ray emission intensity of 237 Np, from the decay of 241 Am, with a relative uncertainty of 0.32%, and details of 33 L X-ray emission intensities by combining the method inspired by Lépy and coworkers with the performances of a metallic magnetic calorimeter. The emission intensities were determined by measuring the ratio between the L X-ray rate and the particle emissions rate from two 241 Am sources with the same detection system. These measurements are deemed accurate assuming the intrinsic detection efficiency of the photons is close to 100%.

It has been proved that, with the current detection system, photon emission intensities of other -emitting radionuclides from a few keV to 25 keV could be measured with the same level of uncertainty. Thus, the obtained emission intensities are free of any efficiency calibration from other emission intensities and free of standard sources established by other primary methods. This makes the present results truly absolute emission intensities. 237 Np from 100 decays of 241 Am for some Siegbahn groups and lines obtained in this work with those measured or evaluated in the literature. The references of the measured data are cited in [START_REF] Chechev | Decay data evaluation project (DDEP): Updated evaluations of the 233Th and 241Am decay characteristics[END_REF]. The combined uncertainties are given for one standard deviation.

Table 2. Comparison between the L X-ray emission intensities of

Figure 1 .

 1 Figure 1. a) and b) Schemes of the MMC SMX3 with its four pixel absorbers and its read-out by two SQUID channels. c) Photograph of the MMC and the SQUID chips (b) 1 .

Figure 2 .

 2 Figure 2. Left axis: intrinsic efficiencies calculated by the MC simulations, for a 70 µm thick gold absorber and for a Au-Ag absorber with 54 µm thick gold and 16 µm thick silver. Right axis: transmission of photon through the 37 µm thick beryllium window calculated by MC simulations.

Figure 3 .

 3 Figure 3. Left, a cross-sectional view of the experimental set-up at scale. Right, view of the square absorbers through the collimator. All parts are cylindrically symmetrical along the z-axis, except for the absorbers and chips.

Figure 4 .

 4 Figure 4. Left: activity distribution 𝑎 of the -particle source. Right: activity distribution 𝑎 of the X-ray source. The two top panels show the surface normalized activity distribution per elementary surface of 100×100 µm² at the position 𝑥, 𝑦 . The two bottom panels show 1-D activity distributions along the dashed lines. The arrows show the HWHM resolution of the profile.

Figure 5 .

 5 Figure 5. Geometrical efficiency 𝑓 𝑥, 𝑦, 𝑍 𝑋 of the detector SMX3 obtained by MC simulations for each elementary area of 100×100 µm² at the positions 𝑥, 𝑦, 𝑍 𝑋 . All these dimensions of the detection geometry set-up were unchanged between the measurements of the two sources, except for the distance 𝑍 . The distance 𝑍 was modified by the different source backing made of stainless steel disks: 𝑍 is 𝑍 16.339 (8) mm and A c c e p t e d M a n u s c r i p t

Figure 6 .

 6 Figure 6. Left y-axis: deviations of the sums 𝑆 and 𝑆 from the sum of a source image with a zero HWHM spatial resolution. Right y-axis: correction on the factor 𝐹 𝑆 /𝑆 . The dashed lines are the limits observed on the HWHM spatial resolution in figure 4.

Figure 7 .

 7 Figure 7. Pulses of 5.5 MeV -particles and their truncated pulse template scaled by least squares fitting. Top, a regular pulse. Bottom, a pulse with a flux jump of 1 0.

Figure 9 .

 9 Figure 9. The spectrum of -particles obtained with the MMC SMX3. The FWHM instrumental resolution is about 3.3 keV. The dashed lines represent the fit of the five main peaks.

Figure 10 .

 10 Figure 10. Top, non-linearities of each pixel given by the difference between the measured energies and the tabulated energies. Bottom, energy resolution of each pixel. Each marker type represents the experimental data of one pixel. The lines correspond to the fit of the experimental data with a 2 nd order polynomial.

Figure 11 .

 11 Figure 11. Detailed spectrum processing of the L X-ray peaks in three energy ranges: L -L, Land L. The solid lines are the diagram transitions and the dashed lines are the satellites. The other Voigt functions are fluorescence and escape peaks. Left tail components are shown in figure 12 for clarity.

Figure 12 .

 12 Figure 12. Top, experimental L X-ray energy spectrum and its total fit. The step functions fit the background and the exponential functions fit the long left tails of the main peaks. The fit of the individual peaks is detailed in figure 11 for more clarity. Bottom, resulting residuals between the fit and the experimental data.

Figure 13 .

 13 Figure 13. Spectrum processing of the -ray peaks at 26.3 keV (top) and 59.5 keV (bottom) and their left tails. The -ray FEPs are fitted with one Gaussian function and two exponential functions for the left tails. The step function fits the background. The dashed Voigt function has the same area as the Gaussian.

Figure 14 .

 14 Figure 14. Total absolute emission intensities referenced in [21] and the result of the present work. The uncertainty bars are plotted for a coverage factor k = 2.

Figure 15 .

 15 Figure 15. Absolute emission intensities of the groups L, L, L and L referenced in [21] and the results from the present work. The uncertainty bars are plotted for a coverage factor k = 2.

  A c c e p t e d M a n u s c r i p t

Table 1 .

 1 Characteristics of the two measured 241 Am sources.

	Source for:	Activity / Bq	Measure-ment date	Distance 𝑍 / mm	Active diameter / mm

-particles 1816.4 (11) 14/01/2022 15.845 (12) 10.5 X-rays 32169 (34) 08/05/2021 16.339 (8) 6.5

  ,

	𝑆	∑	∑	𝑎 , 𝑥, 𝑦	𝑓 , 𝑥, 𝑦, 𝑍	(9)
	𝑆	∑	∑	𝑎 , 𝑥, 𝑦	𝑓

, 𝑥, 𝑦, 𝑍

Table 3 .

 3 Photon emission intensities of L X-rays emitted by237 Np from the decay of 241 Am per 100 decays. The two last columns show the two partial relative uncertainties from the counting statistics and fitting procedure; a third contribution related to the detection efficiencies is 0.33% (not shown) equal for all the transitions. The uncertainties are given for one standard deviation.

	Line or group	Gehrke and Lokken	Watson and Li	Campbell and McNelles	Gunninck et al.	Cohen*	Bland et al.	Lépy et al. [45]	Lépy et al. [18]	Chechev and Kuzmenko** [21]	This work
		1971	1971	1974	1976	1988	1992	1994	2008	2009
	L	0.81 (7)	0.87 (6)	0.86 (2)	0.806 (40)	0.858 (28)	0.837 (10)	0.864 (12)	0.837 (9)	0.844 (9)	0.8989 (38)
	Ls	-	-	-	-	0.017 (5)	0.0073 (13)	-	-	-	0.01024 (26)
	Lt	-	-	-	-	0.0302 (37)	0.032 (10)	-	-	-	0.0101 (8)
	L	12.6 (9)	13.5 (12)	13.20 (25)	13.2 (7)	13.12 (42)	13.01 (10)	13.03 (13)	13.00 (12)	13.02 (10)	13.046 (41)
	L L	19.1 (14)	19.1 (14)	19.25 (40)	19.2 (10)	0.380 (12) 18.9 (6)	0.377 (15) 18.61 (15)	0.369 (12) 18.39 (19)	0.404 (5) 18.65 (13)	0.384 (20) 18.58 (13)	0.3745 (23) 18.68 (6)
	L	4.75 (35)	4.75 (35)	4.85 (15)	4.96 (25)	4.96 (16)	4.815 (38)	4.74 (8)	4.84 (3)	4.83 (3)	4.883 (20)
	Total	37.3 (18)	38.2 (20)	38.2 (8)	38.2 (2.0)	38.2 (12)	37.69 (30)	37.39 (24)	37.73 (26)	37.66 (17)	37.90 (12)
	*relative measurement normalized to the L intensity from this work.
	**evaluated data

A c c e p t e d M a n u s c r i p t

Table 4 .

 4 Uncertainty budget of all the quantities used to determine the photon emission intensities from equation[START_REF] Pommé | The uncertainty of counting at a defined solid angle[END_REF]. Weight and area of Be window <0.01% *The most favorable case has been chosen for the relative uncertainties of L emission intensity.

			𝑛	0.14%	𝑁 ∆𝑡	0.13% 0.056%	Counting statistics Background extrapolation Clock Pile-up rejection	0.13% 0.020% 0.050% 0.019%
		𝑛 *	>0.12%	𝑁 * ∆𝑡	>0.084% 0.080%	Counting statistics* Spectrum processing* Clock Pile-up rejection	>0.058% >0.061% 0.050% 0.085%
	PEI I	>0.32%	𝐹	0.12%	X-ray source activity -particle source activity	0.11% 0.061%	Counting Source geometry and positioning Counting Source geometry and positioning	0.10% 0.030% 0.053% 0.030%
							Eccentricity and orientation	0.033%
		𝐹		0.17%			Disk thicknesses	0.17%
							Source image	<0.01%
		Intrinsic efficiencies	0.16%			𝜀 , 𝜀 ,	0.12% 0.11%
			𝑡	0.03%			Attenuation coefficients of Be	0.030%

The L1 -L3 transition at 4.82 keV is not considered in the energy range between 11.8 keV and 22.4 keV .

0 is the magnetic flux quantum, 1 Φ 2.067833848 10 Wb

It is not necessary to use an 241 Am source to measure 𝑛 , another -emitting radionuclide can be used since the measurement of 𝑛 is equivalent to calibrating the geometrical efficiency.

Because 𝐹 is the ratio between the two activities, an activity standardization is not necessary and a relative measurement of the source activities would have been sufficient.

A flux jump occurs when the variation of flux in the SQUID is faster than the maximum slew rate of the SQUID electronics, the working point of the SQUID imposed by the feedback reaction becomes unstable and the SQUID may

The X-ray line L1-L3 presented in table 3 is not included in the total L X-ray emission intensity in order to be comparable with published data.

Acknowledgements

This work was performed as part of the EMPIR Project 17FUN02 MetroMMC. This project has received funding from the EMPIR program co-financed by the Participating States and from the European Union's Horizon 2020 research and innovation program.

Author et al [START_REF] Chechev | Decay data evaluation project (DDEP): Updated evaluations of the 233Th and 241Am decay characteristics[END_REF]


Wijdane Kaiss
email: wijdane.kaiss@univ-ubs.fr

Khalifa Mansouri

Franck Poirier

Pre-Evaluation with a Personalized Feedback Conversational Agent Integrated in Moodle

Keywords: Evaluation, Conversational Agent, chatbot, Personalized Feedback, LMS, Moodle

Pre-evaluation of the learner's level is a common learning strategy designed to determine the prior knowledge and skills of learners. A pre-evaluation is carried out at the beginning of the course and based on the results obtained, personalized resources will be provided that respond to individual learner needs. This paper presents a pre-evaluation for a C programming language course by providing, at the end of the quiz, a personalized formative feedback and recommendation to the learners. We have developed our conversational chatbot named QuizCbot, which allows learners to go directly to the parts where they need the most help through the personalized feedback provided to them, including their final scores, the questions they answered correctly and the questions they answered incorrectly with the correct answer and explanation. Hence, the chatbot makes a recommendation on the concepts in which the learner did not obtain the average, identifying the concepts not mastered where the learner needs more (or less) support. Determining what learners know and don't know can help to improve the learning experience. We have integrated our QuizCbot chatbot, which is based on Natural Language Understanding (NLU), into the Moodle learning environment.

Introduction

Evaluation plays a critical role in providing meaningful information to guide teaching, help learners achieve next steps, and verify accomplishments and progress. Evaluation should be planned with these aims: evaluation for learning, evaluation as learning, and evaluation of learning, each has a role to play in supporting and enhancing student learning. Evaluation for learning informs teachers and the online learning environment about what learners understand and allows them to know what learning objects to adjust and to plan and guide teaching while providing useful feedback to learners. Evaluation as learning allows learners to become aware of how they are learning, to adjust and progress their learning with increased responsibility. Evaluation of learning allows learners, teachers and the online learning environment to be informed of the learning outcomes achieved at a specific time to highlight successes, plan interventions and continue to promote success.

Three of the most popular types of evaluation are: Pre-evaluation, Formative evaluation, Summative evaluation. Before starting learning, it is essential to know what type of students it is for, by situating their level of knowledge through the Pre-evaluation. Tracking learners' progress through Formative evaluations. A Summative evaluation aims to assess if the most important knowledge has been acquired at the end of the training, in order to adjust the continuation of his/her teaching according to the level reached.

Formative feedback is considered an essential approach to facilitating the development of students as independent learners to monitor, evaluate, and regulate their own learning [START_REF] Md | The Value and Effectiveness of Feedback in Improving Students' Learning and Professionalizing Teaching in Higher Education[END_REF]. Formative feedback involves the feedback given to learners during evaluations to improve their learning [START_REF] Dekker | Effective learning methods: The importance of formative feedback[END_REF]. Thus, helping learners who need more support, and recommending them the contents, can help to improve the learning experience [START_REF] Manouselis | Recommender Systems for Learning[END_REF].

In this article, we will address the first type of evaluation to determine the level of knowledge of learners and rank them in order to identify individual difficulties with the diversity of learners to provide individualized formative feedback and recommendations.

Determining the level of knowledge of each learner and providing individualized feedback and recommendations would be difficult to do by teachers who do not have the time or availability for this task.

To solve this problem, the new form of evaluation is made, which is the use of conversational chatbot. In most of the previous researches, the simple chatbot solutions are widely used in many fields such as medicine, product and service industries. However, the use of chatbots in the educational context is still limited [START_REF] Winkler | Unleashing the Potential of Chatbots in Education: A State-Of-The-Art Analysis[END_REF] [START_REF] Yang | Opportunities and Challenges in Using AI Chatbots in Higher Education[END_REF]. With the integration of our conversational chatbot, multiple choice questions become amusing and interactive.

The objective of this contribution is to improve and personalize the learner's learning experience based on a pre-evaluation to determine what learners know and don't know and situate them in the appropriate level and recommend them to the appropriate content and provide them with personalized feedback. The solution developed is a conversational chatbot that uses Natural Language Understanding (NLU) to make the learning process engaging and motivating for learners. To facilitate the use of our solution we have integrated our chatbot, named QuizCbot, into the Moodle platform.

The rest of this paper is organized as follows: section 2 describes the state of the art, section 3 describes the architecture and design of our solution, section 4 explains the details of the experimental design for the C language programming quiz and population and we will discuss the results obtained and section 5 is reserved for the conclusion.

2

Related works

Quizzes and Feedback

Due to the intense critique of evaluation and its inability to reflect the real state of learners' competence level in a particular subject or skill due to problems such as test validity, the theory of evaluation was developed [START_REF] Black | Developing the theory of formative assessment[END_REF]. In this context, the learner will receive formative feedback before, during, or after an evaluation. The feedback should then be adapted to the user, the task and the environment in order to facilitate the learner's improvement in a subject or a skill.

In general, the feedback has one of the most persuasive influences on performance and learning, but this impact can be negative or positive [START_REF] Hattie | The power of feedback[END_REF]. Educational research has revealed dependencies between variables such as the learner's skill level, the learner's motivation, the properties of the task and the effectiveness of feedback [START_REF] Black | Developing the theory of formative assessment[END_REF]. Additionally, it has been determined that adaptive feedback is more beneficial to the learner than generic feedback. When a learner uses the information he/she receives in the form of feedback to enhance his/her performance, this is called the formative feedback [8]. There are mainly two types of feedback, called formative and summative feedback.

Formative feedback includes feedback given to learners during evaluations to improve their learning [START_REF] Dekker | Effective learning methods: The importance of formative feedback[END_REF]. To be effective, formative feedback must be constructive, timely, personal and motivating. There are two types of formative feedback, namely directive and facilitative. To let students know about their mistakes and learning improvements, directive feedback is used. The facilitative feedback guides learners in their revision by providing suggestions, advice and comments.

Summative feedback involves feedback given in the form of a mark or grade after an evaluation has been completed. It assesses what students have learned at the end of a subject or semester [START_REF] Dekker | Effective learning methods: The importance of formative feedback[END_REF]. A study indicates that summative evaluations allow learners to study more, learn more, and feel more inspired. Along with the grade, summative evaluation also ensures that learners have certain knowledge, abilities, and skills where strengths and weaknesses are identified [START_REF] States | Summative Assessment (Wing Institute Original Paper)[END_REF].

In [START_REF] Bälter | The effect of short formative diagnostic web quizzes with minimal feedback[END_REF], study the effect of correct/incorrect feedback in generic quizzes and they demonstrated that simple quizzes combined with simple feedback are effective. This gives an idea about the ideal placement of this type of activity.

The validity of the results of the tests is an important prerequisite for meaningful feedback. Evaluation based on multiple-choice questions allows learners to easily guess the correct answer. For example, the study [START_REF] Novacek | Confidence-Based Assessments within an Adult Learning Environment[END_REF] demonstrates how multiple-choice questions can be passed when learners simply guess the answers. Therefore, the success of such a form of evaluation depends on the honesty of the learner and is therefore suitable as a self-feedback tool without any consequences for official test scores or course results. In such cases, an opportunity to reflect on their self-confidence can create an environment for learners in which they develop a deeper level of self-regulation.

The study presented in [START_REF] Roediger | The Power of Testing Memory: Basic Research and Implications for Educational Practice[END_REF] illustrates that quizzing helps learners grasp more information than rereading. This is also known as the "test effect" or "retrieval practice". The authors considered the concepts of dynamic testing and evaluation to enhance learning.

Chatbots in Education

Conversational AI provides new possibilities for alternative and innovative information and communication technologies tools, such as AI chatbots. The explosive development of information and communication technology will inevitably have a profound impact on every sector, including education [START_REF] Khoroshko | The Use CAD/CAE Systems to Create E-Learning Courses on Technical Subjects at University[END_REF], [START_REF] Svetsky | The Personalized Computer Support of Teaching[END_REF]. Today, integrating information and communication technology to facilitate online learning is crucial [START_REF] Fewella | Impact of Integrated E-learning: Traditional Approach to Teaching Engineering Perspective Courses[END_REF].

Artificial intelligence (AI) chatbots have gained popularity over time and have been widely used in e-commerce, online banking, and healthcare, among others. In general, the use of chatbots is gaining popularity in several sectors.

However, in the field of education, chatbot as a learning tool to improve learning is still in its infancy [START_REF] Gonda | Evaluation of Developing Educational Chatbots Based on the Seven Principles for Good Teaching[END_REF]. Most studies on chatbot in education are based on online foreign language learning [START_REF] Rahman | Programming challenges chatbot: Current and future prospective[END_REF], [START_REF] Ruan | BookBuddy: Turning Digital Materials Into Interactive Foreign Language Lessons Through a Voice Chatbot[END_REF]. It has been identified that a chatbot can help learning with the same benefits as those obtained from a "real" interview [START_REF] Pérez | Rediscovering the use of chatbots in education: A systematic literature review[END_REF]. In addition to making the learning process enjoyable, the conversational chatbot could make learners more likely to self-evaluate and improve their level, because they do not feel judged.

Our approach is to evaluate students through the chatbot in order to track each learner individually, to guide them based on their deficiencies to the appropriate content, and to provide them a personalized feedback based on the results of the evaluation. The following section describes the architecture and design of our solution.

Proposed design and architectural design

Figure 1 describes the schematic representation of our chatbot that allows to have a conversation with learners by detecting their intentions based on natural language understanding (NLU). We developed our conversational chatbot named QuizCbot that performs a pre-evaluation, online ranking test, for a C programming language course integrated into the Moodle platform to evaluate learners' skills.

Our chatbot is based on the open source version of Google's Dialogflow Machine Learning framework that allows users to develop human-computer interaction technologies that can handle natural language understanding (NLU). Basically, this allows us to create digital programs that interact with the final users via natural languages. When the learner sends a message to QuizCbot in Moodle to start the quiz, the chatbot transmits it to Dialogflow which tries to understand the received text by associating it to an intention using Natural Language Understanding. Once the intention is detected by Dialogflow, an action to be executed is chosen. The Webhook sends a formatted response corresponding to the intention. All actions are coded in Node.js and hosted by the fulfillment Webhook. The fulfillment webhook is a service that allows a dynamic response by searching for response elements in an external database. At the Webhook stage, questions and answers are processed, the learner's level is detected (learner's classification as shown in Figure 2), a recommendation and a personalized feedback are provided to the learner. The webhook records all this information and data in the Mongodb database. Figure 3 shows the interaction between the different components.

QuizCbot evaluation

This section describes the evaluation of the QuizCbot in terms of the participants' perception of the usefulness of the personalized feedback provided to them and the recommendation that was given. Each learner was asked to participate in a survey at the end of the quiz. Section 4.1 explains the details of the experimental design for the C language programming quiz and the population. In Section 4.2 we discuss the results obtained.

Design of the experiment

We have chosen the Ecole Normale Supérieure de l'Enseignement Technique de Mohammedia (ENSET), an engineering school in Morocco to conduct our experiment. The participants are first-year engineering students in the Software Engineering and Distributed Computing Systems (GLSID) and Computer Engineering Big Data and Cloud Computing (BDCC) fields. The experiment was conducted on the C programming techniques module.

The pre-evaluation consists of 40 questions of different levels of difficulty and in different concepts of the course (see Table 1), validated by the professor experienced in the C programming language, to correctly classify the level of knowledge of the learner and then assign him/her to the appropriate group. We have integrated our QuizCbot chatbot into Moodle and the students of GLSID and BDCC access in, before starting the course, to pass the pre-evaluation on the C programming language via our chatbot to determine their level of knowledge and at the end of the test, it provides them recommendations on the concepts not mastered where the learners need more (or less) support and provides them a personalized formative feedback, i.e., giving the learners the opportunity to use the feedback information to regulate their learning process to improve their skills.

The sample included 71 students (52 males and 19 females), who participated in this study and passed the test on our chatbot QuizCbot. As mentioned above, the participants are first-year engineering students in the Software Engineering and Distributed Computing Systems (GLSID) and Computer Engineering Big Data and Cloud Computing (BDCC) fields, and are between the ages of 20 and 21 years old. Participants were allowed to use the QuizCbot on any device of their choice. Although the chatbot offers the option to restart the quiz, only the first fully completed attempt is considered for this study. An important observation is that none of the students needed a demonstration or explanation on how to use the chatbot, adoption of the technology was on the fly due to familiarity with messengers and quizzes.

Results and discussion

As mentioned above, learners were allowed to use QuizCbot on any device of their choice. As shown in Figure 4 In both cases, the chatbot greets the learner and asks him/her to start the quiz in step 1 and then, to identify the learner, the chatbot asks the learner for his/her email in step 2. When the learner provides it, the chatbot starts the conversational quiz permitting the pre-evaluation in the C programming language, as shown in Figure 5, with the associated choices. The learner answers by making sentences or by giving the options (A, B…). The chatbot successfully retrieved each student's score for each question and stored it in the database (Mongodb database), and then it provided learners personalized feedback at the end of the test, as shown in Figure 6, including his/her final score, the questions he/she answered correctly, and the questions he/she answered incorrectly, and it also provided a QuizC-Solution.pdf document containing the answers to the questions with explanation. We then categorized each student into the appropriate level (beginner, intermediate, advanced) to provide personalized resources that respond to individual learners' needs. Analyzing these results, we can see that for the advanced level questions, no students answered correctly. For intermediate level questions, 43 of the learners scored 0 or 1 out of 10, 13 learners scored 2 out of 10, 8 learners scored 3 out of 10, and only 7 out of 71 learners scored 4 out of 10. And for the beginner level questions, 51 of the learners scored between 1 and 10 out of 20, 19 learners scored between 11 and 15 out of 20, and only one learner scored 16 out of 20, so all of these learners still lack mastery of some concepts at this beginner level in C programming language. Hence the conclusion of this part is that all learners are clearly classified at the beginner level.

But we are not stopping there because, for example, there is a learner of beginner level who has a score of 16 out of 20 (he/she still needs support for some notions), and another learner in the same level who has a score of 7 out of 20, the concepts that these two learners master are completely different even if they are classified in the same level. Therefore, since our approach aims to personalize learning subsequently by providing each learner with concepts not mastered, we decided to divide this beginning level into three supplementary levels (low, medium, high) in order to provide each learner with recommendations on the concepts that need more support according to the level he/she belongs.

We wanted to do this method to perfectly personalize the recommendation. Figure 8 shows a pie chart on the learners' final classification. There are 51 learners classified as low beginner level, 18 learners as medium beginner level and only two learners as high beginner level. At the end of this pre-evaluation, after our chatbot provides personalized feedback to each learner and ranks them in the level they belong to, the chatbot recommends the concepts in which the learner did not get the average (see Figure 9), identifying the non-mastered concepts where learners need more (or less) support only in the level in which he/she is classified. This means that, for example, if a learner is classified in the beginner level, our chatbot will first recommend the concepts in which he/she did not get the average in the level he/she belongs to, no need to recommend him/her, for example, to the intermediate level concepts and he/she has not mastered the beginner level concepts yet. In all survey questions, all students selected the very interesting or interesting responses. Table 2 shows the distribution of responses to each survey question. Based on these results, we conclude that our chatbot QuizCbot was perceived as helpful and interesting, which shows a positive attitude of learners towards artificial learning companions.

Conclusion

In this paper, we have presented a research study involving the design and implementation of a pre-evaluation chatbot, integrated into Moodle, that allows learners to pass a test at the beginning of the course to determine and classify their knowledge level. Based on the results obtained of the evaluation, our conversational chatbot named QuizCbot provides personalized feedback to learners including their final score, the questions they answered correctly and the questions they answered incorrectly with the correct answer and explanation. It also provides a recommendation for the concepts in which the learner did not achieve the average, identifying the concepts not mastered where learners need more (or less) support. However, on the basis of the results obtained from the survey conducted to evaluate QuizCbot, we concluded that our chatbot QuizCbot was perceived as interesting and helpful and shows a positive attitude from learners towards the chatbot-based evaluation. The learners also mentioned that the feedback, explanations of wrong answers, and recommendations provided by QuizCbot are interesting or very interesting to them. It allows learners to self-evaluate and can create an environment in which they improve their learning experience, which allows them to become aware of how they learn, adjust and advance their learning by assuming more responsibility. For our future work, we will address the design and implementation of a chatbot to personalize the formative evaluation questions for each learner according to the level in which he/she belongs, in order to guide him/her towards the resources most adapted to his/her needs.

Fig. 1 .

 1 Fig. 1. Schematic representation of our chatbot.

Fig. 2 .

 2 Fig. 2. Learner classification process.

Fig. 3 .

 3 Fig. 3. Interaction between the different components.

  , an example of a learner connected through their mobile phone (Fig 4, (a)), and another learner connected through their computer (Fig 4, (b)).

Fig. 4 .

 4 Fig. 4. Student identification.

Fig. 5 .

 5 Fig. 5. Pre-evaluation in C programming language.

Fig. 6 .

 6 Fig. 6. An example of personalized Feedback.

Figure 7

 7 illustrates three histograms of learners' scores for questions answered correctly at different levels (left histogram for beginner level, middle histogram for intermediate level, and right histogram for advanced level).

Fig. 7 .

 7 Fig. 7. Learners' scores for correctly answered questions at different levels.

Fig. 8 .

 8 Fig. 8. Learner level classification.

Fig. 9 .

 9 Fig. 9. Examples of Personalized recommendations.

Table 1 .

 1 The different course concepts addressed in QuizCbot

		• Introduction to programming in C
		• Primitive types and variable declarations
		• Affectation instruction
	20 questions classified as Beginner Level	• Arithmetic operators • Increment/decrement operators • Relational operators
		• Logical operators
		• Standard Input/Output functions
		• The Control Structures
		• The arrays
	10 questions classified	• The Pointers
	as Intermediate Level	• The structures
		• The functions
		• Pointers and dynamic memory allocation (Func-
	10 questions classified as Advanced Level	tion pointer, Array of pointers, Dynamic memory management, ...) • Unions
		• File management in C

Table 2 .

 2 QuizCbot evaluation questions

	Questions	Very inter-esting	Interesting	Not at all interesting
	How would you rate the feedback	57%	43%	0%
	provided by QuizCbot?
	How would you rate the recommen-
	dation provided by QuizCbot?	97%	3%	0%
	How would you rate the explanation
	of wrong answers provided by the	98%	2%	0%
	chatbot?
	How would you rate the quiz in chat	86%	14%	0%
	format?
	How would you rate the overall ex-	95%	5%	0%
	perience with QuizCbot?

Acknowledgment

This work is supported by the University Hassan II of Casablanca-Morocco and Professor Mohammed Qbadou.