Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
  • G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
  • G01T1/16—Measuring radiation intensity
  • G01T1/167—Measuring radioactive content of objects, e.g. contamination
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
  • G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
  • G01T1/16—Measuring radiation intensity
  • G01T1/169—Exploration, location of contaminated surface areas
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
  • G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
  • G01T1/36—Measuring spectral distribution of X-rays or of nuclear radiation spectrometry

Definitions

• the technical field of the invention is the characterization of a depth of activity of a radionuclide in a solid medium, in particular a concrete wall.
• a first object of the invention is a method for estimating a depth along which a radionuclide extends in a solid medium, from a surface, the solid medium being delimited by the surface, the radionuclide emitting radiation gamma at at least one emission energy, the method comprising:
• spectrometric detector facing the surface of the solid medium, and measurement, by the spectrometric detector of an energy spectrum of gamma radiation, emitted by the radionuclide and emanating from the surface, the measured spectrum comprising a number of pulses detected by the detector for different energy values, the energy spectrum including a peak at the emission energy;
• each calibration coefficient corresponding to a ratio, in each energy band, between a predetermined activity of the solid medium and an estimate of a spectral value corresponding to said predetermined activity;
• step d) application of a calibration function to the comparison indicator resulting from e), so as to estimate the depth at which the radionuclide extends in the medium solid, the calibration function being established beforehand, considering an activity of the radionuclide decreasing as a function of depth; the method being characterized in that during step d), the first calibration coefficient and the second calibration coefficient are determined, in each energy band, by digital modeling of a spectrum detected by the spectrometric detector, the solid medium being considered, during modeling, as having said predetermined activity.
• the first spectral value and the second spectral value are a number of pulses or a count rate in the first energy band and the second energy band, respectively.
• the unit activity can be a uniform surface activity or a uniform specific activity in the analyzed medium or a predetermined activity distributed according to a predefined activity gradient.
• the process may comprise, prior to step c):
• step a correction of the spectrum measured during step a), so as to remove the contribution of the natural radionuclide, at least in the first energy band.
• the representative spectrum of the solid medium can be any suitable spectrum of the solid medium.
• the process may include, prior to step d):
• the process may include, prior to step f):
• the determination of the density of the solid medium examined comprises the following sub-steps:
• each activity estimation being carried out taking into account a density of the solid medium
• the representative spectrum of the solid medium can be:
• the process may include:
• the comparison indicator may be a ratio or a difference between the first calibrated spectral value and the second calibrated spectral value.
• the solid medium can be concrete or earth or sand.
• a second object of the invention is a device intended to estimate a depth along which a radionuclide extends in a solid medium, from a surface, the solid medium being delimited by the surface, the device comprising:
• spectrometric detector configured to measure a spectrum of gamma radiation emanating from the surface; a processing unit, programmed to implement steps b) to f), and possibly step g), of a process according to the first embodiment from the spectrum measured by the spectrometric detector.
• Figure 1 schematizes the main components of a device according to the invention.
• Figure 2 shows the main steps of a method of implementing the invention.
• Figure 3 illustrates two energy bands applied to a spectrum.
• Figure 4A shows a spectrum of the natural activity of a concrete wall.
• Figure 4B is a spectrum of the activity of a concrete wall lightly contaminated with 137 Cs.
• Figure 5A shows an evolution of a first calibrated spectral quantity and a second calibrated spectral quantity (y axis) as a function of the activity depth (x axis).
• Figure 5B represents a calibration function (curve 1) and a correction function (curve 2).
• Figure 6A shows a measuring device whose detector is a cooled Germanium crystal.
• Figure 6B shows models of a spectrum of a concrete wall with density 2.3 g.crrr 3 for the same total activity of 137 Cs and different depths of the activity.
• Figure 6C shows models of a spectrum of a barium concrete wall with a density of 3.35 g.crrr 3 for the same total activity of 137 Cs and different depths of the activity.
• Figure 6D shows models of a spectrum of a concrete wall with density 2.3 g.crrr 3 for the same total activity of 60 Co and different depths of the activity.
• Figure 6E shows models of a spectrum of a barium concrete wall with a density of 3.35 g.crrr 3 for the same total activity of 60 Co and different depths of the activity.
• Figure 7A shows calibration functions established by taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 137 Cs.
• Figure 7B shows calibration functions established taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 60 Co.
• Figure 7C shows correction functions established by taking into account two different densities (2.3 g.crrr 3 and 3.35 g.crrr 3 ) and an activity of 137 Cs.
• Figure 7D shows correction functions established by taking into account two different densities (2.3 g.cm -3 and 3.35 g.cm -3 ) and an activity of 60 Co.
• Figure 1 describes a device 1 adapted to an implementation of the invention.
• the device comprises a spectrometric detector 10, intended to be placed facing a surface S delimiting a solid medium M.
• the solid medium is a medium likely to have been contaminated by a radionuclide. It may in particular be an environment comprising concrete or earth or sand.
• An objective of the invention is to estimate a thickness Zo of the medium capable of containing a major part of the activity. By major part, we mean more than 80% or more than 90% of the activity of the radionuclide.
• the spectrometric detector 10 is placed at a distance D from the surface S of the medium M. It is a detector sensitive to X or gamma radiation.
• the implementation of the invention assumes that the radionuclide is an X or gamma emitter.
• the radionuclide may be, without limitation, 137 Cs (for example in fuel reprocessing installations) or 60 Co (for example in nuclear reactors).
• the detector 10 When a gamma photon interacts in the detector 10, the latter generates a pulse whose amplitude depends, preferably linearly, on the energy released by the photon during its interaction in the detector.
• the detector 10 is connected to an electronic spectrometry circuit 12. During a measurement period, which can last a few seconds to a few minutes or tens of minutes, the pulses generated by the detector 10 are counted and classified according to their amplitude, so to form an amplitude spectrum.
• an energy calibration function establishing a relationship between the amplitude of the pulse and the energy released in the detector, we obtain an energy spectrum.
• the energy spectrum is discretized into different energy channels k, the number K of channels generally being between several hundred and several thousand.
• the device 1 makes it possible to form an energy spectrum of the photons emitted by the medium M.
• a gamma emitting radionuclide When a gamma emitting radionuclide is present in or on the wall, in a detectable quantity, it produces, in the measured spectrum, a spectral signature comprising one or more peaks whose energy is known. The energy of each peak corresponds to the energy of the photons emitted by the radionuclide.
• the emission energies of the main radionuclides are known and available in nuclear databases.
• the detector is a scintillation detector, of the Nal type coupled to a scintillation photon/charge carrier converter. Other types of detectors can be used, for example a LaBrs scintillator detector.
• Germanium detector is described below, in connection with Figures 6A to 6E.
• the measured spectrum may include a background noise component, which corresponds to the radiological background to which the detector 10 is exposed.
• the background noise may have several components.
• a first component is the natural background noise, due to the natural radioactivity of the environment examined. This is particularly the case when the medium is made of concrete or earth.
• the natural background noise comes from radioactive isotopes, gamma emitters, naturally present in the medium M.
• a natural gamma emitter usually encountered is 40 K, knowing that other gamma emitters, resulting from the decay chains of 238 U or 232 Th can be encountered. Taking into account natural background noise constitutes an interesting aspect of the invention, described below.
• a second component is the background noise induced by the vicinity of the controlled wall.
• the detector is usually surrounded by shielding 14.
• the shielding forms a collimator delimiting an opening angle so as to limit the field of observation of the detector 10.
• the shielding does not act all or nothing and certain photons, emitted in the vicinity of the detector, can pass through the shielding and be detected by the detector. And this particularly when the neighboring background noise is more intense than the signal emitted by the medium M, in the field of observation of the detector.
• the shielding 14 may include a removable plug 14', configured to close the field of observation of the detector 10.
• the neighboring background noise is taken into account by carrying out two successive measurements with and without a plug. The measurement carried out with the cap is then considered representative of the neighborhood background noise. It can thus be subtracted from the measurement carried out without a cap.
• the device 1 comprises a processing unit 20, intended to carry out processing of each spectrum resulting from the spectrometry circuit 12.
• the processing unit 20 can by example include a microprocessor.
• the processing unit is programmed to implement certain steps of the process described below, in connection with Figure 2.
• FIG. 2 represents the main stages of implementing the process, which are now described.
• the solid medium is a concrete wall. acquisition of a neighborhood background noise spectrum. This step is optional.
• the plug 14' closes the field of observation of the detector.
• a spectrum representative of the neighborhood background noise is acquired.
• the acquisition duration can be between a few tens of seconds and a few tens of minutes.
• step 130 taking into account neighborhood background noise.
• This step is implemented when a background noise spectrum is available, resulting from step 110.
• the neighborhood background noise spectrum is subtracted from the measurement spectrum, so as to obtain a corrected spectrum.
• the acquisition times of the measurement spectrum (step 120) and the neighborhood background noise spectrum (step 110) are identical. Otherwise, the spectra are readjusted so as to correspond to the same acquisition duration.
• step 120 we have an energy spectrum of the gamma radiation emanating from the surface.
• this spectrum is designated spectrum of interest. This is either the spectrum resulting from step 120, or the corrected spectrum resulting from step 130.
• two different energy bands are selected in the spectrum of interest.
• Part of the invention is based on a different evolution of the content of the spectrum of interest in two different energy bands, depending on the depth of contamination.
• Each energy band was determined during a preliminary calibration phase 70, described below.
• a first energy band EE extends on either side of a spectral zone corresponding to the Compton front.
• the width of the first energy band EE depends on the energy resolution of the detector, the maximum energy of the energy band EE can correspond to the minimum energy of the energy band AE 2 - It generally extends over a few hundred keV.
• a particularity of the first energy band is that the spectral value changes little with the depth of the contamination.
• spectral value we mean the number of pulses detected, the energy of which belongs to the first energy band. The number of pulses detected is usually referred to as “number of shots”.
• a spectrum is shown, obtained by a Nal scintillator detector with a volume of 1 inch by 1 inch, simulated using a particle transport calculation code (MCNP code).
• the detector is placed facing a concrete wall delimited by a surface S, and comprising an activity of 137 Cs whose gradient, according to the depth z, is modeled by a decreasing exponential function.
• the first energy band EE extends between 290 keV and 600 keV.
• the first energy band EE is formed by interactions having two origins: interactions corresponding to the Compton diffusion, in the detector, of gamma photons not or only weakly attenuated by the concrete wall: these interactions form a first component of the spectrum in the first energy band atE 1 .
• such interactions are represented by solid arrows.
• interactions corresponding to an absorption, in the detector, by photoelectric effect, of gamma photons having diffused, according to diffusion angles between 0° and 90° by the concrete wall these interactions form a second component of the spectrum in the first EE energy band.
• such an interaction is represented by a dotted arrow.
• the first component In the presence of a shallow contamination depth, the first component is predominant. In the presence of a high depth of contamination, the second component becomes predominant.
• the spectral content in the first energy band EE is weakly dependent, for example within ⁇ 20%, of the contamination depth.
• the first energy band EE can be defined beforehand and be optimized by modeling spectra detected by the detector by considering different activity gradients in the wall and, for the same activity gradient, different contamination depths. This aspect is described below in connection with Figures 6A to 6E.
• a second energy band AE 2 includes an emission energy of the radionuclide. We know that, subject to a sufficient branching rate, each emission energy of a radionuclide results in the appearance, on the spectrum, of a peak, called a total energy peak.
• the second energy band AE 2 corresponds to all or part of the total energy peak. Depending on the energy resolution of the detector, the second energy band AE 2 is more or less wide.
• the second energy band AE 2 is centered on the emission energy of the radionuclide.
• the spectral content, in the second energy band varies strongly depending on the contamination depth. This is due to the photoelectric absorption, in the solid medium M, of photons emitted at the emission energy.
• the second energy band AE 2 extends on either side of the emission energy of 137 Cs, or 662 keV. In this example, the second energy band AE 2 extends between 577 keV and 747 keV.
• the first energy band and the second energy band do not overlap, or only slightly.
• the first energy band can extend between a first minimum terminal and a first maximum terminal.
• the second energy band can extend between a second minimum terminal and a second maximum terminal.
• the second minimum limit is greater than or equal to the first maximum limit.
• Pulse counts are generally expressed per unit of time, in which case it is count rate: number of pulses detected per second.
• spectral value designates a number of pulses, or a number of pulses per unit of time, in an energy band of the spectrum.
• This step is optional but it is advantageous in particular for low levels of contamination of the medium M.
• the method is intended for use on materials such as concrete or earth.
• This type of material is likely to contain natural radionuclides, some of which are gamma emitters. The presence of the latter can induce a measurement error. Indeed, the quantity of natural radionuclides can have an influence on the first spectral value N ⁇ .
• the contribution of natural gamma-emitting isotopes, particularly in the first energy band must be quantified and removed.
• the presence of natural radionuclides can have an influence on the second spectral value N 2 .
• the contribution of natural gamma-emitting isotopes, in the second energy band AE 2 be quantified and removed.
• the main natural emitters can easily be identified by their photoelectric emission peaks. These are descendants of 232 Th, 238 U. It is also 40 K.
• Taking into account natural radioactivity corresponds to sub-steps 151 to 154. These steps are carried out by taking into account a representative spectrum Sp' of the volume examined.
• the representative spectrum may be the spectrum Sp acquired during step 120 or a different spectrum, for example acquired with the same detector and a longer acquisition duration, so as to obtain a more precise quantification of the natural activity.
• the representative spectrum is carried out on the wall examined or on a wall considered to be representative of the wall examined.
• the representative spectrum can also be acquired by a different detector.
• the following table lists natural radionuclides (first column) and their gamma-emitting descendants (second column), as well as their emission energies (third column - keV) and branching rates (fourth column - %). This list is not exhaustive. Only the highest intensity energy lines are taken into account.
• Figure 4A represents a spectrum, measured by a Germanium spectrometric detector, on a clean concrete wall.
• the spectrum is representative of natural radioactivity. We observe the peaks corresponding to the energies mentioned in Table 1. The duration of the spectrum acquisition was 12 hours.
• Such a spectrum can be considered representative of all or part of the walls of the same installation. It allows an estimation of an average activity of the main natural radionuclides composing the concrete, as described below. The contribution of the activity of each radionuclide can be taken into account to correct spectra measured on the walls of the installation, in particular in the first AEi energy band.
• Sub-step 152 Estimation of a specific activity of 232 Th, 238 U and 40 K.
• the mass activity of 232 Th and 238 U is estimated from average mass activities calculated from peaks of the spectrum detected at each emission energy. It is assumed that the radioactive descendants of 232 Th and 238 U are in radioactive equilibrium with their respective fathers.
• a specific activity A( is of a natural radionuclide RN( is obtained by applying the expression: where N Et) is the counting rate at the emission energy Et of the radionuclide RN( considered and FT(i, Et, d) is a transfer function, obtained by modeling, corresponding to a number of counts detected per unit of time for a predetermined activity of the wall considered, for example a unit activity of 1 Bq. g 1.
• the transfer function is considered taking into account an assumption of homogeneous distribution in the wall, which is relevant with regard to natural radioactivity.
• the transfer function FT(i, Ei, d) depends on the density d of the concrete. The latter can be determined a priori, or be the subject of an experimental determination as described below.
• the modeling of the detector was previously verified in the laboratory, using standard irradiating sources.
• the average activity A m of each parent radionuclide is estimated by averaging the specific activities A( of each radionuclide RN( descendants of said parent radionuclide: where Ai corresponds to the mass activities of the descendant radionuclides of each parent radionuclide and o Aj 2 is the variance assigned to A t .
• the specific activity is obtained by applying expression (1) to the emission peak at 1460 keV.
• Sub-step 153 Simulation of the contribution of 232 Th, 238 U and 40 K.
• the contribution of natural activity in the spectrum, and more particularly in the first energy band AE lt is estimated.
• the contribution of the natural activity is then obtained by weighting each unit contribution of each natural radionuclide by the mass activity of said radionuclide, resulting from substep 152.
• the contribution of natural activity is subtracted from the first spectral value: the value N ⁇ is replaced by N ⁇ — N l nat .
• the value N 2 can be replaced by /V 2 - N 2 nat
• Figure 4B shows a spectrum of a concrete wall lightly contaminated with 137 Cs. We observe the emission peak of 137 Cs, at energy 661.6 keV.
• the first energy band AE 17 is shown which was defined between 300 keV and 659 keV.
• the second energy band AE 2 corresponds to the emission peak of 137 Cs, taking into account the spectral resolution of the detector. In this example, it extends between 659.5 keV and 663.1 keV.
• the first spectral value N and the second spectral value N 2 are multiplied respectively by a first calibration coefficient and by a second calibration coefficient.
• Each calibration coefficient is determined during a prior calibration step 50. During this step, a first reference value N 10 and a second reference value N 20 are determined.
• Each reference value corresponds to an estimate of a spectral value (counting or counting rate) which would be detected by the detector, in the same measurement configuration (same collimator, same position and orientation relative to the surface S), in considering a reference activity A o of the wall.
• the reference activity A o is a purely surface, homogeneous activity of predetermined value. It can for example be a uniform surface activity equal to 1 Bq. cm -2 , which corresponds to a so-called unitary surface activity.
• the reference activity is a specific activity of 1 Bq. g 1 taken into account on a predetermined thickness of the wall, for example 1 cm.
• the reference activity can also be a mass activity of 1 Bq.g 1 which is considered distributed along a predetermined gradient, up to an arbitrary depth.
• each calibration coefficient is carried out by digital modeling, implementing a particle transport code, for example the MCNP code previously cited. Determining the first calibration coefficient and the second calibration coefficient using a digital model, based on a reference activity, makes it possible to obtain precise values of each coefficient, which improves the precision of the measurement.
• step 140 the first spectral value N multiplied by the first calibration coefficient a, and the second spectral value N 2 multiplied by the second calibration coefficient p.
• G and A can be considered as equivalent surface activities estimated on the basis of A ⁇ and N 2 , assuming an absence of contamination depth.
• Figure 5A shows the evolution of the first calibrated quantity G and the second calibrated value A as a function of the contamination depth Z (x-axis).
• the magnitude G is relatively stable, and varies within a margin of ⁇ 10% up to a depth of approximately 15 cm.
• a ratio of the first calibrated value G to the second is calculated calibrated value A.
• a ratio - corresponds to a comparison indicator.
• step 180 the ratio - resulting from step 180 is used as an argument for a calibration function f, previously defined, so as to estimate a contamination depth Z o in the wall examined.
• ct(z) Act tot P z) (9) where: z corresponds to a depth, along the Z axis, perpendicular to the surface S delimiting the solid medium M;
• Act z is a surface activity at depth z
• Act tot is total activity.
• the depth Z o corresponds to the depth up to which it is estimated that 90% of the activity of the radionuclide is contained. So,
• the definition of the calibration function f consists of taking into account, for the same analytical form of the contamination gradient, and for the same total activity, different contamination depths Z o .
• a spectrum resulting from the detector is simulated, from which the spectral values ⁇ (ZQ) and N 2 (Z 0 ) are estimated.
• the calibration function f corresponds to the evolution of the quantity as a function of Z o . It (Z 0 ) is obtained by digital modeling, using a calculation code modeling the transport of photons in matter, and taking into account the geometry of the measurement: modeling of the detector, the possible collimator, the wall of concrete, and the position of the detector by relation to the concrete wall. Modeling can be carried out with the calculation code
• Figure 5B (curve 1 - left y-axis) shows an example of a calibration function f obtained by considering a decreasing activity gradient following an exponential function as explained in (8).
• the abscissa axis corresponds to the magnitude G/A and the left ordinate axis corresponds to the activity depth Z o as defined in expression (10).
• the models making it possible to simulate the detected spectrum are also based on an assumption relating to the density of the concrete. Different modeling can be carried out, taking into account different values of the density d of the material forming the solid medium. This makes it possible to obtain a calibration function for each density value considered.
• Step 200 Estimation of total activity.
• the total activity is estimated from the first calibrated value G.
• the total activity Act tot can be estimated using G directly.
• the correction function K corr is established beforehand, on the basis of modeling.
• the total activity Act tot can be estimated by the first calibrated value G: Act tot “G
• the function K corr is determined beforehand, during a step 80, on the basis of modeling, taking into account several activity gradients.
• Steps 50, 70 and 80 form calibration steps of the device, making it possible to define the first calibration coefficient a, and the second calibration coefficient /3 (step 50), the calibration function f (step 70) and the function correction K corr (step 80). Practically, steps 50, 70 and 80 can be carried out simultaneously, based on the same modeling.
• Figure 5B (curve 2 - right y-axis) shows an example of a correction function obtained by considering a decreasing activity gradient following an exponential function as described in (8).
• the right y-axis corresponds to the value of the correction function K corr .
• K corr varies within a narrow range of variation, between 0.9 and 1.2.
• the modeling is carried out taking into account a hypothesis as to the density of the concrete. Different modeling can be carried out, taking into account different concrete density values. This makes it possible to obtain a correction function for each concrete density value considered.
• the method may include a step 170 of estimating the density of the material forming the volume examined.
• the method may include an estimation of the density of the material forming the medium examined. To do this, we take advantage of the natural activity of the material and select different emission peaks of the same natural radionuclide, for example 214 Bi covering a wide energy range to exploit the contrast linked to the attenuation more or less. less important emission lines in the medium as a function of their energy
• the mass activity of the selected natural radionuclide is estimated, based on different emission peaks, based on expression (1).
• the transfer function FT (i, d) depends on the density of the concrete.
• the specific activities A ⁇ Ei) of the natural radionuclide i are determined, using different transfer functions FT (i, E ⁇ d) established by taking into account different values of the density of the concrete. We then determine the density d for which the different specific activities of the same radionuclide are closest.
• the mass activities determined from the lowest emission energy peaks are greater than the mass activities determined from the highest emission energy peaks. Conversely, when the density taken into account in the transfer function is lower than the real density, the mass activities determined from the lowest emission energy peaks are lower than the mass activities determined from the energy peaks highest emissions.
• Estimating the density of the material forming the examined medium is beneficial because it allows selection of the calibration function and the correction function when we have previously established different calibration functions and/or different correction functions based on different density values.
• Density estimation is also applicable to any other material likely to contain natural radioactivity, for example concrete or earth.
• the density estimate is established from a spectrum considered representative of the wall or walls of an installation.
• the representative spectrum can be measured on a wall considered representative of the installation.
• the density determined from the representative spectrum is then used for processing different spectra acquired on the same wall, or even on several walls of the same installation.
• the density is estimated from each measured spectrum. However, this assumes that the acquisition time is long enough so that the density can be estimated precisely and that the presence of artificial radioactivity is low or of the same order of magnitude as natural radioactivity so that the lines characteristic of natural radioactivity can be identified. .
• Figure 6A illustrates a modeling configuration. Each modeling assumes a description of the geometry: of the detector; shielding and collimator arranged around the detector; of the material examined: thickness, density, activity gradient as a function of depth; position of the detector relative to the material examined, in particular the distance of the detector relative to the surface delimiting the material examined.
• the detector used is a detector based on a Germanium crystal cooled by a tank of liquid nitrogen.
• Figure 6B represents simulated spectra taking into account the same activity of 137 Cs purely surface (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d).
• the activity gradient taken into account was an exponential gradient.
• Figure 6B we have taken into account a concrete with a density of 2.3 g.crrr 3 . This type of simulation makes it possible to define the limits of the first energy band EE.
• the upper limit of the first energy band corresponds to the lower limit of the second energy band AE 2 -
• the lower limit of the first energy band EE corresponds to an energy at which the spectrum obtained by simulation of a surface activity (curve a) crosses the spectrum obtained by simulation of an activity in depth, for example curve b.
• the spectrum the lower limit of the first energy band EE is 290 keV. Feedback has shown that the lower limit of the first energy band can vary between 290 keV and 400 keV, or even more, depending on the radioelements considered and the measurement conditions.
• Figure 6C represents simulated spectra taking into account the same activity of 137 Cs purely surface (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d).
• the activity gradient taken into account was an exponential gradient.
• Figure 6C we have taken into account a concrete with a density of 3.35 g. cm -3 , which corresponds to barium concrete.
• the spectra in Figure 6C are different from those in Figure 6B. This comes from the difference in the densities considered.
• this lower limit is here equal to 310 keV.
• spectra are represented taking into account a purely surface activity (curve a) or extending, according to a decreasing gradient, over 100 mm (curve b), 200 mm (curve c) and 300 mm (curve d).
• the lower limit of the first energy band is respectively 340 keV ( Figure 6D) and 360 keV ( Figure 6E).
• a varies with density because the limits of the first energy band at E 1 vary as a function of density, as described in connection with Figures 6B to 6E.
• Figures 7A and 7B show calibration functions established respectively by taking into account ordinary concrete (curve a) and barium concrete (curve b), for activities of 137 Cs and 60 Co respectively.
• the abscissa axis corresponds to the GG ratio
• the difference between the two depths Z o estimated by taking into account the calibration functions, corresponding to each density, shows the impact of ignorance of the density on the estimation of the depth Z o .
• Figures 7C and 7D show correction functions established respectively by taking into account ordinary concrete (curve a) and barium concrete (curve b), for an activity of 137 Cs and 60 Co respectively.
• the abscissa axis corresponds to the ratio
• Figures 6B to 6E and 7A to 7D illustrate the importance of the measurement modeling phase, so as to establish, as precisely as possible, the calibration function and the correction function.
• the models are based on hypotheses concerning the density of the concrete or the shape of the activity gradient as a function of depth. As previously described, the hypotheses relating to density can be confirmed by a density estimation phase (see step 170). Concerning the activity gradient, it is difficult to estimate it precisely, because this requires an analysis of samples.
• the inventors consider that a gradient of exponential shape, as described in connection with expression (8), is appropriate. More generally, when the real activity gradient deviates from the activity gradient taken into account in the models, the measurement uncertainty increases. It is however considered that subject to taking into account a decreasing activity gradient, the method makes it possible to obtain a sufficient order of magnitude of the depth Z o .
• the “limit” depth depends on the material observed, in particular its density, as well as the duration of acquisition of each spectrum. It is preferable that the latter be a few minutes, and preferably less than 10 min or 15 minutes if we wish to remain compatible with an industrial measurement rate. The limiting depth also depends on the emission energy of the radionuclide whose depth we seek to evaluate in the environment examined. The limiting depth is higher for 60 Co (emission energies of 1173 keV and 1332 keV) than for 137 Cs (emission energy of 662 keV).
• the invention can be implemented for the control of nuclear installation structures, in support of maintenance or dismantling operations. It can also be deployed to carry out radiological monitoring on contaminated land.

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