R Coulon

V Kondrasovs

Quentin Lecomte

Jonathan Dumazert

Multilayer phoswich scintillators for neutron / gamma discrimination

A multi-layer phoswich scintillator is studied by the CEA LIST to address the issue of fast neutron detection. In the proposed approach the neutron are discriminated from gamma background using recoil-particle range differentiation. A simulation study of such a system has been realized using MCNPX Monte-Carlo transport code and a specific program has been developed to extract and process the PTRAC output files. It has been observed a strong anisotropic effect when thin layers are used (<1 mm) and two antagonist effects (neutron induced signal vs. gamma induced signal) which allow us to define the optimal range of operability around 300 µm. Despite of a poor discrimination strength compared to conventional PSD scintillators, the multilayer phoswich can find its interest for neutron source localization thanks to its high direction dependence with neutron angle of incidence.

I. INTRODUCTION

EUTRON measurement is a major issue in many applications as for security (radiological treat), fuel manufacturing and processing, Nuclear Power Plant safety and operating. Thermal neutrons are efficiently detected using helium 3 gas detectors which exhibit an excellent discrimination between neutron and gamma events. In a context of shortage in helium 3, alternative solutions have been developed using thermal neutron capture into Boron, Lithium or Gadolinium [1][2][3][4][5][6]. These systems require the implementation of moderator whereas fast neutron detectors enable neutron from Special Nuclear Materials (SNM) to be directly detected using light ion recoil consecutively to elastic scattering (n,n'). Fast neutron based detectors are therefore more suitable for compact systems or to be used in cluster for implementing coincidence techniques [7,[START_REF] Deyglun | Proceeding of ANIMMA[END_REF]. The discrimination mechanism exploits energy transfer between two triplet state called intersystem crossings. This Triplet-Triplet Annihilation (TTA) is allowed only when a sufficient energy density is achieved in a given polymer matrix [START_REF] Birks | The Theory and Practice of Scintillation Counting[END_REF][START_REF] Brooks | [END_REF]. Indeed, the density of energy released by recoil protons from neutron elastic scattering is superior to the energy density of recoil electrons from gamma-rays Compton scattering. As a consequence, gamma rays will induced fluorescence (direct radiative transition from the first exited singlet state to the fundamental state) whereas neutron particles will produced delayed fluorescence (due to delay time in the triplet state before TTA) in some polymers and for a given deposited energy. The impulse response is therefore dissociated between neutron and gamma rays thanks to the implementation of Pulse Shape Discrimination PSD technique in the Digital Signal Processing DSP of the system. This approach is known to be very efficient in liquid state scintillators where intermolecular energy transfer is fostered [11,12]. However, liquid scintillators have to be carefully encapsulated due to their N toxicity, their low flash point and their oxygen adsorption damaging scintillator performances over the time. Therefore plastic scintillators are more suited for handle and long term of use and some recent works show promising results [13,14].

Another discrimination technique has been proposed by M.A. Kovash for solid state plastic scintillator [START_REF] Kovash | Proceeding of ANIMMA[END_REF]. Recoil protons and electrons have the property to possess distinct path lengths for a given kinetic energy. As presented in the fig. 1, the range of recoil electrons from gamma-rays is two orders of magnitude higher than the range of recoil protons from neutrons for a given energy.

The system proposed by the authors of [START_REF] Kovash | Proceeding of ANIMMA[END_REF] is composed of thin layers (100 µm) optically isolated to each over and associated to a coincidence electronics. Pulse detected in coincidence between adjacent layers is considered as gamma-rays and are then rejected. Fig. 1. Range of electrons calculated by Katz and Penfold formula [START_REF] Katz | [END_REF] and protons calculated by SRIM [17].

The CEA LIST has patented and implemented a layered scintillator in an alternative configuration where the layers are nonoptically insulated, composed of a polymer matrix doped with different fluorophores (inducing fast and slow scintillators) and associated with PSD electronics [18]. On the first hand, output pulses resulting from proton recoils comes from single layer interactions and they can be shape fast or slow (neutron interaction). On the other hand, a mixed pulse shape is observed for recoil electrons slowing-down through adjacent layers (gamma interaction). The fig. 2 illustrates the concept of the system. The multilayer phoswich scintillator has been studied by particle transport simulation. This study is detailed in following sections.

II. MATERIAL AND METHOD

The simulation study has been realized using MCNPX Monte-Carlo particle transport code [19]. The geometry is composed of twenty alternating layers (25 x 25 mm). Source particles (neutron or gamma) are generated next to the scintillator and data associated with recoil particle collisions are recorded into the MCNPX PTRAC file.

Interaction models in 𝛾/𝑒 and n/p modes

We consider first the formatting of electron broken line path in the 𝛾/𝑒 mode. Let 𝑁 the number of the collision 𝛿, 1 ≤ 𝛿 ≤ 𝑁 associated with the history number ℎ. PTRAC file is processed to extract in each history ℎ:

 the coordinate 𝑋 of 𝛿 collisions, ∀𝛿 ∈ [1; 𝑁 ], 𝑋 = 𝑥 , ; 𝑦 , ; 𝑧 , (1)
 the final position of delta-rays coming from the 𝛿 collisions,

∀𝛿 ∈ [1; 𝑁 ], 𝑌 = 𝑥 , ; 𝑦 , ; 𝑧 , (2)
 the initial kinetic energy 𝐸 , of the recoil electron coming from Compton scattering,  the kinetic energy 𝐸 , of each delta electrons,  the cell number 𝐶 in which 𝛿 collision has occurred.

MCNP code ensures electron transport up to 1 keV. As we know, the electron collision threshold is close below 1 keV, we can then consider that ionization and excitation induced by the recoil electron are described along the track path described here. At the end of the electron slowing down, the deposited energy 𝐸 , is spread along the delta electron path in one hand. On the other hand, the energy 𝐸 , is released in the path of the primary recoil electron between two collisions 𝛿 and 𝛿 + 1 as described in the following equations where 𝑑 is the distance path between collisions:

∀𝛿 ∈ [1, 𝑁 -1], 𝑑 = 𝑥 , -𝑥 , + 𝑦 , -𝑦 , + 𝑧 , -𝑧 , (3)
𝐸 , = 𝐸 , -∑ 𝐸 , 𝑑 ∑ 𝑑 (4)
Let 𝜌 = {𝑆 ; 𝑆 } the scintillator type numbers (fast / slow pulse time constant), quantities of deposited energy 𝐸 , in each scintillator type 𝜌 is calculated such as:

∀𝛿 ∈ [1, 𝑁 -1] & ∀𝜌 ∈ [𝑆 ; 𝑆 ], 𝐸 , = 𝐸 , + 𝐸 , , (5)
In n/p mode, the neutron cross-section library ENDF B-VI and the proton cross-section library la150h are used. Protons are decelerated in straight line mainly by Coulomb force and all the energy 𝐸 is considered to be released along its path. In this mode, delta electron production is considered as neglected (𝑁 = 1), then PTRAC processing allow us to calculate directly released energies 𝐸 , into the two types of scintillator.

∀𝜌 ∈ [𝑆 ; 𝑆 ], 𝐸 , = 𝐸 , ( 6
)
Figs. 3 and4 show an example of a recoil electron and a recoil proton path.

Model of the scintillation

A particularity of scintillation is the quenching effect in which the light yield 𝐿 is reduced as a function of the type of polymer and the type of particles (cf. the semi-empirical Birks formula [20]). The quenching phenomenon is increase for hadronic recoil particles compared to leptonic ones, respectively protons and electrons in our case. The reduced energy 𝐸 ̇ in MeVee is calculated for proton particles using the empirical relation proposed by [21] such as:

𝐸 ̇ = -0.0685 + 0.223𝐸 (7)
Scintillation is a quantum phenomenon where the expected number of photon quanta is proportional to the deposited energy from charges particles. As quanta are uncorrelated together, the effective number of quanta governing the scintillation pulse area

𝐸 ̈ , ~ 𝒫 𝐿 𝐸 , 𝐿

Pulse shape discrimination matrix calculation

The PSD matrix called 𝑀 is an n x n matrix, where rows correspond to energies measured in the type 𝑆 scintillator and columns correspond to energies measured in the type 𝑆 scintillator. Let 𝑒 , the energy vector, 𝜌 the scintillator type 𝑆 or 𝑆 , and ∆𝐸 the energy bins.

𝑀 , , , ≔ 𝑀 , , , +

Fig. 5 illustrates the theoretical composition of the discrimination matrix. Three areas can be distinguished:

 a neutron interaction area where recoil protons have released their kinetic energies in a type A scintillation layer (I),  a gamma interaction area where recoil electrons have released their kinetic energies in both types of scintillation layer (II),  a neutron interaction area where recoil protons have released their kinetic energies in a type B scintillation layer (III),

If the two types of layer are with the same thickness, we can predict that the PSD matrix will presents a diagonal line of symmetry.

Fig. 5. Theoretical composition of the discrimination matrix.

Figure of merit & intrinsic neutron efficiency

The discrimination strength of the system is estimated using a Figure Of Merit 𝐹𝑂𝑀 defined as the distance between mean energy of neutron 𝐸 and gamma 𝐸 lobes divided by the sum of associated standard deviations 𝜎 𝐸 and 𝜎 𝐸 at a given energy 𝑒 .

𝐹𝑂𝑀 = 𝐸 -𝐸 𝜎(𝐸 ) + 𝜎 𝐸 (13)

As a 𝐹𝑂𝑀 value above the unit allows the system to be considered as a potential neutron counter [22], the intrinsic neutron efficiency 𝜂 (i.e proton efficiency) is calculated as the sum of neutron counted above an energy threshold 𝛼 corresponding to the minimum energy ensuring discrimination (𝐹𝑂𝑀 > 1).

𝛼 = argmin

, (𝐹𝑂𝑀 > 1) ( 14)

𝜂 = ∑ ∑ 𝑀 , ℎ (15)
III. RESULTS

The simulation study has been conducted in order to determine the behavior of layered phoswich scintillator as a function of the layer thickness 𝛿. PSD matrixes have been calculated for different values of layer thickness such as: 𝛿 = {0.025; 0.050; 0.100; 0.300; 0.500; 1.000} mm for both source positions A and B (cf. fig. 2). The energy binning ∆𝐸 has been taken equal to 5 keVee. high energy protons (>650 keVee) go through more than one layer. Moreover the anisotropy is maximized in this particular case, where discrimination is enabled between 250 and 650 keVee in position B, whereas discrimination is completely impossible in position A. More the layers grow in thickness, more the discrimination strength becomes flat as a function of the energy, and more the isotropic behavior is increased. It can be observed in fig. 10, that 𝐹𝑂𝑀 values between 100 keVee and 1 MeVee and for a layer thickness equal to 1 mm are constant (𝐹𝑂𝑀 ≈ 1.5) and identical for both positions A and B. The homogeneity behavior achieved for 𝛿 = 1 mm against energy range and source position is balanced by low discrimination power while a more efficient discrimination is enable as seen for 𝛿 = 300 µm (𝐹𝑂𝑀 > 2 in position B and for e𝑒 ∈ [0.4; 1] MeVee) if a part of inhomogeneity is accepted (cf. fig. 9). We can conclude that it will be not probably possible to maintain as well discrimination capability and homogeneity (isotropy and energy stability). The proton efficiency 𝜂 (i.e. intrinsic neutron efficiency) has been calculated with 𝛼 estimations as a function of layer thickness for both source positions (average). Fig. 13 shows proton efficiencies estimation using 137 Cs interference source and 252 Cf as neutron source. According to this simulation study, we can conclude that proton efficiency is maximized for a layer thickness equal to 300 µm. In this case, an anisotropic effect is observed above 0.8 MeVee (fig. 9) but only concerns a small amount of recoil protons from fission neutrons. Proton efficiency about 0.2 % could be achieved by the proposed techniques.

IV. DISCUSSION

An interest in such approach could consist in neutron source localization using the anisotropic properties of the scintillator. For instance, a multilayered phoswich can be installed on a rotor fixed on a mobile robot as inspired by [23].

V. CONCLUSION A model allowing simulating neutron measurement of a multilayer phoswich scintillator has been developed. The behavior of the system as a function of the layer thickness has been investigated and strong incidence angle dependence has been predicted especially when layer are below 100 µm. Moreover, the optimum discrimination efficiency has been estimated at 300 µm but the system still shows a low discrimination strength due to the high dispersion of gamma event into PSD matrixes whatever layer thickness or incident energy are. A localization device is under study using this innovative component as a direction sensitive neutron detector.

Fig. 2 .

 2 Fig.2. Principle of the multilayer scintillator.

Fig. 3 .

 3 Fig.3. Scheme of a recoil electron path into the multilayer system.

Fig. 4 .

 4 Fig.4. Scheme of a recoil proton path into the multilayer system.

(

  and amplitude) takes its value in Poison distribution. Measured energies 𝐸 ̈ and 𝐸 ̈ associated to each individual interaction, are obtained by sampling into a Poisson distribution 𝒫 where 𝐸 ̇ and 𝐸 are expected deposited energy values. ∀𝜌 ∈ [𝑆 ; 𝑆 ],

  The figs. 6 and 7 show matrixes obtained with gamma and neutron irradiations. The shapes are in accordance with the expected phenomena introduced in the fig.5with a concentration of gamma events in the central part of the PSD matrix whereas neutron events are mainly located along edges of the PSD matrix.

Fig. 6 .Fig. 7 .

 67 Fig. 6. PSD matrix obtained by simulation of a 60 Co source located in position B for a layer thickness equal to 300 µm.

Fig. 8 .

 8 Fig. 8. 𝐹𝑂𝑀 estimation as a function of the deposited energy 𝑒 for a layer thickness equal to 25 µm ( 60 Co + 252 Cf).

Fig. 9 .

 9 Fig. 9. 𝐹𝑂𝑀 estimation as a function of the deposited energy 𝑒 for a layer thickness equal to 300 µm ( 60 Co + 252 Cf).

Fig. 10 .

 10 Fig. 10. 𝐹𝑂𝑀 estimation as a function of the deposited energy 𝑒 for a layer thickness equal to 1 mm ( 60 Co + 252 Cf).

Fig. 11 .

 11 Fig. 11. Scheme of the discrimination technique principle.

Fig. 12 .

 12 Fig. 12. Electron equivalent energy threshold 𝛼 as a function of layer thickness 𝛿 ( 60 Co + 252 Cf).

Fig. 13 .

 13 Fig. 13. Proton efficiency 𝜂 as a function of the layer thickness 𝛿 ( 137 Cs + 252 Cf).