Elsevier

Radiation Measurements

Volume 123, April 2019, Pages 1-12
Radiation Measurements

Microdosimetric specific energy probability distribution in nanometric targets and its correlation with the efficiency of thermoluminescent detectors exposed to charged particles

https://doi.org/10.1016/j.radmeas.2018.12.010Get rights and content

Highlights

  • A model based on microdosimetry was developed for predicting TLD efficiency.

  • LiF:Mg, Ti and LiF:Mg,Cu,P efficiency was determined for particles from 1H to 132Xe.

  • The determined efficiencies depend on the site size of the calculations.

  • For a site size of 40 nm, very good agreement with experimental data was found.

Abstract

Due to their common use for dose measurements in space and hadron therapy facilities, it is of fundamental importance to know the efficiency of luminescent detectors for measuring a wide range of particles and energies. However, due to experimental limitations it is often not possible to irradiate the detectors with very high energies, less common isotopes or exotic particles. Furthermore, the efficiency determination at low energies is biased with associated large uncertainties in range, linear energy transfer and dose. This paper presents the recently developed Microdosimetric d(z) Model able to assess the relative efficiency of thermoluminescent detectors for measuring different radiation qualities by relating the simulated dose probability distribution of the specific energy in nanometric targets with an experimentally determined response function. The model was tested in case of LiF:Mg, Ti (MTS) and LiF:Mg,Cu,P (MCP) thermoluminescent detectors exposed to charged particles from 1H to 132Xe in the energy range 3–1000 MeV/u. A comparison with experimentally determined efficiency results showed a very good agreement in case of calculations performed in a simulated target size of 40 nm. This validated model can be used to assess detector efficiency to exotic particles, unavailable radiation qualities and energies at ground level accelerators or complex mixed fields. The assumptions behind the model, its methodology and results are discussed in detail. Furthermore, a systematic investigation on the effect of simulation parameters on the calculated efficiency values is included in the manuscript.

Introduction

Because of their safe, light, small and passive nature (Olko, 2010), radiation detectors based on the thermoluminescence technique (McKeever, 1988; Chen and Pagonis, 2011; Bos, 2017) are commonly used for space dose mapping experiments (Reitz et al., 2005; Hajek et al., 2006; Szántó et al., 2015; Berger et al., 2016), astronaut personal dosimetry (Deme et al., 1999; Straube et al., 2010, Apáthy et al., 2002) stratospheric studies (Katona et al., 2007; Zábori et al., 2016), in-phantom organ dose measurements inside and outside shuttles, the International Space Station and commercial flights (Yasuda, 2009; Berger et al., 2008, 2013), space dosimetry of biological experiments (Vanhavere et al., 2008; Berger et al., 2012, 2015), aircrew monitoring (Hajek et al., 2002; Bilski et al., 2004 a; Hajek et al., 2004), radiotherapy mailed audits (Kron, 1999; Kunst et al., 2017), in field (Geiβ et al., 1998 b; Berger et al., 2006a) and out of field (Mukherjee et al., 2011; Knežević et al., 2017; Stolarczyk et al., 2018) dose assessment in hadron therapy. However, radiation measurements in these complex radiation environments (Mayles et al., 2007; Bagshaw, 2008; Nelson, 2016) require an in depth knowledge of detector response in measuring a wide range of particles and energies.

Among all materials available, thermoluminescent detectors based on lithium fluoride are the most diffused and studied worldwide, especially in the form of lithium fluoride doped with magnesium and titanium (LiF:Mg,Ti) or with magnesium, copper and phosphorus (LiF:Mg,Cu,P) (Horowitz, 1993; McKeever et al., 1995; Bilski, 2002). The experimental investigation of the efficiency of these detectors has been carried out during the years by means of calibrated ion beam exposures at ground level particle accelerators (Horowitz, 1981, Benton et al., 2000; Berger et al., 2006b; Bilski, 2006; Berger and Hajek, 2008; Bilski and Puchalska, 2010; Bilski et al., 2011; Gieszczyk et al., 2013; Sądel et al., 2015b; Parisi et al., 2017 b; Parisi et al., 2018).

Due to the complexity of the physical processes taking part in the thermoluminescent phenomenon (McKeever, 1988; Chen and Pagonis, 2011; Bos, 2017), the determination of an absolute luminescence efficiency η (Equation (1)), namely the ratio between the average energy emitted by the detector as form of light (εTL) and the mean energy imparted to the detector by the radiation field (ε), is biased by intrinsic difficulties.η=εTLε

Consequently, during the years researchers focused their efforts in the determination of the relative luminescence efficiency ηrel. The latter quantity is defined as in Equation (2) as the intensity of the luminescence signal S per unit of absorbed dose D for the radiation under investigation over the same quantity for a reference radiation.ηrel=(SD)radiation(SD)referenceradiation

It was concluded that this relative efficiency is not a unique function of the linear energy transfer (LET) of the incident radiation, but depends strongly also on the particle type (Horowitz, 1981; Berger et al., 2006b; Berger and Hajek, 2008). This happens because, in order to have the same LET, two different particles must have different velocities: the heavier the particle, the higher the velocity. Consequently, the heavier particle will produce δ-rays with higher energies (so longer range in matter) which will deposit their energy in a radially less dense way around the track of the charged particle (Olko, 2007). It follows that, being the response of the detector generally inversely related to the energy deposition density of the impinging radiation, the efficiency of the detector in measuring two different particles characterized by the same LET value will be higher for the heavier particle.

Unfortunately, the experimental determination of the relative efficiency of luminescent detectors through irradiations in charged particle accelerators is time consuming and very expensive. Furthermore, due to technical limitations it is often not possible to irradiate the detectors with energies above 1 GeV/u or with less common isotopes. In addition, the efficiency determination for low energies is biased with big uncertainties of all parameters (i.e. LET, range, absorbed dose). However, a complete characterization of the efficiency of these detectors is needed, especially for space applications where particles with a really broad energy spectrum and exotic isotopes are present. As consequence, during the years, many models have been developed in order to explain and predict the efficiency of thermoluminescent detectors for different radiation qualities. Among all of them, the most common ones are based on track structure theory (Larsson and Katz, 1976; Waligórski and Katz, 1980; Kalef-Ezra and Horowitz, 1982; Geiβ et al., 1998 a; Ávila et al., 1999; Boscolo et al., 2015). Two ingredients are needed for those calculations: the radial dose distribution and a dose response function. The first one can be evaluated through analytical models (Butts and Katz, 1967; Faïn et al., 1974; Waligórski et al., 1986; Katz et al., 1990; Katz et al., 1996; Chen and Kellerer, 1997; Cucinotta et al., 1997; Geiβ et al., 1998 a, Greilich et al., 2014) or Monte Carlo simulations (Krämer and Kraft, 1994; Waligórski et al., 1986; Ávila et al., 1996) and represents the dose distribution around the track of the particle while traveling through the detector. The second one represents the response of the detector when irradiated at different dose levels with a sparsely ionizing radiation such as photons or electrons (Horowitz, 1990, Gamboa-deBuen et al., 1998, Bilski, 2002, Massillon-Jl et al., 2006, Bilski et al., 2007, Massillon-Jl et al., 2011).

In depth studies were performed to investigate how the assessment of the radial dose distribution and the dose response function could affect the calculated efficiency (Ávila and Brandan, 2002; Ávila et al., 2008, Massillon-Jl et al., 2011). Efficiency values were determined for response functions obtained exposing the detectors to 8.1 keV X-rays, β-particles, 100 keV X-rays and photons from a60Co γ-ray source. Furthermore, artificial response functions were also included in the study. On the other hand, the radial dose distribution was evaluated by means of both analytical formulations or Monte Carlo simulations. It was concluded that, for all radial dose distribution and dose response function combinations, the quantitative agreement between the calculated and the experimental efficiency values was poor (Massillon-Jl et al., 2011). Similar conclusions were drawn in a separate work (Horowitz et al., 2012) which underlined the necessity of improving the evaluation of the radial dose distribution, i.e. implementing accurate models for the transport of low energy ions and secondary electrons, and reducing the uncertainties associated with the assessment of the dose response function at high dose levels. Furthermore, as the concept of radial dose distribution is inapplicable to photons, neutrons or electrons, one should remember that track structure models cannot be applied for efficiency determination for these radiation qualities (Olko et al., 2002b).

However, an alternative approach based on microdosimetry (International Commission on Radiation Units and Measurements, 1983; Kellerer, 1985; Rossi and Zaider, 1996) was proposed by Olko (Olko, 2002a; Olko, 2002b; Olko, 2004; Olko, 2007). The key idea of his methodology was to use microdosimetric specific energy probability distributions in place of radial dose distributions to quantify the changes in the local ionization density. The detector is supposed being composed by many independent structures, called targets, which act as sensitive volumes for measuring radiation. The size of these targets is a free parameter in Olko's methodology.

In Olko's model, the relative efficiency was evaluated using Equation (3) as the ratio of the specific energy frequency probability distribution f(z) folded into a specific energy response function r(z), over the same quantity for a reference radiation. The factor 1/zF¯ was used to change the normalization from per single event to per unit of dose (Olko, 2002a). Here and in the following, probability distributions and expectation values are relative to single event microdosimetric spectra (International Commission on Radiation Units and Measurements, 1983).ηrel=[1zF¯0+f(z)r(z)dz]radiation[1zF¯0+f(z)r(z)dz]referenceradiation

The reference radiation was chosen to be the photons from a137Cs γ-ray source and zF¯ is the frequency mean specific energy defined as in Equation (4) (International Commission on Radiation Units and Measurements, 1983).zF¯=0+zf(z)dz0+f(z)dz

The frequency distribution of the specific energy f(z) induced by charged particles was assessed using an analytical approach (Olko and Booz, 1990) obtained parametrizing the results of simulations performed with the MOCA-14 code (Paretzke, 1988). In case of photons, the initial distribution of secondary electrons was calculated using the Monte Carlo code PHOEL-2 (Turner et al., 1980). Afterwards, electron track structure simulations were performed using the TRION code (Lappa et al., 1993) for obtaining the microdosimetric probability distributions. All the calculations were performed in an infinitesimal layer of water (the slowing down of the particle within the real detector was neglected) and the results were afterwards converted from targets in water to lithium fluoride using a density scaling approach. More details can be found elsewhere (Olko, 1989; Olko, 2002a; Olko, 2002b). Olko's model was used to calculate the efficiency of several detector types for measuring photons (Olko and Waligórski, 2002; Olko et al., 2002a; Olko et al., 2006) and charged particles from 1H to 16O with a maximum energy of 20 MeV/u (Olko et al., 2002b; Olko et al., 2004; Olko et al., 2006).

A similar model, called Microdosimetric d(z) Model, has been recently developed using the Monte Carlo Particle and Heavy Ion Transport code System (PHITS, Sato et al., 2018) in order to extend the validity of the microdosimetric approach to energies and particles relevant for hadron therapy and space applications. Differences with Olko's model can be found in the formalism used in evaluating the relative efficiency, the assessment of the microdosimetric probability distributions, the specific energy response function and the reference radiation. Furthermore, in this work, the particle slowing down within the detector and the creation of secondary particle were considered in the Monte Carlo calculations. The model was shortly presented in Parisi et al. (2017) c, Parisi et al. (2017) d together with a preliminary comparison between its results for target sizes of 10, 40 and 100 nm and experimental data from the Institute of Nuclear Physics (IFJ, Krakow, Poland: Bilski, 2006, Bilski and Puchalska, 2010, Bilski et al., 2011, Gieszczyk et al., 2013 and Sądel et al., 2015b) for LiF:Mg, Ti (MTS) and LiF:Mg,Cu,P (MCP) detectors. In this paper, the Microdosimetric d(z) Model is presented in detail including a complete description of the methodology used for the assessment of the dose distribution of the specific energy, an in depth comparison between results of the model in case of 10, 20, 30, 40 and 50 nm target sizes and experimentally determined efficiency data including results also from the Belgian Nuclear Research Centre (SCK•CEN, Mol, Belgium: Parisi et al., 2017 a and Parisi et al., 2018), the German Aerospace Centre (DLR, Cologne, Germany: Berger and Hajek, 2008) and the Atomic Institute (ATI, Vienna, Austria: Berger et al., 2006b and Berger and Hajek, 2008), a comparison between the methodology used for assessing LET values using the Monte Carlo code PHITS (Sato et al., 2018) with a similar approach employing the Stopping and Range of Ions in Matter (SRIM) software suite (Ziegler et al., 2010) and a systematic analysis on the effect of simulation parameters on the final calculated relative efficiency values.

Section snippets

Methodology

The relative luminescence efficiency of the detectors was evaluated using Equation (5), where d(z) is the dose probability distribution of the specific energy and r(z) is the specific energy response function.ηrel=[0+d(z)r(z)dz]radiation[0+d(z)r(z)dz]referenceradiation

Differently from Olko's methodology (Olko, 2002a), the reference radiation was chosen to be the photons from a60Co γ-ray source instead of a137Cs γ-ray source. This was done because:

a. The most recent and complete set of high

Relative luminescence efficiency of LiF:Mg, Ti (MTS) and LiF:Mg,Cu,P (MCP) detectors

Using Equation (5), the relative efficiency of LiF:Mg, Ti (MTS) and LiF:Mg,Cu,P (MCP) detectors for measuring particles from 1H to 132Xe was determined in the energy range 3–1000 MeV/u as function of the microdosimetric site size. The site sizes in which the Monte Carlo simulations were performed ranged from 1 nm to 2 μm. The obtained efficiency values were compared with experimental data from literature (Berger et al., 2006b; Bilski, 2006; Berger and Hajek, 2008; Bilski and Puchalska, 2010;

Conclusions

Due to technical limitations, the relative efficiency determination of luminescent detectors for very high and low energy particles, uncommon isotopes and exotic radiation qualities is often strongly limited. Furthermore, the assessment of detector efficiency in complex mixed fields is still very challenging. However, the use of these detectors for space and hadron therapy applications requires an accurate knowledge of their response for measuring a broad spectrum of particles and energies.

In

Author contribution statement

AP conceived, developed and validated the Microdosimetric d(z) Model. The other authors revised the manuscript, written by AP.

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