Y.S. Horowitz

Theory of heavy charged particle response (efficiency and supralinearity) in TL materials

Abstract We describe the theory of heavy charged particle (HCP) response (efficiency and supralinearity) in thermoluminescent (TL) materials. The HCP TL relative efficiency is treated in the framework of modified track structure theory (MTST) using Monte Carlo (MC) calculations of radial dose distributions in condensed phase LiF. HCP TL fluence response is modelled in the framework of the extended track interaction model (ETIM) which treats both HCP fluence response supralinearity and saturation using trapping centre (TC) and luminescent centre (LC) radial occupation density profiles. These are based on the MC radial dose distributions and experimental measurements of optical absorption and sensitisation dose response. Analytical ETIM calculations (up to fourth-order nearest-neighbour track interactions) are used to model the TL fluence response of the components of composite peak 5 in LiF:Mg,Ti (TLD-100). Monte Carlo track interaction calculations (MCTIM) are also described which can model even higher-order nearest-neighbour track interactions appropriate to the high temperature peaks in LiF:Mg,Ti (TLD-100), and as well, model the HCP TL fluence response in both parallel and non-parallel HCP beam geometries.

The unified interaction model applied to the gamma ray induced supralinearity and sensitization of peak 5 in LiF:Mg,Ti (TLD-100)

We describe the development of a comprehensive theory of thermoluminescence (TL) supralinearity and sensitization, the unified interaction model (UNIM), based on both radiation absorption stage and recombination stage mechanisms. The UNIM incorporates both the track interaction model (TIM) for heavy charged particles (HCPs) and the defect interaction model (DIM) for isotropically ionizing gamma rays and electrons, in a unified and self-consistent conceptual and mathematical formalism. The model is applied to explain the unique features of gamma-induced supralinearity and sensitization of peak 5 in LiF:Mg,Ti, especially the strictly linear, then supralinear behaviour and the dependence of the supralinearity on ionization density (gamma ray energy and particle type). Both features arise from a localized trapping entity (the track for HCPs, spatially correlated trapping centres and luminescent centres (TC/LC pairs) for gamma rays and electrons, which dominate the dose response at low dose and are not subject to intra-track competitive processes, thus leading to linear dose response behaviour. The decreasing efficiency of the competitive processes relative to the luminescence recombination processes, as a function of dose, leads to the supralinear behaviour. The decrease of the supralinearity with decreasing gamma ray energy (increasing ionization density) arises from the increasing probability of the TC/LC pair to simultaneously capture an electron - hole pair, leading to geminate recombination not subject to competitive processes. The UNIM is shown to be capable of yielding excellent fits to the experimental data with many of the variable parameters of the model strongly constrained by ancillary optical absorption and sensitization measurements.

Theory of thermoluminescence gamma dose response: The unified interaction model

Abstract We describe the development of a comprehensive theory of thermoluminescence (TL) dose response, the unified interaction model (UNIM). The UNIM is based on both radiation absorption stage and recombination stage mechanisms and can describe dose response for heavy charged particles (in the framework of the extended track interaction model – ETIM) as well as for isotropically ionising gamma rays and electrons (in the framework of the TC/LC geminate recombination model) in a unified and self-consistent conceptual and mathematical formalism. A theory of optical absorption dose response is also incorporated in the UNIM to describe the radiation absorption stage. The UNIM is applied to the dose response supralinearity characteristics of LiF:Mg,Ti and is especially and uniquely successful in explaining the ionisation density dependence of the supralinearity of composite peak 5 in TLD-100. The UNIM is demonstrated to be capable of explaining either qualitatively or quantitatively all of the major features of TL dose response with many of the variable parameters of the model strongly constrained by ancilliary optical absorption and sensitisation measurements.

Heavy charged particle thermoluminescence dosimetry: Track structure theory and experiments

The factors that influence the thermoluminescence (TL) yield of “tissue-equivalent” TL dosimeters (TLDs) following heavy charged particle (HCP) and neutron irradiation are evaluated. The relative TL response, η, the dose-TL response, f(D) , and the relative glow peak intensities (in LiF) appear to be significantly dependent on the HCP charge, mass and energy and not only on the LET ¯ ∞ as is widely believed. Previous studies, which have established the batch dependence of η following 81-meV neutron irradiation and 4-MeV alpha-particle irradiation, have indicated the importance of material characteristics (impurity and defect composition). This finding is now supported by additional studies illustrating a further dependence of the relative TL properties on details of the high-temperature annealing procedure. These HCP-TL properties can be described in the framework of a modified track structure theory (TST) via their relationship to low energy electron TL response. The major premise of TST is that the concentration of liberated charge carriers around the path of the HCP is the only parameter that governs the dependence of the relative TL properties on the type of HCP radiation. In conventional TST the bulk response of the system following γ-irradiation (usually 60 Co or 137 Cs) is folded into the radial distribution of absorbed dose D ( r , HCP, E ) around the axis of the HCP track to determine the relative TL response. This approach has achieved considerable success in HCP radiation yield calculations but the choice of high energy γ-rays or electrons is particularly unfortunate in TL yield calculations because of the well-known dependence of f(D) on electron energy. This latter dependence therefore requires that the test electron spectrum be matched as closely as possible to the initial energy spectrum of the electrons ejected during the HCP slowing down E max ≅ a few keV for ∼MeV/a.m.u. HCP). Further refinements incorporated into our modified TST approach are careful matching of all the relevant experimental parameters in the measurement of η and f(D) and simulation of the density of “low-energy” charge carriers around the HCP path in “tissue-equivalent” dosimeters using published experimental data for “tissue-equivalent” gas rather than the use of approximate analytic calculations. Our experimental measurements of η have encompassed a variety of radiation fields (alpha particles, meV neutrons, fission fragments, etc.), and f(D) has been measured for X-rays, electrons of various energies and 60 Co γ-rays. The overall agreement between theory and experiment is excellent, but considering our inadequate understanding of electron-induced TL it would be premature to conclude that TST is the whole truth underlying HCP-induced TL. TST does provide a convincing and convenient framework to understand HCP- and the neutron-induced TL.

Localized transitions in the thermoluminescence of LiF:Mg,Ti: potential for nanoscale dosimetry

We describe the effect of nanoscale spatially coupled trapping centre (TC)–luminescent centre (LC) pairs on the thermoluminescence (TL) properties of LiF : Mg,Ti. It is shown that glow peak 5a (a low-temperature satellite of the major glow peak 5) arises from localized electron–hole (e–h) recombination in a TC–LC pair believed to be based on Mg 2+ –Livac trimers (the TCs) coupled to Ti(OH)n molecules (the LCs). Due to the localized nature of the e–h pair, two important properties are affected: (i) heavy charged particle (HCP) TL efficiency: the intensity of peak 5a relative to peak 5 following HCP high-ionization density irradiation is greater than that following low ionization density irradiation in a manner somewhat similar to the ionization density dependence of the yield of double-strand breaks (DSBs) induced in DNA. Our experimental measurements in a variety of HCP and fast neutron radiation fields have demonstrated that the ratio of glow peaks 5a/5 is nearly independent of particle species for the protons, deuterons and He ions investigated, is somewhat dependent on HCP energy, and is roughly 2–3 times greater than the peak 5a/5 ratio in low ionization density electron and photon fields. The intensity ratio of peak 5a/5 thus has the potential of estimating the ratio of dose deposited via high ionization density interactions compared to low ionization density interactions in a nanoscale volume without any prior knowledge of the characteristics of the radiation field, (ii) non-linear TL dose response: the relative lack of competitive processes in the localized recombination transitions leading to the TL of composite peak 5 versus the dose-dependent competitive processes in conduction band-mediated delocalized luminescence recombination leads to non-linear dose response (supralinearity) for composite peak 5 and a dependence of the supralinearity on ionization density. This behaviour is modelled in the framework of the unified interaction model (UNIM).

A Unified and Comprehensive Theory of the TL Dose Response of Thermoluminescent Systems Applied to LiF:Mg,Ti

Radiation induced effects in biological and solid-state systems, especially the effects of ionization density, continue to be of far-reaching implications and intensive investigation. In radiobiological systems of impressive complexity such as DNA, the study of the consequence of single strand breaks (SSBs), double strand breaks (DSBs) and clusters of ionization, on radiobiological mechanisms is still in its infancy. Solid-state systems are considerably less complex and the physical/mathematical modelling of radiation induced effects in these systems has reached a more mature stage with significant successes. A good example is the trapping center (TC), luminescent center (LC) and competitive center (CC) system giving rise to glow peaks 4 and 5 in the thermoluminescence (TL) of LiF:Mg,Ti, and the effects of ionization density in this system. Although simpler than the biological mechanisms leading to cancer or cell death, TL is also a multi-stage process in which the interplay between localized and delocalized recombination mechanisms can give rise to many complex phenomena. In the radiation absorption stage, charge carriers released by ionizing radiation are trapped at the various defect centers in metastable states. In the second stage, the recombination stage, the LCs and the non-radiative CCs compete for the thermally released charge carriers. Radiation effects on this system have been intensively studied; a consequence of the decades—long prominence of LiF:Mg,Ti in applications to passive radiation dosimetry. In the 1960s and 1970s early investigations of this material, specifically—the dosimetric glow peaks 4 and 5, quickly revealed a surprising number of phenomena which could be directly related to ionization density. The most famous of these included: (a) A linear, then supralinear, dose response (i.e, increased TL efficiency) beginning at a critical dose level, D c ∼0.1 Gy.

A microdosimetric track interaction model applied to alpha-particle-induced supralinearity and linearity in thermoluminescent LiF:Mg, Ti

A microdosimetric track interaction model for heavy charged particles has been developed which is capable of quantitatively predicting the experimentally observed supralinearity of the alpha particle TL dose response of peak 8 in LiF:Mg, Ti (TLD-100, Harshaw/Filtrol) as well as the linear behaviour of the lower temperature glow peaks. The linear behaviour at low dose is due to lack of track interaction arising from the highly localised nature of the alpha particle dose deposition profile (98% of the dose is deposited within 200 AA of the track axis). Track dose overlap in the radiation absorption stage is shown to be incapable of significantly increasing the thermoluminescence efficiency of intersecting tracks. The alpha-induced supralinearity of peak 8 can, therefore, be explained only via greatly increased charge carrier migration lengths in the glow curve heating stage which brings about significant nearest-neighbour track interactions above a fluence of approximately 108 particles cm-2 (approximately 10 Gy in LiF). The increase in TL efficiency arises from the increased population of luminescence recombination centres available to the migrating charge carriers released from the TL trapping centres. The linear behaviour of the lower temperature peaks (up to a fluence of approximately 1010 particles cm-2 followed by exponential saturation) yields a charge carrier average migration distance of approximately 250AA (cf 5000 AA for peak 8) which implies that at low sample temperatures there is little inter-track migration of charge carriers in the luminescence recombination stage.

Computerized glow curve deconvolution applied to ultralow dose LiF thermoluminescence dosimetry

Abstract A computerized glow curve deconvolution technique (CGCD) and its application to the ultralow dose thermoluminescence (TL) glow curve of LiF:Mg, Ti (TLD-100) are described. The benefits in precision and minimum measurable dose (MMD) applied to TLD-100 are considerable. The CGCD analysis interpolatively estimates the background signal under peaks 4 and 5 which greatly reduces the errors introduced by inaccurate background subtraction due to second readout as well as eliminating the need for second readout. In addition, the error introduced via inaccurate separation of peak 3 is reduced and post-irradiation annealing is rendered unnecessary. An additional important feature of the CGCD method is the ability to reject/correct outliers in the glow curve. Assuming an MMD criterion of ±20% (1 SD) precision yields an MMD of 1.9 μGy (0.19 mrad) and 27 μGy (2.7 mrad) for CGCD and routine analysis respectively, i.e., an improvement in MMD of a factor 14.2.

EXPERIMENTAL INVESTIGATION OF THE 100 keV X-RAY DOSE RESPONSE OF THE HIGH-TEMPERATURE THERMOLUMINESCENCE IN LIF:MG,TI (TLD-100): THEORETICAL INTERPRETATION USING THE UNIFIED INTERACTION MODEL

The dose response of LiF:Mg,Ti (TLD-100) chips was measured from 1 to 50,000 Gy using 100 keV X rays at the European Synchroton Radiation Facility. Glow curves were deconvoluted into component glow peaks using a computerised glow curve deconvolution (CGCD) code based on first-order kinetics. The normalised dose response, f(D), of glow peaks 4 and 5 and 5b (the major components of composite peak 5), as well as peaks 7 and 8 (two of the major components of the high-temperature thermoluminescence (HTTL) at high levels of dose) was separately determined and theoretically interpreted using the unified interaction model (UNIM). The UNIM is a nine-parameter model encompassing both the irradiation/absorption stage and the thermally induced relaxation/recombination stage with an admixture of both localised and delocalised recombination mechanisms. The effects of radiation damage are included in the present modelling via the exponential removal of luminescent centres (LCs) at high dose levels. The main features of the experimentally measured dose response are: (i) increase in f(D)(max) with glow peak temperature, (ii) increase in D(max) (the dose level at which f(D)(max) occurs) with increasing glow peak temperature, and (iii) decreased effects of radiation damage with increasing glow peak temperature. The UNIM interpretation of this behaviour requires both strongly decreasing values of ks (the relative contribution of localised recombination) as a function of glow peak temperature and, as well, significantly different values of the dose-filling constants of the trapping centre (TC) and LC for peaks 7 and 8 than those used for peaks 4 and 5. This suggests that different TC/LC configurations are responsible for HTTL. The relative intensity of peak 5a (a low-temperature satellite of peak 5 arising from localised recombination) was found to significantly increase at higher dose levels due to preferential electron and hole population of the trapping/recombination complex giving rise to composite glow peak 5. It is also demonstrated that possible changes in the trapping cross section of the LC and the competitive centres due to increasing sample/glow peak temperature do not significantly influence these observations/conclusions.

Optical absorption in LiF : Mg,Ti and its relationship to thermoluminescence and thermoluminescence dose response

Abstract The optical absorption (OA) spectrum of LiF : Mg,Ti has been investigated by optical bleaching and I m – T stop pulsed annealing in steps of 3–4°C over the temperature range from 100°C to 300°C. In agreement with previous investigations, the 5.45 eV OA band is identified as a likely candidate for the recombination stage competitor responsible for composite peak 5 supralinearity. An additional OA band at 5.7 eV is also identified as a possible recombination stage competitor. First-order kinetic analysis yields an activation energy of 0.8±0.13 eV for the 4.0 eV band usually associated with peak 5, an energy which is similar in value to the binding energy of the Mg–Li vac trimer believed to form the peak 5 trapping structure. Dose response measurements result in dose filling constants of β TC =0.9±0.1×10 −3 Gy −1 and β CC =3.8±0.8×10 −4 Gy −1 for the 4.0 and 5.45 eV OA bands, respectively. These dose filling constants deduced from OA measurements can be used in the framework of the unified interaction model (UNIM) to study the dose response supralinearity of composite dosimetric peak 5.