Efficiency of thermoluminescent detectors to heavy charged particles

Nuclear Instruments and Methods in Physics Research B 142 (1998) 592±598

Eciency of thermoluminescent detectors to heavy charged particles O.B. Geiû *, M. Kr amer, G. Kraft GSI Biophysik, Planckstrasse 1, D-64291 Darmstadt, Germany Received 3 March 1998

Abstract The eciency of TLD-700 thermoluminescent detectors is studied for various ions as a function of energy. A new model for calculation of eciency has been developed, based on the detector response to reference radiation, and the radial dose distribution of heavy ions only. No free parameters have to be used to calculate the thermoluminescence detector (TLD) eciency as a function of ion species and energy. Comparison between model calculations and experimental results will be presented. Ó 1998 Published by Elsevier Science B.V. All rights reserved. Keywords: Heavy charged particles; Thermoluminescent detectors; TLD-700

1. Introduction Thermoluminescence detectors (TLDs) are widely used in conventional radiation detection and dose veri®cation (for a review see e.g. [14]). Their main advantages are tissue equivalent composition and small dimensions. The recently started radiotherapy at GSI [11] has stimulated investigations whether TLDs could be used for dose veri®cation in heavy ion irradiation. For this purpose the knowledge of the detector eciency g is essential. As already shown in earlier investigations this eciency strongly depends on ion charge Z and energy E [1,3,5±7,13,15±20,23±26]. Getting

* Corresponding author. Fax: +49 6159 712106; e-mail: [email protected].

experimental data on the TLD eciency to heavy ions ± especially carbon and its lighter fragments ± was one aim of our work. On the other hand it was necessary to develop a model to calculate g…E; Z† for ions and energies not available to the experiment. 2. Experiments LiF chips (TLD-700) of Harshaw Chemical Co. (3 ´ 3 ´ 0.38 mm3 ) were used in the experiments. The readout system was a Harshaw Series 8800. After irradiation TLDs were preheated at a temperature of 100 C for 10 s, then heated to a temperature of 300 C with a constant heating rate of 25 C/s. Chips were held at this temperature for 20 s, followed by a 400 C annealing for 20 s. No

0168-583X/98/$19.00 Ó 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 3 2 5 - 5

O.B. Geiû et al. / Nucl. Instr. and Meth. in Phys. Res. B 142 (1998) 592±598

pre-irradiation heating was done. Glow-curves were recorded between t1 ˆ 10 s and t2 ˆ 30 s (after beginning of readout analysis) R t in 200 channels. We used the integral lightsum t12 I…t† dt for glowcurve analysis. A 250 kV X-ray tube was used as a reference radiation source. The dose rate for all radiations was around 5 Gy/min. The dose rate of the irradiations with 137 Cs and 60 Co sources was about 0.5 Gy/min. Irradiations with heavy ions were performed at di€erent facilities, the UNILAC and SIS accelerator of GSI and the tandem accelerator at the MPI Heidelberg (cf. Table 1). In most cases various ion energies were provided by the accelerator. Avoiding energy degraders kept unwanted contributions from projectile fragmentation (see e.g. [22]) at a minimum. The radiation dose was calculated from the measured particle ¯uence according to D …Gy† ˆ 1:602  10ÿ10 1  …dE=dx†LiF …MeV cm2 =g† q  U …particles=cm2 †

…1†

using the mean energy loss …dE=dx†LiF in LiF calculated according to Eq. (7) and the particle ¯uence U measured with transmission counters that have been calibrated using CR39 nuclear track detectors. The radiation dose was lower than 2 Gy in all cases to avoid e€ects of supralinearity. The dose rate was around 10 Gy/min. The eciency g was derived according to gˆ

…TLHI =D† …TLX =D†

…2†

using TLHI and TLX , the integral lightsum of detectors irradiated with heavy ions and X-rays, respectively. Due to the limitations of our TLD readout system it was not possible to measure the thermoluminescence signal up to saturation doses. We therefore parametrized experimental data of Majborn et al. [13], because they also used TLD-700 detectors but a di€erent readout system. Fig. 1 shows their experimental X-ray data as well as our parametrization

h   ÿ4 TLX …D† ˆ const 0:59 1 ÿ eÿ510 D  i ÿ6 2 ‡0:41 1 ÿ eÿ210 D :

593

…3†

3. Calculations It is not possible to measure TLD eciencies for all ions and energies that are necessary for medical dose veri®cation. For that reason an algorithm to calculate g as a function of ion charge Z and energy E is needed. There already exist a number of models working on this purpose [8,9,19]. In contrast to them our model does not use any free parameter-like the radius of a sensitive volumeand therefore requires no experimental heavy ion data as input. The calculations are based on the assumption that the local dose at each electron trapping center is important for the probability of electron trapping. Because of their small size these centers are activated independently of each other. Their responses to the local dose is assumed to be the same as that measured with X-rays. Therefore, the radial dose distribution D…r† around the particle track has to be folded with the detector response TLX …D† to X-rays in order to calculate the dose response to a particle of a given energy and atomic number. For that purpose the detector volume has to be divided into layers of thickness Dzi , so that the energy variation of the primary beam inside each layer is small. The volume around each ion path is divided into concentrical cylindrical shells DVi ˆ 2pri Dri Dzi , resulting in a small variation of dose inside each shell (e.g. 1±5%, depending on the acceptable calculation time and the desired accuracy). For the radial dose distribution at the distance r from the ions path, we parametrized results of track structure calculations [12] leading to  k r 6 r0 ˆ 0:1 nm; …4† D…r† ˆ 2 k…r0 =r† r0 < r < Rel with the constant k normalized to the energy loss ZRel 2p 0

1 D…r†r dr ˆ q



 dE : dx

…5†

594

O.B. Geiû et al. / Nucl. Instr. and Meth. in Phys. Res. B 142 (1998) 592±598

Table 1 Eciency of TLD-700 detectors Ion

1

H

4

He

7

Li

11

B

12

C

59

Ni

122 131 a b c

Sb Xe

Energy (MeV/u)

1/q (dE/dX)LiF (MeV cm2 /g)

3.3 4.0 5.2 5.8 6.3 10.0 2.5 4.2 5.7 7.3 3.7 4.6 5.4 6.1 3.1 4.7 5.6 4.3 5.9 7.0 8.3 10.2 11.0 50.0 60.0 64.8 70.0 77.8 94.8 100.0 142.5 195.0 270.0 2.0 3.5 5.1 10.0 10.0 9.8

148.5 130.0 107.9 99.6 93.7 45.9 709.8 506.5 407.6 339.2 1199.0 1035.0 907.0 846.0 3140.0 2542.0 2299.0 3644.1 3095.8 2804.7 2523.4 2202.2 2090.6 375.1 322.4 303.2 285.0 262.5 227.7 215.7 167.8 143.8 110.3 27699.5 30234.3 30372.5 27352.8 55555.6 63241.4

a

Eciency g Experiment

Calculation

0.230.02 0.260.08 0.480.06 0.60.2 0.520.06 0.90.2 0.040.01 0.090.02 0.240.05 0.350.07 0.0570.01 0.0820.008 0.1340.02 0.1780.02 0.0120.002 0.0330.004 0.0480.01 0.0190.005 0.050.01 0.0820.01 0.120.02 0.190.03 0.230.03 0.650.06 0.690.07 0.710.07 0.740.07 0.780.08 0.800.08 0.790.08 0.890.09 0.990.1 1.00.1 0.0010.001 0.0050.003 0.0050.003 0.0250.01 0.0320.006 0.0230.005

0.21 0.31 0.43 0.55 0.60 0.76 0.036 0.11 0.25 0.42 0.042 0.081 0.12 0.16 0.011 0.035 0.064 0.024 0.06 0.089 0.12 0.22 0.26 0.67 0.70 0.72 0.73 0.75 0.78 0.79 0.85 0.91 0.90 0.002 0.004 0.01 0.039 0.045 0.040

b

Irradiation facility c III III III III III III III III III III III III III III III III III I I I I I I II II II II II II II II II II I I I I I I

Calculated according to Eq. (7). Eciency calculated with our code ECLaT. I ˆ UNILAC (GSI), II ˆ SIS (GSI), III ˆ Tandem (MPI Heidelberg).

The heavy ion energy loss dE…E†=dx has been calculated using the code ATIMA [21]. The Monte Carlo calculations mentioned above yield a relationship between the maximum range of secondary electrons Rel and the electron energy Eel

3=2

Rel / Eel :

…6†

Using Eq. (4) it is possible to calculate the dose deposited in a volume DVi . Because the dose variation is small over the size of the volumes DVi , the

O.B. Geiû et al. / Nucl. Instr. and Meth. in Phys. Res. B 142 (1998) 592±598

595

Fig. 1. Dose dependence of thermoluminescence after irradiation with X-rays. Experimental data () are taken from [13]. The parametrization used for our calculations (according to Eq. (3)) is shown as a solid line.

thermoluminescence signal of each volume can be calculated from the detector response to X-rays as reference radiation TLX …D†. The TL signal after irradiation with X-rays is taken from Eq. (3). Summing up the contributions of all volumes DVi in all layers Dzi yields the thermoluminescence signal TLHI after heavy ion irradiation. The eciency g for particles can then be calculated according to its de®nition (2). This procedure is implemented in a computer code called ECLaT. This enables to calculate the eciency g…E; Z† for all ions and energies. The results of this calculation are presented in Section 4. 4. Results and discussion A comparison between the measured and calculated eciencies is shown in Figs. 2 and 3. The experimental parameters as well as results of experiments and calculations are also compiled in Table 1. As shown in Fig. 2 the TLD eciency decreases steeply with decreasing energy (especially for energies below 10 MeV/u). It is not constant even for

hydrogen ions. This is explained as a saturation effect due to the very high local doses around the ion path. For a given energy the eciency decreases with projectile charge Z due to the ionisation density, which is proportional to the square of the ef2 . The di€erence fective projectile charge Zeff between g…E; Z† and g…E; Z  1† curves becomes smaller with increasing charge. Eciency curves for di€erent ions are separated more clearly if plotted as a function of the mean energy loss dE=dx. Therefore the results of Fig. 2 are replotted in Fig. 3. The mean energy loss is calculated according to dE=dx

…MeV cm2 =g† ˆ

…E0 ÿ Ef †…MeV† 3

q…g=cm †  Dx…cm†

…7†

with the initial and ®nal beam energies E0 and Ef , respectively, and the detector density q. For stopping particles (Ef ˆ 0) Dx equals the ion range Rp , whereas for higher energies Dx has to be replaced by the detector thickness d. The shape of these curves is very similar, especially for ions with Z P 18. The branches are merely shifted against each other, intersecting the g ˆ 0:1 level at di€erent dE=dx0:1 values. These

596

O.B. Geiû et al. / Nucl. Instr. and Meth. in Phys. Res. B 142 (1998) 592±598

Fig. 2. Eciency of TLD-700 detectors as a function of energy. Comparison between experimental (symbols) and calculated (lines) results. Experimental errors are mainly due to the CR39 ¯uence measurement, whereas statistical errors are smaller than 10%. The shaded area represents energies (including 20% uncertainty) for which the ion range equals the detector thickness (d ˆ 0:38 mm).

values scale approximately according to dE=dx0:1  Z 3=2 . Figs. 2 and 3 show both a good overall agreement between experiments and calculations for

all ions. Discrepancies larger than the experimental error only occur for very low energies (below some MeV/u) and heavier projectile ions. There are some reasons for the di€erences between exper-

Fig. 3. Eciency of TLD-700 detectors as a function of the mean energy loss. Comparison between experimental (symbols) and calculated (lines) results. The mean energy loss …dE=dx†LiF is calculated according to Eq. (7).

O.B. Geiû et al. / Nucl. Instr. and Meth. in Phys. Res. B 142 (1998) 592±598

iment and calculation. First of all the calculation of the energy loss by the code ATIMA is not precise for very low energies. Therefore the calculation of dose according to Eq. (1) and hence the calculation of g according to Eq. (2) could be a source of errors. Furthermore the radial distribution of dose around the ion path deviates from the parametrization given in Eq. (4). Especially for very low energies (below some MeV/u) the radial dose strongly di€ers from the 1=r2 dependency (see e.g. Fig. 6 in [12]). In order to improve the accuracy of the calculations in the low energy region the radial dose distribution D…r; E; Z† for all relevant ions and energies has to be improved. In contrast to the approach of Katz et al. our calculations are based on the radial dose distribution D…r† and the detector response TLX …D† only, and do not use any free parameter [8,9]. There is no arbitrary distinction between gamma-kill and ion-kill. Chernov et al. described a model based on the heavy ion spur [2]. The introduction of phenomenological parameters like spur radius and energy leads to eciency values which cannot be veri®ed in experiment. Our model calculations show that the measured TLD response can be predicted/calculated with great accuracy, without the use of any free parameter or input data from heavy ion experiments. However because of the integration over the radial dose distribution as well as over the contribution from primary ions and fragments it is not possible to determine the absolute dose from a TLD measurement in a complex particle ®eld. Therefore, for absolute dose measurement of heavy ion beams TLDs cannot be used due to their charge and energy dependent eciency. However, since we are able to calculate g…E; Z†, at least the dose distribution can be veri®ed. For this purpose the TL signal at an arbitrary position ~ r of a mixed radiation ®eld has to be calculated according to TL…~ r† ZE0 1 X dE…E; Zi † dN …~ r; Zi ; E† g…E; Zi † dE ˆ const q dx dE 0

…8†

597

using the target density q, the initial projectile energy E0 , the fragment energy spectra dN …~ r; Zi ; E†=dE and the eciencies g…E; Zi †. A comparison between the experimental and calculated TL signals then gives information on the distribution of dose in the radiation ®eld. A more detailed description of this dose veri®cation method including some experimental examples is given in [4] and will be published in detail.

5. Conclusion For particles the eciency of TLDs strongly depends on charge and energy. This can be explained as a saturation e€ect caused by recombination events which are due to the very high local doses in the center of the track [10]. A model based on track structure and the dose response to X-rays was developed and implemented in the computer code ECLaT, which is able to calculate the eciency of thermoluminescent detectors for all ions and energies. The calculated eciency values are in excellent agreement with a comprehensive set of data, including new measurements especially for light ions like carbon and its fragmentation products. Using these eciencies g…E; Z†, it is possible to use TLDs for absolute dosimetry in the case of monoenergetic beams or under track segment conditions. However, in mixed radiation ®elds no absolute dose measurement but dose veri®cations are possible.

Acknowledgements The authors want to thank Dr. R. Repnow, MPI Heidelberg, for providing us beam time at the Tandem accelerator, as well as Prof. Kober, Stadtische Kliniken Darmstadt, for irradiations at the 60 Co source. We would like to thank G. Lenz and W. Becher for their technical assistance. We are very thankful to Prof. K. Schwartz, Heidelberg, and Dr. M. Scholz, Darmstadt, for many fruitful discussions.

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