Radiation Measurements

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1 Rdition Mesurements 43 (28) Contents lists ville t ScienceDirect Rdition Mesurements journl homepge: Performnce of GEANT4 in dosimetry pplictions: Clcultion of X-ry spectr nd kerm-to-dose equivlent conversion coefficients Crl C. Guimrães, Murício Morlles, Emico Okuno, * Lortório de Dosimetri, Instituto de Físic d Universidde de São Pulo, DFN, CP 66318, CEP São Pulo, SP, Brzil Centro do Retor de Pesquiss, Instituto de Pesquiss Energétics e Nucleres, CP 1149, CEP São Pulo, SP, Brzil rticle info strct Article history: Received 2 Octoer 27 Received in revised form 1 April 28 Accepted 9 July 28 PACS: 87.8.Sp A Keywords: Monte Crlo GEANT4 Dose equivlent Conversion coefficient In order to vlidte the Gent4 toolkit for dosimetry pplictions, simultions were performed to clculte conversion coefficients h(1, ) from ir kerm free-in-ir to personl dose equivlent H p (1, ). The simultions consisted of two prts: the production of X-rys with rdition qulities of nrrow nd wide spectr, nd the interction of rdition with ICRU tissue-equivlent nd ISO wter sl phntoms. The hlf-vlue lyers of the X-ry spectr otined y simultion were compred with experimentl results. Men energy, spectrl resolution, hlf-vlue lyers nd conversion coefficients were compred with ISO reference vlues. The good greement etween results from simultion nd reference dt shows tht the Gent4 is suitle for dosimetry pplictions which involve photons with energies in the rnge of ten to few hundreds of kev. Ó 28 Elsevier Ltd. All rights reserved. 1. Introduction Stimulted y the continuous dvnces in computer technology, the employment of Monte Crlo methods in simultions of complex prolems hs een incresed in the lst decdes. Continuous efforts of severl groups in the world culminted with vriety of Monte Crlo codes tht tret the rdition trnsport in mtter llowing precise clcultions in the fields of medicl physics, dosimetry nd rdition protection. The personl dose equivlent H p (d, ) is protection quntity tht cn e evluted using Monte Crlo clcultions. According to the ICRU Report 7 (ICRU, 1998), for monitoring purposes, the opertionl quntity H p (d, ) provides resonle evlution of the dose equivlent in the soft tissue t depth d, where is the ngle etween the norml reference direction of the dosimeter nd the direction of rdition incidence. Since the protection quntities re not directly mesurle nd the instruments for rdition monitoring need to e clirted in terms of mesurle quntity, conversion coefficients h(d, ) re clculted to relte some sic physicl quntities, like fluence or ir kerm free-in-ir (K ir ), to the opertionl quntities. In ddition, H p (d, ), originlly defined s * Corresponding uthor. Tel.: þ ; fx: þ E-mil ddress: emico.okuno@dfn.if.usp.r (E. Okuno). quntity in the humn ody, is extended to phntoms for prcticl resons in clirtion procedures. These reference conversion coefficients were clculted y severl methods nd they re descried in ICRU Report 7 (ICRU, 1998), nd ISO reports (ISO, 1999) nd (ISO, 24), for phntoms irrdited under idel conditions using unidirectionl ems of stndrd rdition qulities. Although the reference conversion coefficients re useful in clirtion procedures, difficulties rise when the conditions of irrdition differ from the ones recommended in technicl reports. In relistic situtions, workers re exposed to rdition with rod spectrum, nd their personl dosimeters receive photons from ll directions. Thus, the vilility of confident tool for the clcultion of conversion coefficients for customised conditions of irrdition would e very pproprite nd useful. The potentil ppliction of this tool cn e found in recently pulished studies. To mention two exmples, predictions of the response of commercilly ville H p (1) chmers (Mikmi et l., 27) nd conversion coefficients for new proposed rdition qulities (Ankerhold, 27) could e performed with Monte Crlo clcultions. In this study, the Gent4 Monte Crlo toolkit (Agostinelli et l., 23) ws employed to clculte conversion coefficients for severl irrdition conditions. Differently from other clcultions, which used either monoenergetic rdition (Grosswendt, 1991,) or /$ see front mtter Ó 28 Elsevier Ltd. All rights reserved. doi:1.116/j.rdmes

2 126 C.C. Guimrães et l. / Rdition Mesurements 43 (28) photons with energy distriutions determined experimentlly (Grosswendt, 1992; Ankerhold et l., 1999), in the present work the X-ry spectr were lso otined using the Monte Crlo method. In this wy, the performnce of Gent4 to tret the physicl processes tht re predominnt in dosimetry of X-rys ws verified. The simultion ws performed in two stges. In the first one, the primry prticles consist of electrons tht interct with the node of the X-ry tue y ionistion, remsstrhlung nd multiple scttering processes. The trnsport of remsstrhlung nd chrcteristic rdition through the node nd sorers is lso performed to produce the X-ry spectr of stndrd rdition qulities. In the second prt, the interction of photons with phntoms ws simulted for different incidence ngles, nd conversion coefficients were clculted for the depth of 1 mm. events of chnnels round 9 kev corresponding to 89., 89.7, 9 nd 9.2 kev sum to 464 with sttisticl uncertinty of 4.6%. The clcultions were run on PC (Pentium IV, 2.4 GHz, 12 MB RAM, Linux) using electrons tht produced spectr with typicl numer of photons rnging from 1 4 (kvp ¼ 2 kv) to (kvp ¼ 3 kv). For ech rdition qulity, the filtrtion of the generted spectrum ws simulted y directing the photon em to one or more sorers of Al, Cu, Sn nd P with the thickness corresponding to tht used in the experiment. The filtered spectrum ws lso recorded in chnnels with width of.2 kev. The low-energy extension of the electromgnetic processes provided y Gent4 ws used in ll simultions. More detils out the simultion of X-ry production is descried in Morlles et l. (2). 2. X-ry spectr In this section, chrcteristics of X-ry spectr of the ISO nrrow nd rdition qulities otined y simultion re compred with experimentl results nd lso with reference vlues of the ISO reports (ISO, 1997, 24), hereinfter referred s reference dt Experiment The X-ry ems were produced with Philips MG 4 system, which hs tungsten node with ngle of 22 nd inherent filtrtion of 2.2 mm eryllium. Aluminium, copper, tin nd led sorers were employed to produce ems with the ISO rdition qulities (ISO, 1997). The HVLs were otined using luminium nd copper sorers, nd two cylindricl ionistion chmers: the.6 cc Frmer type NE 271 (Nucler Enterprise) nd the 1 6 Rdcl ion chmer (Rdcl Corportion) plced t the distnce of 1.2 m from the focl point. The purity of the sorers is 99.98% for Al nd pproximtely 99.% for Cu sorers nd dditionl filtrtion. The dependence of the mesured ir kerm on the thickness x of the sorer ws djusted with two exponentils, ccording to the eqution K ir ¼ A 1 exp x þ A t 2 exp xt2 ; (1) 1 where the prmeters A i nd t i were determined using the Levenerg Mrqurdt lest-squres lgorithm of non-liner fit. The goodness of the fit ws verified y the reduced c 2 vlues, which rnged etween.6 nd 1.2 for ll rdition qulities. The first nd second HVLs were clculted with n itertive lgorithm to solve x from Eq. (1) for K ir ¼ K /2 nd K ir ¼ K /4, where K is the ir kerm mesured without ttenution. The uncertinties were estimted s 3% nd 4% for the first nd second HVL, respectively Simultion The X-ry production ws simulted eginning with em of electrons impinging t n ngle of 22 with the norml to the tungsten node surfce. A eryllium disc with the thickness of 2.2 mm, plced etween the trget nd the region where the energy of the photon is registered, ws used to simulte the inherent filtrtion. For ech vlue of selected pek voltge (kvp), the spectrum of emitted photons from the trget within n perture ngle of 3 ws recorded in chnnels with width of.2 kev. The numer of histories ws chosen to produce sttisticl uncertinty of less thn % for the totl events contined in 1. kev intervl centred t 9% of the mximum energy. Considering the spectrum with mximum energy of 1 kev, for exmple, the 2.3. Anlysis Hlf-vlue lyers nd ttenution curves The first nd second HVLs of the simulted spectr were clculted ccording to the procedure descried y Ankerhold et l. (1999), using the sorption coefficients of Huell nd Seltzer (199). Simulted vlues hve sttisticl uncertinties of less thn 1%; errors of the cross-sections of the interctions used y Gent4 were not tken into ccount. Tle 1 presents results otined from experiment, simultion nd reference vlues. In generl, the greement of our experimentl nd simulted results with tht of reference dt is similr to those otined y Seelentg et l. (1979) from mesurements of X-ry spectr with high-purity germnium detector. According to criterion of ISO (ISO, 1997), if the first nd second HVLs in given mteril gree within % for two X-ry ems, then these two ems shll e considered to e essentilly of the sme qulity. Differences etween experimentl nd simulted results for the first nd second HVLs re shown in Fig. 1() nd (), respectively. Tking into ccount the uncertinties, one oserves tht five (N2, N2, N4, N6 nd W2) of the 16 spectr hve the first HVL with differences of more thn %, nd in the cse of second HVL, only one spectrum (N6) does not gree within %. This result shows tht the performnce of Gent4 cn e considered dequte to simulte the experiment. Fig. 1(c) nd (d) show the sme comprisons etween reference vlues nd simulted results, considering sttisticl uncertinty of 1%. Tle 1 First nd second HVLs of X-ry with rdition qulities of the ISO nrrow (N) nd wide (W) spectrum series (ISO, 1997): results from experiment, simultion with Gent4, nd reference vlues (ISO) Qulity First HVL (mm) Second HVL (mm) Experiment Simultion ISO Experiment Simultion ISO N N N N N N N N N N N W W W W W Aluminium is used s ttenutor mteril for N2, N2 nd N3 rdition qulities. Copper is used for the others.

3 C.C. Guimrães et l. / Rdition Mesurements 43 (28) st HVL difference (%) frction of trnsmitted kerm 1. N2 N2 Gent4 experimentl results N3 1 st HVL difference (%) 2 nd HVL difference (%) 2 nd HVL difference (%) c d nrrow series thickness of luminium (mm) Fig. 2. Trnsmission curves otined with simulted spectr nd experimentl points for ISO nrrow series using luminium sorers. filtrtion nd thickness of ir tht they used, it is expected tht X-ry spectr produced with different vlues of these prmeters present systemtic chnges in comprison with the reference spectr. The prticulr comintion of these prmeters in the experimentl setup, which re proly not the sme of tht employed to estlish the reference vlues, could e the cuse of the undnce of low-energy photons in the simulted spectr. The result for rdition qulity N2 deserves some comments, since Fig. 1(c) shows tht the difference for N2 is quite fr from the systemtic ehviour presented y the other rdition qulities. The more recent ISO (ISO, 24) presents corrected vlues for the men energies of N1, N2 nd N3 rdition qulities tht were tken from the work of Ankerhold et l. (1999). These uthors mesured men energy nd first HVL for N2 tht re 2. nd 9% greter thn the vlues presented in the ISO 437-1, respectively. If the HVL vlue mesured y Ankerhold (.348 mm Al) is used insted of the ISO vlue (.32 mm Al), the difference from the vlue otined y simultion (.33 mm Al) for N2 chnges from 4.7 to þ3.7%, which is comptile with the verge difference of the other rdition qulities, s shown y the open squre point in Fig. 1(c). Results for N3 do not show significtive chnges. Besides the HVL vlues, ttenution curves provide useful informtion tht re influenced y the shpes of the spectr. Figs. 2 nd 3 show comprisons of trnsmitted kerm curves for luminium nd copper ttenutors, respectively. One oserves resonle greement etween the ttenution otined with the simulted spectr nd experimentlly. In fct, the dt revel n N2 N2 N3 N4 N6 N8 N1 N12 N2 N2 N3 W8 W11 W1 W2 W2 rdition qulity Fig. 1. Differences in HVLs etween results of: () experiment nd simultion, 1st HVL; () experiment nd simultion, 2nd HVL; (c) reference (ISO, 1997) nd simultion, 1st HVL; (d) reference nd simultion, 2nd HVL. Horizontl segmented lines indicte the difference rnge etween %. The open squre point in (c) corresponds to the difference etween simultion nd the result of Ankerhold et l. (1999) for N2 (see text). In this cse, results of six spectr (N3, N6, N1, W8, W11 nd W1) do not comply with the ISO requirements. Furthermore, one oserves tht the discrepncies show systemtic ehviour, since lmost ll HVLs otined in the simultions re smller thn the reference vlues. This is n indiction tht the simulted spectr hve more contriutions from low-energy photons when compred with the reference spectr. Considering tht the ISO report does not specify the exct vlues for node ngle, inherent frction of trnsmitted kerm 1..1 W8 N8 N1 W2 N12 Gent4 experimentl results W thickness of copper (mm) N3 Fig. 3. Trnsmission curves otined with simulted spectr nd experimentl points for ISO nrrow nd using copper sorers.

4 128 C.C. Guimrães et l. / Rdition Mesurements 43 (28) Tle 2 Men energy nd spectrl resolution of nrrow (N) nd wide (W) rdition qulities of simulted spectr nd ISO reference (ISO, 1997; ISO, 24) Qulity Men energy (kev) Resolution (%) Simulted ISO Simulted ISO N N N N N N N N N N N W W W W W W Typicl uncertinties of men energies nd spectrl resolutions of the simulted spectr re.1 nd 1%, respectively. Tken from reference (ISO, 24). verge difference of 4% etween experimentl points nd simulted dt. We ttriute the min contriution for these discrepncies to impurities tht must e present in dditionl filters nd in the copper sorers. Previous studies concerning the influence of impurities in the ttenutors used in HVL mesurements reported similr verge differences (Wgner et l., 199; Terry et l., 1999) Men energy nd resolution Tle 2 presents men energy nd spectrl resolution of the simulted spectr s defined in the ISO specifictions (ISO, 1997). Since the inherent filtrtion of the tue is 2.2 mm eryllium, this reference sttes tht the greement must e within nd 1% for men energy nd spectrl resolution, respectively. The differences in these prmeters etween results from simulted spectr nd reference vlues re presented in Fig. 4. One oserves tht ll simulted spectr oey the ISO conditions. However, the men energies of the simulted spectr re systemticlly lower thn tht of reference vlues. This is nother indiction tht, in comprison with the ISO reference, the spectr otined y simultion contin more contriutions from low-energy photons. difference (%): reference - simulted 1-1 men energy spectrl resolution nrrow series N2 N2 N3 N4 N6 N8 N1 N12 N2 N2 N3 W6 W8 W11 W1 W2 W2 rdition qulity Fig. 4. Differences in men energy nd spectrl resolution etween reference vlues nd simulted spectr nd reference vlues. Uncertinties re of the order or smller thn the point size. Horizontl segmented lines indicte the difference rnge etween %. The fct tht ll simulted spectr oey the ISO requirements concerning the men energy nd spectrl resolution ut mny of them fil to oey the HVL conditions indictes tht these requirements re not equivlent in prctice. 3. Conversion coefficients The conversion coefficient h(d, ) for photons incident on phntoms is defined y hðd; Þ ¼ H pðd; Þ (2) K ir where H p (d, ) is the personl dose equivlent t depth d nd ngle of rdition incidence on the dosimeter, nd K ir the ir kerm free-in-ir. Recommended conversion coefficients for sl phntom re pulished in the ISO reference (ISO, 1999) for nrrow nd wide spectrum series. In this section we report the conversion coefficients clculted with the Gent4 for the ICRU tissue-equivlent nd ISO wter sl phntoms t the depth of 1 mm, nd compre them with ISO reference vlues Simultion The kerm-to-dose equivlent conversion coefficients were clculted for two types of phntoms: ICRU sl phntom (ICRU, 1998) nd ISO wter sl phntom (ISO, 1999). In the simultion, h(1,α ) (Sv/Gy) nrrow men energy (kev) Fig.. () Conversion coefficients h(1, ) of the ISO nrrow spectr simulted with Gent4 toolkit for the ICRU tissue-equivlent solid sl t severl incidence ngles. Segmented lines represent h(1, ) reference vlues (ISO, 1999). () Men differences (Eq. ()) over ll ngles. Dispersions (Eq. (6)) re indicted y error rs.

5 C.C. Guimrães et l. / Rdition Mesurements 43 (28) wide 1. nrrow series h(1,α ) (Sv/Gy) incidence ngle (degrees) Fig. 7. Men differences nd dispersion (presented s error rs) etween conversion coefficients otined y simultion nd reference (ISO, 1999) vlues for different ngles. Results for the ICRU tissue-equivlent solid sl men energy (kev) Fig. 6. () Conversion coefficients h(1, ) of the ISO nrrow spectr simulted with Gent4 toolkit for the ICRU tissue-equivlent solid sl t severl incidence ngles. Segmented lines represent h(1, ) reference vlues (ISO, 1999). () Men differences (Eq. ()) over ll ngles. Dispersions (Eq. (6)) re indicted y error rs. the ISO wter sl phntom is prllelepiped with wlls of 1 mm thick except the frontl fce of 2. mm thick mde of polymethyl methcrylte (PMMA) with internl volume of mm 3 full of wter, wheres the ICRU sl phntom is solid prllelepiped mde of ICRU tissue-equivlent mteril hving the sme geometric dimension of the ISO wter sl phntom. The energy distriution of the photons ws tken from the spectr otined in the simultion descried in the previous section. The irrdition with severl ngles of incidence ws simulted y rotting the phntom round the verticl xis tht contins the centre of its frontl fce. The H p (1, ) ws evluted y defining squre grid of 1 1 smll spheres with rdius of.2 mm, uniformly distriuted on mm 2, nd locted t 1 mm from the outer surfce of the frontl wll. The centre of the squre grid of spheres coincides with the centre of the squre rdition field. The totl energy deposited in the 1, spheres divided y their totl mss ws used to represent the H p (1, ) vlue. The energy deposition ws otined y using the method GetTotlEnergyDeposit() of Gent4. The K ir term of Eq. (2) corresponds to the ir kerm free-in-ir of the rdition field t the position of the phntom. It ws evluted y Z Emx mðeþ K ir ¼ fðeþ de; (3) r ir where E mx is the mximum energy of the spectrum, f(e) is the numer of photons of energy E per unit of re, nd ðmðeþ=rþ ir is the mss-energy sorption coefficient for photons of energy E in ir, which ws tken from Huell nd Seltzer (199). The numer of primry photons used in the simultions ws dependent on the rdition qulity. It ws chosen to produce vlues of H p (1, ) with sttisticl uncertinties of less thn % Anlysis ICRU tissue-equivlent sl phntom The conversion coefficients for the ICRU tissue-equivlent sl phntom otined y simultion re shown in Figs. () nd 6() for nrrow nd wide spectr, respectively. Different symols re used to distinguish ech ngle of photon incidence. For resons of clrity, results for ngles of 1,2 nd 3 re not shown in the Figs. () nd 6(). To nlyse the greement with reference vlues, the reltive difference in percentge, D r,, etween reference h r, nd simulted h r, coefficients ws clculted for ech comintion of prmeters (r, ), ccording to h r; h r; D r; ¼ 1 h ; (4) r; where the prmeters r nd refer to the rdition qulity nd irrdition ngle, respectively. The generl greement for specific spectrum series is otined from the men of ll qulities nd incidence ngles of tht series. The greement of the simulted results ws then nlysed reltively to the rdition qulity nd to the incidence ngle y fixing one of the prmeters nd summing over the other to otin the men difference CD p D for the fixed prmeter p. For exmple, the clcultion of the men reltive difference for the nrrow spectrum with 6 kv (r ¼ N6) is performed y

6 13 C.C. Guimrães et l. / Rdition Mesurements 43 (28) nrrow 2. wide h(1,α ) (Sv/Gy) h(1,α ) (Sv/Gy) men energy (kev) Fig. 8. () Conversion coefficients h(1, ) of the ISO nrrow spectr simulted with Gent4 toolkit for the wter sl phntom t severl incidence ngles. Segmented lines represent h(1, ) reference vlues (ISO, 1999). () Men differences (Eq. ()) over ll ngles. Dispersions (Eq. (6)) re indicted y error rs men energy (kev) Fig. 9. () Conversion coefficients h(1, ) of the ISO wide spectr simulted with Gent4 toolkit for the wter sl phntom t severl incidence ngles. Segmented lines represent h(1, ) reference vlues (ISO, 1999). () Men differences (Eq. ()) over ll ngles. Dispersions (Eq. (6)) re indicted y error rs. hd N6 i ¼ 1 N X h N6; h N6; h N6; ; () where ssumes N ¼ 9 vlues, corresponding to the rnge from to 8 in steps of 1. Then, the stndrd devition s DN6 of this difference, is clculted y s DN6 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P DN6; hd N6 i 2 u t ¼ : (6) N 1 The solute vlue of the men difference quntifies the mount tht the simulted results disgree with the reference vlues, while the sign indictes overestimtion (negtive) or underestimtion (positive). The stndrd devition quntifies the dispersion of the men differences. The generl percentges of the men difference (dispersion) for nrrow nd wide spectr were 2.2% (3.8) nd 1.6% (2.1), respectively. Figs. () nd 6() present the men differences with corresponding dispersions for fixed rdition qulities, while Fig. 7 shows the men differences for fixed incidence ngles. From these figures one oserves tht most of the men differences re found within 1 nd 3%. The exceptions with the lrgest discrepncies occur for spectr with lower men energies (N2, N2, N3) nd for lrge ngles (7,8 ). The predominnce of positive differences indictes tht the simultions produce conversion coefficients tht re, in verge, underestimted in reltion to the ISO reference vlues. The origin of this underestimtion is the undnce of lowenergy photons s discussed in Section The effect is more pronounced for the lower energy spectr due to the lrge ttenution of the primry photons, which reduces the numer of photons tht rech the depth of 1 mm. The differences diminish with incresing energy, s cn e seen in Figs. () nd 6(). The sme resoning pplies to the ngulr dependence shown in Fig ISO wter sl phntom Figs. 8() nd 9() show the conversion coefficients otined y simultions (symols) for the ISO wter phntom s function of the men energy of the nrrow nd wide spectr, respectively, compred with reference vlues (segmented lines) (ISO, 1999). For clrity, results for ngles of 1,2 nd 3 re not shown. The generl percentge of the men difference (dispersion) in comprison with the ISO reference ws 2.2% (4.2) nd.9% (3.) for nrrow nd wide spectr, respectively. The solute vlues of these differences re similr to those otined for the ICRU tissueequivlent phntom, ut the signs re opposite. Figs. 8() nd 9() show the men differences nd dispersions of nrrow nd wide spectr, respectively. In this cse lmost ll differences re negtive, indicting tht the coefficients clculted with Gent4 for this phntom re overestimted in reltion to the reference. Negtive men differences re oserved lso for fixed ngles from to 6, shown in Fig. 1. The reson for this overestimtion is tht in the

7 C.C. Guimrães et l. / Rdition Mesurements 43 (28) nrrow series oservtion of lrger differences for low energies nd lrge incidence ngles cn e motivtion for clcultions with other Monte Crlo codes in order to determine if the origin of these discrepncies lie in the mthemticl tretment of the physicl processes or in the cross-section dt. In summry, Gent4 seems dequte to e employed in simultions of dosimetry of photons with energies of ten to few hundreds of kev. Acknowledgement C.C. Guimrães thnks CAPES (Brzil) for scholrship... wter sl phntom more photons rech the depth of 1 mm thn in the ICRU sl phntom. Differences etween the cksctter fctors for these two phntoms, which were extensively studied y Tru et l. (1997), explin tht the conversion coefficients for the ISO wter sl phntom re lrger thn for the ICRU tissue sl phntom. 4. Conclusion incidence ngle (degrees) Fig. 1. Men differences nd dispersion (presented s error rs) etween conversion coefficients otined y simultion nd reference (ISO, 1999) vlues for different ngles. Results for the wter sl phntom. The results of this work show tht nrrow nd wide X-ry spectr produced with Gent4 present men energy nd resolution tht gree with tht of reference rditions. Furthermore, the HVLs of the simulted spectr re comptile with experimentl results within the uncertinties. The simultion of spectr with lower vlues of men energies nd HVLs revels tht Gent4 presents smll tendency to produce more photons of low energy thn the corresponding reference spectr. The results of our simultions show tht lmost ll conversion coefficients of the ISO reference (ISO, 1999) lie etween the results otined with the ICRU tissue-equivlent sl phntom nd the ISO wter sl phntom. The conversion coefficients clculted with Gent4 present differences of the order of 1 3% when compred with reference vlues for most of the rdition qulities nd incidence ngles. The References Agostinelli, S., Allison, J., Amko, K., et l., 23. GEANT4 simultion toolkit. Nucl. Instrum. Methods A 6, Ankerhold, U., Behrens, B., Amrosi, P., X ry spectrometry of low energy photons for determining conversion coefficients from ir kerm, K, to personl dose equivlent, H p (1), for rdition qulities of the ISO nrrow spectrum series. Rdit. Prot. Dosimetry 81, Ankerhold, U., 27. X reference rdition qulities produced with tue voltges ove 3 kv for the clirtion nd testing of dosemeters. Rdit. Prot. Dosimetry 123, Grosswendt, B., The influence of the photon em direction on the dose equivlent in the IAEA 3 cm wter cue phntom. Rdit. Prot. Dosimetry 3, 12. Grosswendt, B., The ngulr dependence nd irrdition geometry fctor for the dose equivlent for photons in sl phntoms of tissue-equivlent mteril nd PMMA. Rdit. Prot. Dosimetry 3, Grosswendt, B., Coefficients for the conversion of ir collision kerm to dose equivlent for the clirtion of individul dosemeters in X ry fields. Rdit. Prot. Dosimetry 4, Huell, J.H., Seltzer, S.M., 199. Tles of mss ttenution coefficients nd mss energy sorption coefficients 1 kev to 2 MeV for elements Z ¼ 1 to 92 nd 48 dditionl sustnces of dosimetric interests. NIST, NISTIR 632. Updted versions of these tles re presently ville from: ICRU, Conversion Coefficients for Use in Rdiologicl Protection Aginst Externl Rdition. ICRU Report 7. ICRU Pulictions, Bethesd, MD. ISO, X nd Gmm Reference Rditions for Clirting Dosemeters nd Doserte Meters nd for Determining Their Response s Function of Photon Energy Prt 1: Rdition Chrcteristics nd Production Methods. ISO 437-1, Genev, Switzerlnd. ISO, X nd Gmm Reference Rditions for Clirting Dosemeters nd Doserte Meters nd for Determining Their Response s Function of Photon Energy Prt 3: Clirtion of Are nd Personl Dosemeters nd the Mesurement of their Response s Function of Energy nd Angle of Incidence. ISO 437-3, Genev, Switzerlnd. ISO, 24. X nd Gmm Reference Rditions for Clirting Dosemeters nd Doserte Meters nd for Determining Their Response s Function of Photon Energy Prt 4: Clirtion of Are nd Personl Dosemeters in Low Energy X Reference Rdition Fields. ISO 437-4, Genev, Switzerlnd. Mikmi, S., Itié, C., Texier, C., 27. Considertion on clirtion nd correction fctors of n H p (1) chmer for different rdition qulities nd ngles of incidence. Rdit. Prot. Dosimetry 123, Morlles, M., Guimrães, C.C., Okuno, E., 2. Response of thermoluminescent dosemeters to photons simulted with the Monte Crlo method. Nucl. Instrum. Methods A 4, Seelentg, W.W., Pnzer, W., Drexler, G., Pltz, L., Sntner, F.A. Ctlogue of Spectr for the Clirtion of Dosemeters. GSF-Bericht 6. Terry, J.A., Wggener, R.G., Miller Blough, M.A., Hlf-vlue lyer nd intensity vritions s function of position in the rdition field for film-screen mmmogrphy. Med. Phys. 26, Tru, R.J., McDonld, J.C., Murphy, M.K., Determintion of photon cksctter from severl clirtion phntoms. Rdit. Prot. Dosimetry 74, Wgner, L.K., Archer, B.R., Cerr, F., 199. On the mesurement of hlf-vlue lyer in film-screen mmmogrphy. Med. Phys. 17,