Radiation Measurements

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1 Rdition Mesurements xxx (2012) 1e7 Contents lists ville t SciVerse ScienceDirect Rdition Mesurements journl homepge: Modeling of the shpe of infrred stimulted luminescence signls in feldsprs Vsilis Pgonis, *, Mynk Jin, Andrew S. Murry c, Christin Ankjærgrd d, Reuven Chen e McDniel College, Physics Deprtment, Westminster, MD 21157, USA Rdition Reserch Division, Risø Ntionl Lortory for Sustinle Energy, Technicl University of Denmrk, DK-4000 Roskilde, Denmrk c Nordic Lortory for Luminescence Dting, Deprtment of Erth Science, Arhus University, Risø Ntionl Lortory for Sustinle Energy, DK-4000 Roskilde, Denmrk d Netherlnds Centre for Luminescence Dting, Technicl University of Delft, The Netherlnds e Rymond nd Beverly Sckler School of Physics nd Astronomy, Tel Aviv University, Tel Aviv 69978, Isrel rticle info strct Article history: Received 20 Septemer 2011 Received in revised form 30 Jnury 2012 Accepted 24 Ferury 2012 Keywords: Infrred stimulted luminescence IRSL Feldsprs Power lw of luminescence Kinetic rte equtions Kinetic model Tunneling This pper presents new empiricl model descriing infrred (IR) stimultion phenomen in feldsprs. In the model electrons from the ground stte of n electron trp re rised y infrred opticl stimultion to the excited stte, nd susequently recomine with nerest-neighor hole vi tunneling process, leding to the emission of light. The model explins the experimentlly oserved existence of two distinct time intervls in the luminescence intensity; rpid initil decy of the signl followed y much slower grdul decy of the signl with time. The initil fst decy region corresponds to fst rte of recomintion processes tking plce long the infrred stimulted luminescence (IRSL) curves. The susequent decy of the simulted IRSL signl is chrcterized y much slower recomintion rte, which cn e descried y power-lw type of eqution. Severl simultions of IRSL experiments re crried out y vrying the prmeters in the model. It is found tht the shpe of the IRSL signl is remrkly stle when the kinetic prmeters re chnged within the model; this is in greement with severl previous studies of these signls on feldsprs, which showed tht the shpe of the IRSL curves does not chnge significntly under different experimentl conditions. The reltionship etween the simulted IRSL signl nd the well-known power-lw dependence of relxtion processes in solids is lso explored, y fitting the IRSL signl t long times with power-lw type of eqution. The exponent in this power-lw is found to depend very wekly on the vrious prmeters in the model, in greement with the results of experimentl studies. The results from the model re compred with experimentl IRSL curves otined using different IR stimulting power, nd good quntittive greement is found etween the simultion results nd experimentl dt. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The phenomenon of nomlous fding in feldspr smples hs een studied extensively oth experimentlly nd y modeling, due to its importnce in dting studies of these mterils (Wintle, 1973; Visoceks, 1985; Templer, 1986; Duller nd Bøtter-Jensen, 1993; Bøtter-Jensen et l., 2003). These studies hve suggested tht nomlous fding is due to quntum mechnicl tunneling from the ground stte of the trp (Huntley nd Lmothe, 2001; Poolton et l., 2002, ; Li nd Li, 2008; Krs et l., 2008; Lrsen et l., 2009; Li nd Li, 2010 nd references therein). Furthermore, it hs een shown tht this ground stte tunneling process in * Corresponding uthor. Tel.: þ ; fx: þ E-mil ddress: vpgonis@mcdniel.edu (V. Pgonis). vrious mterils cn e descried y power-lw decy (Delecq et l., 1974; Huntley, 2006). Some studies hve suggested tht in K-feldsprs the infrred stimulted luminescence (IRSL) signl origintes from single trp corresponding to the thermoluminescence pek t w400 C (s mesured with heting rte of 5 C/ s) (Bril, 2002; Bril nd Huntley, 2003; Murry et l., 2009). The experimentl nd modeling work y Poolton et l. (2002,, 2009) nd more recently y Ankjærgrd et l. (2009) nd Jin nd Ankjærgrd (2011), provide solid understnding of the trnsport processes giving rise to the IRSL from feldsprs. These complex processes re elieved to consist of loclized recomintion y tunneling from the excited stte of the trp, s well s chrge migrtion through the conduction nd-til sttes into the recomintion centre. The ville experimentl dt is consistent with nd-tils occupying continuum of energy sttes from w0.4 ev elow the conduction nd (Poolton et l., 2009). The /$ e see front mtter Ó 2012 Elsevier Ltd. All rights reserved. doi: /j.rdmes

2 2 V. Pgonis et l. / Rdition Mesurements xxx (2012) 1e7 continuous-wve IRSL signls (CWeIRSL, lso known s infrred shine down curves) from feldsprs, re known to hve remrkly stle shpe. Their shpe chnges very little with experimentl conditions like the irrdition dose nd prehet temperture. However, significnt chnges tke plce in the CWeIRSL signl shpe when the intensity of stimulting IR light is vried experimentlly (Thomsen et l., 2008, 2011). It is lso noted tht significnt ut smller chnges tke plce in the CWeIRSL when the stimultion temperture is vried (see e.g. nd Jin nd Ankjærgrd, 2011; nd references therein). CWeIRSL signls from feldsprs re known to decy in nonexponentil mnner. Biliff nd Poolton (1991) showed tht the IRSL decy follows power-lw. Poolton et l. (1994) explined IRSL in feldsprs using donorecceptor model, in which electron tunneling occurs from the excited stte of the IRSL trp t out 1.4 ev Poolton et l. (1995, 2002, ) refined this model y including the possiility of chrge trnsfer from the excited stte of the IRSL trp into the nd-til sttes. Thomsen et l. (2008) pointed out tht this model implies tht the IRSL decy curve is function of tunneling proility, which is exponentilly relted to the distnce etween the donorecceptor recomintion pir. These uthors lso suggested tht in this model, the eginning of the IRSL decy curve origintes with the luminescence emitted from close donorecceptor pirs, while the end of the IRSL curve most likely represents the tunneling of distnt pirs. In this pper we present new kinetic model sed on loclized electronic trnsitions, in n ttempt to descrie the phenomenon of tunneling in feldsprs. This model is sed on new empiricl function used to descrie vrition in the tunneling proility with time in feldsprs. Our gol is to compre the results from the model with experimentl CWeIRSL dt, nd to ttempt chrcteriztion of the different prts of the IRSL decy curves from feldsprs. Furthermore, the model provides us with n insight from the vrious processes tking plce during the mesurement of IRSL signls in feldsprs t room temperture. 2. The new tunneling model for feldsprs The purpose of this pper is to simulte IRSL signls from feldsprs, lso known s infrred shine down curves. In the model shown in Fig. 1 we simulte IRSL experiments, y ssuming tht IR stimultion does not rise ny electrons into the conduction nd (CB), nd y neglecting the effect of the nd-til sttes. Insted, ll trnsitions tke plce within the loclity of the electronehole (eeh) pir. The IR stimultion rises electrons from the ground stte into the excited stte (trnsition 1); some of these electrons will e retrpped in the ground stte (trnsition 2), while others will recomine rditively with holes (trnsition 3). The vrious trnsitions in the model re shown in Fig. 1, nd the equtions in the model re: dn t dt dn e dt ¼ l IR n t ðtþþn e ðtþs (1) ¼ l IR n t ðtþ n e ðtþs n e ðtþg (2) LðtÞ ¼ dm=dt ¼ n e ðtþg (3) In these equtions n t (t) nd n e (t) represent the concentrtions of electrons t ny instnt in the ground stte nd the excited stte, correspondingly. The term l IR n t (t) represents the rte of chnge of n t (t) due to the IR stimultion. Here l IR ¼ s IR I is the infrred opticl stimultion proility (s 1 ) which is proportionl to the intensity I of the IR light (photons per cm 2 per s), nd to the IR stimultion cross section s IR (cm 2 ). The term n e (t)s in equtions (1) nd (2) descries the rte of chnge of the concentrtion of excited electrons n e (t), due to the possiility of electronic trnsitions from the excited stte ck into the ground stte. The mthemticl form of this term is determined from the principle of detiled lnce (see for exmple, Chen nd McKeever, 1997; Chen nd Pgonis, 2011). Eqution (3) expresses the oserved luminescence intensity s the product of the concentrtion of electrons n e (t) in the excited stte, nd the proility of recomintion G (in s 1 ). The timedependent concentrtion of holes is denoted y m(t), nd is relted to the electron concentrtions t ll times y the conservtion of chrge: mðtþ ¼n t ðtþþn e ðtþ (4) In pulished loclized models for thermoluminescence (TL), the proility of recomintion G is usully considered to e constnt quntity, since the electron in the excited stte is ssumed to e le to interct only with the next neighoring holes/recomintion centers. In the cse of feldsprs this recomintion proility G vries ccording to the tunneling process (see the extensive discussion in Thomsen et l., 2008). From the quntum mechnicl theory of tunneling, it is known tht the men lifetime s of the tunneling process is relted to frequency fctor s 0 nd to the tunneling distnce r y the eqution (Huntley, 2006): s ¼ 1 s 0er (5) where is constnt with the dimensions of inverse distnce. The proility of recomintion G (in s 1 ) is given y the inverse of the luminescence lifetime: G ¼ s 0 e r (6) From physicl point of view, we my expect tht the tunneling distnce r etween the electron nd hole will depend on the concentrtion of holes m(t) in the mteril. This suggests the possiility of using time-dependent empiricl function GðtÞ of the form: GðtÞ ¼ge f ðmþ ; (7) Fig. 1. The electronic trnsitions tking plce during the infrred stimultion of feldspr smples. Electrons re excited y the IR stimultion from the ground stte into the excited stte of the electron trp, nd tunneling tkes plce from the excited stte into the recomintion center. where g is n empiricl constnt to e determined y fitting the experimentl dt, nd the time-dependent function f(m) represents some lgeric function of the concentrtion of holes m(t) t ny instnt t.

3 V. Pgonis et l. / Rdition Mesurements xxx (2012) 1e7 3 We further require tht this recomintion proility GðtÞ vry ccording to the following physicl properties: t very long times t the concentrtion of holes m(t) should pproch zero, nd therefore the corresponding recomintion proility GðtÞ should lso pproch zero. Also t time t ¼ 0 the concentrtions of ville holes nd electrons n t (0) ¼ m(0) must e t mximum, hence the recomintion proility GðtÞ should lso e t its mximum vlue. These conditions led us to use the following simple empiricl mthemticl form for the recomintion proility: mð0þ 1=3 1 GðtÞ ¼ge mðtþ 2e+11 1e (8) where is dimensionless positive proportionlity fctor which chrcterizes n unknown physicl property of the electronehole pir. Eqution (8) hs the desired mthemticl form similr to eqution (6), nd lso hs the required physicl properties t lrge nd smll times: Gð0Þ ¼ g ¼ mximum; nd GðNÞ ¼ 0: (9) The constnts g nd in eqution (8) re treted s djustle prmeters in the model, in order to otin the est possile fit to the experimentl dt. It is emphsized tht s in ll empiriclly derived models, it is not possile to prove tht eqution (8) is the correct mthemticl form of the recomintion proility. We introduce this specific expression on n empiricl sis, nd its usefulness is shown y compring it with the experimentl dt. Perhps the most detiled study of the pplicility of the power-lw type decy in luminescence signls from feldsprs hs een crried out y Bril (2002). Huntley (2006) developed model for tunneling processes in solids, nd showed tht the luminescence intensity I(t) oserved during the tunneling process follows power-lw type expression of the form: IðtÞ ¼ct k (10) where c is constnt, nd the power-lw exponent k hs vlue round 1.0. By tking the logrithms of oth sides in eqution (10) we otin: lni ¼ lnc klnt: (11) In this pper we show tht the results from the simultions re consistent with the experimentlly reported power-lw decy of luminescence from feldsprs t longer times. Furthermore, we investigte how the power-lw exponent k in eqution (11) depends on the kinetic prmeters of the model. 3. Results from the model We simulte the IR stimultion of the feldspr smple y solving the system of differentil equtions (1)e(4), for the time intervl t ¼ 0 to t ¼ 5000 s. The numericl vlues chosen for the prmeters in the model re: l IR ¼ 0.06 s 1, s ¼ 10 5 s 1, g ¼ 10 5 s 1, ¼ 35 nd the initil conditions re n t (0) ¼ m(0) ¼ 6 cm 3, n e (0) ¼ 0cm 3. The numericl vlues of the vrious prmeters nd their effect on the results of the simultion re discussed in the next section of this pper. Fig. 2 shows the simulted IRSL signl with the ove prmeters, on semilog scle. The inset of Fig. 2 shows the sme simulted dt on liner-log scle. The simulted dt in Fig. 2 shows clerly the existence of two distinct time intervls. The first intervl corresponds to short IR stimultion times (t n Simulted IRSL fitted power lw k= Fig. 2. () The simulted IRSL signl s function of time on semilog scle. The inset shows the sme simulted dt on liner-log scle. The two distinct time regions cn e clerly seen. () The sme simulted dt s in (), on logelog scle. The dshed line indictes power-lw fit to the dt ccording to eqution (11). pproximte vlue of t < 10 s), nd is chrcterized y very fst initil decy of the signl with time. The second intervl for t > 10 s shows much slower decy of the luminescence intensity with time. The existence of these two distinct time intervls in the simultion is in greement with experimentl results of Thomsen et l. (2011). Fig. 2 shows the simulted dt from Fig. 2 on logelog scle. For lrge stimultion times, the lnivslnt grph is liner, indicting tht the decy of the IRSL signl t lrge times follows power-lw type of decy, s descried ove in equtions (10) nd (11). The dshed line in Fig. 2 shows the est fit of the simulted dt t lrge times with power-lw exponent k ¼ We cn otin some physicl insight into the nture of these two distinct time intervls in the IRSL signl, y exmining the vrition of the concentrtions of electrons s function of time. In Fig. 3 we show the concentrtion of trpped electrons n t (t) in the ground stte nd the corresponding concentrtion n e (t) of electrons in the excited stte, s function of time during the IRstimultion process. The concentrtion n e (t) hs een multiplied y fctor of 10 6 for esier visuliztion of the dt. The concentrtion n t (t) in the ground stte decreses continuously with time, due to the recomintions tking plce etween eeh pirs. The corresponding concentrtion n e (t) in the excited stte increses initilly, reches mximum t w10 s, nd susequently decreses continuously with time t pproximtely the sme time rte s n t (t).

4 4 V. Pgonis et l. / Rdition Mesurements xxx (2012) 1e7 n t, n e x10 6 (cm -3 ) sn e, λn t (cm -3 s -1 ) 1e+13 9e+11 6e+11 3e+11 n t n e x10 6 1e λn t sn e % of remining electron-hole pirs, n t /n t IR-Stimultion proility λ IR (s -1 ) IR-Stimultion proility λ IR (s -1 ) Fig. 3. () The concentrtions of electrons in the ground stte n t (t), nd in the excited stte n e (t)s function of time during the IR stimultion. The ltter is multiplied y fctor of 10 6 for visuliztion purposes. () The two terms ppering in eqution (1) re plotted s function of time. Fig. 3 shows similr ehvior for the two terms l IR n t (t) nd n e (t)s ppering in eqution (1), s function of time. For smll times (t < 10 s), the infrred stimultion term l IR n t (t) decreses with time, while the excited-to-ground stte trnsition term n e (t)s increses within the sme time intervl. At tw100 s the two terms ecome prcticlly equl nd for t > 100 s they remin prcticlly equl to ech other, while they oth decrese t the sme rte. After the initil intervl in which rpid chnge tkes plce, the two terms l IR n t (t) nd n e (t)s in eqution (1) rech equilirium. For long times these two terms remin in equilirium, while they oth decrese t much slower rte. We conclude tht the simulted dt of Fig. 3 explin the existence of two distinct time intervls in the IRSL signl. The initil fst decy corresponds to the two terms in eqution (1) grdully reching equilirium. After equilirium is reched etween the two terms, the decy of the simulted IRSL signl is chrcterized y much slower recomintion rte, which cn e descried y power-lw type of eqution. Further insight into the processes tking plce during the tunneling trnsitions is otined from Fig. 4, which shows the time vrition of the percent rtio n t (t)/n t (0) of the remining electronehole pirs (eeh) during the simulted IRSL process. Severl simulted curves n t (t)/n t (0) re shown in Fig. 4; these were otined y chnging the proility of IR stimultion l IR in eqution (1), y few orders of mgnitude. Fig. 4 showssimilrly severl of the corresponding IRSL signls otined y vrying l IR IR-stimultion time, s Fig. 4. () Simulted results showing the percent of remining electronehole pirs during the IR stimultion process, for different IR-stimultion proilities. Experimentlly this type of mesurement is crried out y vrying the power of the IR stimulting source. () Simulted IRSL curves for different IR-stimultion proilities. The overll shpe of the curves does not chnge significntly t longer stimultion times. By inspection of the dotted curve otined with l IR ¼ 0.12 s 1 in Fig. 4, we cn otin physicl insight into how the rte of the recomintion processes chnges long the IRSL curves. During the initil time intervl, the percent rtio of remining electronehole pirs decreses rpidly, from 100% t time t ¼ 0 decresing to 65% of electronehole pirs remining t longer times t ¼ 200 s. Clerly in this initil time intervl only 35% of the initil concentrtion of eeh pirs hve tunneled through the energy rrier, nd hve recomined rditively. For lrge IR stimultion times the tunneling process tkes plce t very reduced rte, so tht the percent rtio of remining eeh pirs decreses to w50% within this lrge time intervl. Therefore only n dditionl 15% of eeh pirs hs tunneled within the time intervl t ¼ 200 s to t ¼ 5000 s. Most notly, Fig. 4 shows tht even fter time intervl of 5000 s there re still w40% of eeh pirs remining in the system. This very slow recomintion process occurring t long times explins why it is so difficult to completely erse the IRSL signl from feldsprs; initilly lrge percentge of trpped electrons nd holes recomines rpidly, ut t longer times the tunneling process ecomes very slow. In the next section we will show tht within the simple model presented here, the slowly decying prt of the IRSL signl lwys follows power-lw type of decy. Experimentlly the type of mesurement shown in Fig. 4 is crried out y vrying the power of the IR stimulting source.

5 V. Pgonis et l. / Rdition Mesurements xxx (2012) 1e7 5 Fig. 5 shows experimentl dt otined y Thomsen et l. (2011), using different IR-stimultion powers in their LED system. A corsegrin sedimentry K-feldspr smple ws mesured (l code: ). An liquot of smple ws given dose of 7 Gy, preheted t 280 C for 60 s nd stimulted with IR t 50 C for 10,000 s using LED power settings rnging etween 1 nd 100% (w1.35ew135 mw/cm 2 ). The experimentl dt re compred with the simulted dt from the model, nd very good greement is found etween the model nd experiment. The simulted solid curves in Fig. 5 hve een multiplied y n pproprite scling fctor, for comprison purposes. By incresing the power of the IReLEDs, very significnt chnges occur mostly in the initil prt of the IRSL signl, in which the rpid recomintion rte previls. The slower prt of the IRSL signl t longer times is ffected much less y chnges in the IR power, in oth the simulted nd experimentl dt. The model prmeters used to otin the simulted dt in Fig. 5 re: s ¼ 10 5 s 1, g ¼ s 1, ¼ 35 nd the initil conditions re n t (0) ¼ m(0) ¼ 6 cm 3, n e (0) ¼ 0cm 3. Another detiled exmple of compring experimentl nd simulted dt is shown in Fig. 5, for different feldspr smple. The luminescence signls of this K-rich sediment extrct (lortory code ), were recently studied in Jin nd Ankjærgrd (2011). The smple ws given dose of 45 Gy nd susequently Fig. 5. () The experimentl dt of Thomsen et l. (2011), otined using different powers of their IR LEDs. The simulted dt re shown s solid lines. () A different set of experimentl dt for K-rich feldspr smple. The experimentl IR power is set t 100%. The inset shows the sme experimentl dt for short IR stimultion times, on liner scle. The offset is equl to the verge of the lst 100 chnnels in the IRSL signl. preheted to 250 C for 60 s, prior to mesurement of the IRSL signl t 50 C. An excellent fit shown s solid line through the experimentl dt is otined using the model, for the complete time intervl t ¼ 0tot ¼ 5000 s. The simulted nd experimentl dt in Fig. 5 re normlized to the first point in the experimentl dt. A smll ut finite constnt signl hs een dded to the simulted dt; this smll signl could represent the experimentl ckground, ut lso could represent significnt contriution from the nd-til sttes. The model prmeters used to otin the simulted dt in Fig. 5 re:l IR ¼ 0.06 s 1, s ¼ 10 5 s 1, g ¼ 10 5 s 1, ¼ 35, nd the initil conditions re n t (0) ¼ m(0) ¼ 6 cm 3, n e (0) ¼ 0cm 3. In the next section we study the effect of the vrious prmeters on the results from the model. Our gol is () to determine which prmeters hve the most effect on the shpe of the simulted IRSL signls, nd () to further investigte the power-lw of decy of the IRSL signl. 4. Effects of the vrious prmeters on the simulted IRSL signls We strt y exmining the numericl vlues of the frequency prmeters l IR, s which pper in the system of equtions (1)e(3). Wht is importnt in descriing the ehvior of the system of equtions is not so much the solute vlues of these prmeters, ut rther their numericl dimensionless rtio g/s. These rtios represent the rtios of possile trnsition proilities for electrons in the ground stte nd the excited stte, correspondingly. The vlue of the IR-stimultion prmeter l IR ¼ 0.12 s 1 ws chosen in the simultion so tht the simulted IRSL curve in Fig. 2 decys t similr rtes s in typicl experimentl IRSL curves. The vlue of the frequency fctors s ¼ g ¼ 10 5 s 1 ws chosen ritrrily in the model, ut is typicl of frequency fctors for loclized processes. The vlue of the dimensionless prmeter ¼ 35 in eqution (8) ws chosen so tht the simulted dt fits est the typicl experimentl dt. In Fig. 6 we show the effect of chnging the rtio g/s on the results of the model, y vrying this rtio from g/s ¼ 10 3 up to vlue of The simultion results show tht this rtio ffects mostly the initil prt of the IRSL curve; for lrge stimultion times t, ll simulted IRSL curves in Fig. 6 exhiit the power-lw of luminescence decy. The vlues of the power exponent k otined y fitting the simulted dt of Fig. 6 re prcticlly constnt, with very smll rndom vrition etween k ¼ 1.03 nd We conclude tht within this model, the power-lw exponent k depends very wekly on the rtio g/s, even though this rtio is vried over 5 orders of mgnitude in the simultions. It is noted tht the quntity g/s does not depend on the experimentl conditions, ut rther is physicl property of the eeh pir. In Fig. 6 we show the effect of chnging the dimensionless prmeter on the results of the simultion. This prmeter descries the unknown physicl properties of the eeh pir relting to the tunneling process. The vlues of the power exponent k otined y fitting the simulted dt of Fig. 6 show very smll systemtic decrese with the vlue of, from k ¼ 1.09 nd k ¼ We conclude tht within this model, the power-lw exponent k depends rther wekly on the kinetic prmeter. Finlly we consider the effect of chnging the initil concentrtion n t (0) ¼ m(0) of eeh pirs on the results of the model, y vrying this prmeter within severl orders of mgnitude. The simultions show tht chnging the initil concentrtions ffects the mgnitude of the IRSL signl, while the shpe of the IRSL curve remins the sme. In conclusion, the simulted dt in this pper show clerly tht in ll cses simulted here, nd for wide rnge of numericl vlues

6 6 V. Pgonis et l. / Rdition Mesurements xxx (2012) 1e7 γ/s = = description of the effect of stimulting temperture on the shpe of CWeIRSL curves. For exmple, Poolton et l. (2009) nd Jin nd Ankjærgrd (2011) demonstrted in their experimentl work tht nd-til sttes ply sustntil role in the IRSL mechnism. At low tempertures w10 K it is elieved tht the nd-til sttes re frozen nd tunneling constitutes the min IRSL mechnism (Poolton et l., 2009). It hs lso een suggested tht t higher tempertures the contriution of the nd-til sttes to the IRSL signl ecomes more importnt. In the model presented in this pper, the initil fst decy of the IRSL signl is explined on the sis of equilirium eing reched grdully etween the two mthemticl terms in eqution (1). In the work of Thomsen et l. (2008), this initil fst decy ws interpreted s due to recomintions tking plce etween nery eeh pirs, while the slower prt of the IRSL signl ws due to recomintions etween pirs locted frther prt. It is uncler whether these two explntions of the shpe of the IRSL curves re equivlent from physicl point of view, nd further experimentl nd modeling work is necessry to clrify these points. In this pper only experimentl dt otined from K-feldspr re used for comprison, nd other types of feldspr IRSL signls hve not een tested. Clerly more extensive experimentl nd simultion work is needed to scertin whether the simple model in this pper lso descries the IRSL decy curves from other feldspr smples Fig. 6. () Simulted IRSL curves for different vlues of the rtio g/s, from 10 3 to () Simulted IRSL curves for different vlues of n unknown physicl property of eeh pir in eqution (9), on logelog scle showing the liner regions of the power-lw decy. The power-lw exponent k otined y fitting the power-lw eqution (10) to the simulted dt in () nd () depends only very wekly on the vlue of the prmeters g/s nd in the model. of the prmeters in the model, the shpe of the IRSL curves does not chnge drsticlly. Of ll the prmeters vried in the model, the dimensionless prmeter hs the lrgest effect on the shpe of the IRSL curves. 5. Discussion nd conclusions The exct mthemticl shpe of the CWeIRSL curves is n open reserch question. Specificlly, it is uncler whether the luminescence signls t long excittion times re etter fitted with the power-lw, or with stretched exponentil function, or even with some other long-tiled mthemticl function. However, it is interesting to note tht there hs een some previous work on this suject: the PhD work y Bril (2002) contins rther extensive discussion nd study of the power-lw, s pplied to severl types of luminescence signls from feldsprs. In this pper we exmined the possiility of otining the luminescence decy lw sed on the system of differentil equtions descriing electronic trfficking etween the excited stte, the ground stte nd the luminescence center. The model explins the experimentl fct tht the initil prt of IRSL decy curves does not follow the power-lw of luminescence decy. Two limittions of the current model re: () the sence of role in the model for the nd-til sttes which re known to e present in feldsprs, nd () the sence of mthemticl Acknowledgements We thnk Dr. Kristin Thomsen for providing us with digitl copy of the experimentl dt shown in Fig. 5. Dr. Vsilis Pgonis is lso grteful for the finncil support of the Ntionl Lortory for Sustinle Energy, in Roskilde, Denmrk during his visit in Octoer References Ankjærgrd, C., Jin, M., Klchgruer, R., Lpp, T., Klein, D., McKeever, S.W.S., Murry, A.S., Mortheki, P., Further investigtions into pulsed opticlly stimulted luminescence from feldsprs using lue nd green light. Rdit. Mes. 44, 576e581. Biliff, I.K., Poolton, N.R.J., Studies of chrge trnsfer mechnisms in feldsprs. Nucl. Trcks Rdit. Mes. 18, 111e118. Bril, M.R., Spectrl investigtions of luminescence in feldsprs. 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