Determining the probability of locating peaks using computerized peak-location methods in gamma-ray spectra as a function of the relative peak-area uncertainty

Applied Radia ion and Iso opes 155 (2020) 108920 A ailable online 4 Oc obe 2019 0969-8043/© 2019 Else ie L d. All igh s ese ed. De e mining he p obabili y o loca ing peaks using compu e ized peak-loca ion me hods in gamma- ay spec a as a unc ion o he ela i e peak-a ea unce ain y M.C. Ali San o o c , M.J. Anagnos akis o , T. Boshko a a , A. Camacho b , M.C. Fo nacia i Iljadica c , S.M. Collins d , R. Diaz Pe ez e , J.U. Delgado , M. Đu a� sa i� c g , M.A. Duch b , V.H. El i a p , R. S. Gomes , A. Gudelis h , D. Gu au n , S. Hu ado Be mudez e , R. Idoe a i , A. Je emo i� c g , A. Kandi� c g , M. Ko un j , * , K. Ka opoulos k , M. Laubens ein l , S. Long m , R.M. Ma gineanu n , I. Mi sios o , D. Mulas b , J.K. Nikoli� c , A. Pan elica n , V. Pey es Medina p , L. Pibida q , C. Po i iadis k , R.L. Sil a , S. Si i c , B. � Se� slak g , L. Ve heyen , B. Vodenik j , I. Vukanac , H. Wiedne s , B. Zo ko j a Facul y o Physics, S . Klimen Oh idsky Uni e si y o So ia, 5 James Bou chie Bl d., 1164 So ia, Bulga ia b Uni e si a Poli � ecnica de Ca alunya (UPC), Ins i u de Tecniques Ene ge iques, Diagonal 647, 08028, Ba celona, Spain c Di isi� on Radioquimica B� asica y Da os Nuclea es, Depa amen o Quimica Nuclea , Comisi� on Nacional de Ene gia A � omica, A gen ina d Na ional Physical Labo a o y, Tedding on, Middlesex, TW11 0LW, UK e CITIUS, Uni e sidad de Se illa, A da. Reina Me cedes 4B, 41012, Se illa, Spain Labo a � o io Nacional de Me ologia das Radiaç~ oes Ionizan es – LNMRI, Ins i u o de Radiop o eç~ ao e Dosime ia – IRD / CNEN, B asilia, B azil g Vin� ca Ins i u e o Nuclea Sciences, Labo a o y o Nuclea and Plasma Physics, Uni e si y o Belg ade, Belg ade, Se bia h Cen e o Physical Sciences End Technology, Sa ano iu A e. 231, Vilnus, Li huania i Esquela de Ingenie ia de Bilbao, Uni e sidad del Pais Vasco UPV/EHU, Plaza Ingenie o To es Que edo 1, 48013, Bilbao, Spain j “Jo� ze S e an” Ins i u e, Jamo a Ces a 39, 1000, Ljubljana, Slo enia k G eek A omic Ene gy Commission, Agia Pa aske i, A hens, G eece l Labo a o i Nazionali del G an Sasso, Ins i u o Nazionale di Fisica Nuclea e, Via G. Aci elli 22, I-67100, Asse gi (AQ), I aly m Aus alian Radia ion P o ec ion and Nuclea Sa e y Agency, 619 Lowe Plen y Road, Yallambie, 3085, Aus alia n Ho ia Hulubei Na ional Ins i u e o Resea ch and De elopmen in Physics and Nuclea Enginee ing (IFIN_HH), 30 Reac o ului S ., POB MG-6, RO-0077125, Bucha es -Magu ele, Romania o Nuclea Enginee ing Depa men , Na ional Technical Uni e si y o A hens, 15780, A hens, G eece p Labo a o io de Me ologia de Radiaciones Ionizan es, A da. Complu ense 40, 28040, Mad id, Spain q Na ional Ins i u e o S anda ds and Technology, 100 Bu eau DR, MS8462, Gai he sbu g, MD, 20899-8462, USA Belgian Nuclea Resea ch Cen e, Boe e ang 200, BE-2400, Mol, Belgium s BEV - Bundesam ü Eich- und Ve messungswesen, Physikalisch- echnische P ü diens , A l gasse 35, 1160, Wien, Aus ia Vin� ca Ins i u e o Nuclea Sciences, Labo a o y o Radia ion and En i onmen al P o ec ion, Uni e si y o Belg ade, Belg ade, Se bia ARTICLE INFO Keywo ds: Gamma- ay spec ome y Rela i e peak-a ea unce ain y Peak loca ion Decision h eshold ABSTRACT The p obabili ies o loca ing peaks wi h a high ela i e peak-a ea unce ain y we e de e mined empi ically wi h nine ypes o peak-loca ion so wa e used in labo a o ies engaged in gamma- ay spec ome y measu emen s. I was ound ha i is no possible o loca e peaks wi h a p obabili y o 0.95, when hey ha e a ela i e peak-a ea unce ain y in excess o 50%. Loca ing peaks a hese ela i ely high peak-a ea unce ain ies wi h a p obabili y g ea e han 0.95 is only possible in he lib a y-d i en mode, whe e he peak posi ions a e supposed a-p io i. The de iciencies o he lib a y-d i en mode and he possibili ies o imp o e he p obabili ies o loca ing peaks a e b ie ly discussed. * Co esponding au ho . E-mail add ess: [email p o ec ed] (M. Ko un). Con en s lis s a ailable a ScienceDi ec Applied Radia ion and Iso opes jou nal homepage: h p://www.else ie .com/loca e/ap adiso h ps://doi.o g/10.1016/j.ap adiso.2019.108920 Recei ed 6 Feb ua y 2019; Recei ed in e ised o m 18 Sep embe 2019; Accep ed 2 Oc obe 2019 Applied Radia ion and Iso opes 155 (2020) 108920 2 1. In oduc ion In gamma- ay spec ome y measu emen s i is equen ly necessa y o e alua e peaks ha canno be easily dis inguished om luc ua ions in he con inuous backg ound on which hey a e supe imposed. Since he p esence o peaks in he spec um e lec s he p esence o gamma- ay emi e s, ob ious c i e ia o be used in he loca ion o small peaks, in o de o signal he p esence o a gamma- ay emi e , should conside he posi ion o he peak and i s shape. The peak posi ion should co espond o he ene gy whe e he gamma- ays om he emi e a e egis e ed, and he peak wid h should ollow he ene gy esolu ion o he spec ome e . Howe e , since s a is ical luc ua ions in he con inuous backg ound can a ise a any posi ion in he spec um and can ake on any wid h, hose wo c i e ia a e no su icien o di e en ia e be ween s a is ical luc- ua ions and small signals. The e o e, i is necessa y o es ablish a c i- e ion based on he exp essi eness o he peak. I he peak is small enough, compa ed o he s a is ical luc ua ions ha can be easonably expec ed, i is supposed o ep esen a s a is ical luc ua ion and no a signal due o he p esence o a gamma- ay emi e . The s anda d de i- a ion o he numbe o coun s in an ene gy in e al, co esponding o he esolu ion o he spec ome e , is gene ally used o de ine a quan i a i e c i e ion on he p esence o peaks. This s anda d de ia ion ep esen s he unce ain y o a peak a ea ha ing a alue o ze o, i.e., he null measu emen unce ain y (ISO/IEC, 2007). This c i e ion, o mula ed by Cu ie in 1968, s a es ha excu sions o he con inuous backg ound ha ing an a ea exceeding he c i ical limi , n*, de ined as n* ¼k 1- α ⋅u(n ¼0) (1) a e classi ied as loca ed peaks, signaling he p esence o gamma- ay emi e s. In Eq. (1) u(n ¼0) deno es he null measu emen unce ain y o he indica ion and he p opo ionali y ac o k 1- α desc ibes he p ob- abili y o making e o s o ype I, i.e., co esponding o he alse posi i e, meaning ha he peak is ac ually caused by a s a is ical luc ua ion. Usually, c i ical limi s a e calcula ed allowing 5% o alse posi i es, implying ha k 1- α ¼1.65. In he s anda d ISO 11929 (ISO, 2010) he c i ical limi , which e e s o he numbe o coun s, i.e., he indica ion, is subs i u ed by he deci- sion h eshold y*, which exp esses he p obabili y o he occu ence o ype-I e o s wi h he alue o he measu and y as ollows: y* ¼k 1- α ⋅u(y ¼0), (2) whe e u(y ¼0) deno es he null measu emen unce ain y o he measu and. The s anda d equi es documen ing whe he he indica ion, signal- ling he p esence o he measu and, was ecognized o no and doc- umen ing he co esponding decision h eshold in epo s on measu emen s o es i ems. The decision h eshold should be epo ed, ega dless o whe he a peak signalling he p esence o he gamma- ay emi e was loca ed in he spec um o no . Howe e , he me hod o he calcula ion o he decision h eshold di e s in bo h cases. In he i s case (peak p esen ) he heigh o he con inuous backg ound is de e - mined om he spec al egions ha do no o e lap wi h he peak e- gion. In he second case he con inuous backg ound is compu ed om a egion o in e es comp ising he egion whe e he peak is expec ed (Canbe a, 2004; DIN, 2014). The e o e, he compu ed decision h eshold can be di e en o he loca ed and o he no -loca ed peaks esiding on equal backg ounds and ha ing equal a eas. Al e na i ely, o loca ed peaks, he decision h eshold can be calcula ed om he peak da a (Ko un e al., 2016). I is ob ious ha o comply wi h he equi emen o he s anda d, i.e. o pe o m he calcula ion o he decision h eshold co ec ly, he loca ion o he peaks, deno ing he p esence o he measu and, should be pe o med wi h a eliabili y ha is de ined by he p obabili y α o making e o s o ype I. The s a is ical signi icance o he peak ha should be ecognized wi h his p obabili y is de e mined by he de ini ion o he decision h eshold. Since he measu e o he s a is ical signi icance o a peak is he ela i e unce ain y o i s a ea, he ela i e limi , which s ic ly co esponds o he espec i e decision h eshold (Boshko a, 2018), may be used. I he ROI (Region o In e es ) me hod is used o he peak a ea e alua ion, his limi ( ela i e decision h eshold) ends o 1/k 1- α , a a numbe o coun s co esponding o he decision h eshold, which is much la ge han k 1- α 2 . Fo a 0.05 p obabili y o ype-I e o s 1/k 1- α akes on a alue o 0.608 (60.8%), while o he numbe o coun s co esponding o he decision h eshold o 50 coun s, he ela i e decision h eshold has a alue o 0.628. (Boshko a, 2018). Howe e , i is no possible o calcula e he decision h eshold and he ela i e decision h eshold om he peak a ea and i s unce ain y only, since i also de- pends on he me hod o he peak a ea e alua ion and on he egion o in e es used o de e mining he con inuous backg ound. The e o e he app oxima e ela ion nea he decision h eshold uðyÞ y¼1 k1 α (3) be ween he ela i e peak a ea unce ain y and he decision h eshold was used, which a ises om he de ini ion o he decision h eshold, by assuming u(y ¼0) �u(y*). I ollows hen, ha o a 0.05 p obabili y o making ype-I e o s, peaks wi h a ela i e unce ain y o 60.8% should be loca ed wi h a p obabili y o 0.95. To examine he abili y o he so wa e, ha is cu en ly used in labo a o ies engaged in gamma- ay spec ome y measu emen s, an ac ion was ini ia ed wi hin he Low-Le el Measu emen Techniques Wo king G oup o he ICRM (In e na ional Commi ee o Radionuclide Me ology), wi h he aim o de e mine he p obabili y o loca ing peaks in gamma- ay spec a as a unc ion o hei ela i e peak-a ea unce - ain y. The ac ion ep esen s he ollow-up o a p e ious ac ion pe - o med wi h he pu pose o de e mining he sys ema ic in luences on peak a eas when he peaks a e no exp essi e (B uggeman e al., 2018). The analyses wi hin he ollow-up ac ion we e pe o med on he same se o spec a as he ac ion on he sys ema ic in luences, a ailable a he URL add ess h ps://www.d opbox.com/sh/ 9ws2 6g5mn0nqd /AABiO5-yq1IC 76EYd MCZq6a?dl¼0. I is he pu pose o his a icle o p esen he esul s o his ollow up and o d aw some conclusions abou he so wa e and on he way he labo a o ies use i . 2. Me hods The pa icipa ing labo a o ies we e asked o analyze a se o 35 spec a and o en e he esul s o he analyses in an Excel ile a ailable a he same URL add ess as he spec a. Twen y labo a o ies epo ed wen y- i e se s o esul s. Thi een se s we e ob ained wi h Canbe a’s peak-loca ion Genie 2000 2nd Di e ences P og am (Canbe a, 2004). These analyses we e pe o med wi h he alues o he sensi i i y pa ame e se be ween 2.07 and 2.55. O he ypes o so wa e ha we e used we e he Genie 2000 VMS S anda d Peak Sea ch P og am (Can- be a, 2006), wo se s; APTEC (Ap ec, 2000), wo se s; ANGES (Mishe , 2016), wo se s; Gamma Vision (O ec, 2016), wo se s; Maes o (O ec, 2008), one se ; Silena (2000), one se ; Gamma-W (Gamma-W 2008; IAEA, 1998), one se ; and SPUNAL (Simopoulos, 1989), one se . The analyses wi h he Genie 2000 VMS p og am we e made a he sensi i i y 2.2, wi h Silena a he sensi i i y 2.4 and wi h he Gamma-Vision so - wa e a he mos sensi i e alue o he peak signi icance pa ame e o uni y (one). Fo o he analyses i can be concluded on he basis o he numbe o peaks loca ed, ha he peak analyses we e made a simila sensi i i ies, excep o he ANGES so wa e, whe e he analyses we e less sensi i e. The p obabili ies o loca ing a peak a he ene gy E, p(E) we e calcula ed as p(E) ¼n(E)/N (4) M.C. Ali San o o e al. Applied Radia ion and Iso opes 155 (2020) 108920 3 whe e n(E) deno es he numbe o spec a wi hin a speci ic se o esul s, whe e a peak a he ene gy E was loca ed, and N is he numbe o spec a in he se . The unce ain y o his p obabili y was calcula ed as (Gilmo e, 2008; Ko un e al., 2015) u½pðEÞ� ¼ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i pðEÞ⋅½1pðEÞ� N (5) The ela i e unce ain y, a ibu ed o he mean peak a ea o a peak occu ing a an ene gy E, was calcula ed as he mean ela i e unce - ain y o he peak a eas calcula ed a he ene gy E wi hin a se u el�npðEÞ�¼1 nðEÞX nðEÞ i¼1 u el�npiðEÞ�(6) whe e n pi (E) deno es he numbe o coun s in he peak a he ene gy E in he i- h spec um wi hin a se o esul s and u el [n pi (E)] is i s ela i e unce ain y. The unce ain y was calcula ed as he a-pos e io i unce - ain y om he wid hs o he dis ibu ions o he ela i e unce ain ies occu ing a he ene gy E wi hin he se : u�u el�npðEÞ��¼ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i P nðEÞ i¼1�u el�npiðEÞ�u el�npðEÞ�� ½nðEÞ  1�⋅nðEÞ 2 u u u u (7) 3. Resul s The esul s epo ed by he pa icipan s a e p esen ed as he p oba- bili y o loca e peaks a speci ied loca ions as unc ions o he mean ela i e unce ain y and a e shown in Figs. 1 and 2 o he a ious ypes o so wa e used o he peak analysis. I is a common obse a ion ha o all he da a se s ecei ed, ha a small ela i e peak-a ea unce ain ies he p obabili y o de ec ion ends o uni y. The dis ibu ion o se s o e he mean se -speci ic numbe o ene gies in one spec um, whe e a peak was loca ed, is p esen ed in Fig. 3. Howe e , i is di icul o compa e he a ious da a se s, because he unce ain ies a ibu ed o he peak a eas a y signi ican ly. Fig. 4 p esen s he dis ibu ion o he da a se s e- po ed o e he mean ela i e unce ain y epo ed o his se . I is ob ious ha when compa ing he esul s om di e en se s he mean ela i e peak-speci ic peak-a ea unce ain ies epo ed canno be in e - p e ed di ec ly, bu needs o be e alua ed ela i e o he da a-se -speci ic mean ela i e peak-a ea unce ain y u el u el ¼1 MX M j¼1 u el�npEj�� (8) whe e M deno es he numbe o ene gies wi hin a da a se whe e he peaks we e loca ed and u el½npðEjÞ� is he mean ela i e peak-a ea un- ce ain y o he peaks loca ed a he ene gy E j . The a iabili y o he da a-se -speci ic mean ela i e peak-a ea un- ce ain ies canno be explained using he me hods o e alua ion o he peak a eas only, i.e., depending on whe he he peak a eas we e calcu- la ed using he ROI me hod o using he leas -squa es me hod. I is ob ious, he e o e, ha he a iabili y o igina es in he a iabili y o he spec al egions used o de e mining he backg ound. Howe e , all he ela i e unce ain ies epo ed exceeded he lowe limi o he ela i e unce ain y implied by he Poisson s a is ics o he case o a e y wide spec al in e al used o de e mining he heigh o he con inuous backg ound, i.e., u el >n g 1/2 , whe e n g deno es he g oss numbe o coun s in he peak egion. Since he co ela ion be ween he p obabili y o loca e peaks and he ela i e peak-a ea unce ain y is a he sca e ed, i is di icul o es ablish a quan i a i e c i e ion o exp ess he uppe limi o he in- e al o he ela i e unce ain ies whe e he p obabili y o he loca ion alls below 0.95. I can be obse ed ha a egion o ela i e peak-a ea unce ain ies exis s, whe e he p obabili ies o he peak loca ion Fig. 1. Co ela ions be ween he mean ela i e peak-a ea unce ain ies and he p obabili ies o loca ing he peaks o di e en ypes o so wa e used in he peak analysis. Fig. 2. Co ela ions be ween he mean ela i e peak-a ea unce ain ies and he p obabili ies o loca ing he peaks o da a se s comp ising la ge ela i e peak- a ea unce ain ies. M.C. Ali San o o e al. Applied Radia ion and Iso opes 155 (2020) 108920 4 being equal o uni y a e con iguous, and ha ano he egion o ela i e unce ain ies exis s whe e he p obabili ies o loca ing peaks, being smalle han uni y, a e con iguous. The uppe and lowe bounda ies o hese wo in e als a e deno ed by u el,Max and u el,Min , espec i ely. In his way he egion o alues u el /u el was di ided in h ee in e als, he i s one ex ending om ze o o u el,Max , he second one ex ending om u el,Max o u el,Min and he hi d ex ending om u el,Min o in ini y. Fig. 5a and b p esen he co ela ion be ween u el,Max /u el and he numbe o peaks ha ing u el <u el,Max and he co ela ion be ween he numbe o peaks wi h u el >u el,Min and u el,Min /u el, espec i ely. I is ob ious ha he co ela ions desc ibe he obus ness o he peak analysis. Fig. 5a p esen s he uppe limi s o he anges o he ela i e unce ain ies comp ising only peaks wi h a p obabili y o uni y o loca ion. The wide his ange is, he smalle is he p obabili y o ype-II e o s, i.e., he mo e obus is he peak-loca ion algo i hm o loca ing exp essi e peaks and he mo e peaks encompass he in e al [0,u el, Max ]. Fig. 5b p esen s he la ges mean ela i e peak-a ea unce ain y o a peak, loca ed wi h a p obabili y o uni y. The la ge his ela i e unce ain y is, he smalle is he p obabili y o ype-II e o s in he case o unexp essi e peaks, i.e., he mo e sensi i e he peak-loca ion algo i hm is. Also, he la ge u el,Min is, he ewe peaks occu wi h he mean peak-a ea unce ain y exceeding u el,Min . I is ob ious ha he ela i e peak-a ea unce ain y co esponding o he p obabili y o loca ing a peak wi h he p obabili y o 0.95 mus lie in he in e al [u el,Max , u el, Min ]. To de e mine his unce ain y, he dependence o he p obabili y o peak loca ion as a unc ion o he ela i e unce ain y was smoo hed, and om hese esul s he smalles ela i e unce ain y was de e mined, a he condi ion whe e he p ob- abili y o de ec ion d ops below 0.95. The dis ibu ion o he da ase s o e his ela i e unce ain y is shown in Fig. 6. 4. Discussion I can be seen in Fig. 6 ha he mean ela i e peak-a ea unce ain ies, needed o loca ing a peak wi h a p obabili y o 0.95, a e smalle han 60% in all he da a se s, excep one. The main pa ame e , which in- luences he p obabili y o peak loca ion and he da a-se -speci ic mean ela i e peak-a ea unce ain y, is he alue o he sensi i i y pa ame e , which in luences he peak loca ion p obabili y o he inexp essi e peaks. High p obabili ies o loca ing peaks inc ease he incidence o he peak loca ion o unexp essi e peaks, ha ing a high ela i e peak-a ea un- ce ain y. The e o e, in he da a se s hey inc ease he mean peak-a ea unce ain y. The co ela ion among he numbe o ene gies whe e he peaks we e loca ed wi hin a da a se and u el is p esen ed in Fig. 7. He e, he da a se s whe e he peak a eas we e calcula ed wi h he leas -squa e me hod and he da a se s calcula ed wi h he ROI me hod a e deno ed wi h open iangles and ull do s, espec i ely. I can be obse ed ha a he same numbe o loca ed peaks, i.e., o da a se s analyzed wi h he same e ec i e alue o he sensi i i y pa ame e , he mean ela i e unce ain ies ob ained wi h he LSQ me hod a e smalle han hese Fig. 3. Dis ibu ion o he da a se s o e he se -speci ic mean numbe o en- e gies in one spec um, whe e a peak was loca ed. Fig. 4. Dis ibu ion o da a se s o e he se -speci ic mean ela i e unce - ain y u el. Fig. 5. Co ela ion be ween he numbe o peaks ha ing u el <u el,Max and u el, Max /u el(a) and he co ela ion be ween he numbe o peaks wi h u el >u el,Min and u el,Min /u el (b). M.C. Ali San o o e al. Applied Radia ion and Iso opes 155 (2020) 108920 5 ob ained by he ROI me hod, as expec ed (Ko un e al., 2018). Fo he da a se s comp ising mo e han 100 peaks, he ype o so wa e used is iden i ied. In Fig. 8 he co ela ion among u el and he ela i e unce - ain y needed o loca e a peak wi h a p obabili y o 0.95 is p esen ed. I ollows om Fig. 8 ha some ypes o so wa e achie e a la ge mean ela i e peak-a ea unce ain y wi h a p obabili y o de ec ion o 0.95, despi e a smalle u el. By compa ing Figs. 7 and 8 i is clea ha his occu s al hough he numbe o ene gies whe e he peaks we e loca ed was app oxima ely he same. The eason o his is he be e selec i i y o ecognizing inexp essi e peaks. These da a se s a e, in Fig. 6, loca ed a he mean ela i e peak-a ea unce ain ies, which a e ecognized wi h a p obabili y o 0.95, in excess o 30%. I should be men ioned he e ha he da a se ob ained wi h he Gamma-Vision so wa e di e s quali a i ely om he o he da a se s (Fig. 2). This se was calcula ed in he lib a y-d i en mode. He e, he spec um is no scanned o he p esence o peaks, bu he peak a eas a e only e alua ed a p ede ined ene gies ha a e speci ied in a nuclide li- b a y. Wi h his app oach he spec um is decomposed in o he con in- uous backg ound and a peak a each ene gy, speci ied in he lib a y, using he leas -squa es me hod. In his way, by a-p io i supposing he p esence o a peak, he so wa e is “ o ced” o calcula e he peak’s p ope ies. The ad an age o his me hod was ecognized al eady, since he e he p obabili y o de ec ion is no gi en by he alue o he sensi i i y pa ame e , bu by he c i e ia o ejec ing he supposed peak (e.g., on he basis o he ene gy ole ance o he sign o he peak a ea). In he case o Gamma-Vision i can be seen ha he es ing o whe he a peak is p esen a a speci ic ene gy was no p e o med op imally. Fig. 9 p esen s he p obabili ies o loca ing he peaks, whe e he peaks loca ed wi h a p obabili y subs an ially less han uni y a e iden i ied by hei ene gy. I is ob ious ha he peaks a he highes ene gies we e loca ed wi h a compa a i ely low p obabili y, which poin s o he c i e ia ha ejec high-ene gy peaks. Howe e , he e is a p ice o be paid o he good pe o mance in ecognizing unexp essi e peaks. By compelling he so wa e o ecog- nize peaks ha would no be loca ed o he wise he quali y o he esul s is educed, since in hese cases he shape o he i ed spec um is less compa ible wi h a peak on a con inuous backg ound. This has he consequence ha he unce ain ies o he calcula ed peak pa ame e s inc ease, and wi h hem he ela i e peak-a ea unce ain ies. The e o e, hei dispe sion inc eases and wi h i also he mean ela i e peak-a ea unce ain y and i s ep oducibili y. I can be seen in Figs. 1 and 2 ha he la ges mean ela i e peak-a ea unce ain ies we e ob ained wi h he Fig. 6. Dis ibu ion o da a se s o e he ela i e peak-a ea unce ain y needed o loca e a peak wi h a p obabili y exceeding 95%. Fig. 7. Co ela ion be ween he numbe o ene gies whe e peaks we e loca ed wi hin a da a se and he se -speci ic mean ela i e unce ain y u el. The da a se s calcula ed wi h he ROI me hod a e deno ed wi h ull do s and he da a se s calcula ed wi h he LSQ me hod wi h emp y iangles. Fig. 8. Co ela ion be ween he se -speci ic mean ela i e unce ain y and he ela i e peak-a ea unce ain y needed o loca e a peak wi h a p obabili y o 0.95. The da a se s calcula ed wi h he ROI me hod a e deno ed wi h ull do s and he da a se s calcula ed wi h he LSQ me hod wi h emp y iangles. Fig. 9. Co ela ion be ween he mean ela i e peak-a ea unce ain y and he p obabili y o loca ing a peak in he da a se calcula ed in he lib a y- d i en mode. M.C. Ali San o o e al. Applied Radia ion and Iso opes 155 (2020) 108920 6 lib a y-d i en analysis. This de iciency could be imp o ed by using he penalized leas -squa es me hod (Kanisch, 2017). I ollows om Fig. 1, ha mos o he peak-analysis p og ams using he peak-loca ion me hod do no loca e peaks wi h he mean ela i e unce ain y o 61% wi h he p obabili y exceeding 0.5. To inc ease his p obabili y, he ollowing h ee possible ways can be ollowed: To inc ease he p obabili y o loca ing unexp essi e peaks, a smalle alue o he peak-signi icance pa ame e should be used, bu his can cause an unaccep able incidence o spu ious peaks, i.e., ype-I e o s (Ko un e al., 2017). The e o e his me hod should be complemen ed wi h il e s o iden i ica ion o alse posi i es on he basis o e.g. he peak’s ela i e a ea unce ain y and he ag eemen o he peak’s FWHM wi h he calib a ed FWHM (Ko un e al., 2013). I should be no ed howe e , ha he alue o he peak signi icance pa ame e can be dec eased only o a alue, whe e o e lapping o peaks is excluded, since hen he quali y o he peak-analysis esul s de e io a es. Ano he way o inc easing he p obabili y o loca ing peaks close o he decision h eshold is o inc ease he unce ain y o he peak a eas. This can be done only on he basis o plausibly ounded a gumen s. Many peak e alua ing algo i hms ake in o accoun only he s a is ical unce ain y o he numbe o coun s in he peak and he backg ound whe e he peak is supe imposed, bu do no conside he unce ain y esul ing om he choice o he peak s a and peak end channels o he ROI used o he e alua ion o he peak a ea (Ko un, 2008). When his unce ain y is aken in o accoun mo e eliable decisions on he p esence o a peak can be made. To dec ease he occu ence o de ec ion o spu ious peaks, he peak wid hs, as hey a e obse ed in he spec um, could be inc eased, i.e., by acqui ing spec a a a highe con e sion gain se ing, co esponding o a lowe ene gy pe channel alue. Then, o loca e a peak, he con en s o mo e consecu i e channels mus exceed he a e age channel con en , which diminishes he p obabili y o ecognizing s a is ical luc ua ions as peaks. I ollows ha by a combina ion o he h ee me hods men ioned i may be possible o inc ease he p obabili y o loca ing peaks wi h a la ge ela i e peak a eas unce ain y. 5. Conclusion I has been shown ha peaks wi h ela i e peak-a ea unce ain ies in excess o 50% a e no loca ed wi h a p obabili y o 95%, excep in he lib a y-d i en peak-analysis mode. Howe e , he disad an age o his mode is ha in he case o unexp essi e peaks he peak-a ea un- ce ain ies inc ease subs an ially, making hese peak a eas o limi ed use o u he analysis. An al e na i e possibili y o inc ease he p obabili y o loca ing small peaks is o use a smalle alue o he sensi i i y pa ame e , bu his should be used in combina ion by app opia e il e ing o dec ease he occu ance o spu ious peaks. Decla a ion o compe ing in e es The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Re e ences Ap ec, 2000. Ap ec MCA Applica ion Mul ichannel Analyze Ve sion 7.00.01. Ap ec Ins umen s L d. Boshko a, T., 2018. Decision h eshold and ela i e unce ain y o he measu ed ne signal in adia ion measu emen . Appl. Radia . Iso . 139, 146–150. B uggeman, M., e al., 2018. Sys ema ic in luences on he a eas o peaks in gamma- ay spec a ha ha e a la ge s a is ical unce ain y. Appl. Radia . Iso . 134, 51–55. Canbe a, 2004. Genie 2000 Spec oscopy So wa e, Cus omiza ion Tools. Canbe a Indus ies Inc., Me iden, USA. Canbe a, 2006. Genie 2000 Spec oscopy So wa e Ope a ions. Canbe a Indus ies Inc., Me iden, USA. Cu ie, L.A., 1968. Limi s o quali a i e de ec ion and quan i a i e de e mina ion – applica ion o adiochemis y. Anal. Chem. 40, 586–593. DIN, 2014. 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