EX PER I MEN TAL VER I FI CA TION OF GAMMA-EF FI CIENCYCAL CU LA TIONS FOR SCIN TIL LA TION DE TEC TORS

IN AN GLE 4 SOFT WARE

by

Abouzeid A. THABET 1, Aleksandar D. DLABAC 2, Slobodan I. JOVANOVIC 2, 3*,Mohamed S. BADAWI 4, Nikola N. MIHALJEVIC 2, 5, Ahmed M. EL-KHATIB 4,

Mona M. GOUDA 4, and Mahmoud I. ABBAS 4

1 De part ment of Med i cal Equip ment Tech nol ogy, Fac ulty of Al lied Med i cal Sci ences,Phar os Uni ver sity, Al ex an dria, Egypt

2 Cen tre for Nu clear Com pe tence and Knowl edge Man age ment, Uni ver sity of Montenegro, Podgorica, Montenegro3 De part ment of Phys ics, Fac ulty of Math e mat ics and Nat u ral Sci ences,

Uni ver sity of Montenegro, Podgorica, Montenegro4 De part ment of Phys ics, Fac ulty of Sci ence, Al ex an dria Uni ver sity, Al ex an dria, Egypt

5 De part ment of Math e mat ics, Mar i time Fac ulty, Uni ver sity of Montenegro, Kotor, Montenegro

Sci en tific pa perDOI: 10.2298/NTRP1501035T

AN GLE soft ware for semi con duc tor de tec tor ef fi ciency cal cu la tions – long ex ist ing andwidely ac cepted tool in quan ti ta tive gamma spec trom e try – has been re cently ex tended toscin til la tion NaI de tec tors. The ex ten sion fea tures in the lat est edi tion (AN GLE 4) and it isbriefly out lined. Discretization of ref er ence ef fi ciency curve, mean ing pos si bil ity of us ing AN -GLE 4 for par tic u lar gamma en er gies with out con struct ing the com plete ref er ence ef fi ciencycurve, is par tic u larly em pha sized. This yields both in en hanced prac ti cal ity and higher ac cu -racy, while re duc ing the po ten tial for sys tem atic er rors. The pres ent work is pri mar ily fo -cussed on ex per i men tal ver i fi ca tion of AN GLE 4 for NaI de tec tors. Two de tec tors (2 ́ 2 and3 ´ 3 inches) were em ployed in the ex per i ment. Com mer cially cal i brated gamma sources (inthe forms of quasi point and cyl in der) and home made so lu tions (di luted from cal i bratedones) were mea sured at var i ous dis tances from the de tec tor(s), rang ing 0 cm to 50 cm. En -ergy range ob served was 59 keV to 1408 keV. Ver sa til ity of count ing con di tions, in terms ofde tec tors and sources used, gamma en er gies ob served, source de tec tor sep a ra tions, etc., wasaimed at cre at ing as large ex per i men tal ev i dence as pos si ble for ver i fi ca tion pur poses. Ex per i -men tally ob tained ef fi cien cies are com pared with those cal cu lated by AN GLE 4. Very goodagree ment is ob tained – well within the ex per i men tal un cer tain ties – thus prov ing the re li abil -ity of the soft ware.

Key words: gamma spec trom e try, scin til la tion de tec tor, ef fi ciency cal cu la tion, AN GLE soft ware,ex per i men tal ver i fi ca tion

IN TRO DUC TION

AN GLE soft ware for semi con duc tor de tec torgamma ef fi ciency cal cu la tions in its var i ous forms hasbeen in use for more than 20 years now [1-3]. It is gen -er ally re garded as a so phis ti cated/ad vanced tool inquan ti ta tive gamma spec trom e try – now a days rou -tinely ex ploited in hun dreds of gamma spec trom e trybased lab o ra to ries world wide, in clud ing the mostprom i nent ones [4]. AN GLE al lows ac cu rate de ter mi -na tion of the ac tiv i ties of gamma spec tro scopic sam -ples for which no rep li cate stan dard ex ists, in terms ofge om e try and ma trix. A semi em pir i cal ef fi ciencytrans fer (ET) ap proach is em ployed, com bin ing ad -

van tages of both ab so lute (Monte Carlo) and rel a tive(trace able source based) meth ods to de ter mine thesam ple ac tiv ity by gamma spec trom e try [2, 5-15] – inthis way the prac ti cal lim i ta tions of rel a tive meth odsare re duced, while the po ten tial for sys tem atic er rorsin the ab so lute ones is min i mized.

The phys i cal model be hind ET is the con cept ofthe ef fec tive solid an gle (W ) – a com pound pa ram e ter,cal cu lated upon the in put data on geo met ri cal, phys i -cal, and chem i cal (com po si tion) char ac ter is tics of (1)the source (incl. its con tainer ves sel), (2) the de tec tor(incl. crys tal hous ing and endcap), and (3) count ing ar -range ment (incl. in ter cept ing lay ers be tween the lat tertwo) [1, 12, 16-18].

The pro gram is broadly ap pli ca ble (prac ti cally to allmost com mon sit u a tions en coun tered in gamma-spec -trom e try prac tice), e. g., in nu clear in dus try, en vi ron men -

A. A. Thabet, et al.: Ex per i men tal Ver i fi ca tion of Gamma-Ef fi ciency ...Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46 35

* Cor re spond ing au thor; e-mail: bobo_jovanovic@ya hoo.co.uk jogi@rc.pmf.ac.me

tal mon i tor ing, ra dio ac tiv ity con trol, food safety, med i -cine, ra dio ac tive waste man age ment, safety/se cu rity/safe guards, sci en tific re search (e. g., neu tron ac ti va tionanal y sis, nu clear data stan dard iza tion, re ac tor phys ics),ed u ca tion and train ing, etc. [19-26]. Point, disc, cy lin dri -cal or Marinelli sam ples, small or large, of any ma trixcom po si tion, mea sured on co ax ial, pla nar or well type de -tec tors, HPGe or Ge(Li) – and now NaI – can be ac com -mo dated. No stan dards are re quired, but a start up ref er -ence ef fi ciency curve (REC) must be ob tained, gen er allyas a one time cal i bra tion pro ce dure. Time and ef fort putinto ob tain ing a re li able REC is largely paid off in sub se -quent AN GLE uti li za tion, through the sim plic ity, speedand pro duc tiv ity in ob tain ing an a lyt i cal re sults – lead ing to im proved lab o ra tory per for mance.

AN GLE is thus char ac ter ized by its (1) widerange of ap pli ca bil ity, (2) high ac cu racy, (3) ease ofuse, (4) flex i bil ity in re spect to in put pa ram e ters andout put data, (5) short com pu ta tion times, (6) easy com -mu ni ca tion with an other soft ware, (7) suit abil ity forteach ing/train ing pur poses, (8) po ten tial for ac com -mo dat ing – into its ar chi tec ture – other ef fi ciency cal -cu la tion meth ods of semi em pir i cal or ab so lute (Monte Carlo) types, and (9) pos si bil ity of ex pand ing its cur -rent scope of ap pli ca bil ity to fur ther/par tic u lar user'sneeds and/or fields of in ter est. A key as pect and dif fer -ence from other ap proaches, which greatly en hances

prac ti cal ity, is the fact that no fac tory char ac ter iza tionof the de tec tor re sponse is re quired – any de tec tor maybe ac com mo dated as long as some ba sic knowl edgecon cern ing its con struc tion is avail able (which is nor -mally the case – de tec tor man u fac tur ers do sup ply rel -e vant data sheets).

Be sides the de cades of prac ti cal uti li za tion, ac -cu racy of the soft ware is suc cess fully tested in anIAEA or ga nized gamma spec trom e try soft wareintercomparison ex er cise [10] – AN GLE scored0.65% av er age de vi a tion from the ex er cise mean (forEg > 20 keV en er gies). AN GLE is avail able from thede vel op ers, while com mer cially dis trib uted byAMETEK/ORTEC, USA as well [4, 27].

NEW VER SION OF AN GLE ANDEX TEN SION TO SCIN TIL LA TIONDE TEC TORS

De tails about AN GLE soft ware prin ci ples, in -clud ing the o ret i cal back ground and ap pli ca tion to var -i ous types of semi con duc tor de tec tors, as well as thede scrip tion of the soft ware, are elab o rated in de tailelse where [1, 4, 12, 16-18, 27]. New ver sion, AN GLE4, is about to be re leased [4]. As com pared to pre vi ousver sion, AN GLE 3, the new ver sion brings many new

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...36 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Fig ure 1. AN GLE 4 main screen

fea tures, among which (1) sup port for scin til la tion NaI de tec tors (both cy lin dri cal and well type), (2) newXML based file for mat which al lows easy ma nip u la -tion of both in put and out put files by a third party soft -ware, and thus, (3) au to ma tion and com plex anal y ses,(4) scaled graph i cal pre view of in put and out put pa -ram e ters, which can be ex ported to bitmap or vec torfile for mats, (5) multilanguage sup port, (6) ad di tionalin put pa ram e ters for de tec tors, (7) user in ter face im -prove ments, (8) dis crete ref er ence ef fi cien cies, etc.AN GLE 4 main screen is shown in fig. 1.

The op tion of NaI de tec tors was con sid ered from the very be gin ning of AN GLE de vel op ment. It wasbe lieved, how ever, that the con cept of ad vanced soft -ware for semi con duc tor de tec tors does not al low forscin til la tion ones, re gard ing (wrongly) the lat ter as in -ad e quate and ob so lete. Nev er the less, in house ver sionof AN GLE which sup ports NaI de tec tors ex ists since2002 and was suc cess fully tested in geo chron ol ogy re -search [24].

The idea of cre at ing a sep a rate, much less elab o -rate soft ware (for NaI de tec tors only) was an other pos -si bil ity, but that was deemed a sort of triv ial and over -sim pli fied AN GLE vari a tion to ex ist on its own. Itcame even tu ally as a re sult of AN GLE us ers' feed backand grow ing in ter est, that this op tion should be in cor -po rated within the new ver sion of AN GLE – as it isnow the case in AN GLE 4. The fact that NaI de tec torsdo not be long to semi con duc tor fam ily is largely over -shad owed by the at trib utes they have in com monand/or com ple ment each other.

The use of NaI de tec tors for gamma spec trom e -try is steadily in creas ing, de spite their ap par ent draw -backs (most of all the poor res o lu tion) as com pared tosemi con duc tor ones (HPGe in par tic u lar) which madeNaI look like a his tor i cal rel ict 30 years ago. How ever,in many fields of ap pli ca tion, only a few tar getedradionuclides are be ing mea sured (most no ta blyCs-137 in en vi ron men tal mon i tor ing), of ten on “in -dus trial scale”, i. e., for huge num ber of sam ples ofsim i lar or i gin (e. g., food, soil, air fil ters, con struc tionma te ri als, consumables, etc.). An or der of mag ni tudelower price, sim ple main te nance and high ef fi ciency(short count ing times) then come de ci sively in NaI fa -vour – when lab o ra tory per for mance and out put arepar a mount.

Ap pli ca bil ity of AN GLE con cept to NaI de tec -tors is straight for ward, es pe cially for those al ready fa -mil iar with AN GLE ar chi tec ture. This co mes as a con -se quence of ap par ent fun da men tal sim i lar ity be tweenthe two types of de tec tors, HPGe and NaI. Of course,AN GLE 4 ac counts for NaI as gamma ray ab sorb ingma te rial which gives rise to im pulses/count in agamma spec trum. The use of REC – as one time cal i -bra tion – which is typ i cal for AN GLE, is still rec om -mended. Care must be taken, how ever, that not somany ex per i men tal cal i bra tion points can be ob tainedwithin the gamma en ergy re gion of in ter est (e. g.

50 keV to 2000 keV), due to the fact these have to besep a rated by con sid er able mar gins (in gamma en er -gies) to avoid over lap ping of the peaks. This is par tic u -larly valid when REC is ob tained from a sin gle multigamma source, but can be avoided us ing sev eral sin gle gamma sources mea sured suc ces sively/sep a rately.

Con cern ing ref er ence cal i bra tion, i. e. REC,there is a very im por tant ad van tage that AN GLE 4 of -fers. Namely, given the na ture of NaI mea sure ments, itwent in most cases about mea sur ing only one nu clideat a time, even just one en ergy (e. g., 661.6 keV ofCs-137). In such case, AN GLE 4 al lows REC to becon sid ered as sep a rate/sin gle points (thus not as acurve in ter po lated be tween ex per i men tal cal i bra tionpoints). Let us call it “REC discretization”. One ormore dis crete points can be cho sen/used for par tic u largamma en ergy (or en er gies) of in ter est.

Ap par ently REC discretization makes AN GLEap pli ca tion not only ex tremely sim ple, but also moreac cu rate. It can fairly be said this is quasi rel a tive ap -proach to quan ti ta tive gamma spec trom e try on its best– pre serv ing most of the ac cu racy of rel a tive method,yet al low ing for un lim ited flex i bil ity in sam ple type,ma trix, size, its con tainer char ac ter is tics and other in -ter cept ing lay ers, count ing ar range ment, etc. Twomost com mon types of NaI de tec tors are avail able inAN GLE 4: stan dard (with cy lin dri cal crys tal as the ac -tive body) and well type (a hole is drilled in the crys talto en able place ment of small sources, in or der to max i -mize the ef fi ciency). De tec tor data in put is or ga nizedin the same way as for semi con duc tor de tec tors. Userori ented and er ror cor rect ing graph i cal in ter face is in -struc tive and self ex plan a tory (fig. 2). Much less de -tec tor pa ram e ters are re quired, as com pared withsemi con duc tor de tec tors, due to sim plic ity of NaI de -tec tor con struc tion. Some new de tec tor pa ram e ters are in tro duced, spe cific for this de tec tor type, such as re -flect ing layer, op ti cal cou pling and photomultipliertubes.

EX PER I MEN TAL

Ex per i men tal ver i fi ca tion of AN GLE 4 soft ware for NaI de tec tors was ef fec tu ated at Prof. Younis S.Selim Lab o ra tory for Ra di a tion Phys ics, Phys ics De -part ment, Fac ulty of Sci ence, Al ex an dria Uni ver sity(Al ex an dria, Egypt). For the sake of ver i fi ca tion, thelab o ra tory was sup plied with the pre re lease ver sion ofAN GLE 4. Two NaI de tec tors with cy lin dri cal crys -tals, 2 ´ 2 and 3 ´ 3 inches were used in the ex per i -ments. All the de tails about the de tec tors are listed intab. 1; some of the pa ram e ters (con cern ing the op ti calcou pling and photomultiplier tube) were ir rel e vant foref fi ciency cal cu la tions per formed by AN GLE 4.

The first set of ac tiv ity stan dards in the form ofpoint sources was used for cal i bra tion of gamma spec -trom e ters. Ra dio ac tive sub stance it self is a very thin,

A. A. Thabet, et al.: Ex per i men tal Ver i fi ca tion of Gamma-Ef fi ciency ...Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46 37

com pact grained layer, ap plied to a small cir cu lar area(5 mm in di am e ter, i. e., “quasi point”), in the mid dle of the source, be tween two poly eth yl ene foils and eachhav ing a mass per unit area of 21.3 ± 1.8 mg/cm2. Byheat ing un der pres sure, the two foils were welded to -gether over the whole area, so that they are leak proof.To fa cil i tate han dling, the foil 26 mm in di am e ter ismounted in a cir cu lar alu mi num ring (outer di am e ter30 mm and height 3 mm), from which it can eas ily bere moved if and when re quired. These point sources(241Am, 137Cs, 133Ba, 60Co, and 152Eu) were pur chasedfrom the Physikalisch Technische Bundesanstalt(PTB) in Braunschweig and Berlin, which is na tionalin sti tute for sci ence and tech nol ogy and the high esttech ni cal au thor ity of Ger many in the field of me trol -ogy and cer tain sec tors of safety en gi neer ing. The cer -tif i cates show ing the ac tiv i ties of the sources and cor -re spond ing un cer tain ties are listed in tab. 2. The datasheet stat ing the val ues of half life pho ton en er gies and pho ton emis sion prob a bil i ties per de cay for allradionuclides used in the cal i bra tion pro cess is givenin tab. 3.

The sec ond set of ac tiv ity stan dards was home -made vol u met ric from stan dard so lu tion. The de tailsof the prep a ra tion are listed in tab. 4. Poly propy lene500 ml vial was filled with 200 ml, 300 ml, and 400 mlof 152Eu aque ous so lu tion of known ac tiv ity.

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...38 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Fig ure 2. Data in put di a log for cy lin dri cal NaI detector

Ta ble 1. Char ac ter is tics of NaI de tec tors used in theex per i ments

ItemDe tec tor

3 ´ 3De tec tor

2 ´ 2

Man u fac turer Can berra

Se rial num ber 09L 652 09L 654

De tec tor model 802

Type Cy lin dri cal

Mount ing Ver ti cal

Res o lu tion (FWHM) at 661 keV 8.5% 7.5%

Cath ode to an ode volt age +800 V DC +900 V DC

Dynode to dynode +80 V DC

Cath ode to dynode +150 V DC

Tube base Model 2007

Shap ing mode Gaussi an

De tec tor type NaI(Tl)

Crys tal di am e ter [mm] 76.2 50.8

Crys tal length [mm] 76.2 50.8

Top cover thick ness [mm] Al (0.5)

Side cover thick ness [mm] Al (0.5)

Re flec tor – ox ide [mm] 2.5

Weight [kg] 1.8 0.77

Outer di am e ter [mm] 80.9 57.2

Outer length [mm] 79.4 53.9

Crys tal vol ume [cm3] 347.49 102.96

The prep a ra tion method of the home madesources was based on the orig i nal (PTB) aque oussource ac tiv ity and its prop er ties which are known [to -tal ac tiv ity 202 ± 4 kBq at Jan. 1, 2010, with a to talweight 1000.41 g) – sim ply di vid ing the so lu tion ac -tiv ity by the to tal mass of the so lu tion, the ac tiv ity foreach gram will be known from the spe cific ac tiv ity law

aA

m= (1)

where a [Bqg–1] is the spe cific ac tiv ity, A [Bq] – the ac -tiv ity, and m [g] – the mass of the ma te rial. So, to pre -pare the source with the needed ac tiv ity one just cal cu -lates how many grams to take from the par ent so lu tion.In the pres ent work, in or der to pre pare var i ous vol -umes of so lu tions with the ac tiv ity of 5 kBq, each timewe took 25 g from the par ent so lu tion and com pletedthe rest of the vi als by the car rier so lu tion; car rier so lu -tion was pre pared from 0.1 M HCl in aque ous form.

Mea sure ments were car ried out to ob tain sta tis ti -cally sig nif i cant main peaks in the spec tra; spec tra arere corded and pro cessed by winTMCA32 soft waremade by ICx Tech nol o gies. Mea sured spec trum wassaved as spec trum ORTEC files which can be openedby ISO 9001 Ge nie 2000 data ac qui si tion and anal y sissoft ware made by Can berra where the peak anal y sis isac com plished. Ac qui si tion time is set high enough toget the num ber of counts to be at least (or more than)10,000, which makes the sta tis ti cal un cer tain ties lessthan 1%. The spec tra were an a lyzed with the pro gramus ing its au to matic peak search and peak area cal cu la -tions, along with the changes in the peak fit us ing thein ter ac tive peak fit in ter face, when nec es sary to re -duce the re sid u als and er ror in the peak area val ues.The peak ar eas, the live time, the run time and the starttime for each spec trum are en tered in the spread sheetsthat are used to per form the cal cu la tions nec es sary togen er ate the ex per i men tal ef fi ciency curves [28-40].Some rep re sen ta tive spec tra, in clud ing all sources andboth de tec tors, can be found at a ded i cated web pageac com pa ny ing this pa per [41].

The ex per i men tal full en ergy peak ef fi ciency aten ergy E, for a given set of mea sur ing con di tions canbe com puted by the equa tion

e( )( )

( )E

N E

TA P EC=

Si (2)

where N (E) is the num ber of counts in the full en ergypeak, T [s] – the mea sur ing time, P(E) – the pho tonemis sion prob a bil ity at en ergy E, AS – the radionuclideac tiv ity, and Ci – the cor rec tion fac tor due to dead timeand radionuclide de cay. In these mea sure ments of thelow ac tiv ity sources, the dead time had been al waysless than 2%, so the cor re spond ing fac tor was ob tained sim ply by us ing ADC live time. The de cay cor rec tion,Cd, for the cal i brat ing source from the ref er ence timeto the run time is given by

C Td e= lD (3)

where l is the de cay con stant and DT – the time in ter -val over which the source de cays cor re spond ing to therun time. The un cer tainty in the ex per i men tal full en -ergy peak ef fi ciency, se, is given by [40]

s ee

se

se

se =æ

èç

ö

ø÷ +

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷

¶

¶

¶

¶

¶

¶A P NA P N

22

22

22 (4)

where sA, sP, and sN, are the un cer tain ties as so ci atedwith the quan ti ties AS, P(E), and N(E), re spec tively, as -sum ing that the only cor rec tion made is due to thesource ac tiv ity de cay.

While mea sur ing vol u met ric sources, a thickplexi glas cover was placed di rectly on the de tec tor en -trance win dow as an ab sorber, so as to avoid the ef fectof b- and X-rays and to pro tect de tec tor endcaps.There fore, no cor rec tion was needed for X-gamma co -in ci dences, since in most cases the ac com pa ny ingX-rays were soft enough to be ab sorbed com pletelybe fore en ter ing the de tec tor. In ad di tion, an gu lar cor -re la tion ef fects were neg li gi ble for low source to de -tec tor dis tances.

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Ta ble 2. PTB point sources' ac tiv i ties and their un cer tain ties

PTB – Nu clide Ac tiv ity[kBq] Ref er ence date Un cer tainty

[kBq]241Am 259.0

June 1, 2009

±2.6133Ba 275.3 ±2.8152Eu 290.0 ±4.0137Cs 385.0 ±4.060Co 212.1 ±1.5

Ta ble 3. Half-lives, pho ton en er gies and pho ton emis sionprob a bil i ties per de cay for the radionuclides used inthis work

PTB –Nu clide

En ergy[keV]

Emis sionprob a bil ity [%]

Half life[d]

241Am 59.52 35.9 157861.05133Ba 80.99 34.1 3847.91

152Eu

121.78 28.4

4943.29

244.69 7.49

344.28 26.6

778.95 12.96

964.13 14.0

1408.01 20.87137Cs 661.66 85.21 11004.98

60Co1173.23 99.9

1925.311332.50 99.982

Ta ble 4. Prop er ties of vol u met ric ra dio ac tive sourcesused in the mea sure ments

Items152Eu so lu tion sources de scrip tion

(home made)

Vol ume [ml] 200 300 400

Ac tiv ity [kBq] 5

Un cer tainty [%] 1.98

Ref er ence date January 1, 2010

Vial manufacturer Nalgene

Vial material Poly propy lene

As to g-g true co in ci dence sum ming (TCS), nocor rec tions were deemed to be made nei ther. It is ap -par ent that for point sources the sum ming is neg li gi ble– the clos est count ing po si tion (P4) is more than 20 cmfrom the de tec tor top. For vo lu mi nous sources it is notneg li gi ble, but it is fair to es ti mate that it does not ex -ceed a few per cent, nei ther. Namely, all three vo lu mi -nous sources had the di am e ter (11.15 cm) much largerthan that of the de tec tor(s) (5.08 cm to 7.62 cm). To -gether with source height (2.145 cm to 4.183 cm), thismakes a few cm ef fec tive dis tance from the de tec tor.In ad di tion, vo lu mi nous sources were mea sured at~0.8 cm from the de tec tor top (in clud ing con tainerbot tom thick ness of 2.03 mm, con tainer foot height of2.00 mm, and source sup port thick ness of 3.36 mm to3.63 mm). When com par ing with lit er a ture val ues forEu-152 cor rec tion fac tors (all six sig nif i cant g-lines,but mostly prom i nent for 122 keV), we came to thecon clu sion that this ef fect could not pro duce more than ~5% sys tem atic er ror. This is within ex per i men tal un -cer tainty bud get (~2% on fac tory cal i bra tion of the so -lu tion, a few per cent on home made di lu tion, and an -

other few per cent on count ing sta tis tics). Last but notleast, AN GLE soft ware – based upon ef fi ciency trans -fer (ET) prin ci ple – in her ently tends to re duce sys tem -atic er rors of this type, due to sim i lar ity of count ing ar -range ments (par tial er ror cancelling); this is es pe cially valid when count ing ar range ments are sim i lar (e. g.,com par ing vo lu mi nous sources among them selves).

In or der to pre vent dead time and pile up ef fects,source ac tiv i ties were kept be low a few kBq for eachradionuclide. High count rates were, hence, avoidedwhen mea sur ing at close dis tances; how ever, this im -pli cated long count ing times at higher dis tances [37].The ex per i ments were set so as to ex tract max i mum in -for ma tion pos si ble for AN GLE 4 soft ware val i da tionfor NaI de tec tors. Sources were po si tioned co ax i allywith de tec tor when mea sured. All the de tails about thesource to de tec tor con fig u ra tions for us ing point andvol u met ric ra dio ac tive sources are listed in tab. 5,while figs. 3 and 4 show sche matic di a grams of NaIde tec tors with an iso tro pic ra di at ing point and vol u -met ric sources, re spec tively.

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...40 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Ta ble 5. Rel e vant data for the de tec tors, ra dio ac tive sources and count ing ge om e tries used in the ex per i ment

ItemDe tec tor

2 ´ 2 [mm]De tec tor

3 ´ 3 [mm]

De tec tor di men sions

Dd (de tec tor di am e ter) 50.80 76.20

Dl (de tec tor height) 50.80 76.20

ECth (end cap thick ness) 0.50 0.50

Rth1 (face re flec tor layer thick ness) 2.50 2.50

Rth2 (side re flec tor layer thick ness) 2.70 1.85

Plexi glas holder di men sions

A 7.08 12.16

B 13.09 16.57

C 22.61 36.99

D 3.36 3.63

E 4.42 6.83

F 35.06 22.82

G 4.13 4.65

H 31.28 46.73

I 42.14 34.98

J 149.92 160.09

K 135.75 135.75

L 27.31 27.31

M 81.00 81.00

N 9.85 9.85

O 2.38 2.38

Point sources height

P 1.50 1.50

P4 204.15 204.42

P5 254.34 254.61

P6 305.10 305.37

P7 355.63 355.90

P8 405.73 406.00

P9 456.39 456.66

P10 506.90 507.17

Vol u met ric sourcesdi men sions

Sd (source di am e ter) 111.50 mm

Sh (source height) 21.45/31.59/41.83 mm

Wth (wall thick ness) 2.03

Bth (bot tom thick ness) 2.03

Fth (foot height) 2.00

Source vol ume 200/300/400 ml

A. A. Thabet, et al.: Ex per i men tal Ver i fi ca tion of Gamma-Ef fi ciency ...Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46 41

Fig ure 3. Sche matic di a gram of NaI de tec tors us ing iso tro pic ra di at ing point sources mea sured....................from po si tion P4 up to po si tion P10

Fig ure 4. Sche matic di a gram of NaIde tec tors us ing vol u met ric sourcesmea sured on the top of the hold ers;an gu lar cor re la tionef fects can be ne glected forlow source to de tec tor dis tances

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...42 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Fig ure 5. AN GLE 4 cal cu la tion vs. ex per i ment for 2 ´ 2 inch de tec tor and var i ous count ing ar range ments

A. A. Thabet, et al.: Ex per i men tal Ver i fi ca tion of Gamma-Ef fi ciency ...Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46 43

Fig ure 6. AN GLE 4 cal cu la tion vs. ex per i ment for 3 × 3 inch de tec tor and var i ous count ing ar range ments

CAL CU LA TIONS AND RE SULTS

De tec tion ef fi cien cies are cal cu lated us ing AN -GLE 4 soft ware. Var i ous sources are tried as ref er ence(cal i bra tion) ones, from which the de tec tion ef fi cien -cies are cal cu lated for the un known sources – ac tu allycal i brated ones as well, thus with known ac tiv i ties.

Very good agree ment is ob tained be tween ex per -i men tally de ter mined and cal cu lated (us ing AN GLE4) de tec tion ef fi cien cies for NaI de tec tors. The agree -ment is ap par ently within ex per i men tal un cer tain ties.There is no in di ca tion of bias or sys tem atic er rors.

Re sults for each de tec tor and count ing ar range -ment are given in figs. 5 and 6 (for 2 ´ 2 and 3 ´ 3inches de tec tors, re spec tively). Sum ma rized re sultsare pre sented in tab. 6. De tails can be found in the form of ex ten sive Ex cel file, which is avail able for down -loading [41].

CON CLU SIONS

Ex per i men tal ver i fi ca tion of AN GLE 4 soft ware for NaI de tec tors proved the re li abil ity of the soft ware. As a mat ter of fact, this was ex pected with pretty muchcon fi dence, since the core soft ware per forms muchmore com plex task of the same type – ef fi ciency cal cu -la tions for semi con duc tor de tec tors, the lat ter be ingex ten sively tested dur ing more than twenty years ofprac ti cal ap pli ca tion in gamma-spec trom e try labs allaround.

From the other side, this work also proved the re -li abil ity of both ex per i men tal set-up and pro ce dure ap -plied. These are in tended to be fur ther used in test ingand val i dat ing new up grades of AN GLE soft ware –within sci en tific col lab o ra tion be tween the uni ver si -ties of Al ex an dria and of Montenegro.

AU THOR CON TRI BU TIONS

AN GLE 4 soft ware ex ten sion to NaI de tec torswas de vel oped by A. D. Dlabac. Ex per i men tal part ofthe ver i fi ca tion work was car ried out by A. A. Thabetand M. S. Badawi. All au thors took part in plan ningthe work and in dis cus sions dur ing all phases of itselab o ra tion. The manu script was con ceived and writ -ten by S. I. Jovanovi}, M. S. Badawi, A. M. El Khatib,and M. I. Abbas. A. D. Dlabac per formed data elab o ra -tion and the graph i cal rep re sen ta tion of re sults.

REF ER ENCES

[1] Jovanovi}, S., et al., AN GLE: A PC Code for Semi con -duc tor De tec tor Ef fi ciency Cal cu la tions, J. Radioanal.Nucl. Chem., 218 (1997), 1, pp. 13-20

[2] Jovanovi}, S., Dlabac, A., Mihaljevi}, N., AN GLEv2.1 – New Ver sion of the Com puter Code for Semi -con duc tor De tec tor Gamma Ef fi ciency Cal cu la tions,Nucl. Instr. and Meth., A 622 (2010), 2, pp. 385-391

[3] Mihaljevi}, N., et al., “EXTSANGLE” – An Ex ten -sion of the Ef fi ciency Con ver sion Pro gram“SOLANG” to Sources with a Di am e ter Larger thanthat of the Ge De tec tor, J. Radioanal. Nucl. Chem.,Ar ti cles, 169 (1993), 1, pp. 209-218

[4] Jovanovi}, S., Dlabac, A., AN GLE Soft ware,www.angle4.com

[5] Lepy, M. C., et al., Intercomparison of Ef fi ciencyTrans fer Soft ware for Gamma-Ray Spec trom e try,Appl. Radiat. Isot., 55 (2001), 4, pp. 493-503

[6] Sima, O., Ar nold, D., Trans fer of the Ef fi ciency Cal i -bra tion of Ger ma nium Gamma-Ray De tec tors Us ingthe GESPECOR Soft ware, Appl. Rad. Isot., 56(2002), 1-2, pp. 71-75

[7] Pi ton, F., et al., Ef fi ciency Trans fer and Co in ci denceSum ming Cor rec tions for g-Ray Spec trom e try, Appl.Radiat. Isot., 52 (2000), 3, pp. 791-795

[8] Vidmar, T., EFFTRAN – A Monte Carlo Ef fi ciencyTrans fer Code for Gamma Ray Spec trom e try, Nucl.Instr. and Meth., A 550 (2005), 3, pp. 603-608

[9] Abbas, K., et al., Re li abil ity of Two Cal cu la tionCodes for Ef fi ciency Cal i bra tions of HPGe De tec tors, Appl. Radiat. Isot., 56 (2002), 5, pp. 703-709

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...44 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Ta ble 6. Com par i son be tween ex per i men tal and cal cu lated (by AN GLE 4) de tec tion ef fi cien cies – sum mary

Source/ref er encesource

En ergy range[keV]

Num ber ofen er gies

De tec tor 2 ´ 2 De tec tor 3 × 3

Av er age arith me ticdis crep ancy

Av er age ab so lutedis crep ancy

Av er age arith me ticdis crep ancy

Av er age ab so lutedis crep ancy

P5/P4 59.53-1408.01 11 1.01% 1.01% 0.50% 1.44%

P6/P4 59.53-1408.01 11 0.62% 1.62% 0.51% 1.72%

P7/P4 59.53-1408.01 11 1.53% 1.91% 1.40% 2.01%

P8/P4 59.53-1408.01 11 0.56% 1.96% –0.19% 2.19%

P9/P4 59.53-1408.01 11 –0.03% 2.71% 0.87% 2.57%

P10/P4 59.53-1408.01 11 0.73% 3.01% 0.94% 3.06%

200 ml/P4 121.78-1408.01 6 5.78% 5.78% –1.30% 1.48%

300 ml/P4 121.78-1408.01 6 5.59% 5.59% –0.69% 1.03%

300 ml/200 ml 121.78-1408.01 6 –0.24% 0.49% 0.56% 0.66%

400 ml/P4 121.78-1408.01 6 5.32% 5.32% –1.61% 1.61%

400 ml/200 ml 121.78-1408.01 6 –0.52% 0.55% –0.36% 0.95%

400 ml/300 ml 121.78-1408.01 6 –0.28% 0.44% –0.92% 0.92%

Mean 1.67% 2.53% –0.03% 1.64%

[10] Vidmar, T., et al., Test ing Ef fi ciency Trans fer Codesfor Equiv a lence, Appl. Radiat. Isot., 68 (2010), 2, pp.355-359

[11] Stelji}, M., Milo{evi}, M., Beli~ev, P., Mod el ing ofGer ma nium De tec tor and Its Sourceless Cal i bra tion,Nucl Technol Radiat, 23 (2008), 2, pp. 51-57

[12] Moens, L., et al., Cal cu la tion of the Ab so lute Peak Ef -fi ciency of Ge and Ge(Li) De tec tors for Dif fer entCount ing Ge om e tries, J. Radioanal. Chem. Ar ti cles,70 (1982), 1-2, pp. 539-550

[13] Erten, H. N., Aksoyoglu, S., Gokturk, H., Ef fi ciencyCal i bra tion and Sum ma tion Ef fects in Gamma RaySpec trom e try, J. Radioanal. Nucl. Chem. Articles,125 (1988), 1, pp. 3-10

[14] Vidmar, T., Likar, A., On the In vari abil ity of the To talto Peak Ra tio in Gamma-Ray Spec trom e try, Appl.Radiat. Isot., 60 (2004), 2-4, pp. 191-195

[15] Vidmar, T., Likar, A., On the In vari abil ity of the To talto Peak Ra tio in Gamma-Ray Spec trom e try, Appl.Radiat. Isot., 60 (2004), 2-4, pp. 191-195

[16] Moens, L., et al., Cal cu la tion of the Ab so lute Peak Ef -fi ciency of Gamma-Ray De tec tors for Dif fer entCount ing Ge om e tries, Nucl. Instr. and Meth., 187(1981), 2-3, pp. 451-472

[17] Vukotic, P., et al., On the Ap pli ca bil ity of the Ef fec -tive Solid An gle Con cept in Ac tiv ity De ter mi na tionof Large Cy lin dri cal Sources, J. Radioanal. Nucl.Chem., 218 (1997), 1, pp. 21-26

[18] Moens, L., Hoste, J., Cal cu la tion of the Peak Ef fi -ciency of High Pu rity Ger ma nium De tec tors, Appl.Radiat. Isot., 34 (1983), 8, pp. 1085-1095

[19] Mihaljevi}, N., Dlaba~, A., Jovanovi}, S., Ac count ing for De tec tor Crys tal Edge Round ing in Gamma Ef fi -ciency Cal cu la tions, The o ret i cal Elab o ra tion, andAp pli ca tion in AN GLE Soft ware, Nucl TechnolRadiat, 27 (2012), 1, pp. 1-12

[20] Jackman, K. R., Biegalski, R., Meth ods and Soft warefor Pre dict ing Ger ma nium De tec tor Ab so lute FullEn ergy Peak Ef fi cien cies, J. Radioanal. Nucl. Chem.,279 (2009), 1, pp. 355-360

[21] Slivka, J., Eval u a tion of Ef fi ciency Cal i bra tion Meth -ods of Semi con duc tor Gamma Spec trom e ters, Jour -nal of Re search in Phys ics, 31 (2007), 1, pp. 19-30

[22] Bell, S. J., Judge, S. M., Regan, P. H., An In ves ti ga -tion of HPGe Gamma Ef fi ciency Cal i bra tion Soft -ware (AN GLE v.3) for Ap pli ca tions in Nu clear De -com mis sion ing, Ap plied Ra di a tion and Iso topes, 70(2012), 12, pp. 2737-2741

[23] Miller, M., Voutchkov, M., Mod el ing the Im pact ofUn cer tainty in De tec tor Spec i fi ca tion on Ef fi ciencyVal ues of a HPGe De tec tor Us ing AN GLE Soft ware, Nucl Technol Radiat, 28 (2013), 2, pp. 169-181

[24] De Corte, F., et al., In tro duc tion of Marinelli Ef fec tive Solid An gles for Cor rect ing the Cal i bra tion of NaI(Tl) Field Gamma-Ray Spec trom e try in TL/OSL Dat ing,J. Radioanal. Nucl. Chem., 257 (2003), 3, pp. 551-555

[25] Mrdja, D., et al., Con tri bu tion of 210Pb Brems strah -lung to the Back ground of Lead Shielded GammaSpec trom e ters, Nucl. Instr. Meth. Phys. Res., A, 572(2007), 2, pp. 739-744

[26] Bikit, I., et al., Pro duc tion of X-Rays by Cos mic RayMuons in Heavily Shielded Gamma-Ray Spec trom e -ters, Nucl. Instr. Meth., A, 606 (2009), 3, pp. 495-500

[27] ***, ORTEC, AN GLE Soft ware, www.ortec on line.com/So lu tions/Soft ware/in dex.aspx?tab=3#An gle

[28] Badawi, M. S., et al., New Al go rithm for Study ing theEf fect of Self At ten u a tion Fac tor on the Ef fi ciency ofg-Ray De tec tors, Nucl. Instr. Meth., A, 696 (2012), 1,pp. 164-170

[29] Badawi, M. S., et al., New An a lyt i cal Ap proach toCal i brate the Co-Ax ial HPGe De tec tors In clud ingCor rec tion for Source Ma trix Self At ten u a tion, Appl.Radiat. Isot., 70 (2012), 12, pp. 2661-2668

[30] Badawi, M. S., et al., An Em pir i cal For mula to Cal cu -late the Full En ergy Peak Ef fi ciency of Scin til la tionDe tec tors, Appl. Radiat. Isot., 74 (2013), 1, pp. 46-49

[31] El Khatib, A. M., et al., New An a lyt i cal Ap proach toCal i brate the NaI(Tl) De tec tors Us ing Spher i cal Ra -dio ac tive Sources, Rad. Prot. Do sim e try, 156 (2013),1, pp. 109-117

[32] El Khatib, A. M., et al., Com pu ta tion of the Full En -ergy Peak Ef fi ciency of an HPGe De tec tor Us ing aNew Com pact Sim u la tion An a lyt i cal Ap proach forSpher i cal Sources, Jour nal of En gi neer ing Sci ence &Tech nol ogy, 8 (2013), 5, pp. 623-638

[33] El Khatib, A. M., Krar, M. E., Badawi, M. S., Study -ing the Full En ergy Peak Ef fi ciency for a Two g-De -tec tors Com bi na tion of a Dif fer ent Di men sions, Nucl.Instrum. Meth ods, A, 719 (2013), 1, pp. 50-56

[34] Badawi, M. S., et al., A New Math e mat i cal Model forDe ter min ing the Full En ergy Peak Ef fi ciency of anAr ray of Two Gamma De tec tors Count ing Rect an gu -lar Parallelepiped Sources, Nucl Technol Radiat, 28(2013), 4, pp. 370-380

[35] Badawi, M. S., El Khatib, A. M., Krar, M. E., NewNu mer i cal Sim u la tion Ap proach to Cal i brate theNaI(Tl) De tec tors Ar ray Us ing Non Ax ial Ex tendedSpher i cal Sources, Jour nal of In stru men ta tion, 8(2013), 11, P11005

[36] Krar, M. E., El Khatib, A. M., Badawi, M. S., NewNu mer i cal Al go rithm Method Con sid er ing the SelfAb sorp tion of the Spher i cal Ra dio ac tive Sources Ma -trix to Cal i brate a Sys tem of Two NaI g-De tec tors,Jour nal of Nu clear Tech nol ogy, Amer i can Nu clearSo ci ety, 187 (2014), 2, pp. 208-219

[37] Badawi, M. S., et al., An Ap proach to Eval u ate the Ef -fi ciency of g-Ray De tec tors to Use It for De ter min ingRa dio ac tiv ity in En vi ron men tal Sam ples, Jour nal ofChi nese Phys ics C., 38 (2014), 6, 066203

[38] El Khatib, A. M., et al., Study on the Ef fect of the SelfAt ten u a tion Co ef fi cient on g-Ray De tec tor Ef fi ciency Cal cu lated at Low and High En ergy Re gions, Jour nalof Nu clear En gi neer ing and Tech nol ogy., 46 (2014),2, p. 217

[39] Badawi, M. S., et al., A Nu mer i cal Ap proach to Cal -cu late the Full En ergy Peak Ef fi ciency of HPGe WellType De tec tors Us ing the Ef fec tive Solid An gle Ra -tio, Jour nal of In stru men ta tion, 9 (2014), 7, P07030

[40] Abbas, M. I., et al., Cal i bra tion of a Sin gle Hex ag o nalNaI(Tl) De tec tor Us ing a New Nu mer i cal Sim u la tionMethod Based on the Ef fi ciency Trans fer Method,Nucl. Instrum. Meth ods. Phys. Res. A., 771 (2015), 1,pp. 110-114

[41] Dlabac, D. A., et al., AN GLE 4 for NaI Ver i fi ca tion,Ex per i men tal Data, an gle.dlabac.com/angle4_nai_ver i fi ca tion.html

Re ceived on Feb ru ary 1, 2015Ac cepted on March 18, 2015

A. A. Thabet, et al.: Ex per i men tal Ver i fi ca tion of Gamma-Ef fi ciency ...Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46 45

A. A. Thabet, et al.: Ex per i men tal Verification of Gamma-Ef fi ciency ...46 Nu clear Tech nol ogy & Ra di a tion Pro tec tion: Year 2015, Vol. 30, No. 1, pp. 35-46

Abuzeid A. TABET, Aleksandar D. DLABA^, Slobodan I. JOVANOVI],Mohamed S. BADAVI, Nikola N. MIHAQEVI], Ahmed M. EL-HATIB,

Mona M. GAUDA, Mahmud I. ABAZ

EKSPERIMENTALNA PROVERA SOFTVERA ANGLE 4 U DELUPRORA^UNA EFIKASNOSTI SCINTILACIONIH DETEKTORA

GAMA ZRA^EWA

Softver AN GLE za prora~un efikasnosti poluprovodni~kih detektora gama zra~ewa, {iroko rasprostawen i odavno u upotrebi, nedavno je nadgra|en za kori{}ewe kod scintilacionih NaI detektora. Ova opcija figuri{e u posledwoj verziji AN GLE 4 i u radu je ukratko prikazana.Posebno je nagla{ena tzv. “diskretizacija” krive referentne efikasnosti, {to otvara mogu}nostupotrebe softvera AN GLE 4 na pojedina~nim gama-energijama, tj. bez prethodnog odre|ivawareferentne krive. Ovo doprinosi ne samo boqoj upotrebqivosti i ve}oj pouzdanosti metode isoftvera, nego i smawuje mogu}nosti za sistematske gre{ke. Rad je prvenstveno usmeren naeksperimentalnu proveru softvera AN GLE 4 kod NaI detektora. Kori{}ena su dva detektorarazli~itih karakteristika (2 ́ 2 i 3 ́ 3 in~a). Komercijalni kalibrisani gama-izvori (ta~kasti icilindri~ni) i rastvori pripremqeni u sopstvenoj izradi (razbla`ivawem kalibrisanihrastvora), mereni su na razli~itim rastojawima od detektora, u opsegu 0-50 cm. Posmatran jeenergetski opseg 59-1408 keV. Ova raznovrsnost uslova merewa koja se ti~e detektora, izvora,rastojawa izvor-detektor, razmatranih gama-energija i drugog, imala je za ciq da obezbedi {to{iru eksperimentalnu osnovu za proveru metode i softvera. Eksperimentalno dobijeneefikasnosti upore|ivane su sa onim dobijenim prora~unom pomo}u AN GLE 4. Postignuta je veomadobra saglasnost – uvek u granicama merne nesigurnosti – ~ime je potvr|ena pouzdanost softvera za kori{}ewa u NaI kvantitativnoj gama-spektrometriji.

Kqu~ne re~i: gama-spektrometrija, scintilacioni detektor, prora~un efikasnosti,..........................softver AN GLE, eksperimentalna provera