các phương pháp hiệu chỉnh hiệu suất cho hệ phổ kế gamma

8/11/2019 Cc phng php hiu chnh hiu sut cho h ph k gamma

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Cc phng php hiu chnh hiu sut cho h ph k gamma

ng Nguyn Phng

[email protected]

Ngy 13 thng 9 nm 2014

1 M u

Hiu sut ghi ca mt detector i vi mt ngun phng x ph thuc vo cc yu t sau

Khong cch t ngun o n detector

Hnh dng ca ngun o

S t hp th bn trong ngun o

Trng phng ngu nhin do hot ca ngun ln

Trng phng tht khi ngun o t gn

Tc phn r ca ngun trong thi gian o

H in t

Bn cnh , i vi mu o l mu mi trng, cc nhn t khc cng gy nh hng ln hiusut l cu hnh o ca h, mt v thnh phn ha hc ca mu o.

i vi mi nhn t gy nh hng, ta cn s dng mt phng thc hiu chnh thch hp. Dos lng nhn t nh hng l kh nhiu khng th bao qut ht ch trong mt ti liu ngn,v vy nn trong ti liu ny tc gi ch xin gii thiu qua mt s phng php hiu chnh hiusut ghi ca h ph k gamma cho hai hiu ng trng phng v t hp th trong ngun o.

2 Hiu chnh trng phng

2.1 nh ngha trng phng

Hiu ng trng phng (coincidence effect) l hiu ng xy ra khi hai hoc nhiu hn hai tiagamma c pht ra cng n detector trong khong thi gian phn gii ca detector v cghi nhn nh l mt xung duy nht.

Ta bit rng tia gamma c sinh ra do s dch chuyn ca ht nhn khng bn trng thikch thch v trng thi c bn hoc l nhng trng thi thp hn. Ty vo mi ng v phngx m mt ht nhn c th bao gm mt s mc nng lng trung gian pht tia gamma tngng vi mc nng lng . V mi chui pht gamma lin tip nh vy c gi l hin tngni tng (cascade transition) (Hnh1).

Trong qu trnh dch chuyn ni tng, c nhng mc trung gian ht nhn tn ti rt ngn, vo

c1010

n1020

s, trc khi pht tia gamma tr v trng thi bn hn. Bn cnh , trongcc h ph k gamma, c bit l cc h ph k bn dn o phng x mi trng, p ng thigian ca h o l vo cs c th thu thp c nng lng m tia gamma li trong vng

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ng Nguyn Phng Ti liu ni b NMTP

Hnh 1: Minh ha hin tng pht gamma ni tng trong phn r 60Co (tri) v 133Ba (phi)

nhy ca detector v to khong thi gian cht h o c th phn bit c nng lng catng bc x ring bit. Do s chnh lch kh ln gia thi gian tn ti ca cc trng thi kchthch ca ht nhn v thi gian phn gii ca h o s lm xut hin hin tng trng phngkhi c hai hay nhiu hn cc tia gamma i vo trong detector v c ghi nhn mt cch ngthi.

2.2 Phn loi hiu ng trng phng

Hiu ng trng phng c chia lm hai loi l hiu ng trng phng ngu nhin (randomcoincidence effect) v hiu ng trng phng thc (true coincidence effect) hay cn gi l hiung trng phng tng (summing coincidence effect). Bng1trnh by s so snh gia hai hiung trng phng ny.

Bng 1: Phn loi hiu ng trng phng

Trng phng thc Trng phng ngu nhin

(true-coincidence summing) (random summing)

Trng phng bi cc tia gamma ca cngmt ht nhn

Trng phng bi cc tia gamma khngcng mt ht nhn

Khng ph thuc vo hot ngun Ph thuc vo hot ngun

Hiu chnh trng phng:

Gim tc mGamma gamma

Gamma tia X (K, L)

Gamma bremsstrahlung

Ti liu ny ch trnh by cc cch thc hiu chnh trng phng thc, cho thun tin tht nay v sau thut ng trng phng thc s c gi tt l trng phng

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2.3 Trng phng thc

Trng phng thc l trng phng bi cc tia gamma ca cng mt ht nhn v n khng phthuc vo hot ngun, xy ra i vi ht nhn phn r hai hay nhiu photon trong khongthi gian phn gii ca detector.

Hu ht nhng trng hp phn r ca ht nhn m n nhng trng thi bn ca ht nhncon th pht ra mt vi tia gamma hoc tia X trong tng mc phn r. Nu nh hai tia gammavi nng lng khc nhau c pht ra trong cng mt lc ca mt ht nhn phn r, v chngc pht hin trong thi gian m h o c th nhn bit c chng, hai tia gamma ny gyra hin tng trng phng thc. Detector s tch ly nhng nng lng ca hai gamma phtra li vng hot ng detector. Kt qu l, nhng hin tng ny gy ra hin tng trngphng thm v trng phng mt t nng lng nh ton phn ca tia gamma v nh vy vicphn tch xc nh nng lng nh ton phn s sai. Do , s hiu chnh nng lng nh tonphn cho hiu ng trng phng thc l cn thit.

Khi nng lng nh ton phn ca gamma 1 v gamma 2 b mt trong trng hp ny c s

sut hin ca nng lng nh ton phn ca gamma 3 dn n lm tng s m nh. Hnna detector c th tch ly nng lng ton phn ca gamma 1 v mt phn nng lng tgamma 2 dn n mt s m nng lng ton phn ca gamma 1 hoc gamma 2. Do khihiu chnh cn phi xc nh hiu sut tng ca tng gamma hiu chnh cho tng trnghp tng mt.

H s hiu chnh trng phng thc ph thuc vo tng loi detector, yu t hnh hc v chuiphn r ca tng ht nhn, trng phng c th xy ra gia mt tia gamma vi tia gamma khc,tia X (K, L) hoc bc x bremsstrahlung.

Phn loi trng phng thc

Trng phng thm (summing in): l hin tng trng phng lm tng s m nh.Trng hp cc tia gamma i vo detector, cng li ton b nng lng trong vnghot ng detector v nng lng tng cng ny cng bng vi nng lng ca mt tiagamma khc pht ra t ngun th ta s c hin tng trng phng thm, ng ngha vivic mt s m c cng thm vo trong mt nh gamma ca ph (Hnh2).

(a) (b) (c)

Hnh 2: Minh ha hin tng trng phng thm, nh gamma 30c ng gp thm s mt cc s kin trng phng ca cc nh (a) 32v 20(b) 31v 10(c)32,21v 10.

Trng phng mt (summing out): l hin tng trng phng lm mt s m nh. l trng hp m mt tia gamma i vo trong detector v li ton b nng lng trongvng nhy ca detector nhng li b trng phng vi cc tia gamma khc cng li ton

b hay ch mt phn nng lng trong detector, iu ny s lm mt i s m nhnng lng ton phn ca tia gamma quan tm (Hnh 3).

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(a) (b) (c)

Hnh 3: Minh ha hin tng trng phng mt, gia cc nh (a) 30v31(b) 31v20(c)20,21v 10.

Trng hp cc tia gamma vo detector v lm mt ton b nng lng ca mnh trongvng nhy m nng lng ny khng ng vi bt k mt tia gamma no khc cng phtra t ngun th trn ph s xut hin mt nh mi tng ng vi tng nng lng ca

cc tia gamma, nh ny c gi l nh tng (sum peak) (Hnh4).

2.4 V d n gin

Ta xt mt v d hiu ng trng phng khi o ngun 60Co (Hnh4), hai tia gamma c nnglng 1173v 1332keVpht ra t ngun ny xut hin trong khong thi gian cch nhau rtnh nn detector ghi nhn nh mt tia gamma c nng lng bng tng nng lng hai tia ringbit. Khi hiu sut ghi hai tia ring bit gim i v trn ph sut hin thm mt nh ngvi nng lng tng (2505keV).

Hnh 4: Minh ha hin tng trng phng thc trong ghi nhn ph 60Co

Gi 1, 1 ln lt l hiu sut thc ca tia 1, 2 v1, 2, s ln lt l hiu sut ghi nhnc ca tia 1,2v nh tng. Ta c th vit

1= 1(1 a2T2) (1)

Trong ,a2T2l xc sut ghi tia2(a2l t s phn nhnh ca 2vT2l hiu sut tng ghinhn tia 2)

2= 2(1 a1T1) (2)

Trong , a1T1l xc sut ghi nhn tia 1v(1 a1T1)l xc sut khng ghi nhn tia 1.

T ta c th suy ra hiu sut ghi nhn nh tng

s = 12 (3)

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Vi trng hp s phn r phc tp ta c cng thc phc tp hn nhiu v vic tnh tonc thc hin bi mt phn mm chuyn dng cho php ta hiu chnh hiu sut ghi cc nhkhi c trng phng.

2.5 Hiu chnh trng phng thc

C kh nhiu phng php hiu chnh cho trng phng thc, di y l mt s phngphp tiu biu nht

Phng php t s theo khong cch c a ra bi Kafala (1994), v c p dng hiu chnh trng phng cho trng hp ngun im. Phng php ny da trn quan strng t s hiu sut nh c o cc khong cch khc nhau th khng i theo nng lng(Hnh5).

Hnh 5: T s ca ca hiu sut nh c theo nng lng c o bi detector HPGe ngtrc cc khong cch khc nhau

hiu chnh trng phng trong thc nghim ngi ta thng lm nh sau

Dng mt ngun chun kt hp vi ngun cn hiu chnh trng phng v o hai ngunny cch nhau cc khong cch xa v gn i vi detector.

Gi N l tc m ca gamma ti nh sau khi hiu chnh thi gian cht v s phn

r trong qu trnh o vi ch s di l ch ngun chun khng trng phng (r) hayngun o (s)

Nr/s =

C

(1 etc)etd

r/s

(4)

ViCl din tch nh, tcl thi gian o, tdl thi gian phn r v l hng s phn r.

Sau khi tnh c tc m i vi ngun chun v ngun o, lp t s cc khongcch gn v xa detector ta suy ra c cng thc

Rf =

NrNs

f

vRn=NrNs

n

(5)

ViNr l tc m ca ngun chun khng trng phng, Ns l tc m ca nguno,RnvRfln lt l t s ca tc m ti v tr gn v xa detector.

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Vi ngun c trng phng xy ra, tc m ti v tr gn u d s chu nh hng catrng phng do s thp hn tc m ti v tr xa. Nu ngun chun l ngun khngc trng phng th khng c s mt s m do trng phng. Khi h s trng phngc nh ngha nh l t s RntrnRfi vi cu hnh tng t nhau

Cf = RnRf (6)

Trng phng khng ng k khi Cf = 1v ngc li ng k khi Cf= 1.

Phng php ny c u im d s dng, khng cn n thng tin v chui phn r ca ngunv din tch nh.

Phng php ng cong P/T trong phng php ny, bn cnh vic s dng thng tinv hiu sut nh ta cn cn s dng thm thng tin hiu sut tng. Hiu sut tng l h srt quan trng trong vic tnh ton h s hiu chnh, bi v s mt tc m trong nh nng

lng ton phn cho mt tia gamma th t l vi hiu sut tng cho nhng tia gamma khctrong tng trng hp.

Hiu sut nh nng lng ton phn (p) v hiu sut tng (t) c mi quan h vi nhau bit s nh trn tng P /T (Hnh6)

P/T =pt

(7)

Hnh 6: ng cong P /T theo nng lng c o bi detector HPGe ng trc

Bng cch xy dng ng cong t s P /Ttheo nng lng, ta c th xc nh c hiu sutnh khi khng xy ra hin tng trng phng thng qua hiu sut tng (t ph thuc vo hintng ny), t c th d dng xc nh c h s hiu chnh trng phng.

Phng php ma trn xc sut dch chuyn phng php ny da trn vic tnh toncc ma trn dch chuyn nhm tnh ra cc xc sut m hai hay nhiu tia gamma trng nhau.Ngoi ra ta cng cn lu rng khng ch c bc x gamma gy hiu ng trng phng mnhng bc x khc cng gy ra hiu ng trng phng thc vi tia gamma, chng hn nh tiaX (do bin hon trong hay bt electron), bc x hm, bc x hy cp. Do cng cn a ccxc sut ny vo trong tnh ton.

Trong phng php ny, hiu chnh bc 1 ch lin quan ti s kt hp ca hai tia gamma trngphng, v cc hiu chnh bc cao hn lin quan ti s trng phng ca nhiu hn hai tia gamma.

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Gi s ta c mt s phn r tng qut nh trong Hnh 7,ng vi phn r beta, bt electronhay tia gamma kh kch thch. i vi phn r + s c mt mc o ti v tr 511keV. Nu khiu cc mc vi ch s i, ta c vector dng fth hin xc sut ht nhn m phn r n tngmc tng ng theo ch s ic dng

f=f0 f1 fn

(8)

vin l tng s mc trn mc c bn, i = 0,...,n.

Hnh 7: S phn r tng qut

Cc xc sut dch chuyn c k hiu l xji tng ng vi dch chuyn t mc thjn mcthi, trong trng hp ny xji l mt phn t trong ma trn tam gic vung di

x=

0 0 0 0 0

x10 0 0 0 0

x20 x21 0 0 0...

... ...

... . . .

...

xn0 xn1 xn2 xn1 0

(9)

Cc phn tfivxji tha iu kinn

i=1 fi = 1 (10)

j1i=1

xji = 1 vij= 1,...,n (11)

Chng ta s tip tc xy dng cc ma trn

Ma trncth hin s gamma thc s pht ra hiu chnh h s bin hon trong (internalconversion coefficient) ji

cji = xji1 + ji

(12)

Ma trn a th hin xc sut ghi nhn nh quang in v l hm ca hiu sut nh

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nng lng ton phnpjiaji = cji

pji (13)

Ma trneth hin xc sut gamma c ghi nhn trong detector v l hm ca hiu suttng tji

eji = cjitji (14)

Ma trnb th hin xc sut khng ghi nhn gamma

bji = xji eji (15)

m hnh ha ton b cc nhnh phn r v trng phng chng ta a vo ma trn Ath hin cho chui phn r c ghi nhn

A=n

k=1

ak (16)

Ma trnB h hin cho chui phn r khng c ghi nhn

B = E+n

k=1

bk (17)

ViEl ma trn n v E= diag(1)

Ta xy dng hai ma trn NvMl hm ca ma trn B

N = diag ([fB]i) (18)M = diag(Bi0) (19)

Trong Nl ma trn th hin xc sut dch chuyn v cc mc thp hn v Ml matrn th hin xc sut dch chuyn v mc c bn.

ph cp ca nh quan tm c cho bi ma trn S

S= RNAM (20)

viR l i lng v hng th hin tc pht ca ngun.

i lng S th hin ph cp quan tm khi c hiu ng trng phng. Ngoi ra chng ta

cng xy dng thm mt i lng S0 th hin khi hiu chnh bc khng tc l khng c trngphngS0 =RN0A0M0 (21)

H s hiu chnh trng phng chnh l t s gia SvS0

fji =SjiS0ji

= (NAM)ji(N0A0M0)ji

(22)

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3 Hiu chnh hiu ng t hp th

3.1 Hiu ng t hp th

i vi ngun th tch hay mu o mi trng th mt s tia gamma pht ra b mt mt phnhay ton b nng lng ca chng trong ngun (mu) trc khi ri khi ngun (hp ng mu).Kt qu ny lm gim bt s tia gamma c ghi nhn bi detector. nh hng ny gi l s tsuy gim (self-attenuation) hay s t hp th (self-absorption). Mc t hp th ph thucvo hnh hc (b dy, th tch mu) v cht nn (matrix) ca mu.

Hot ca cc ng v phng x trong ngun (mu) c tnh ton t ng cong hiu sut(E) c xc nh bng cch s dng ngun/mu chun (standard source). Trong thc t,khng phi lc no vt liu mu o v mu chun l hon ton ging nhau. Cc mu mi trngc th thay i rt ln v thnh phn ho hc, mt ca chng c th thay i t gn 0 chon gn 2.0g/cm3. Nu cc mu chun v cc mu cn kho st c s khc nhau v tnh cht tsuy gim ca photon (thng thng l khc nhau v cht nn hay mt ) th ta cn phi avo h s hiu chnh hiu sut ghi nhn cho khc bit t hp th gia cc mu ny vi nhau.

3.2 Phng trnh t hp th

hiu chnh s t hp th cho tc m ca nh ph gamma Rchng ta c th s dngphng trnh n gin

R0= Rt

1 et (23)

vitl b dy ca mu v l h s suy gim tuyn tnh nng lng thch hp ca vt liulm thnh mu. Vic p dng phng trnh (23) l n gin khi m h s suy gim cbit. Nu matrix ca mu khng phi l mt hp cht n gin, gi tr ca hu nh khngbit. i vi nhiu loi matrix gi tr hiu dng c th c c lng t nhng vt liu tngt. Nu hp cht ca mu c thit lp hp l mt phng php c lng h s hp thkhi/cho hp cht t cc h s hp th khi ca cc thnh phn (/)ic trnh by theocng thc

=

fi

i

(24)

vifil t s ca mi thnh phn ring bit v l mt tng ng.

3.3 Cc phng php hiu chnh t hp th cho ngun/mu hnh tr

Phng php truyn qua (transmission method) c a ra bi N.H. Cutshall v cng s

(1983) da trn nguyn l ca s suy gim tia gamma khi truyn qua vt chtI=I0e

x (25)

trong Il cng ca chm tia sau khi truyn qua, I0l cng chm tia ban u, lh s suy gim ton phn (total attenuation coefficient) (cm2/g), l mt vt cht (g/cm3)vx l b dy ca lp vt cht truyn qua.

Phng trnh t hp th

R= R01 ex

x (26)

trong R l cng pht ca ngun khi c hiu ng t hp th cn R0l cng pht khikhng c hiu ng t hp th.

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H s hiu chnh t hp th c tnh nh sau

f=R0R

= x

1 ex =

ln(I/I0)

I/I0 1 (27)

Nh vy, xc nh c h s hiu chnh t hp th fta cn tnh c t s I/I0 =e

x.i vi mt ngun hay mu phng x bit trc thnh phn, vic xc nh cc h s , vxl ht sc n gin. Tuy nhin i vi nhng ngun khng xc nh c thnh phn (khngxc nh c ), ta c th xc nh bng cch s dng mt ngun im c nng lng gammatng ng vi nh nng lng m ta ang cn quan tm hiu chnh t hp th. Ngun imny c t bn trn mu nh trong Hnh 8.

Hnh 8: Minh ha h o hiu chnh t hp th bng phng php truyn qua

Nu chm tia pht ra t ngun im c chun trc, ta c th d dng xc nh c t sI/I0cng nh h s

(E) =ln(N/N0)

x (28)

viN vN0 l s m ghi nhn c nh nng lng Ekhi c v khng c mu (sau khi tr i ph ghi nhn ca mu trong trng hp ca N).

Trong trng hp chm tia pht ra t ngun im khng c chun trc, vic xc nh chnhxc t s I/I0 cng nh h s s kh khn hn bi v khng phi tt c cc tia gamma utruyn qua lp vt cht x mt khong nh nhau. Trong trng hp , ta c th tin hnh oc thc nghim hoc nh s tr gip ca m phng Monte Carlo xy dng cc mi quanh gia h s truyn qua T = N/N0 v, sau ni suy ra gi tr ca tng ng vi h struyn qua c o vi mu (Hnh9).

Phng php gii tch (bn thc nghim) (semi-empirical method) c xut bi M.Noguchi cng cng s (1980s)

Cch 1: theo cch ny ta s dng mt mu chun c h s suy gim s, cha cng ng v

phng x vi mu cn o (hot bit trc). Mu chun c o vi cc b dy khc nhauv hiu sut ghi nhn ca mu chun sau c lm khp theo hm ph thuc vo b dy

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Hnh 9: Minh ha ng lm khp tng quan gia ln(T)v

mu (Hnh10)

(H) =F

H

1 eAH

A +

1 eBH

B

(29)

viA = + vA = + (trong trng hp ny = s). Cc h s c lm khp y l(,,F).

Hiu sut ghi nhn ca mu o c thnh phn khc vi mu chun (h s suy gim x) c thc tnh da vo cng thc (29) vi gi tr = x.

Hnh 10: S ph thuc ca hiu sut ghi nhn mu chun theo b dy mu

Cch 2:vi cch ny, ta c th xp x cng thc ng cong hiu sut theo b dy mu theo

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GESPECOR(Germanium Spectrometry Correction): phn mm hiu chnh trung phngv t hp th cho ph k germaniumhttp://www.gespecor.de/en/home.html

Cc chng trnh m phng Monte Carlo nh MCNP, GEANT4, EGS,...

Ti liu

[1] K. Debertin, R.G. Helmer,Gamma and X-Ray Spectrometry with Semiconductor Detector,North-Holland, Amsterdam (1988).

[2] Nguyn V Hoi Th,Xy dng chng trnh hiu chnh trng phng cho h ph k gamma,Kha lun tt nghip i hc (2008).

[3] Nguyn Th Cm Thu, Kho st phng nn v ti u ho hiu sut cho h ph k gammaHPGe trong php o mu mi trng, Lun vn tt nghip Thc s (2010).

[4] M LAnnunziata,Handbook of Radioactivity Analysis, 3rd Edition, Academic Press (2012).

[5] M. Noguchi,-ray Spectrometry with a Ge Detector for Environmental Radioactivity Anal-ysishttp://nutec.jaea.go.jp/fnca/common/images/e3.pdf

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http://www.gespecor.de/en/home.htmlhttp://nutec.jaea.go.jp/fnca/common/images/e3.pdfhttp://nutec.jaea.go.jp/fnca/common/images/e3.pdfhttp://www.gespecor.de/en/home.html

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