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Cc c trng ca ph gamma

ng Nguyn [email protected]

Ngy 21 thng 5 nm 2014

1 S hnh thnh ph gamma

Phn ln cc ng v phng x u c kh nng pht ra bc x gamma vi cc mc nng lngv cng khc nhau. ghi nhn ph gamma do mt ng v pht ra phi da vo tngtc gia tia gamma vi vt cht, y chnh l cc detector. Do tng tc gia vt cht trongdetector vi tia gamma rt phc tp nn thay v ch ghi nhn c 1 vch nng lng tngng vi nng lng gamma, ta s ghi nhn c mt ph phn b (spectrum) nh trong Hnh 1.Ph gamma trong thc nghim l mt s phn b lin tc ca cc cao xung (pulse height)trong c cha cc nh nng lng ton phn c b rng xc nh.

Hnh 1: Minh ha ph gamma l tng (hnh trn) v ph gamma thc t (hnh di) ghi nhnc bi detector

Hnh 2 m t mt v d s h thit b ghi nhn ph gamma. Cc qu trnh hnh thnh phgamma gm c

Mt tia (photon) c nng lng E0 i vo detector.

Cc electron s cp (primary electron) vi tng ng nng E sinh ra trong vng nhy

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ng Nguyn Phng Ti liu ni b NMTP

(sensitive volume)1 bi s tng tc ca photon vi vt cht (ch yu l cc electron mitrng) trong vng ny.

Cc electron s cp ny li tip tc to ra mt lng ln cc cp electron th cp (secondaryelectron) l trng thng qua cc phn ng ion ha hay kch thch.

Mt tn hiu xung c bin V c sinh ra u vo tin khuch i (pre-amplifier)vi in dung C.

in th V c khuch i v bin i thnh s ch v tr knh bi Thit b chuyn itng t - s (Analog-to-Digital Converter ADC) ca B phn tch a knh (Multi-Channel Analyzer MCA), mt s m c cng vo s m tng ti v tr knh tngng.

Nhiu tia gamma c ghi nhn v s phn b cao ca xung c hnh thnh (phgamma).

Hnh 2: S tiu biu cho h thit b ghi nhn ph gamma

2 ng chun nng lng theo knh

Mc ch ca vic chun nng lng (energy calibration) l tm ra mi quan h gia v tr knh(channel) trong ph v nng lng ghi nhn tng ng trong detector. Cng vic ny thngc tin hnh trc khi thc hin vic o c ph ca ngun hay mu phng x cn quan tm.

Vic chun nng lng c tin hnh bng cch o ph gamma ca mt s ngun pht gamma bit chnh xc nng lng, sau thit lp mi quan h gia nng lng v v tr knh (khiu l ch). Hm biu din s ph thuc ca nng lng theo knh thng c dng bc nht

E = A+B ch (1)

hoc bc haiE = A+B ch+ C ch2 (2)

trong A, B v C l cc h s thu c t vic lm khp.

1cn gi l vng ghi nhn (detection volume) hay vng hot ng (active volume)

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Hnh 3: V d ng chun nng lng theo knh c lm khp theo hm bc hai (quadratic)

3 Cc nh c trng ca ph gamma

nh nng lng ton phn hay cn gi l nh quang in (photo-peak) c hnh thnhbi cc tng tc m photon b mt ton b nng lng ca n bn trong detector. S mtnng lng ca photon c th thng qua duy nht mt tng tc hp th quang in hoc mtchui tn x Compton (c th cng vi to cp) v kt thc bng hiu ng hp th quang in.

Hnh 4: Minh ha nh quang in

Vng Compton ph ca cc s kin nm trc nh nng lng ton phn c hnh thnhbi cc tn x Compton m photon mt mt phn nng lng ca n trong detector. Ch dcca phn b Compton c gi l cnh Compton (Compton edge), y l v tr ng vi nnglng cc i m photon c th chuyn cho electron trong mt tn x Compton (ng vi gctn x 180).

Khu vc nm gia cnh Compton v nh quang in c gi l vng tn x nhiu ln (multipleCompton scattering hay Compton valley) c hnh thnh do cc s kin tn x nhiu ln bn

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trong detector hoc do cc photon tn x vi gc nh trc khi vo v mt nng lng honton bn trong detector.

Hnh 5: Minh ha vng Compton

nh thot n khi cc photon c nng lng ln hn 2mec2 = 1.022MeV (vi me l khilng ngh ca electron) i vo trong detector, chng c th to ra cc cp electron-positronthng qua hiu ng to cp. Cc electron v positron ny s nhanh chng c lm chm trongmi trng. Sau khi c lm chm, cc positron s kt hp vi cc electron to ra s hy cp(annihilation), qu trnh ny s to ra hai tia gamma vi cng nng lng 0.511MeV , nhngtia gamma ny c th tip tc tng tc vi vt cht trong detector hoc thot ra ngoi. Trnghp mt trong hai tia gamma hy thot ra ngoi s to nn nh thot n (single-escape peak),nh ny nm cch nh quang in mt khong ng bng 0.511MeV (tng ng vi nnglng tia gamma thot ra khi detector).

Hnh 6: Minh ha nh thot n

nh thot i Tng t nh trng hp ca nh thot n nhng trong trng hp nyc hai tia gamma hy thot ra ngoi to nn nh thot i (double-escape peak), nh ny nmcch nh quang in mt khong 1.022MeV (tng ng vi nng lng ca c hai tia gammathot ra khi detector). Ngoi ra, trong trng hp m c hai tia gamma u b hp th, tngtc s ng gp vo trong nh nng lng ton phn ca ph ghi nhn.

nh hy trng hp ny c th c xem nh l trng hp ngc li ca hai nh thot.Trong trng hp ny positron c to ra v hy cp mi trng bn ngoi detector, mttrong hai tia gamma hy lt vo detector v to nn nh hy nm ti v tr ng vi nng lng0.511MeV .

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Hnh 7: Minh ha nh thot i

Hnh 8: Minh ha nh hy

nh tn x ngc c hnh thnh sau khi tia gamma tn x vi mt gc ln ( 120180)vi vt cht mi trng xung quanh detector v sau b hp th trong detector. Tng nnglng ca nh tn x ngc v cnh Compton s bng vi nng lng ca nh quang in, biv c hai u l kt qu ca tn x Compton gc ln ca tia gamma ti. Cc s kin ng gpcho nh tn x ngc ch khi tia gamma mt nng lng ca n trong detector, cn ng gpcho cnh Compton khi electron mt nng lng ca n trong detector.

Hnh 9: Minh ha nh tn x ngc

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4 Cc c trng ca nh ph gamma

4.1 Dng ca nh

Dng chi tit ca cc nh trong ph gamma l quan trng nu chng ta mun din tch nhc tnh mt cch chnh xc, c bit l i vi cc detector c phn gii cao (Hnh 10).

Hnh 10: Minh ha tnh din tch nh ph gamma c ghi nhn bi detector nhp nhy

Trong cc tnh ton n gin, nh ph gamma thng c xp x theo dng phn b Gauss

f(x) = Aexp

[(x x0)

2

22

](3)

trong A l cao nh, x0 l v tr ca nh v l lch chun ca phn b nh.

Tuy nhin, trong nhiu trng hp ta c th thc hin cc m t chi tit cho nh ph bngcch s dng phn b Gauss c hiu chnh m t phn ui pha nng lng thp ca phnb. Phn ui c th xut hin do nhiu hiu ng vt l, bao gm s thu gom in tch khnghon ho trong mt s vng ca detector, hay do cc electron th cp v bc x bremsstrahlungtrong vng th tch hot ng. Hnh 11 trnh by mt v d cho s m t nh gamma cng viui ca n, bn cnh phn m t nh i xng phn b dng Gauss theo nh cng thc (3),ta cn s dng thm mt hm khc m t phn ui phn b c to ra do vic thu thpin tch khng hon ho bn trong vng nhy ca detector

t(x) =1

2exp

(x x0

)erfc

(x x0

+

2

)(4)

Trong , l tham s lm khp m t dc ca phn b, x0 l v tr ca nh, l lchchun ca phn b nh Gauss v hm sai s b tr (complementary error function) erfc(x) cdng

erfc(x) =2pi

x

exp(t2)dt (5)

S khc bit gia ui ngn v ui di trong cu hnh l ui ngn c nhiu hiu ng quantrng hn trn dng ca nh gn y ca n, trong khi ui di thng c th c xem nhl phn ng gp thm vo ca phng nn.

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Hnh 11: Minh ha lm khp ph gamma vi ui phn b, hm G(E) m t phn b nh dngGauss, hm T (E) m t phn b ui v hm B(E) m t phn b phng nn dng bc thang

4.2 Dng ca cnh Compton

Trong mt s trng hp chng hn nh khi xy dng ng chun nng lng cho ph gamma,nu s lng ngun chun khng , ta c th s dng thm thng tin nng lng ca cnhCompton chun. lm c iu ny ta cn phi lm khp xc nh chnh xc nnglng tng ng vi cnh Compton trong ph.

V mt l thuyt, cnh Compton c dng bc thang (step function), tuy nhin do s thngging trong vic ghi nhn nng lng, dng ca cnh Compton l s kt hp gia phn b bcthang v phn b Gauss

f(x) = y0 +A erfc

(x x0

2

)(6)

4.3 phn gii nng lng

Mt trong nhng i lng quan trng nht nh gi ph nng lng ca tia gamma chnh l phn gii nng lng (energy resolution)

R =E

E(7)

i lng ny c s dng nh gi s n rng nh ph do ng gp ca cc nhiu cngnh qu trnh thu thp in tch khng hon ton v s mt mt nng lng khng ging nhauti ca s vo ca detector cng gp phn lm m rng nh ph, do lm gim kh nngphn gii ca detector.

phn gii nng lng khng ch ph thuc vo bn thn detector m cn ph thuc vo ccthit b in t i km theo (ch yu l b tin khuch i) theo cng thc

E2total = E2detector + E

2electronics (8)

i vi cc detector bn dn, lch chun cho thng k ca in tch c to ra bn trongdetector do qu trnh hp th gamma c cho bi

detector =FJ (9)

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vi J l s trung bnh cc cp electron l trng c to ra v F l h s Fano (Fano factor)2. phn gii tng i ca detector c th biu din qua cng thc

Rdetector = 2.35

FJ

J= 2.35

Fw

E(10)

trong , w l nng lng trung bnh cn thit to 1 cp electron l trng (vd: i vigermanium l 2.96eV ) v E l nng lng photon li trong detector.

phn gii tt khng nhng gip ta nhn bit c cc nh k nhau, m cn gip ghi nhnc cc ngun yu c nng lng ring bit khi n nm chng ln min lin tc. Cc detectorc hiu sut bng nhau s c kt qu l cc din tch nh bng nhau, nhng vi nhng detectorc phn gii nng lng tt th s to nn cc nh nng lng hp v cao m n c th nhln cao vng nhiu thng k ca min lin tc. Cc ph so snh c a ra Hnh 12 minhho r v u th ca cc detector c phn gii tt trong trng hp c nhiu cc nh nnglng gamma gn nhau cn c tch ra.

Hnh 12: So snh phn gii gia hai loi detector NaI(Tl) v HPGe

4.4 FWHM

i lng thng uc s dng nh gi phn gii nng lng ca nh ph n nng lb rng ton phn ti mt na chiu cao (full width at half maximum FWHM).

Nu gi s rng nh ph c dng phn b Gauss nh m t trong cng thc (3) vi l lch chun ca phn b, ta c th d dng tnh c mi quan h gia FWHM v

FWHM = 2

2ln2 2.355 (11)

FWHM thay i ty thuc vo loi detector cng nh nng lng gamma ti, gi tr caFWHM ca mt s loi detector thng dng nh

2H s Fano c a ra hiu chnh gia phng sai ca gi tr quan st c (N) vi phng sai cathng k Poisson l thuyt, h s ny c trng cho mi loi vt liu. Gii hn thng k ca phn gii ctnh theo cng thc

Rstatistical limit = 2.35(F/N)

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Hnh 13: Minh ha FWHM

NaI(Tl): gi tr FWHM tng i ti nh 661.7keV (137Cs) l vo khong 67%, tngng vi khong 40keV

HPGe: c gi tr FWHM ti nh 1332keV l vo khong khong 1.5 2.0keV . phngii nng lng ca cc detector germanium tinh khit i vi bc x gamma thng lnh hn 1%.

Cc gi tr ca FWHM thng c lm khp theo nng lng hoc theo knh vi cc dngsau

FWHM =A+B E (12)

FWHM = A+BE (13)

FWHM = A+B E + C E2 + . . . (14)

Hnh 14: V d FWHM c lm khp theo nng lng vi dng hm bc hai (quadratic)

4.5 FWTM

Nh cp n trong Phn 4.1, dng ca nh ph khng hon ton tun theo phn bGauss. Mt phng php ch ra c trng ca phn ui ca mt nh ph l s dng b

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rng ton phn mt phn mi chiu cao (full width at one-tenth maxium FWTM hayFW.1M) ca nh nng lng ton phn. i vi cc detector c cht lng tt vi ui nh,FWTM s nh hn hai ln FWHM (t l FWTM/FWHM i vi nh dng Gauss thuntu l 1.823).

Ngoi ra, mt ch s khc cng thng c s dng l t l ca b rng ton phn 1/50 chiucao (FWFM) trn FWHM , thng thng c o 1.333MeV . Cc detector germanium ttc gi tr ca t l ny nm gia 2.5 v 3.0, t l ny l 2.376 ca dng Gauss thun tu.

Hnh 15: Minh ha cc gi tr phn gii nh FWHM , FWTM v FWFM

5 Phng nn ph gamma

5.1 Phng nn Compton

Vng phng nn Compton xut hin khi nng lng ton phn ca photon ti khng c hpth hon ton trong detector v thot ra khi detector vi ch mt phn nng lng ca nc ghi. Cc nh nng lng ring phn ny xut hin trong ph gamma nh l cc s kinngu nhin trc nh nng lng ton phn v c gi l min Compton hay lng Compton(Compton continuum).

T s ca din tch nh nng lng ton phn trn lng Compton c gi l t s nh/Compton(peak-to-Compton hay P/C ratio). i vi cc detector hin i chng hn nh cc detectorgermanium, t s P/C thng thng nm trong khong gia 40:1 v 60:1 i vi nh nnglng 1.332MeV ca ngun 60Co. Cc detector c kch thc ln c th t c t s P/C gn100:1.

lm tng t s nh/Compton, ngi ta xy dng cc h thng kh nhiu Compton(Compton suppression). Do nng lng thot ra thng di dng cc photon, cho nn ta cth thu li nng lng tht thot bng mt detector khc. Detector ny thng l cc tinhth c kch thc ln lm bng mt vt liu r tin hn chng hn nh NaI, plastic,... v thngc gi l detector che chn (shield detector). Bng cch thit lp mi tng quan gia cc skin trong detector ghi nhn v detector che chn vi cc thit b in t o thi gian (timingelectronics), cc s kin c ghi nhn trong detector che chn c th c s dng loi b

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ng thi cc s kin trong detector ghi nhn. Kt qu s lm trit tiu vng lng Comptonca ph gamma c ghi nhn, v lm gim phng mt cch ng k (Hnh 16). Trong mt sh thng kh nhiu Compton, t s P/C c th t ti 800:1.

Hnh 16: So snh ph ca ngun 60Co trc v sau khi trit Compton, detector ghi nhn lmbng tinh th Ge v detector che chn lm bng BGO (bismuth germanate)

Ngoi t s P/C, ngi ta cn s dng mt t s khc nh gi phng nn Compton, lt s nh/ton phn (peak-to-total hay P/T ratio).

5.2 Phng nn bc x hm

Bc x hm (bremsstrahlung) l bc x in t sinh ra tng tc gia electron nhanh vi trngCoulomb ca ht nhn. Bc x hm cng sinh ra trong trng hp cc ht mang in khc blm chm trong mi trng vt cht. Tuy nhin, bc x hm ch ng k i vi cc ht nhmang in. Bc x in t ny c ph lin tc v phn ln nm vng tia X.

S sinh ra bc x hm cng ng k khi nng lng ca electron cng ln v mi trng lmchm c nguyn t s Z cng ln. V d nh electron c nng lng 1MeV sinh ra bc x hmng k trong ch (Z = 82) nhng khng ng k trong nhm (Z = 13).

S xut hin bc x hm s lm vng ph c nng lng thp b dng cao. iu ny lm tngphng nn ca cc nh c nng lng thp v nh hng n chnh xc ca php o. Trongtrng hp ca ngun 28Al, do electron pht ra c nng lng cc i 2.8MeV nn lm tngphng vng nng lng thp ng k (Hnh 17).

5.3 Phng nn phng x t nhin

Mi trng xung quanh chng ta lun tn ti cc ht nhn phng x. Cc ht nhn ny c thc to ra do tia v tr tng tc vi cc ht nhn khc trong bu kh quyn xung quanhTri t, do s tin b ca khoa hc trong lnh vc ht nhn, hay c ngun gc t thu tora v tr. Thng thng, cc ht nhn ny thng c hot thp. Tuy nhin, do s tn tikhp mi ni ca chng, trong c mu o, ngay bn trong v xung quanh detector nn cngnh hng ng k n cc php o cc mu mi trng c hot thp. Vic nm vng cc

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Hnh 17: Ph bc x hm ca electron c nng lng cc i 2.8MeV ca 28Al

tia gamma do cc ht nhn phng x pht ra s gip chng ta c nhng hiu chnh cn thitkhi xc nh din tch ca nhng nh gamma m chng ta quan tm. Hnh 18 trnh by phphng nn phng x t nhin c o bng nhiu loi detector khc nhau.

Hnh 18: So snh ph phng nn phng x t nhin ca cc loi detector khc nhau

Ngun phng x trong mi trng c chia lm hai loi: ngun phng x t nhin v ngunphng x nhn to. Cc ngun phng x t nghin gm hai nhm: nhm cc ng v phng xnguyn thy (c t khi to thnh tri t) v v tr v nhm cc ng v phng x c ngungc t v tr (c tia v tr to ra). Ngun phng x nhn to do con ngi ch to bngcch chiu cc cht trong l phn ng ht nhn hay my gia tc hoc t cc v th nghim vkh ht nhn

Phng x c ngun gc do bc x v tr cc bc x n t v tr, ch yu l t ngoih Mt tri ca chng ta, c th l chm ht photon nng nng lng cao, ht muon, hay chmht nng mang in. Cc bc x ny tng tc vi cc ht nhn nit v oxi trong tng caoca kh quyn v to ra cc ht nhn phng x nh 3T, 14C, 7Be,. . . vi tc khng i. Ccht nhn phng x ny theo nc ma n b mt ca Tri t. Mc d mt cc ht nhnphng x ny nh nhng xt trn ton cu th lng ht nhn phng x ny khng nh. Chng

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c chu k bn r di nhng phn ln u nh hn chu k ca cc ht nhn phng x nguynthy. Trong s cc ht nhn phng x do bc x v tr to ra, ba ht nhn ph bin nht l3T, 14C v 7Be.

Phng x nguyn thu cc ht nhn phng x nguyn thy c t lc to ra v tr. a scc ht nhn ny c chu k bn r rt ln, khong hng trm triu nm. Nu tnh t lc Trit c to thnh, cc ht nhn no tri qua khong vi chc chu k bn r th hu nhkhng cn tn ti na. Ch nhng ht nhn c chu k bn r ln, so snh c vi tui ca Trit th vn cn tn ti nh 238U, 235U, 232Th v 40K. Ngoi tr 40K, cc sn phm ca cc htnhn ny cng khng bn nn chng tip tc phn r to thnh ba chui phng x trong tnhin.

Phng x nhn to Trong qu trnh s dng phng x, hn mt trm nm nay, loi ngi a vo t nhin nhng ht nhn phng x mi, ng gp vo lng phng x t nhin. Ccngun pht phng x nhn to c th k n nh l cc nh my in ht nhn, cc v thv kh ht nhn, cc khu cha cht thi phng x, cht thi rn hay ng v phng x nhdu,. . . Nhng ht nhn phng x ny ngy cng tng trong nhng ln th v kh ht nhn vtrong nhng s c ht nhn. Tuy nhin chng c chu k bn r ngn hn nhiu so vi cc htnhn phng x nguyn thy.

Ti liu

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

[2] G.F. Knoll, Radiation Detection and Measurement, 3rd Edition, John Wiley & Sons Inc.,New York (1999).

[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] Josef Uher, Greg Roach, James Tickner, Peak fitting and identification software library forhigh resolution gamma-ray spectra, Nuclear Instruments and Methods in Physics ResearchA 619 (2010) 457-459.

[5] G. Gilmore, Practical Gamma-Ray Spectrometry, John Wiley & Sons Ltd., West Sussex(2008)

[6] www.gammaspectrometry.co.uk

[7] http://nsspi.tamu.edu/nsep/courses/basic-radiation-detection/gamma-ray-spectroscopy/gamma-ray-spectra/gamma-ray-spectra-page-two

[8] https://wiki.uio.no/mn/safe/nukwik/index.php/KJM-FYS_5920_Lab_Exercise_2_-_Student_Report

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S hnh thnh ph gammaung chun nang lung theo knhCc inh c trung cua ph gammaCc c trung cua inh ph gammaDang cua inhDang cua canh Compton phn giai nang lungFWHMFWTM

Phng nn ph gammaPhng nn ComptonPhng nn bc xa hmPhng nn phng xa t nhin

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