Đặc trưng phổ gamma

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  • Cc c trng ca ph gamma

    ng Nguyn Phngdnphuong1984@gmail.com

    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

    1

  • 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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  • ng Nguyn Phng Ti liu ni b NMTP

    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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  • ng Nguyn Phng Ti liu ni b NMTP

    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

    5

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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

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