NGHIEN CUtJ TACH D i N H CHAP DUNG THUAT TOAN GIAI CUON GOLD
TRLTONG THI HONG LOAN*'\ NGO QUANG HUY^^^ CAO PHUC LONG HOA'*', TRAN THI MINH M A N " \ DANG NGUYEN PHLTONG*"
^'^Khoa Vgtlyva VgtlyKy thugt - Trudng Dgi hgc Khoa hgc Tunhien, DHQG-TP.HCM
^^Trudng Dgi hgc Cdng nghi?p TP.HCM Email: [email protected]
Abstract: In this work, we study on using Gold unfolding algorithm to deconvolute continuum and to analyze overlaped peaks in the gamma spectra for gamma spectrometry usmg HPGe detector. The results are basic for analyzing overlaped peaks under the study on estimation of low level from environmental samples.
Tir khoa: gidi cugn,hdm ddp «ng, MCNP, HPGe
I. Gidl THIEU
Trong phan tich dinh lugng hay dinh tinh bdng he phd k£ gamma, khi xir ly s6 liSu thu dugc tir viee ghi nhan phd biic xa gamma ngudi ta ddc biet quan tam den cae dinh nang lugng todn phan gay nen bdi hien tugng quang dien.
Tuy nhien, ngodi hieu ling quang dien, biic xa gamma cdn tham gia vao hai tuong tdc khac la hiSu iing tao cap va tan xa Compton, trong do, tin hieu tao ra bdi tan xa Compton dong mdt vai trd ddng ke trong pho ciia biic xa gamma. Do su cd mat cua nen tan xa Compton, viec tinh todn boat do ciia ngudn it nhiSu bi sai l^ch khi dinh nang lugng thap tren nen Compton cao hodc khi cac dinh nang lugng quan tam nam gan nhau trong pham vi nhd hon kha nang phan giai cua he phd k& (sir chap dinh). D^ tang dg chinh xac cho qua trinh phan tich phd thuc nghiem, ngudi ta dua ra nhieu phuong phap de loai bd vung tin hieu do tdn xa Compton gay ra nhu tri|t Compton hoac sii dung eac phuong phdp xir ly so lieu de thu dugc ket qua mong dgi.
Cdng trinh nay xay d\mg chuong trinh giai cugn phd dung thu$t toan Gold, va dp dung chuong trinh gidi cudn dk nghien cihi khii mign lien tuc va tach dinh chdp cua pho gamma.
II. PHU'ONG PHAP THyC HIEN 1. Thuat toan giai cuon Gold [1]
Thuat toan Gold dugc thiet ldp dua tren phuong trinh tich phan:
YQI)= [ "A(v,ti)X(v)dv
• ' V l (1)
Trong dd, X(v) la phan bd butc xa d miic ndng lugng v, Y(^) la s6 buc xa ghi nhan dugc d miic ndng lugng \i ciia thiet bj ghi biic xg, A(v,^) la bam dap ting cua detector, chg bilt xac sudt ma mgt biic xa mang nang lugng v se duge ghi nhan d vi tri ndng lugng p. cua he do.
O phuong trinh (1), p. va v la eac bien Hen tuc ndm tren mien gia tn ndng lugng cdn khdo sat. Tuy nhien, tren thyc tS, thilt kl cua cdc detector khdng cho phep chiing hiln thi cac tin hi§u lien tyc ma chi cho phep phan bd tin bi?u vao cac kSnh rdi rac, do dd, phuong trinh (1) dugc chuyen thanh d^g:
438 Hdi nghi Khoa hoc vd Cdng nghi hgt nhdn todn qudc idn thuIX, Ninh Thudn 18-19/8/2011
Y=AX (2) Tron^ dd, Y la vec to phd do, cdn ggi Id vector dau ra, chiia cac gia tr} rdi rac tuong
ling vdi sd dem timg kenh ciia detector; X la vec to pho dau vao, d^i dien cho phdn b6 ning lugng cua ngudn; A la ma trdn dap ling cua detector, phan anh each ma phd biic xa glc dupe ghi nhan trong detector.
Nhu vdy, phdn tir y, ciia vec to Y se dugc xac dinh bdi:
yt=Z^'''
((3)Vdi Xj Id phdn tii cua vec to X, aj,, la phdn tir cua ma tran dap iing A; n la cap cua ma tran dap iing A.
Phuong trinh (2) cd thi dugc giai bang each nhdn trai hai ve eiia phuong trinh cho ma tran A'V Tuy nhien, khi xay dung mgt ma tran ddp iing de gidi bdi toan trong dieu kien thy;c tl. Gold sir dung phuong phdp lap de tim ra nghiem gan diing cua phuong trinh (2) nhu sau:
2, Xay dung chiroug trinh giai cugn pho gamma bang thuat toan Gold
Viec xay dung chuong trinh giai cudn gdm 2 budc chinh: thii nhat la xay dung ma trdn dap iing, thii hai la tao vdng lap sir dung thuat todn Gold de tim phd gdc tir ngudn.
De xdy dung ma tran dap iing, ta can xdc dinh cae vector ham dap ling A,. Ham dap ling Pi(Ej) la mgt ham sd cho bi§t xdc suat md mpt biic xa cd nang lugng Ei dugc ghi nh(ln tren timg kenh cua mgt detector nhat dinh. Trong tinh todn, ham dap iing Pi(Ej) dugc dai dien bdi vector Aj.
Tren ly thuyet, ta cd the thu dugc mgt ham dap iing bdng cdch sir dung mpt nguon don nang da biet truoc hoat do, ghi nhdn so dem cua ngudn nay bdng detector dang khao sdt, sau dd tinh xac suat ma biic xa duge ghi nhdn tren timg kenh cua detector. Tuy nhien, vi nhiing detector do biic xa gamma trong thuc te cd sd kenh rdt Ion nen viec sir dyng cdc nguon phong xa don nang th^t de xay dung cac ham ddp iing la khong kha thi. D I C6 the xay dung mpt lupng Idn hdm ddp iing nhu vdy, ngudi ta sir dung cdc chuong trinh md phdng bang may tinh. Trong cdng trinh nay, ham dap iing dugc md phdng bdng chuong trinh MCNPS [3].
Viec md phdng cdc ham dap iing tuy dugc thuc hien tren mdy tinh nhung cung tin rdt nhieu thdi gian. De nit ngan thdi gian xay dung cac ham dap ling, ta khdng thuc hien mo ph6ng tCmg kenh nang lugng mgt, md thuc bien mo phdng cdch khoang. Viec lira chpn khoang m giira cac ham dap iing mdt cdch hgp ly se ldm giam thdi gian md phdng ma vdn dam bao mpt miic sai sd chdp nhan dugc. De xac dinh cac ham ddp iing ndm giiia hai ham dap iing mo phdng, ehiing tdi xay dung code ngi suy dua tren co sd thudt toan ngi suy cua cong trinh [1].
Sau khi cd dugc mpt ma tran dap img, xay dung code de giai cudn theo cdng thiic l?p (4)- III. KET QUA VA THAO LUAN
Khd ndng tdch dinh cua thuat toan gidi cudn tuy thugc vdo cip cua ma t r ^ dap iing- Trudng hgp tdt nhat tuong ung vdi khi dd chia nhd nhdt ciia ma tr|n dap ling bdng d6 chia kenh nhd nhat cua he phd kl. CJ ddy he phd kl ma chiing tdi khao sat cd tdi da la 8192 kenh
Hgi nghj Khoa hgc vd Cdng nghe hgt nhdn todn qudc Idn thu IX, Ninh Thugn 18-19/8/2011 439 trong miln ndng lugng tir 6.7 keV den 1942.2 keV. Vi v|.y khoang each trung binh giiia hai kenh Id 0.24 keV.
D I th\rc biSn phep kiem tra miic do tach dinh, ta xay dung mgt phd thii nghiem X gdm hai dinh vdi mpt dinh lam ehuan C dugc cd dinh d kenh 5000, cd dien tich la 10 sd dem.
Dinh dung dl kilm tra K cd dien tich lO', lan lugt dugc phan bd d cac kenh 5002, 5004 va 5006. Tdng dien tich cua phd X la 110000000 so dim.
Hmh 1,2, 3 trinh bay cac phd dau ra cua dinh K, dinh C va dinh chong chap giua C va K \hn lugt t^i sdu vi tri ciia K.
3,5E+05 3.0E+O5 2.5E+05 2.0E>05 l.SE*05 l.OE+OS 5.0E+04 O.OE+00
BiilllC fiiiiliK Diiili ciioiis: cliop
PTinh 1. Dinh C, dinh K vd dinh chdng chdp khi K a kenh 5002.
HO - o t o
3.5E-K)5 3.0E+05 2.5E*05 2.0E-t05 1.5EtOS 1.0E+O5 5.0E+O4 0.0E+OO
4 9 E)2 4 9 9 5 4 9 9 8 5 0 0 1 K . e n l i
Diiili c D i i i l i K
"•"••'•• Diiili cliong cliap
5 0 0 4 5 0 0 7 5 0 1 0 5 0 1 3
• i c w
Hinh 2. Dinh C, dinh K vd dinh chdng chdp khi K a kenh 5004.
3.0E+O5 2 . 5 E t 0 5 2 . 0 E 4 0 5 1.5E+0S 1 . 0 E t 0 5 5.0E+O4 O.OE400 4 9
/ \ D i i U i C / \ ^ — B i n l l K / \ ^ • ^ D i i i l i c h o n g d i g p
J V-^
92 4 9 9 5 4 9 9 8 SOOl 5 0 0 4 5 0 0 7 5 0 1 0
Kenli
5 0 1 3
Hinh 3. Binh C, dinh K va dinh chdng chdp khi K a kenh 5006.
440 Hgi nghi Khoa hgc vd Cdng nghe hgt nhdn tadn quic lin thi IX, Ninh Thudn 18-19/8/2011 Sau khi thu duac cac ph6 diu ra, ta tiSn hanh giai cuOn cho ba ph5 nay va thu dim cac ket qua sau:
- Tmcmg hop K n5m 6 kSnh 5002 (hinh 4), chucmg trinh cho thjy phan bi$t duqrc liai dinh nhung chua tach duoc hai dinh K va C.
- Trucmg hop K nam 6 cac kenh 5004 va 5006 (hinh 5 va hmh 6), chuong trinh clio phep phan biet hai dmh K va C. M4c d0 chdng chap dinh dupe cho 6 bang 4.1.
- Khi khoang each giiia K va C 14 tit 4 kenh tro len (hinh 5 va 6), thu$t toan giai cupn hoan toan tach duoc hai dinh nay.
5.E+05 ,
4.E-KI5 ;
2 3.E+0S
W 2.E+05
l.E+05
4 9 9 0
y
4 9 9 5
A 11
/lu / \
soooK e i i l i
— — P l i d t n i o c sifti niQii
— • • P h o smi giSi ctiQii
V
5 0 0 5 5 0 1 0 5 0 1 5
Hinh 4. Dinh CvdK truac vd sau gidi cugn (K a kinh 5002)
5.E+0S 1
4.E+05 I
1
p 3.Et05 1
"^ !
w 2.E+05 i
1.E-K15 !
4990
y
4995
fl
A/K ll
/(P / \
5000K e i U i
- - — ' P h o t n i d t giai CTIQII
— — P l i o stui gi^i ciioii
> ^
5005 5010 5015
Hinh 5. Dinh CvdK truac vd sau gidi cudn (K a kenh 5004)
I 5.E*05
I " K i o l m o c gi6i CIIQII P)>^ smi giai cuQii
5 0 0 0 5 0 0 5 Kenll
Hinh 6. Dinh CvdK trude vd sau gidi cugn (K a kenh 5006)
Hgi nghi Khoa hgc vd Cdng ngh? hgt nhdn todn qudc Idn thu IX. Ninh Thudn 18-19/8/2011 441 Qua thi nghiem tren, chiing ta nhan thay thuat todn Gold giup ta phdn biet hau nhu moi trudng hgp cac dinh pho ndm each nhau tir hai kenh trd len vd cd kha nang tdch biet hoan toan hai dinh khi khoang cdch giiia chung la tren bdn kenh (tuong iing vdi 0.96 keV).
Bdng 4.1. Do chdng chap dinh C vd Ksau khi gidi cudn.
Vi tri dinh K
5002 5004 5006
Dien tich phan pho xay ra chong chap 1080042090
1401027 0
So kenh chong chap
3 1 0
Ti le di?n tich phan pho chong chap so vai dien
tich dinh K(%) 1080.04
1.40 0.00
IV. KET LUAN
Cdng trinh nay budc ddu nghien ciiu dp dung thuat toan giai cudn Gold trong viec khii mien lien tuc va tach dinh chap cua pho gamma tren h? phd ke HPGe. Ket qua cho thay chuong trinh gidi cupn xay dung dugc dua tr6n thudt todn Gold giup ta phan biet hau nhu mpi trudng hgp cdc dinh phd nam each nhau tii hai kenh trd len va cd khd nang tdch biet hodn todn hai dinh khi khoang each giua chiing la tren bdn kenh (tuong iing vdi 0.96 keV). Cac dinh pho thu dugc tir phep giai cugn bdng thuat todn Gold kha hep, ti so gifl-a be rdng trung binh cua mpt phd giai cudn so vdi be rpng trung binh ciia phd thy:c nghiem chi nam trong khoang 40% den 50%, nhd do nang cao kha ndng phan tach cac dinh chdng chap cua phd do.
TAI LI$U THAM KHAO
[1] M. Jandel, M. Morhd^c, J. Kliman, L'. Krupa, V. Matousek, J.H. Hamiltonc, A.V.
Ramayyac, "Decomposition of continuum g-ray spectra using synthesized response matrix". Nuclear Instruments and Methods in Physics Research A 516 172-183 (2004).
[2] Raymond Gold, "An iterative unfolding method for response matrices", Argonne National Laboratory, Argorme, Illinois (1964).
[3] X-5 Monte Carlo Team, "MCNP - A general Monte Carlo N-particle Transport Code", Version 5, Los Alamos National Laboratory (2003).
