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QUANTUM-MECHANICAL BASED VERSION OF X-RAY CHARACTERISTIC ATTENUATION
COEFFICIENTS
O. Marenkov
To cite this version:
O. Marenkov. QUANTUM-MECHANICAL BASED VERSION OF X-RAY CHARACTERISTIC ATTENUATION COEFFICIENTS. Journal de Physique Colloques, 1984, 45 (C2), pp.C2-51-C2-52.
�10.1051/jphyscol:1984213�. �jpa-00223799�
JOURNAL DE PHYSIQUE
Colloque C2, supplkment au n02, Tome 45, fkvrier 1984 page C2-51
QUANTUM-MECHANICAL BASED VERSION OF X-RAY CHARACTERISTIC ATTENUATION COEFFICIENTS
O.S. Marenkov
VNIIliauchprybor, Leningrad, U.S.S.B.
RBsumE
-
On montre que les valeurs theoriques des coeffi- cients globaux d'absorption massique du rayonnement X carac- tgristique dans un domaine dl&nergie superieur 0,3 keV sont plus exactes que les valeurs empiriques et semi-empiri- ques.
Abstract
-
For the energy E 7 0.3 keV it is demonstrated that the theoretical values of the total attenuation mass coef-
ficients for characteristic X-ray radiation are more accura- te than empirical and semi-empirical values.
The use of modern computers during last 10-15 years enabled to cope with the calculational difficulties of quantum theory of partial photon radiation interaction processes with matter. In the energy intervals ( E30.1-120 keV ) of characteristic X-radiation the total attenuation coefficients can be represented aa a sum of partial
where the photoelectric attenuation coeffitients 4;- (E) being cal- culated by interpolation (E" -power polynomial) of table quantum- mechanical relativistic data of photoionization cross-sections
(Soof ield 1973, Band 1977 ) ; @ (E) by numerical integration of differential Thomson scatteris cross-sections by using relativis- tic Hartree-Fock atomic f om-factor F (Hubbell 1979), corrected for anomalous dispersion effect;
B
incoh (E)-
by numerical integra- tion of differential Kleb-Nishina colllsion cross-section by using non-relativistic Hartree-Pock incoherent scattering function S (Hubbell 1975), e.g.:Quantum-mechanical values of the total mass (cm2g'1 ) attenuation coefficients of K-, L-, M- characteristic X-ray radiation (about 500 lines for E ) 7 keV)of 88 absorbing elements (Z=1-94) are presented in /I/.
The systematic comparison of theoretical values of
fi
in the E=4.5-
150 keV interval with the su er precise experimental data (error less than 1% for 24 elements7 showed, that / theore- tical for most elements are more accurate compared with those empi- rical and sea-empirical values widely used in X-ray analysis, inArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984213
C2-52 JOURNAL DE PHYSIQUE
p a r t i c u l a r electron-microprobe a n a l y s i s (Leroux 1962, 1979; Heinrich 1966; Kelly 1966; Theisen 1967; F r a s e r 1967; Dewey 1969; Bracewell 1971; Hubbell 1974; larenkov 1978; Blokhin 1982).
The r e l a t i v e d e v i a t i o n v a l u e between t h e t h e o r e t i c a l / I / and experi- mental d a t a reachs 1-376 on t h e average. The r e s u l t s of t h e calcu- l a t i o m /2/ have t h e same r e l a t i v e d e v i a t i o n value. They were obtained by i n t e r p o l a t i o n of t h e w e l l known Storm's and I s r a e l ' s d a t a (1970).
The empirical and semi-empirical v a l u e s of JA obtained by t h e men- t i o n e d a u t h o r s of summary r e s e a r c h s have t h e accuracy l e v e l consf- derably lower than t h e d a t a i n /1,2/.
For most elements t h e r e l a t i v e mean e r r o r is more than 3-5%.
The r e s e a r c h of uncertainty in t h e t o t a l a t t e n u a t i o n mass c o e f f i - c i e n t values f o r X-ray r a d i a t i o n i n t h e energy i n t e r n a l 0.1-4.5 keV (Dewey 1969; Bracewell 1971; Henke 1974; 1982; Ruste 1975, 1979;
Loi 1975; Blokhin 1982; Ibfarenkov 1983) was c a r r i e d on experimental
d a t a (West 1976, 1978, w i t h e r r o r 2-3%). From t h i s comparlson we can draw t h e considerable advantage of t h e d a t a /3,4/. The d e t a i - l e d compariaon o f $ v a l u e s from /3,4/ i n narrow energy i n t e r v a l s (0.1
+
0.3; 0.3+
1.5; 1.5+
4.5 keV) shows t h a t e m p i r i c a l d a t a /3/a r e more p r e f e r a b l e f o r a n a l y t i c a l p r a c t i c e than d a t a /4/ only i n t h e energy i n t e r v a l (0.1
+
0.3 keV). Thus the works c a r r i e d on es- t i m a t i o n of 4 u n c e r t a i n t y f o r c h a r a c t e r i s t i c X-ray r a d i a t i o n show t h e evident advantage of t h e o r e t i c a l v a l u e s of $ from /1,2,4/ f o r energy more than 0.3 keV.REFERENCES
1. Marenkov 0.8. e t a l . T a b l i t s y i formuly rentgenospektralnogo ana- l i x a . 1,2, Leningrad, 1981.
2. Montene r o E.C. e t a l . Atomic Data and Nucl. Data Tables, 22(1978? 131.
3. Henke B.L. e t a l . Atomic Data and Hucl. Data Tables, 27(1982) 1.
4, Marenkov O.S. e t a l . Apparatura i metody rentgenovskogo a n a l i z a , 29 (1983) 48-
