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Average M-shell fluorescence yields (ωM ) for Pt, Au and Pb
Radiar.
Pergamon PII: s0969-806x(%)00159-4
Phys. Chem. Vol. 49. No. 4, pp. 503-504. 1997 A 1997 Eiker Science Ltd Printed in Grea;Britain. AI1 rights reserved 0969-806X/97 $17.00 + 0.00
TECHNICAL NOTE AVERAGE
M-SHELL FLUORESCENCE Au AND Pb
YIELDS (OM) FOR Pt,
D. V. RAO,‘,’ R. CESAREO’ and G. E. GIGANTE’,’ ‘Dipartimento
di Fisica, Universita di Roma “La Sapienza”, Piazzale A Moro 2, 00185, Roma, Italy and %entro Interdipartimentale di Ricerca per L’Analisi dei Modelli e dell’hformazione nei Sistemi Biomedici, Corso Vittorio Emanuele 11, 00186, Roma, Italy (Received 28 March 1996; revised 6 September
Experimental fluorescente yields are required in a variety of applications including, for example, atomic physics studies, X-ray fluorescente (XRF) surface chemical analysis, and dosimetric computations for health physics, cancer therapy, and industrial irradiation processing. Especially, fluorescente yield data are required in calculating mass energy absorption coefficients p,,/p, a key parameter in computations of energy deposited in media subjected to photon irradiation (Berger, 1961; Hubbell, 1977; Seltzer, 1993; Hubbell and Seltzer, 1995). Extensive theoretical values of fluorescente yields, Coster-Kronig transition probabilities based on relativistic Dirac-Hartree-Slater theory (Bambynek el al., 1972; Chen et al., 1980, 1983) are available in the literature. If one hopes to check these theoretical values against experimental results, a comprehensive and reliable set of experimental data is required.
1996; accepted 6 September 1996)
fluorescente yields, On, for each element were obtained by taking the weighted average of the We values available at 5.47, 5.96, 6.47, 7.04, 7.57, 8.14, 8.74 and 9.36 keV photon energies, using the expression
where W, denotes the jth experimentally deduced fluorescente yield and (Aw,) represents the quoted uncertainty in the jth experimental value.
RESULTS AND DISCUSSION
The derived experimental M-shell fluorescente yields at different incident photon energies were fitted by least squares to polynomials in Z ( = cu”Z”) using
ESTIMATION OF AVERAGE M-SHELL FLUORESCENCE YIELD (&,)
the Gauss-Seidel iteration method. The differente between the experimental M-shell fluorescente yields and the fitted values is less than 1%. Using these values the average M-shell fluorescente yields were derived in the atomic region 78 I Z 5 82 and are fitted by least squares to polynomials in Z. The average M-shell fluorescente yield can be deduced using the relation given below
Experimental total M X-ray fluorescente cross sections have been measured by US in the energy region 5.47 < E -c 9.36 keV (Rao et al., 1996). M-shell fluorescente yields at each incident photon energy are evaluated using the relation
WM= o$/lrp,
(1)
wW = - 3.6823 x 10-2 + 1.7282
where ah are the measured M X-ray fluorescente sections and the values of the M-subshell photoionization cross sections ah were interpolated from the theoretical tables of Scofield (1973). Total M X-ray fluorescente cross sections were measured at more than one incident photon energy of the exciting particle, the values of the ith shell
x lom4 + 8.1576 x 10-6Z*
(3)
Table 1 shows the comparison of the average M-shell fluorescente yields with theoretical estimates, present fitted values and the fitted values available in the 503
504
Technical Note Table
z
70 79 82
Experimental
1. Comparison
0.0262 f 0.0018 0.0276 f 0.0020 0.0322 + 0.0022
literature.
of experimental
Fitted
values
values
average
average
yields
(&)
with
theoretical
estimates
and fitted
values
Chen pf al. (1983)
Hubbell (1989)
Hubbe.ll er al. (1994)
0.0247 0.0270 0.0320
0.0254 0.0268 0.0313
0.0230 0.0245 0.0292
0.0274 0.0292 0.0346
0.0263 0.0278 0.0322
Experimental
fluorescente
McGuire (1972)
M-shell
fluorescente
yields are in good agreement with the theoretical estimates based on relativistic Dirac-Hartree-Slater theory. The differente between the experimental values and the fitted values is less than 1% in the studied atomic region. However, the experimental yield can also be obtained using these fitted coefficients in the atomic region 71 5 E I 92 with an uncertainty of 24% between the experimental and theoretical values. The experimental average M-shell fluorescente yield is higher by 5% for Pt and 2% for Au, when compared with theoretical data based on AHS [(non-relativistic) approximate Herman-Skillman) calculations of McGuire (1975). However, it is interesting to note that the differente between the experimental M-shell fluorescente yield and the theoretical value is less than 1% for Pb. Experimental average M-shell fluorescente yields are higher than the fitted values of Hubbell(l989) by 9 to 12% in the atomic region 78 I Z I 82. However, experimental average M-shell fluorescente yield are in good agreement with the recent fitted values of Hubbell et al. (1994). Acknowledgements-We are very grateful to Professor Dr G. Furlan for providing financial assistance and also to the Centro Interdipartimentale di Ricerca per L’Analisi dei Modelli e dell’ Informazione nei Sistemi Biomedici for allowing USto carry out this experimental work. One of US (DVR) undertook this work with the support of the ICTP programme for training and research in Italian laboratories, Trieste, Italy.
REFERENCES Bambynek, W., Crasemann, B., Fink, R.W., Freund, H. IJ., Mark, H., Swift, C. D., Price, R. E. and Rao, P. V. (1972). X-ray fluorescente yields. Auger and Coster-Kronig
transition probabilities. Reviews of Modern Physics 44, 716.
Berger, R. T. (1961). The X-or gamma-ray energy absorption or transfer coefficient: tabulations and discussion Radiation Research 15, 1. Chen, M. H., Crasemann, B. and Mark, H. (1980). Relativistic M-shell radiationless transitions. Physics Reviews A21, 449. Chen, M. H., Crasemann, B. and Mark, H. (1983). Radiationless transitions to atomic M-shells. Results of relativistic theory. Physics Reviews A27, 2989. Hubbell, J. H. (1977). Photon mass attenuation and mass-energy absorption coefficients for H, C, N, 0, Ar, and seven mixtures from 0.1 keV to 20 MeV. Radiation Research 70, 58.
Hubbell, J.H. (1989) Bibliography and current status of K, L and higher shell fluorescente yields for computations of photon energy absorption coefficients, NISTIR Report 89-4144, National Institute of Standards and Technology, U.S.A. Hubbell, J. H., Trehan, P. N., Singh, N., Chand, B., Mehta, D., Garg, M. L., Garg, R. R., Singh, S. and Puri, S. (1994). A review, bibliography, and tabulation of K, L, and higher atomic shell X-ray fluorescente yields. Journal of Phy&al and Chemical Reference Data i3, 339.
Hubbell. J.H. and Seltzer. S.M. (1995) . , Tables of X-rav mass attenuation coefficients
coefficients
1
and
mass
energy-absorption
keV to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest, NISTIR Report 5632, National Institute of Standards and Technology, U.S.A. McGuire, E. J. (1975). Atomic M-shell Coster-Kronig, Auger, and radiative rates, and fluorescente yields for Ca-Th. Physics Reviews AS, 1043. Rao, D. V., Cesareo, R. and Gigante, G. E. (1996). M X-ray fluorescente cross sections and yields for Pt, Au and Pb in the energy region 5.47 < E Q 9.36 keV. Nuclear Instruments and Methods BHU3,227. Scofield, J.H. (1973). Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore National Laboratory Report UCRL-51326, U.S.A. Seltzer, S. M. (1993). Calculation of photon mass energy transfer and mass energy absorption coefficients. Radiation Research 136, 147.
Pergamon PII: s0969-806x(%)00159-4
Phys. Chem. Vol. 49. No. 4, pp. 503-504. 1997 A 1997 Eiker Science Ltd Printed in Grea;Britain. AI1 rights reserved 0969-806X/97 $17.00 + 0.00
TECHNICAL NOTE AVERAGE
M-SHELL FLUORESCENCE Au AND Pb
YIELDS (OM) FOR Pt,
D. V. RAO,‘,’ R. CESAREO’ and G. E. GIGANTE’,’ ‘Dipartimento
di Fisica, Universita di Roma “La Sapienza”, Piazzale A Moro 2, 00185, Roma, Italy and %entro Interdipartimentale di Ricerca per L’Analisi dei Modelli e dell’hformazione nei Sistemi Biomedici, Corso Vittorio Emanuele 11, 00186, Roma, Italy (Received 28 March 1996; revised 6 September
Experimental fluorescente yields are required in a variety of applications including, for example, atomic physics studies, X-ray fluorescente (XRF) surface chemical analysis, and dosimetric computations for health physics, cancer therapy, and industrial irradiation processing. Especially, fluorescente yield data are required in calculating mass energy absorption coefficients p,,/p, a key parameter in computations of energy deposited in media subjected to photon irradiation (Berger, 1961; Hubbell, 1977; Seltzer, 1993; Hubbell and Seltzer, 1995). Extensive theoretical values of fluorescente yields, Coster-Kronig transition probabilities based on relativistic Dirac-Hartree-Slater theory (Bambynek el al., 1972; Chen et al., 1980, 1983) are available in the literature. If one hopes to check these theoretical values against experimental results, a comprehensive and reliable set of experimental data is required.
1996; accepted 6 September 1996)
fluorescente yields, On, for each element were obtained by taking the weighted average of the We values available at 5.47, 5.96, 6.47, 7.04, 7.57, 8.14, 8.74 and 9.36 keV photon energies, using the expression
where W, denotes the jth experimentally deduced fluorescente yield and (Aw,) represents the quoted uncertainty in the jth experimental value.
RESULTS AND DISCUSSION
The derived experimental M-shell fluorescente yields at different incident photon energies were fitted by least squares to polynomials in Z ( = cu”Z”) using
ESTIMATION OF AVERAGE M-SHELL FLUORESCENCE YIELD (&,)
the Gauss-Seidel iteration method. The differente between the experimental M-shell fluorescente yields and the fitted values is less than 1%. Using these values the average M-shell fluorescente yields were derived in the atomic region 78 I Z 5 82 and are fitted by least squares to polynomials in Z. The average M-shell fluorescente yield can be deduced using the relation given below
Experimental total M X-ray fluorescente cross sections have been measured by US in the energy region 5.47 < E -c 9.36 keV (Rao et al., 1996). M-shell fluorescente yields at each incident photon energy are evaluated using the relation
WM= o$/lrp,
(1)
wW = - 3.6823 x 10-2 + 1.7282
where ah are the measured M X-ray fluorescente sections and the values of the M-subshell photoionization cross sections ah were interpolated from the theoretical tables of Scofield (1973). Total M X-ray fluorescente cross sections were measured at more than one incident photon energy of the exciting particle, the values of the ith shell
x lom4 + 8.1576 x 10-6Z*
(3)
Table 1 shows the comparison of the average M-shell fluorescente yields with theoretical estimates, present fitted values and the fitted values available in the 503
504
Technical Note Table
z
70 79 82
Experimental
1. Comparison
0.0262 f 0.0018 0.0276 f 0.0020 0.0322 + 0.0022
literature.
of experimental
Fitted
values
values
average
average
yields
(&)
with
theoretical
estimates
and fitted
values
Chen pf al. (1983)
Hubbell (1989)
Hubbe.ll er al. (1994)
0.0247 0.0270 0.0320
0.0254 0.0268 0.0313
0.0230 0.0245 0.0292
0.0274 0.0292 0.0346
0.0263 0.0278 0.0322
Experimental
fluorescente
McGuire (1972)
M-shell
fluorescente
yields are in good agreement with the theoretical estimates based on relativistic Dirac-Hartree-Slater theory. The differente between the experimental values and the fitted values is less than 1% in the studied atomic region. However, the experimental yield can also be obtained using these fitted coefficients in the atomic region 71 5 E I 92 with an uncertainty of 24% between the experimental and theoretical values. The experimental average M-shell fluorescente yield is higher by 5% for Pt and 2% for Au, when compared with theoretical data based on AHS [(non-relativistic) approximate Herman-Skillman) calculations of McGuire (1975). However, it is interesting to note that the differente between the experimental M-shell fluorescente yield and the theoretical value is less than 1% for Pb. Experimental average M-shell fluorescente yields are higher than the fitted values of Hubbell(l989) by 9 to 12% in the atomic region 78 I Z I 82. However, experimental average M-shell fluorescente yield are in good agreement with the recent fitted values of Hubbell et al. (1994). Acknowledgements-We are very grateful to Professor Dr G. Furlan for providing financial assistance and also to the Centro Interdipartimentale di Ricerca per L’Analisi dei Modelli e dell’ Informazione nei Sistemi Biomedici for allowing USto carry out this experimental work. One of US (DVR) undertook this work with the support of the ICTP programme for training and research in Italian laboratories, Trieste, Italy.
REFERENCES Bambynek, W., Crasemann, B., Fink, R.W., Freund, H. IJ., Mark, H., Swift, C. D., Price, R. E. and Rao, P. V. (1972). X-ray fluorescente yields. Auger and Coster-Kronig
transition probabilities. Reviews of Modern Physics 44, 716.
Berger, R. T. (1961). The X-or gamma-ray energy absorption or transfer coefficient: tabulations and discussion Radiation Research 15, 1. Chen, M. H., Crasemann, B. and Mark, H. (1980). Relativistic M-shell radiationless transitions. Physics Reviews A21, 449. Chen, M. H., Crasemann, B. and Mark, H. (1983). Radiationless transitions to atomic M-shells. Results of relativistic theory. Physics Reviews A27, 2989. Hubbell, J. H. (1977). Photon mass attenuation and mass-energy absorption coefficients for H, C, N, 0, Ar, and seven mixtures from 0.1 keV to 20 MeV. Radiation Research 70, 58.
Hubbell, J.H. (1989) Bibliography and current status of K, L and higher shell fluorescente yields for computations of photon energy absorption coefficients, NISTIR Report 89-4144, National Institute of Standards and Technology, U.S.A. Hubbell, J. H., Trehan, P. N., Singh, N., Chand, B., Mehta, D., Garg, M. L., Garg, R. R., Singh, S. and Puri, S. (1994). A review, bibliography, and tabulation of K, L, and higher atomic shell X-ray fluorescente yields. Journal of Phy&al and Chemical Reference Data i3, 339.
Hubbell. J.H. and Seltzer. S.M. (1995) . , Tables of X-rav mass attenuation coefficients
coefficients
1
and
mass
energy-absorption
keV to 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest, NISTIR Report 5632, National Institute of Standards and Technology, U.S.A. McGuire, E. J. (1975). Atomic M-shell Coster-Kronig, Auger, and radiative rates, and fluorescente yields for Ca-Th. Physics Reviews AS, 1043. Rao, D. V., Cesareo, R. and Gigante, G. E. (1996). M X-ray fluorescente cross sections and yields for Pt, Au and Pb in the energy region 5.47 < E Q 9.36 keV. Nuclear Instruments and Methods BHU3,227. Scofield, J.H. (1973). Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore National Laboratory Report UCRL-51326, U.S.A. Seltzer, S. M. (1993). Calculation of photon mass energy transfer and mass energy absorption coefficients. Radiation Research 136, 147.