K shell, L shell–subshell and M shell–subshell photoeffect cross-sections in elements between Tb (Z=65) and U (Z=92) at 123.6 keV

ARTICLE IN PRESS

Radiation Physics and Chemistry 77 (2008) 101–106 www.elsevier.com/locate/radphyschem

K shell, L shell–subshell and M shell–subshell photoeffect cross-sections in elements between Tb (Z ¼ 65) and U (Z ¼ 92) at 123.6 keV N. Kaya, G. Apaydın, V. Aylıkcı, E. Cengiz, E. Tıras- og˘lu Department of Physics, Faculty of Arts and Science, Karadeniz Technical University, 61080 Trabzon, Turkey Received 27 March 2007; accepted 27 June 2007

Abstract In this paper, we report on measurements of K shell, L shell–subshell and M shell–subshell photoeffect cross-sections for 21 highatomic-number elements between Tb (Z ¼ 65) and U (Z ¼ 92) at 123.6 keV. These photoeffect cross-sections have been measured by using our earlier measurements of the K-shell X-ray production cross-sections. The measured photoeffect cross-sections have been compared with calculated theoretical values. It is clear that the results compare well with theoretical values within an experimental average error. At 123.6 keV, these cross-sections have been measured for the first time. The results have been plotted versus atomic number. r 2007 Elsevier Ltd. All rights reserved. Keywords: Photoeffect cross-sections; Si(Li) detector;

57

Co-radioisotope

1. Introduction It is well known that the gamma-ray photons whose energy is in the range from a few keV to MeV can lose their energy in matter predominantly by the photoeffect process, the Compton scattering, and the pair production process. At low energies (100–150 keV) and for high-Z absorbers the photoeffect process is an important process of absorption of gamma photons in matter; in this process a gamma photon is completely absorbed and a bound electron is ejected from the atom. Since the interaction of gamma radiation with matter has wide applications in several fields such as radiation biology, medical physics, nuclear power plant shielding, industrial irradiation and monitoring, in X-ray crystallography and elemental analysis using X-ray fluorescence (XRF), the related parameters should be known accurately (Hubbell, 1999a, b, 2006). In this direction several researchers have compiled the photon cross sections in the form of tables and graphs (Creagh and Hubbell, 1992; Chantler, 1995). Corresponding author. Tel.: +90 462 3773819; fax: +90 462 3253195.

E-mail address: [email protected] (N. Kaya). 0969-806X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2007.06.013

The numerical data of Scofield (1973) on total as well as shell-wise cross-sections of elements are considered to be the most accurate theoretical data. These data include elements of Z ¼ 1–101 in the energy region 1–1500 keV. Berger and Hubbell (1987, 1999) have published the XCOM program for personal computers, which calculates the photon cross-sections corresponding to scattering, photoelectric effect, pair production and total attenuation for elements and compounds in the energy region from 1 keV to 100 GeV. On the other hand, the photoeffect cross-sections have been determined experimentally by many workers (Umesh et al., 1985; Nathuram et al., 1988; Roy et al., 1997; Arora et al., 1981a, b; Karabulut et al., 2002, 2005; Gu¨rol et al., 2003; Nayak and Badiger, 2006). The accurate and reliable data on the L and M XRF cross-sections have an important bearing in the theory for developing more practical models describing the fundamental processes following inner-shell ionization, namely radioactive, Auger and Coster-Kronig. A better approach to check parameters is to measure the XRF cross-sections for the X-rays originating from K shell, L shell and subshell (Li, i ¼ 1, 2, 3) and M shell and subshell (Mj j ¼ 1, 2, 3, 4 and 5). For these reasons, we determined K shell,

ARTICLE IN PRESS N. Kaya et al. / Radiation Physics and Chemistry 77 (2008) 101–106

102

L shell–subshell, M shell–subshell photoeffect crosssections for some elements with 65pZp92 at 123.6 keV by using experimental data from Apaydın and Tıras-og˘lu, (2006).

tM3 ¼ tpe ðrK rL1 rL2 rL3 rM1 rM2 Þ1 ð1  1=rM3 ÞwM3 ðZÞ, tM4 ¼ tpe ðrK rL1 rL2 rL3 rM1 rM2 rM3 Þ1 ð1  1=rM4 Þ  wM4 ðZÞ, tM5 ¼ tpe ðrK rL1 rL2 rL3 rM1 rM2 rM3 rM4 Þ1 ð1  1=rM5 Þ

2. Experimental and calculated procedures

 wM5 ðZÞ,

The experimental set-up, as described earlier (Ertug˘ral et al., 2007), consists of a Si (Li) detector, a 57Co radioisotope source and a target. Pure and compounds of heavy elements were used as samples. The properties of these samples used in the measurements were described in Apaydın and Tıras-og˘lu (2006). The K X-ray production cross-sections were calculated by the relation sKa ðiÞ ¼ sKa1 ðiÞ þ sKa2 ðiÞ,

(1)

where sKa1 ðiÞ and sKa2 ðiÞ cross-sections were introduced and measured in our work (Apaydın and Tıras-og˘lu, 2006). The total atomic photoeffect cross-sections tpe ðiÞ were evaluated by the following equation:   sKa ðiÞ I Kb tpe ðiÞ ¼ 1þ . (2) ð1  1=rK ÞoK I Ka Using this relation, the total atomic photoeffect crosssection of an element at Ei can be determined using the measured value of sKa ðiÞ from Eq. (1), rK, oK and I Kb =I Ka , where rK, oK and I Kb =I Ka are absorption jump ratio, fluorescence yield and the intensity ratio of Kb and Ka X-rays, respectively. rK have been calculated from the values of mass attenuation coefficients taken from XCOM (Berger et al.,2005), oK is the K shell fluorescence yield taken from the standard fitted values of Krause (1979) and I Kb =I Ka is the theoretical values calculated using Hartree–Slater theory of Scofield (1974). We used the following equations to calculate the photoeffect (or photoionisation) cross-sections: tK ¼ tpe ð1  1=rK Þ,

(3)

tL1 ¼ tpe r1 K ð1  1=rL1 ÞwL1 ðZÞ, tL2 ¼ tpe ðrK rL1 Þ1 ð1  1=rL2 ÞwL2 ðZÞ, tL3 ¼ tpe ðrK rL1 rL2 Þ1 ð1  1=rL3 ÞwL3 ðZÞ,

ð4Þ

tM1 ¼ tpe ðrK rL1 rL2 rL3 Þ1 ð1  1=rM1 ÞwM1 ðZÞ, tM2 ¼ tpe ðrK rL1 rL2 rL3 rM1 Þ1 ð1  1=rM2 ÞwM2 ðZÞ,

ð5Þ

where tpe is the total photoeffect cross-section determined from Eq. (2). tK, tLi (i ¼ 1, 2, 3) and tMj (j ¼ 1, 2, 3, 4, 5) are K shell photoeffect cross-sections, Li (i ¼ 1, 2, 3) L subshell photoeffect cross-sections and Mj (j ¼ 1, 2, 3, 4, 5) M subshell photoeffect cross-sections, respectively. rK;Li Mj (i ¼ 1, 2, 3 and j ¼ 1, 2, 3, 4, 5) are the jump ratios. These values were defined as: rk ¼ ðm=rÞS =ðm=rÞL ;

k ¼ K; Li ; Mj

ði ¼ 1; 2; 3 and j ¼ 1; 2; 3; 4; 5Þ subshells; where S and L refer, respectively, to short- and longwavelength sides of the absorption edge, that is, the ‘‘top’’ and ‘‘bottom’’, or maximum and minimum values of mass attenuation coefficients at the absorption edge (Bertin, 1975). The values of these mass attenuation coefficients have been taken from XCOM (Berger et al., 2005). wLi ðZÞ (i ¼ 1, 2, 3) and wMj ðZÞ (j ¼ 1, 2, 3, 4, 5) are the coefficients depending on atomic number Z of target elements. The necessity of using these coefficients has arisen from the complex structure (like a sawtooth) of absorption edges. The coefficients are calculated as follows: t L1 r K , tpe ð1  1=rL1 Þ tL1 rK rL1 wL2 ðZÞ ¼ , tpe ð1  1=rL2 Þ tL1 rK rL1 rL2 wL3 ðZÞ ¼ , tpe ð1  1=rL3 Þ

wL1 ðZÞ ¼

ð6Þ

t L1 r K r L1 r L2 r L3 , tpe ð1  1=rM1 Þ t L r K r L1 r L2 r L3 r M 1 wM2 ðZÞ ¼ 1 , tpe ð1  1=rM2 Þ t L r K r L1 r L2 r L3 r M 1 r M 2 wM3 ðZÞ ¼ 1 , tpe ð1  1=rM3 Þ t L r K r L1 r L2 r L3 r M 1 r M 2 r M 3 wM4 ðZÞ ¼ 1 , tpe ð1  1=rM4 Þ t L r K r L1 r L2 r L3 r M 1 r M 2 r M 3 r M 4 wM5 ðZÞ ¼ 1 , tpe ð1  1=rM5 Þ wM1 ðZÞ ¼

ð7Þ

Table 1 Specifications of wLi ðZÞ (i ¼ 1, 2, 3) and wMj ðZÞ (j ¼ 1, 2, 3, 4, 5)

A B

tL1

tL2

tL3

tM1

tM2

tM3

tM4

tM5

5.43379 0.0308

0.4946 0.01481

0.1525 0.00699

15.8661 0.0887

2.1725 0.06192

0.15535 0.01299

0.00312 0.1297

0.0088 0.65438

ARTICLE IN PRESS N. Kaya et al. / Radiation Physics and Chemistry 77 (2008) 101–106

where tpe, tLi (i ¼ 1, 2, 3) and tMj (j ¼ 1, 2, 3, 4, 5) are theoretical photoeffect cross-sections and are taken from tabulated theoretical values of Scofield (1973). rK;Li ;Mj (i ¼ 1, 2, 3 and j ¼ 1, 2, 3, 4, 5) are the same as mentioned above.wLi ðZÞ (i ¼ 1, 2, 3) and wMj ðZÞ (j ¼ 1, 2, 3, 4, 5) were

103

fitted a linear curve (wLi ðZÞ ¼ Ai þ Bi  Z, i ¼ 1, 2, 3 and wMj ðZÞ ¼ Aj þ Bj  Z, j ¼ 1 ,2, 3, 4, 5) with correlation coefficients of determination R2E0.95, and standard deviation of the fits SDE0.05. The coefficients are introduced in Table 1, where A and B coefficients are the

Table 2 tK and tLi (i ¼ 1,2,3) photoeffect cross sections Element

tK

65

Tb Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au S0 Hg 81 T1 82 Pb 83 Bi 90 Th 92 U 66

tL1

tL2

tL3

Exp.

Theo.

Exp.

Theo.

Exp.

Theo.

Exp.

Theo.

341717 364718 390719 412721 438722 458723 480724 492725 556728 581729 559728 624731 708735 705735 752738 799740 841742 931747 1019751 1220761 1318766

370 391 413 436 458 482 508 534 560 588 615 643 672 702 732 732 763 827 861 1104 1174

35.8272.15 37.5572.25 40.3772.42 42.8572.57 44.6572.68 47.4772.85 49.9673.00 51.0973.07 57.9673.48 60.6173.64 58.0773.48 64.8973.89 73.9074.43 72.2574.34 78.5974.72 84.5275.07 87.7575.27 98.5975.92 105.4876.33 129.8777.79 143.0578.58

37.17 39.37 41.65 44.02 46.47 49.01 51.63 54.34 57.13 60.01 63.00 66.03 69.18 72.41 75.72 79.13 82.62 86.20 89.85 117.89 126.69

8.1470.49 9.2270.55 10.2870.62 11.3570.68 12.3770.74 14.5170.87 14.7870.89 15.7770.95 18.6071.12 20.1771.21 20.1371.21 23.4271.41 27.6971.66 28.2771.70 31.5971.90 34.7472.08 38.1472.29 43.6972.62 48.3172.90 79.5874.77 90.0275.40

8.83 9.73 10.71 11.77 12.91 14.15 15.48 16.92 18.47 20.14 21.98 23.85 25.92 28.13 30.50 33.04 35.75 38.66 41.76 69.95 80.54

9.2070.55 10.0870.60 11.1370.67 12.0870.72 13.1070.79 13.8670.83 15.2870.92 16.1270.97 18.6271.12 20.0671.20 19.7471.1S 22.6771.36 26.2471.57 26.5471.59 29.5071.77 32.3271.94 34.4872.07 39.0872.34 43.0272.5S 61.9373.72 70.9074.25

9.65 10.52 11.44 12.43 13.49 14.61 15.80 17.08 18.41 19.83 21.34 22.93 24.61 26.39 28.26 30.23 32.30 34.48 36.77 56.11 62.85

Exp., experimental; Theo., theoretical. Table 3 tMj (j ¼ 1, 2,3,4,5) photoeffect cross sections Element

65

Tb Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 0s 77 L78 Pt 79 Au 80 Hg 81 T1 82 Pb 83 Bi 90 Th 92 U 56

tM1

tM2

tM3

tM4

tM5

Exp.

Theo.

Exp.

Theo.

Exp.

Theo.

Exp.

Theo.

Exp.

Theo.

7.6170.46 8.0770.48 8.7170.52 9.3170.56 9.7770.59 9.9170.59 10.4470.63 10.9670.66 12.5970.76 13.2770.80 12.8770.77 14.0970.85 15.9670.96 15.8870.95 17.3371.04 18 2571.10 20.3371.22 21.5471.29 24.3871.46 29.0471.74 32.1871.93

7.82 8.29 8.81 9.35 9.91 10.49 11.09 11.71 12.35 13.02 13.70 14.41 15.14 15.90 16.68 17.48 18.30 19.14 20.01 26.74 28.85

1.8770.07 1.8870.08 2.5370.10 2.5670.10 2.8370.11 3.0070.12 3.3970.14 3.6170.14 4.2970.17 4.5770.18 4.6770.19 5.3470.21 6.2370.25 6.3770.25 7.1370.29 7.9370.32 8.3770.33 10.4270.42 10.7570.43 17.8270.71 20.7570.83

1.95 2.16 2.38 2.63 2.89 3.18 3.48 3.81 4.17 4.55 4.96 5.41 5.88 6.39 6.93 7.51 8.14 8.80 9.51 15.90 18.29

2.1070.08 2.3970.10 2.6670.11 2.8770.11 3.0170.12 3.2770.13 3.6870.15 3.7870.15 4.5070.18 4.7470.19 4.6570.19 5.2770.21 6.0670.24 6.1870.25 6.7970.27 7.3870.30 8.1170.32 9.2270.37 10.1170.40 15.3870.62 17.9070.72

2.19 2.40 2.62 2.86 3.11 3.39 3.68 3.93 4.31 4.66 5.02 5.41 5.83 6.26 6.72 7.21 7.72 8.26 8.82 13.64 15.32

0.0770.01 0.0870.01 0.1370.01 0.1070.01 0.1670.02 0.1370.01 0.1570.02 0.1670.02 0.2870.03 0.2770.03 0.3070.03 0.3070.03 0.3870.04 0.3670.04 0.4070.04 0.4170.04 0.5970.06 0.5070.05 0.5170.05 1.1070.11 1.4070.14

0.08 0.09 0.11 0.12 0.14 0.16 0.18 0.20 0.22 0.25 0.28 0.31 0.35 0.39 0.43 0.47 0.52 0.58 0.64 1.22 1.45

0.0970.01 0.0870.01 0.1070.01 0.1170.01 0.2070.02 0.2070.02 0.1770.02 0.2870.03 0.1770.02 0.2570.03 0.2870.03 0.3070.03 0.3770.04 0.3870.04 0.4070.04 0.4470.04 0.4970.05 0.6470.06 0.5970.06 1.1070.11 1.3170.13

0.09 0.10 0.12 0.13 0.15 0.17 0.19 0.21 0.24 0.26 0.29 0.33 0.34 0.40 0.44 0.49 0.54 0.59 0.65 1.19 1.40

Exp., experimental; Theo., theoretical.

ARTICLE IN PRESS 104

N. Kaya et al. / Radiation Physics and Chemistry 77 (2008) 101–106

intercept value and slope value of fit, respectively. The values of these coefficients taken from the linear fit equations have been used in Eqs. (4) and (5). 3. Results and discussion In Tables 2 and 3, we present our measured tK, tLi (i=1, 2, 3) and tMj (j=1, 2, 3, 4, 5) photoeffect cross-sections in elements between Tb (Z=65) and U (Z=92) at an energy of 123.6 keV g-photons. Also, the theoretical values of tK, tLi (i=1, 2, 3) and tMj (i=1, 2, 3, 4, 5) are given in same tables. We have compared values of experimental photoeffect cross-sections with theoretical ones. Our experimental total atomic, K shell, L shell–subshell and M shell–subshell photoeffect cross-sections agree to within 0.42–12%, 0.50–18%, 0.22–17% and 0.31–27% of the theoretical values taken from the tabulated theoretical values of Scofield (1973). They are plotted as a function of the atomic number as shown in Figs. 1 and 2. It is clear that, within the

experimental average error, the measured values are in agreement with the theoretical values. The overall error on the measured value (root mean of all error contributions) of the K X-ray production cross-sections is as discussed in Apaydın and Tıras- og˘lu (2006). In this study, the overall error in tK, tLi (i ¼ 1, 2, 3) and tMj (i ¼ 1, 2, 3, 4, 5) is estimated to be E6–14%. These errors result from the uncertainties in the parameters used to calculate tLi (i ¼ 1, 2, 3) and tMj (i ¼ 1, 2, 3, 4,5); that is, uncertainties in the tpe photoeffect cross-sections and the fit coefficients A and B in wLi ðZÞ (i ¼ 1, 2, 3) and wMj ðZÞ (j ¼ 1, 2, 3, 4, 5). As a result, more experimental and theoretical values for the elements from Tb to U are needed for full knowledge of K shell, L shell–subshell and M shell–subshell photoeffect cross-sections, covering a wider range of energy. We believe that the experimental values may serve three purposes. Firstly, they offer an indirect check on the reliability of the available values. Secondly, with the present work it has been established that these experimental values for photoeffect cross-sections can be used with confidence for

Fig. 1. Comparison of results.

ARTICLE IN PRESS N. Kaya et al. / Radiation Physics and Chemistry 77 (2008) 101–106

105

Fig. 2. Comparison of results.

element analysis of different types of samples. Thirdly, these experimental values can be used to calculate experimental absorption jump factors and jump ratios of K shell, L shell–subshell and M shell–subshell. Moreover,

the present agreement between the theoretical and experimental values leads to the conclusion that the data presented here could be of benefit to those using XRF techniques.

ARTICLE IN PRESS 106

N. Kaya et al. / Radiation Physics and Chemistry 77 (2008) 101–106

References Apaydın, G., Tıras-og˘lu, E., 2006. Measurements of K shell X-ray production cross sections and fluorescence yields of elements in the atomic number range 65pZp92 at 123.6 keV. Nucl. Instr. and Meth. B 246, 303–308. Arora, S.K., Allawadhi, K.L., Sood, B.S., 1981. L-shell photoelectric cross section measurements. J. Phys. B 14, 1423. Arora, S.K., Allawadhi, K.L., Sood, B.S., 1981. K-shell photoelectric cross-section measurements. Phys. Rev. A 23, 1147. Berger, M.J., Hubbell, J.H., 1987. XCOM: Photon Crosssections on a Personnel Computer (Version 1.2) NBSIR 87-3597. Berger, M.J., Hubbell, J.H., 1999. XCOM: Photon Crosssections on a Personnel Computer (Version 1.3) NIST MD 20899. Berger, M.J., Hubbell, J.H., Seltzer, S.M., Chang, J., Coursey, J.S., Sukumar, R., Zucker, D.S., 2005. XCOM: Photon Cross-Section Database (Version 1.3). [Online] Available from: /http://physics.nist. gov/xcomS. National Institute of Standards and Technology, Gaithersburg, MD. Bertin, E.P., 1975. Principles and Practice of X-ray Spectrometric Analysis. Plenum Press, New York, p. 59. Chantler, C.T., 1995. Theoretical form factor, attenuation and scattering tabulation for Z ¼ 1–92 from E ¼ 1–10 eV to E ¼ 0.4–1.0 MeV. J. Phys. Chem. Ref. Data 24, 71–643. Creagh, D.C., Hubbell, J.H., 1992. X-ray absorption (or attenuation) coefficients. In: Wilson, A.J.C. (Ed.), International Tables for Crystallography, C Section 4.2.4. Kluwer Academic Publishers, Dordrecht, The Netherlands, p. 189. Ertug˘ral, B., Apaydın, G., C - evik, U., Ertug˘rul, M., Kobya, A.I˙., 2007. Kb/Ka X-ray intensity ratios for elements in the range 16Z92 excited by 5.9, 59.5 and 123.6 keV photons. Radiat. Phys. Chem. 76, 15–22. Gu¨rol, A., Karabulut, A., Polat, R., Budak, G., S- ahin, Y., Ertug˘rul, M., 2003. L-subshell and total L-shell photoeffect cross-sections measurements for Pb, Au, W, and Ta at 59.5 keV. Radiat. Phys. Chem. 66, 197.

Hubbell, J.H., 1999. Compilation of photon cross-sections: some historical remarks and current status. X-ray Spectrom 28, 215. Hubbell, J.H., 1999. Review of photon interaction cross section data in the medical and biological context. Phys. Med. Biol. 44, R1–R22. Hubbell, J.H., 2006. Review and history of photon cross section calculations, Phys. Med. Biol. 51, R245–R262. Karabulut, A., Gu¨rol, A., Budak, G., Ertugrul, M., 2005. K shell and L subshell and L shell photoeffect cross sections in the atomic region 40pZp52 and 58pZp68 at 59.537 keV. Nucl. Instr. and Meth. B 227, 485. Karabulut, A., Gu¨rol, A., Budak, G., Polat, R., 2002. Measurements of L subshell and total L shell photoeffect cross-sections for some elements in 72pZp92. Eur. Phys. J. D. 21, 57. Krause, M.O., 1979. Atomic radiative and radiationless yield for K and L shells. J. Phys. Chem. Ref. Data 8, 307. Nathuram, R., Rao, I.S.S., yMehta, M.K., 1988. Photo effect cross sections for 6–20 keV photons in beryllium, carbon, magnesium, aluminum, silicon, copper, silver, and lead. Phys. Rev. A 374978. Nayak, S.V., Badiger, N.M., 2006. Measurement of K-shell photoelectric absorption parameters of Hf, Ta, Au, and Pb by an alternative method using a weak X-particle source. Phys. Rev. A 73, 032707. Roy, B., Chatterjee, B.K., Roy, S.C., Bhattacharya, N., Choudhury, N., 1997. Photoelectric cross-sections derived from measured total attenuation coefficient of photons near absorption edges of heavier atoms. Appl. Radiat. Isot. 48, 785. Scofield, J.H., 1973. Theoretical photoionization cross sections from 1 to 1500 keV, Lawrence Livermore Laboratory Report UCRL–51326. Scofield, J.H., 1974.Relativistic Hartree–Slater values for K and L X-ray emission rates. Atom Data Tables 14, 121. Umesh, T.K., Ranganathaiah, C., Sanjeevaiah, A., 1985. Photoeffect cross sections of some rare-earth elements at 145.4 keV. Phys. Rev. A 322.