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K-Shell atomic photo effect cross sections at K-edge energies in medium Z--elements.


Among the possible types of interaction of photons with matter below 1 MeV, the atomic photo effect is the predominant one at very low energies. The cross section for this process increases rapidly with decreasing energy and increasing atomic number. An experimental evaluation of the atomic photo effect cross section at K-edge can be carried out by an one of the following methods (i) measurement of K-X ray yield, following the ejection of photo electron, (ii) measurement of the photo electron intensities and (iii) extra polation method. The first method involves corrections such as self-absorption in the target and includes uncertainities associated with the fluorescent yields etc. The second method is relatively complicated and it is not suitable near the threshold as it involves the measurement of the photo electrons of low photon energies. On the other hand, the third method is simple and more accurate as it just involves the measurement of total photon cross sections. Hence, the third method is employed in the present investigations. In the energy region 10-100 keV, where the atomic photo effect cross section is predominant in medium Z- elements (Visweswara Rao et. al. 1981), the indirect method of estimating atomic photo effect cross sections by subtracting a relatively small scattering contribution [ coherent + incoherent ] from the measured total photon cross section preferred (Putta Swamy et. al. 1979). This method is relatively simple and gives fairly accurate results, it has received considerable attention in the past three decades (Sivashankar Rao et. al 1977; Putta Swamy et. al. 1979; Visweswara Rao et. al. 1981). The reliability of the subtraction method depends on the exact knowledge of theoretical (coherent + incoherent) scattering cross section data. Fairly accurate cross section values for coherent and incoherent scattering are available (Hubbell et. al. 1975). Extensive theoretical data on atomic photo effect cross sections have also been published, in the energy region 1-1500 keV, for all elements; they are considered to be highly accurate (Scofield, 1973).

With the motivation, a systematic study of photon attenuation measurements in elements in the energy rage 13--60 keV has been under taken and the results have already been presented (Radhakrishna Murthy and Nageshwar Rao, 2005). In that report the atomic photo effect cross sections of nine elements, Z= 28-50, were obtained and compared with the theoretical values. To supplement the data some of the atomic photo effect cross sections at different energies below K-edge were taken from the available literature (Veigele, 1973). Thus, the energy region studied covers the upper and the lower K-edge of the elements under consideration.


The usual narrow beam geometry is employed in the present investigations and is suitably modified depending on the photon energy and the type of the detector used. For measurements in the low energy region proportional counter with Argon filled is used in geometry already described in an earlier investigation (Radhakrishna Murthy and Nageshwar Rao, 2005). In the energy region 30-660keV a 5.1 cm X 0.4 cm NaI(Tl) scintillation spectrometer in conjection with a narrow beam geometry is employed. The atomic photo effect cross sections above and below the K-edge of each element were fitted by the method of least squares. A typical plot for the elements is shown in Fig.1 (a-d).


The plots above and below the K-edge extrapolated towards the K-edge. The total atomic photo effect cross sections ([[sigma].sub.[tau])],[[sigma].sub.[tau]<]) corresponding to upper and lower K-edge energies were also obtained from the graph. The difference of these two values, at the K-shell binding energy directly gives the K-shell cross section at K-edge. The values so obtained are presented in table-I along with values available in literature (Putta Swamy et. al. 1981; Visweswara Rao 1973).

The K-shell binding energies taken from Hubbell (1975) are given in the second column. The atomic photo effect cross sections of lower and upper K-edge values are presented in columns 3 and 4 respectively, along with the theoretical values (Storm and Isreal 1970; Scofield 1973). The figures in the column 5 corresponds to the K-shell atomic photo effect cross sections of the K-edge energy along with the theoretical values. The values obtained by other authors (Veigele, 1973; Putta Swamy et. al. 1981) are also given. The errors quoted are due to the uncertainties involved in estimating the upper and lower edge cross sections from the graphs, the error on the measurement total cross sections and the error involved in the subtraction procedure to obtain atomic photo effect cross sections. The error on the total atomic photo effect cross section is of the order of 2%.


It can be seen from the table-I that the upper and lower K-edge atomic photo effect cross sections from the present work agree with the values from the Scofield report (1973) with in the experimental errors. A comparison with the values obtained from Veigele's compilation data (1973) shows a general agreement. The upper and lower K-edge and the K-shell cross sections for Ag and Sn measured by Putta Swamy et. al. (1981) are in agreement with the present values.


The author wishes to express his gratitude to Dr. A.S. Nageswara Rao and Dr. P. Anuradha for their valuable support and suggestions.


[1.] Putta Swamy, K.S., Ramakrishna Gowda and Sanjeevaiah, B. 1979. Canadian Journal of Physics, 57 : 92.

[2.] Putta Swamy, K.S., Ramakrishna Gowda and Sanjeevaiah, B. 1981. Canadian Journal of Physics, 59: 853.

[3.] Radhakrishna Murthy, C., Chandra Lingam, S. and Nageshwar Rao, A.S. 2005. Bulletin of Pure and Applied Science, Vol. 24D(No.2):119.

[4.] Scofield, J.H. 1973 .Report UCRL, 51326.

[5.] Storm, E. and Isreal, H.I. 1970. .Nucl. Data Tables, A1; 565.

[6.] Shivashankar Rao, K., Radhakrishna Murthy, V., Parthasaradhi, K., Rama Rao, J. and Laxminarayana, V. 1977. Pramana, 9: 321.

[7.] Visweswara Rao, V., Shahnawaz and Venkateshwara Rao, D. 1981. Physica, 111C: 107.

[8.] Veigele, Wm. J. 1973. At. data tables.

* JNTU, Kukatpalli, Hyderabad, India

C. Radha Krishna Murthy and * S. Chandra Lingam

Dept. of Physics, Kakatiya University, Warangal--506 009, India
Table-I: K-shell total atomic photo effect cross sections at K-edge

Element K-edge K-edge photo effect Total atomic cross section

 keV [[sigma].sub. [[sigma].sub.[tau]<]

Ag 25.67 1577 [+ or -] 34 9684 [+ or -] 212
 1550 (a) 9860 (a)
 1548 (b) 9607 (b)
 1590 (c) 10000 (c)
 1570 d 9832 (d)

Cd 26.87 1448 [+ or -] 32 8944 [+ or -] 196
 1480(a) 9400 (a)
 1487 (b) 9143 (b)
 1500 (c) 9650 (c)

In 28.11 1452 [+ or -] 32 8762 [+ or -] 192
 1420 (a) 8950 (a)
 1428 (b) 8717 (b)
 1470 (c) 9760 (c)

Sn 29.39 1432 [+ or -] 31 8316 [+ or -] 182
 1370 (a) 8510 (a)
 1374 (b) 8318 (b)
 1400 (c) 8650 (c)
 1374 (d) 8450 (d)

Element K-shell cross section
 at K-edge


Ag 8107 [+ or -] 251
 8310 (a)
 8093 (b)
 8410 (c)
 8262 (d)

Cd 7496 [+ or -] 231
 7920 (a)
 7689 (b)
 8150 (c)

In 7334 [+ or -] 226
 7530 (a)
 7320 (b)
 8290 (c)

Sn 6566 [+ or -] 203
 7140 (a)
 6975 (b)
 7250 (c)
 7076 (d)

(a) Storm and Isreal; (b) Scofield; c) Veigele; d) Putta Swamy et. al.
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Author:Murthy, C. Radha Krishna; Lingam, S. Chandra
Publication:Bulletin of Pure & Applied Sciences-Physics
Date:Jan 1, 2006
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