Kβ to Kα Intensity Ratio and Total Vacancy Transfer Probabilities of Molybdenum and Silver

Using a simple method of targets of Mo and Ag being excited by a weak Cs137 γ-ray source it was possible to determine K shell Xray intensity ratios (IKβ/IKα) and the total vacancy transfer probabilities (ηKL) of Moand Ag. The targets of Mo and Ag were excited using barium K X-rays from a weak Cs137 γ-ray source. K shell X-rays were detected using Si (Li) X-ray detector coupled to 8k multichannel analyzer. The values of IKβ to IKα ratios and ηKL are compared with the theoretical values and experimental data of other experimentalists and the results are found to be in good agreement.


Introduction
X-ray fluorescence (XRF) intensity ratios and vacancy transfer probabilities of elements and compounds have been found to have wide applications in many areas of diverse applications. These applications require the accurate values of K shell X-ray intensity ratios and vacancy transfer probabilities of elements. In the past few decades, several researchers have determined K shell X-ray intensity ratios and vacancy transfer probabilities of various elements and compounds by different methods (For e.g., Apaydin and Tiraşoğlu, 2012;Hopman et al., 2012;Cengiz et al., 2011, Cengiz et al., 2010. However these methods require strong γ-ray sources of the order of 100 to 200 mCi and hence require shielding from strong radiations. Our group has developed a simple method to determine K shell fluorescence parameters of elements and compounds by using 2π-geometrical configuration with weak γ-ray sources of the order of 1 µCi (Horakeri et al., 1997; Gudennavar et al., 2003b;Bennal et al., 2010). The method essentially involves placing the target between the detector and the source. Because of the wide solid angle, source strength requires could be as low as of the order of a few µCi. Recently Tursucu et al., (2012) have determined the K shell intensity ratios and total vacancy probabilities of 9 elements in the atomic range 40 ≤ Z ≤ 50 employing this simple method and they report that the method yields the results comparable with the results of reflection geometry experiments. In the present work, we have determined the I Kβ /I Kα intensity ratios and total vacancy probabilities of Mo and Ag by using Si(Li) detector coupled to a PC based 8k multichannel analyzer and a weak Cs 137 source. The targets of Mo and Ag were excited using barium K X-rays of energy 32.86 keV resulting in the Internal Conversion (IC) process in Cs 137 .

Experimental
The experimental set up consists of a Si(Li) X-ray detector, spectroscopy amplifier , a high voltage bias supply and a PC based MCA to detect and measure the intensity of K X-rays emitted from Mo and Ag targets (Fig.1). The Si (Li) detector had an active surface area of 20 mm 2 , 3.5 mm thick and Be window of 12.5 µm thickness. The energy resolution of the detector is 140 eV at 5.9 keV Mn K X-ray. The Si (Li) X-ray detector spectrometer was calibrated using various gamma and X-ray sources. The target materials of pure molybdenum and silver, were purchased in the form of thin foil of required thickness from local company. The Mo and Ag targets were excited using the barium K X-rays of energy 32.86 keV resulting in the IC process of Cs 137 . The weak point Cs 137 γ-ray source (2 µCi) prepared on a thin plastic disc was obtained from Radiopharmaceuticals Division, Therapeutic and Reference Sources Section, BARC, Mumbai.
The total K to L vacancy transfer probability is given (Schönfield and Janßen, 1996) by 84 K β to K α Intensity Ratio and Total Vacancy Transfer Probabilities of Molybdenum and Silver The ratio of the intensity of the characteristic X-ray of type i to type j is given by where i = K β and j = K α ; and are the measured intensities of K shell X-ray of type i and j respectively, ε i and ε j are the efficiencies of the detector for K shell X-ray of type i and j respectively, exp(-μ xiw t w ) and exp(-μ xjw t w ) are the window attenuation correction factors for fluorescence X-rays of type i and j respectively; μ xiw and μ xjw are the mass attenuation coefficients of K shell X-rays of type i and j in the detector window of thickness t w ; β i and β j are the self-attenuation correction factors for the K shell X-ray of type i and type j respectively in the target material and are calculated using the eqn. ( where μ i and μ e are the mass attenuation coefficients (cm 2 /gm) of the incident and emitted K shell X-rays respectively in the target of thickness t (g/cm2) and are computed using WinXcom software (Berger et al., 2005).
The intensities of K shell X-rays of Mo and Ag targets were measured as follows. The 'source spectrum with background' was acquired for the live time of 5000s by placing the source in front of the face of the detector window, as close as possible so as to have wide solid angle (Fig.  2).Tthe target was then placed between the source and the detector window to acquire the 'transmitted spectrum with background' for the same duration of live time (Fig. 3). Subtraction of the former from the latter, gives a clean K shell X-ray fluorescence spectrum of the target element under investigation (Fig. 4). Each K shell X-ray peak is then fitted to a Gaussian distribution function using ORIGIN software and the area under the peak is estimated carefully. The area under each peak gives the intensity of K shell X-ray of given type, which is then corrected for self attenuation in the target, attenuation in the window and the efficiency of the detector to get the total number of K shell X-rays emitted in the forward hemisphere. The I Kβ /I Kα intensity ratios and total vacancy probabilities of Mo and Ag are calculated using the following eqs.

Results and Discussion
The molybdenum and silver targets were excited using barium K x-rays of weighted energy of 32.86 keV from weak 137 Cs gamma source. The K x-rays emitted were detected using Si(Li) detector spectrometer. From the measured K shell X-ray intensity ratios and the ω k values taken from Hubbell tables (Hubbell, 1989), the total vacancy transfer probabilities for pure molybdenum and silver have been determined. The results along with the theoretical values calculated by Scofield (1974) and others' experimental values obtained by adopting reflection geometry for these elements are presented in Table 1.  From the table, it is clear that our results agree with the theoretical and others' experimental values. Thus the present study shows that the simple 2π geometrical configuration method employing weak gamma source can be an alternate method