Measurement of K β / K α x-ray intensity ratios and K to L shell total vacancy transfer probabilities for elements in the range 40 ≤ Z ≤ 50

The K shell x-ray intensity ratios Kβ/Kα for 9 elements in the atomic range 40 ≤ Z ≤ 50 have been determined for an excitation energy of 59.537 keV. The K-L total vacancy transfer probabilities (ηKL) for these elements have been determined, also. K x-rays emitted by samples were detected using a high resolution Si(Li) semiconductor detector. The measured values were compared with the theoretical values calculated using Scofield's tables based on the Hartree-Slater and Hartree-Fock theories, and available experimental values. The agreement of measured values of intensity ratios and vacancy transfer probabilities were quite satisfactory with theoretical calculations. 
 
   
 
 Key words: K shell intensity ratio, vacancy transfer probability, X-ray.


INTRODUCTION
Transition of an inner-shell electron from one shell to another will involve emission or absorption of high energy, short-wavelength radiation (x-rays).Usually, however, all of the energy levels of inner shells are occupied, so, in order to allow a transition to occur at all, a vacancy must be created in one of the inner shells.The energy required to do this can come from either the absorption of a sufficiently energetic photon, or from the impact with a high energy particle (Ewart, 2008).
The measurements of K β /K α x-ray intensity ratios are significant for comparison with theoretical predictions based on atomic models in order to test the validity of these models.The K α x-rays arise from transitions from the L to the K shell.The K β x-rays arise from transitions from the M-, N-, O-, etc. to the K shell.Atoms with vacancies in the inner shells are unstable and their stability can be regained by single or multiple electron transitions from the outer shells.When a single vacancy is created in an inner shell (for example, the K shell), the vacancy is filled up by an electron coming from some higher shell.As a result, the vacancy is shifted to the higher shell.The transfer coefficients, η KL describes the mean number of vacancies produced in the L shell by one vacancy transfer probability and are important in many practical applications, such as nuclear electron capture, internal conversion of gamma rays, photoelectric effect, and atomic processes leading to the emission of xrays, Auger electrons and computations for medical physics and irradiational process.X-ray fluorescence parameters such as intensity ratio and vacancy transfer probability are very important in understanding the ionization of atoms as well as for non-destructive elemental analysis in several fields such as material science, medical physics, industry and environmental science.
K to L shell vacancy transfer probabilities (η KL ) of molybdenum (Mo), Palladium (Pd), and Cadmium (Cd) have been measured by repeatedly exciting them with the K x-rays of Nickel (Ni) and Tin (Sn) induced by bremsstrahlung emanating from x-ray tube (Santra et al., 2005).Radiative vacancy transfer probabilities from the L 3 subshell to M-, N-and O-shells and subshells in the atomic range 72 ≤ Z ≤ 92 have been obtained (Tuzluca et al., 2008).Vacancy transfer probabilities from K to L for high atomic number elements at 123.6 keV had been measured (Ertugral et al., 2005).K x-ray intensity ratios for Tantalum (Ta), Gold (Au), and Lead (Pb) targets by adopting a 2π geometrical configuration with weak radioactive 57 Co gamma source have been measured (Bennal and Badiger, 2006).Total vacancy transfer probabilities from K to L shell of selected elements in the atomic range 42 ≤ Z ≤ 82 have been determined using weak 57 Co gamma source (Bennal et al., 2010).The average vacancy distributions have been calculated by researchers (Rao et al., 1972).K to L shell and L to M shell vacancy transfer probabilities for elements in the atomic range 37  Z  42 and 18  Z  96 have been measured, respectively (Puri et al., 1993).K shell x-ray production cross-sections and fluorescence yields for Neodymium (Nd), Europium (Eu), Gadolinium (Gd), Dysprosium (Dy) and Holmium (Ho) have been measured using radioisotope x-ray fluorescence in the external magnetic field (Demir and Şahin, 2007).
In the present work, K β /K α x-ray intensity ratios, K shell fluorescence yields and radiative vacancy transfer probabilities from K to L shell for Zirconium (Zr), Niobium (Nb), Mo, Ruthenium (Ru), Rhodium (Rh), Pd, Silver (Ag), Cd, and Sn were investigated.The vacancies were produced by the 59.537 keV photons from an 241 Am point source radioisotope.K x-rays emitted by samples were detected using by a Si (Li) detector having a resolution of 180 eV full widths at half maximum at 5.9 keV.

Experimental setup and method of measurement
The experimental arrangement used for the present measurement shown in Figure 1.The parameters used for estimating K α,β x-ray intensity ratios and total vacancy transfer probabilities are provided in Table 1.The samples were placed at a 45° angle with respect to the beam from the source and excited by 59.537 keV gamma rays from an 241 Am point source.The resultant fluorescent x-rays were detected by a Si(Li) detector (an active diameter = 6.2 mm, sensitive crystal depth = 5 mm, Be window thickness = 0.008 mm, FWHM = 180 eV at 5.9 keV) coupled to a analyzing system (Canberra-DSA1000).Spectroscopically high purity targets of Zirconium (Zr), Nb, Mo, Ru, Rh, Pd, Ag, Cd, and Sn foil samples of thickness ranging from 100 µm to 1 mm and Ru (powder sample) have been used for the measurement.A typical K x-ray spectrum of Zr is shown in Figure 2.
The K α x-ray production cross-section at excitation energy are given by: Where, K  is the total K shell ionization cross-section, K w is the K shell fluorescence yield and K f  is given by:  (2) The experimental K β to K α x-ray intensity ratios are evaluated using the following equation: Where,

1
 and 2  are the absorption coefficients, obtained by means of a computer program named WINXCOM (Gerward et al., 2004), at the incident and emitted x-rays photon energy.The product 0 IG  , containing the terms related to the incident photon flux, geometrical factor and the intrinsic absolute efficiency of the xray detector, was determined by collecting the K α and K β x-ray spectra of samples for 241 Am in the same geometry using equation:

Δl
( l is the orbital angular momentum quantum number) for radiative transitions.Theoretical  radiative vacancy transfer probabilities were calculated using the equation:

RESULTS AND DISCUSSION
The measured values of the K β /K α x-ray intensity ratios in the atomic range 40  Z 50 are listed in Table 2 with the  theoretical and other experimental values.Theoretical values are based on relativistic Hartee-Fock and Hartree-Slater theories (Scofield, 1974a, b).As seen from Table 2, the agreement between the present results and theoretical prediction of Scofield is within the range 3%.

Sample
From Table 2, our measured values closely agree with the values obtained from other researchers (Ertuğrul et al., 2001).The overall error in the experimental parameters is the sum of the uncertainties in different factors, namely, the evaluation of peak areas (2.25 to 6.20%), target mass thickness (1.65 to 4.60%) and statistical error (< 1.00%).Total errors affecting the experimental parameters are calculated between 2.96 to 7.78%.The errors in the evaluation of the areas under the X-and gamma-ray peaks have two main error sources, that is., the errors in the elimination of the background and in the peak fitting procedures.
The measured values of the K shell fluorescence yield K w for elements in the atomic range 40  Z  50 are compared with the theoretical values (Krause, 1979;Hubbell, 1989) and other experimental values (Han et al., 2007;Bennal et al., 2010) in Tables 3. As seen from We believe that the present experimental values may serve three purposes.Firstly, our values confirm the reliability of the existing theoretical values.Secondly, with the vacancy transfer probability values that we have obtained in this study, the elemental analysis of different samples can be calculated with confidence.Thirdly, the experimental values of these vacancy transfer probabilities can be used to calculate the experimental absorption jump factors and jump ratios of K shell, L shell-subshell.In addition, the agreement  Rao et al. (1972).
between experimental and theoretical values indicates that the usage of XRF technique is beneficial for these studies.

Figure 2 .
Figure 2. Typical K x-ray spectrum for Zr.
photons.The values of

L
subshell vacancies produced by one vacancy in the K shell through radiative

Table 1 .
Parameters used for estimating K x-ray intensity ratios and total vacancy transfer probabilities.

Table 4 .
K-L total vacancy transfer probabilities.