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Lβ/L Intensity Ratios of Antimony at Different Azimuthal and Polar Angles

Lβ/L X-ray intensity ratios of antimony (Sb) were investigated at different azimuthal (-30° ≤ φ ≤+30°, at intervals of 10°) and polar scattering angles (85°≤ θ ≤135° at intervals of 10°). In the purpose of exciting to Sb and detecting the X-rays emitted from Sb, 241 Am point source and Si(Li) detector have been used, respectively. The data was analysed by means of Origin 9 Software and it was determined that Lβ/L change by polar scattering angle at a fixed azimuthal scattering angle and by azimuthal scattering angle at a fixed polar scattering angle.


Introduction
Antimony ([Kr] 4d 10 5s 2 5p 3 ) which exists metalic and non-metalic form is an element in 5A group of periodic table. It founds in nature as free or is obtained from ores of Sb2S3 and Sb2O3. The pure form Antimony is used the production of diodes and infrared detectors. The alloyed Antimony and its compounds which have importance for world economy are used in low friction metals, batteries, paints, pottery, make-up and ceramics etc.
The radiation interacts with the matter in different processes. One of the interactions is photoelectric effect. In this interaction, the atom is bombarded by photons and the atom is excited or ionized by moving of any electron of atom to upper energy levels or out of the atom. If this electron ejected is on L subshell, electron transitions occur through upper levels to L sub-shell with radiative or nonradiative. The radiation having different frequencies emits during these transitions and they are called L X-rays. The transitions that make L rays and Lβ rays occurred are shown in Table 1.
X-rays are characterized by alignment (distortion of the charge cloud) and orientation parameters (the sum-angular momentum or circulation). If there are a vacancy states on K, L1, L2, M1 and M2 shells (J=1/2), the transitions to these shells make isotropic and unpolarized emission of X-rays form (Cooper et al., 1969) or on L3, M3, M4 and M5 (J>1/2), the transitions to these shells make anisotropic and polarized emission of X-rays form (Flügge et al., 1972). While (Lβ and L) X rays are isotropic, (L and L) are anisotropic (Kahlon et al., 1991;Ertuğrul, 1996;Seven and Koçak, 2002;Han et al., 2008 and. The depending on the angular and magnetic field of L and L emission (anisotropic) are stronger than Lß (isotropic) emission (Demir and Şahin, 2007). Determining of L X-ray intensity correctly is beneficial to test theoretical predictions and in terms of to be used in a wide area like medical area, sample analysis (Doğan et al., 1998) and geological, nuclear and atomic physics (Yalçın et al., 2008). There are lots of studies about L Xrays before. The some of these studies; Doğan et al. (1998) have measured the L shell X-ray intensity ratios for Ta, W, Re, Au, Hg, T1, Pb, Bi, Th and U at excitation energies of 59.5 and 122 keV with a Si(Li) detector and observed agreement between the experimental and theoretical values. Yalçın et al. (2008) have determined the measurements of the L X-ray intensity ratio for elements Dy, Ho, Yb, W, Hg, Tl and Pb by photon excitation of 241 Am and the radioactive decay of 160 Tb, 160 Er, 173 Lu, 182 Re, 20 1Tl, 203 Pb and 207 Bi. They have found that the conclusions of the search support the theoretical and other experimental results and L X-ray intensity ratios for samples by radioactive decay of radioisotopes deviated significantly from both experimental and theoretical results in literature. Söğüt et al. (1997) have investigated chemical effects on the Lβ/Lα and Lγ/Lα X-ray intensity ratios of Hg, Pb and Bi. They have determined that L X-ray intensity ratios are effected by the chemical environment of atoms and Lβ/Lα intensity ratios are affected less than Lγ/Lα intensity ratios. Cesareo et al. (2009) have studied the depending on the composition and thickness of the layer of X-ray ratios of K/Kβ, L/Lβ and L/Lγ. They have calculated K/Kβ, L/Lβ and L/Lγ as a function of material and thickness of the corresponding layer and shown many examples of using these ratios to identify layers and related thicknesses. Wang et al. (2016) have measured the angular distribution of W-Lα, Lβ1 and Lβ2 X-rays induced by 13.1 keV bremsstrahlung at diffferent emission angles from 110° to 140° at intervals of 10°. They have shown that Lβ1 X-ray yield shows isotropic emission, while the measured Lα and Lβ2 X-ray yields are anisotropic. They have determined the anisotropy parameters for Lα and Lβ2 X-rays.
Kawai has studied chemical effects on the intensity ratio of Lα and Lβ lines of transition metals with an XRF spectrometer and determined to be characterized the bond covalency of compounds with Lβ/Lα intensity ratio.
In this work, since the changes in Lβ/L with respect to angle for Sb have been investigated firstly, this study is important. The aim of the present study is to measure Lβ/L intensity ratios of Sb with different polar and azimuthal scattering angles and to observe whether there is a change or not at this value.

Materials and Methods
In this study, Sb (powder form) was turned into pellet which radius is with 13 mm by applying pressure. The angle between the γ rays coming from point source and normal of sample was fixed at 45°. The source and sample were rotated together. The data was obtained at six different polar scattering angles (85°≤ θ ≤135° with steps of 10°) for a fixed azimuthal scattering angle and at seven different azimuthal scattering angles (-30° ≤ φ ≤+30°, with steps of 10°) for fixed polar scattering angle on the experimental setup ( Figure 1). 100 mCi 241 Am point source having γ photons with 59.54 keV of energy in order to excite the sample and Si(Li) detector for counting to photons emitted from sample were used. The photons coming to the detector was placed to the channels according to energies via multichannel analyzer. The data was analyzed at Origin 9 computer program. Typical Spectrum is seen for L and Lβ rays of Sb in Figure 2.  been calculated by measuring the peak areas of characteristic K X-rays of K, Cr, Co, Ni, Cu, Zn, Y, Zr, Nb and Mo. The detector efficiency graph for the polar scattering angle (θ =115°) is seen in Figure 3. I0 is γ-ray intensity and G is the geometrical contribution changing with the radioactive element-target array.
0 i IG  is given by: The theoretical Ki  (the possibility of Ki X-ray fluorescence) is given by this formula: where () K E  was obtained from (Storm and Israel, 1970),  To minimize the experimental error, the measurement was taken with and without the sample for different azimuthal and polar scattering angles. The measurement without sample was subtracted from the measurement with sample for all angel values. The overall error in the present measurements is estimated to be 1-3 %.
In this work, experimental error was calculated by using equation following: where ∆ , ∆ are counts error of and X-ray intensity peaks; ∆ , ∆ are the βLi errors for and X-ray photons; ∆ 0 and ∆ 0 are the effective photon flux errors at and energies. The total of the uncertainties are sourced from different factors such as the evaluation of peak areas (<0.4%), I0Gε product (<0.5%), absorption correction factor (<0.2%) and experimental geometry (<0.1%).
These results are compatible with the before studies that; Seven and Koçak (2002) have measured the Ll, Lα, Lβ and Lγ X-ray production cross-sections in U, Th, Bi, Pb, Tl, Hg and Au using 59.5 keV incident photon energies in the angular range 40-130 • . Lβ and Lγ X-rays were found to be angle independent, those for Ll and Lα X-rays were found to be angle dependent. They have found that ILβ/IL ratios increase with the emission angle (θ= from 40° to 130°, at intervals of 10°) for U, Th, Bi, Pb, Tl, Hg and Au. Ertuğrul (1996) has studied measurement of cross-sections and Coster-Kronig transition effect on L subshell X-rays of some heavy elements in the atomic range 79 ≤ Z ≤92 at 59.5 keV and has determined that ILβ / IL ratios increase with the scatter angle (θ= 45°, 60°, 75°, 90°, 105°, 120° and 135°) for Pb. Kahlon et al. (1990) have measured the angular distribution and polarization of the L-shell fluorescent X-rays excited by 59.57-keV photons in Th and U and found that ILβ / IL ratios increase with emission angle (θ= from 40° to 120°, at interval of 10°) for U and Th.    Han et al. (2008) have been studied angular variations of K and L X-ray fluorescence cross sections for some lanthanides and found that ILβ / IL increase with emission angle (θ= from 120° to 150°, at intervals of 10°) for Sm, Eu, Gd, Tb, Dy, Ho and Er.
When the results evaluate the before studies, we may arrive the conclusion that since Lβ X-rays are independent the angle and Lα is dependent to the angle, the probability of Lα X-rays may decrease the changing of the polar and azimuthal scattering angles. This state may cause of the increasing of ILβ / IL ratios.
In the same way, when Figure 5 and Table  2 are examined, it is seen that ILβ / IL ratios generally increases with the variation of azimuthal scattering angle (from +30° to -30°) at all polar scattering angles.  has found that Kβ/Kα intensity ratios are not dependent on azimuthal scattering angle. Han et al. (2008) have found that Kβ/Kα intensity ratios are constant at all emission angles. Since Kβ/Kα intensity ratio which depends on the physical and chemical environments of the elements in the sample (Raj et al. 1998;Pawloski et al 2002) is consant at all polar and azimuthal scattering angles, it is appropriate for studies made to determine some individual atomic parameters, ILβ / IL ratios which change by depending on the angle may not be appropriate for that.

Results
In this study, Lβ /L X-ray intensity ratios of Sb were investigated at different azimuthal and polar scattering angles. It is seen that ILβ/IL ratios change with the polar and azimuthal scattering angles. This value is not same at different angles. This variation should be taken into account at the studies.
In terms of confidence of the evaluation, this study may be repeated for different polar and azimuthal scattering angles and elements.