Kα, Kβ, Lα, and Lβ X-ray fluorescence cross sections for lanthanides in the atomic range 62 ≤ Z ≤ 68 (Sm, Eu, Gd Tb, Dy, Ho, and Er) were simultaneously measured by 59.54 keV incident photon energy at five angles ranging from 120° to 160°. The measurements were performed using an Am-241 radioisotope as the photon source and a Si(Li) detector. The Lα X-ray fluorescence cross section (σLα) was found to decrease with increasing emission angle and showed an anisotropic distribution of Lα X-rays. Kα, Kβ, and Lβ X-ray fluorescence cross sections (σKα, σKβ, and σLβ) were observed to be angle-independent and showed an isotropic distribution of Kα, Kβ, and Lβ X-rays. The Kα and Kβ X-rays originate from filling of the K shell (J = 1/2) vacancies, Lβ X-rays from filling of the L1 and L2 (J = 1/2) subshell vacancies, and Lα X-rays from filling of the L3 subshell (J = 3/2) vacancy. The fluorescent X-rays originating from the vacancy states with J = 1/2 are isotropic and unpolarized, but fluorescent X-rays originating from the vacancy states with J > 1/2 are anisotropic and polarized. Thus, the atomic inner shells vacancy states with J > 1/2 are aligned whereas vacancy states with J = 1/2 are not aligned. Lα fluorescence X-rays have an anisotropic distribution, while Kα, Kβ, and Lβ fluorescence X-rays have isotropic distribution. Furthermore, the IKβ/IKα, ILα/IKα}, ILβ/IKα, and ILβ/ILα intensity ratios for the elements under investigation were determined. The experimental cross sections and intensity ratios for Kα, Kβ, Lα, and Lβ fluorescence X-rays were also determined, and these experimental values were compared with our calculated theoretical values.PACS Nos.: 32.30.Rj, 32.80.Cy
