Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

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V. K. Garg¹, M. Gupta¹, M. K. Tiwari², A. Sharma<sup>1,*

1</sup> Chitkara School of Engineering and Technology, Chitkara University, Himachal Pradesh, India
² Raja Ramanna Centre for Advanced Technology, Indore, India

^*Corresponding author. E-mail address: ajay.sharma@chitkarauniversity.edu.in

Abstract: A comprehensive theoretical study of the angular anisotropy and linear polarization of characteristic L-shell X-ray emission from high-Z atoms (tantalum, tungsten, rhenium, iridium, gold, and thallium) produced by photoionization with unpolarized photons is reported. The calculations are performed within the non-dipole approximation employing three alternative descriptions of the atomic potential: (i) point Coulomb field, (ii) screened Coulomb field, and (iii) analytical perturbative treatment. To examine only direct L-shell fluorescence, the incident photon energy is limited to the range extending from the L₃ absorption threshold to the K-shell edge, thereby eliminating contributions from K-shell ionization, Coster-Kronig transitions, and inter-shell vacancy transfer processes. The degree of linear polarization for the L_ℓ, L_α1, and L_α2 spectral lines is calculated up to 60 keV to determine their variation with excitation energy. The results indicate that vacancy alignment reaches its maximum close to the threshold, where great changes in subshell ionization amplitudes and photoelectron partial-wave components occur. As the photon energy increases, the alignment progressively decreases, leading to reduced anisotropy and polarization, and gradually approaches a slowly varying high-energy limit. The L_ℓ transition consistently shows greater anisotropy than the L_α lines, while the polarization values of L_ℓ, L_α1, and L_α2 remain transition-specific because of differences in angular momentum coupling and radiative transition matrix elements. A systematic dependence on atomic number is observed throughout the investigated elements, with heavier atoms exhibiting comparatively greater changes in the polarization behaviour. While this trend may reflect the combined influence of relativistic effects, spin-orbit coupling, and electron-correlation effects commonly associated with heavier atomic systems. Although all three theoretical approaches predict similar overall energy-dependent trends, noticeable quantitative differences are obtained in the polarization magnitudes, demonstrating the sensitivity of the results to the adopted potential model and alignment treatment. Comparison with previously published results of Kämpfer et al. and Özdemir et al. confirms the consistency of the present calculations and offers a deeper theoretical understanding of the combined influence of vacancy alignment, multipole mixing, and relativistic dynamics in L-shell X-ray emission.

Keywords: L-shell X-ray emission, polarization, anisotropy, photoionization, high-Z atoms.

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