Analytical evaluation of atomic form factors: Application to Rayleigh scattering
Safari L, Santos J, Amaro P, Jänkälä K, Fratini F. 2015. Analytical evaluation of atomic form factors: Application to Rayleigh scattering. Journal of Mathematical Physics. 56(5), 052105.
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Author
Safari, LalehISTA;
Santos, José;
Amaro, Pedro;
Jänkälä, Kari;
Fratini, Filippo
Department
Abstract
Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wave functions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.
Publishing Year
Date Published
2015-05-20
Journal Title
Journal of Mathematical Physics
Acknowledgement
The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n◦ [291734]. F.F. acknowledges support by Fundação de Amparo à Pesquisa do estado de Minas Gerais (FAPEMIG), by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and by the Austrian Science Fund (FWF) through the START Grant No. Y 591-N16.
Volume
56
Issue
5
Article Number
052105
IST-REx-ID
Cite this
Safari L, Santos J, Amaro P, Jänkälä K, Fratini F. Analytical evaluation of atomic form factors: Application to Rayleigh scattering. Journal of Mathematical Physics. 2015;56(5). doi:10.1063/1.4921227
Safari, L., Santos, J., Amaro, P., Jänkälä, K., & Fratini, F. (2015). Analytical evaluation of atomic form factors: Application to Rayleigh scattering. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4921227
Safari, Laleh, José Santos, Pedro Amaro, Kari Jänkälä, and Filippo Fratini. “Analytical Evaluation of Atomic Form Factors: Application to Rayleigh Scattering.” Journal of Mathematical Physics. American Institute of Physics, 2015. https://doi.org/10.1063/1.4921227.
L. Safari, J. Santos, P. Amaro, K. Jänkälä, and F. Fratini, “Analytical evaluation of atomic form factors: Application to Rayleigh scattering,” Journal of Mathematical Physics, vol. 56, no. 5. American Institute of Physics, 2015.
Safari L, Santos J, Amaro P, Jänkälä K, Fratini F. 2015. Analytical evaluation of atomic form factors: Application to Rayleigh scattering. Journal of Mathematical Physics. 56(5), 052105.
Safari, Laleh, et al. “Analytical Evaluation of Atomic Form Factors: Application to Rayleigh Scattering.” Journal of Mathematical Physics, vol. 56, no. 5, 052105, American Institute of Physics, 2015, doi:10.1063/1.4921227.
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