@article{e72976dec8024209955165bf2cce8932,
title = "Analytical evaluation of atomic form factors: Application to Rayleigh scattering",
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. (C) 2015 AIP Publishing LLC.",
keywords = "SLATER-TYPE ORBITALS, X-RAY-SCATTERING, ELASTIC-SCATTERING, GAMMA-RAYS, LAGUERRE-POLYNOMIALS, SCREENING CONSTANTS, COHERENT SCATTERING, MOMENTUM-TRANSFER, CROSS-SECTIONS, SCF FUNCTIONS",
author = "L. Safari and Santos, {J. P.} and P. Amaro and K. Jankala and F. Fratini",
note = "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 no [291734]. F.F. acknowledges support by Fundacao de Amparo a Pesquisa do estado de Minas Gerais (FAPEMIG), by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), and by the Austrian Science Fund (FWF) through the START Grant No. Y 591-N16. F.F. acknowledges hospitality of the Neel institute in Grenoble (France), where part of the work has been carried out. L.S., K.J., and F.F. acknowledge support by the Research Council for Natural Sciences and Engineering of the Academy of Finland. P.A. acknowledges the support of the German Research Foundation (DFG) within the Emmy Noether program under Contract No. TA 740 1-1 and FCT, under Contract No. SFRH/BPD/92329/2013. J.P.S. and P.A. acknowledge support by Fundacao para a Ciencia e a Tecnologia (FCT) in Portugal, through the Project Nos. PEstOE/FIS/UI0303/2011 and PTDC/FIS/117606/2010. All authors gladly thank Professor Paul Indelicato, Professor Nivaldo Lucio Speziali, and Professor Carmelo Giacovazzo for discussions about possible applications of the presented results in structural crystallography.",
year = "2015",
month = may,
doi = "10.1063/1.4921227",
language = "English",
volume = "56",
journal = "Journal Of Mathematical Physics",
issn = "0022-2488",
publisher = "AMER INST PHYSICS",
number = "5",
}