# 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.

- Authors:

- IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg (Austria)
- (Finland)
- Laboratório de Instrumentação, Engenharia Biomédica e Física da Radiação (LIBPhys-UNL), Departamento de Física, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, 2829-516 Caparica (Portugal)
- (Germany)
- Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu (Finland)
- (Austria)
- (Brazil)

- Publication Date:

- OSTI Identifier:
- 22403141

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL CROSS SECTIONS; FORM FACTORS; HARTREE-FOCK METHOD; RAYLEIGH SCATTERING; SINGLE-PARTICLE MODEL; WAVE FUNCTIONS

### Citation Formats

```
Safari, L., E-mail: laleh.safari@ist.ac.at, Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu, Santos, J. P., Amaro, P., Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Jänkälä, K., Fratini, F., Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien, and Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG.
```*Analytical evaluation of atomic form factors: Application to Rayleigh scattering*. United States: N. p., 2015.
Web. doi:10.1063/1.4921227.

```
Safari, L., E-mail: laleh.safari@ist.ac.at, Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu, Santos, J. P., Amaro, P., Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Jänkälä, K., Fratini, F., Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien, & Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG.
```*Analytical evaluation of atomic form factors: Application to Rayleigh scattering*. United States. doi:10.1063/1.4921227.

```
Safari, L., E-mail: laleh.safari@ist.ac.at, Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu, Santos, J. P., Amaro, P., Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Jänkälä, K., Fratini, F., Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien, and Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG. Fri .
"Analytical evaluation of atomic form factors: Application to Rayleigh scattering". United States. doi:10.1063/1.4921227.
```

```
@article{osti_22403141,
```

title = {Analytical evaluation of atomic form factors: Application to Rayleigh scattering},

author = {Safari, L., E-mail: laleh.safari@ist.ac.at and Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu and Santos, J. P. and Amaro, P. and Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg and Jänkälä, K. and Fratini, F. and Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien and Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG},

abstractNote = {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.},

doi = {10.1063/1.4921227},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 5,

volume = 56,

place = {United States},

year = {2015},

month = {5}

}

DOI: 10.1063/1.4921227

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.