# Reduction of small-angle scattering profiles to finite sets of structural invariants

## Abstract

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters calledK _{n}which are related to the shape of the object of study. TheseK _{n}, together with a radiusR, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and theD _{max}parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1373191

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Acta Crystallographica Section A Foundations and Advances; Journal Volume: 73; Journal Issue: 4

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Houdayer, Jérôme, and Poitevin, Frédéric.
```*Reduction of small-angle scattering profiles to finite sets of structural invariants*. United States: N. p., 2017.
Web. doi:10.1107/S205327331700451X.

```
Houdayer, Jérôme, & Poitevin, Frédéric.
```*Reduction of small-angle scattering profiles to finite sets of structural invariants*. United States. doi:10.1107/S205327331700451X.

```
Houdayer, Jérôme, and Poitevin, Frédéric. Fri .
"Reduction of small-angle scattering profiles to finite sets of structural invariants". United States.
doi:10.1107/S205327331700451X.
```

```
@article{osti_1373191,
```

title = {Reduction of small-angle scattering profiles to finite sets of structural invariants},

author = {Houdayer, Jérôme and Poitevin, Frédéric},

abstractNote = {This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters calledKnwhich are related to the shape of the object of study. TheseKn, together with a radiusR, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and theDmaxparameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.},

doi = {10.1107/S205327331700451X},

journal = {Acta Crystallographica Section A Foundations and Advances},

number = 4,

volume = 73,

place = {United States},

year = {Fri Jun 09 00:00:00 EDT 2017},

month = {Fri Jun 09 00:00:00 EDT 2017}

}