# Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

## Abstract

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general.

- Authors:

- Department of Physics, Faculty of Science and Art, KSUe 46100 K.Maras (Turkey)
- Department of Physics, Faculty of Science and Art, CUe Balcali-Adana (Turkey)

- Publication Date:

- OSTI Identifier:
- 21057098

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 899; Journal Issue: 1; Conference: 6. international conference of the Balkan Physical Union, Istanbul (Turkey), 22-26 Aug 2006; Other Information: DOI: 10.1063/1.2733065; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; CROSS SECTIONS; DIFFUSION; FLUCTUATIONS; LEGENDRE POLYNOMIALS; NEUTRON TRANSPORT; NEUTRON TRANSPORT THEORY; NEUTRONS; SCATTERING; SPHERICAL CONFIGURATION

### Citation Formats

```
Yasa, F., Anli, F., and Guengoer, S.
```*Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry*. United States: N. p., 2007.
Web. doi:10.1063/1.2733065.

```
Yasa, F., Anli, F., & Guengoer, S.
```*Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry*. United States. doi:10.1063/1.2733065.

```
Yasa, F., Anli, F., and Guengoer, S. Mon .
"Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry". United States.
doi:10.1063/1.2733065.
```

```
@article{osti_21057098,
```

title = {Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry},

author = {Yasa, F. and Anli, F. and Guengoer, S.},

abstractNote = {We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general.},

doi = {10.1063/1.2733065},

journal = {AIP Conference Proceedings},

number = 1,

volume = 899,

place = {United States},

year = {Mon Apr 23 00:00:00 EDT 2007},

month = {Mon Apr 23 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2733065

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