# Nuclide Importance and the Steady-State Burnup Equation

## Abstract

Conventional methods for evaluating some characteristic values of nuclides relating to burnup in a given neutron spectrum are reviewed in a mathematically systematic way, and a new method based on the importance theory is proposed. In this method, these characteristic values of a nuclide are equivalent to the importances of the nuclide. By solving the equation adjoint to the steady-state burnup equation with a properly chosen source term, the importances for all nuclides are obtained simultaneously.The fission number importance, net neutron importance, fission neutron importance, and absorbed neutron importance are evaluated and discussed. The net neutron importance is a measure directly estimating neutron economy, and it can be evaluated simply by calculating the fission neutron importance minus the absorbed neutron importance, where only the absorbed neutron importance depends on the fission product. The fission neutron importance and absorbed neutron importance are analyzed separately, and detailed discussions of the fission product effects are given for the absorbed neutron importance.

- Authors:

- Tokyo Institute of Technology (Japan)

- Publication Date:

- OSTI Identifier:
- 20804638

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 135; Journal Issue: 1; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0029-5639

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BURNUP; EQUATIONS; FISSION NEUTRONS; FISSION PRODUCTS; NEUTRON FLUX; NEUTRON SPECTRA; STEADY-STATE CONDITIONS

### Citation Formats

```
Sekimoto, Hiroshi, and Nemoto, Atsushi.
```*Nuclide Importance and the Steady-State Burnup Equation*. United States: N. p., 2000.
Web.

```
Sekimoto, Hiroshi, & Nemoto, Atsushi.
```*Nuclide Importance and the Steady-State Burnup Equation*. United States.

```
Sekimoto, Hiroshi, and Nemoto, Atsushi. Mon .
"Nuclide Importance and the Steady-State Burnup Equation". United States.
```

```
@article{osti_20804638,
```

title = {Nuclide Importance and the Steady-State Burnup Equation},

author = {Sekimoto, Hiroshi and Nemoto, Atsushi},

abstractNote = {Conventional methods for evaluating some characteristic values of nuclides relating to burnup in a given neutron spectrum are reviewed in a mathematically systematic way, and a new method based on the importance theory is proposed. In this method, these characteristic values of a nuclide are equivalent to the importances of the nuclide. By solving the equation adjoint to the steady-state burnup equation with a properly chosen source term, the importances for all nuclides are obtained simultaneously.The fission number importance, net neutron importance, fission neutron importance, and absorbed neutron importance are evaluated and discussed. The net neutron importance is a measure directly estimating neutron economy, and it can be evaluated simply by calculating the fission neutron importance minus the absorbed neutron importance, where only the absorbed neutron importance depends on the fission product. The fission neutron importance and absorbed neutron importance are analyzed separately, and detailed discussions of the fission product effects are given for the absorbed neutron importance.},

doi = {},

journal = {Nuclear Science and Engineering},

issn = {0029-5639},

number = 1,

volume = 135,

place = {United States},

year = {2000},

month = {5}

}