# Analysis of a Breit-Wigner spectrum

In the following table you can see experimental data of the cross section as a function of energy for neutron scattering:

E (MeV) | 0 | 25 | 50 | 75 | 100 | 125 | 150 | 175 | 200 |
---|---|---|---|---|---|---|---|---|---|

σ (mb) | 10.6 | 16.0 | 45.0 | 83.5 | 52.8 | 19.9 | 10.8 | 8.25 | 4.7 |

The cross-section as a function of energy can be described as the Breit-Wigner function:

$\sigma =\frac{{\sigma}_{0}}{(E-{E}_{r}{)}^{2}+{\displaystyle \frac{{\gamma}^{2}}{4}}}$

where E_{r} is the resonance energy (*position of the maximum*), and γ the width at half-maximum height.

**Objective:** to determine the values of E_{r} and γ from the experimental data. Here, three possible methods are shown: Lagrange Interpolators, Cubic Splines and Least Squares.