# 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) σ (mb) 0 25 50 75 100 125 150 175 200 10.6 16 45 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:

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

where Er is the resonance energy (position of the maximum), and γ the width at half-maximum height.

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