Numerical Recipes applied
to
Thermodynamics

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:

Experimental data of neutron scattering cross-sections, where mb = milibarn and 1 barn = 10-28m2
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:

σ=σ0(E-Er)2+γ24

Breit-Wigner curve

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.