$ \chi ^{2}$ Minimisation

$ \chi ^{2}$ is a measure of the deviation of the theoretical spectrum and the experimental spectrum, giving a best fit when it is at a minimum. The analysis programs vary the parameters of the theoretical spectrum to find a minimum in $ \chi ^{2}$ according to the following formula:

$\displaystyle \chi^{2} = \frac{1}{N-n} \sum^{N}_{i=1} \left[ \frac{E_{i}-T_{i}}{\sqrt{E_{i}}} \right]^{2}$ (4.1)

where $ N$ is the number of channels (576 in this case) and $ n$ is the number of parameters that are free to vary. $ E_{i}$ and $ T_{i}$ are the number of counts in the $ i$th channel of the experimental and theoretical spectra respectively.

Dr John Bland, 15/03/2003