Gaussian fits to the MEG LSF

The effects of fitting a Gaussian function to a line spread function which is more complex, a Gaussian core with Lorentzian conponent for the wings, can result in a narrower Gaussian than would be obtained by using the more complete Gaussian plus Lorentzian function. To demonstrate this effect a simulation was generated using a delta function convolved with the RMF for the first order MEG which has both the Gaussian and Lorentzian component. This function was then fit with a Gaussian that was not convolved with the RMF so that the wings would not appear. The region over which the fit was performed was decreased so that only the core was being fit. The columns in table 1 are the energy range being fit, the best fit sigma of the simple Gaussian fit and the absolute value of $\Delta$%

$$\vert\vert ({(\sigma - 3.06\times 10^{-4})\over 3.06 \times 10^{-4}})*100 \vert\vert$$

assuming that the widest energy range is the true Gaussian width.

Figure 13: Full LSF (Gaussian + Lorentzian)

Figure 14: LSF 652 - 656 eV

Energy Range	Gaussian $\sigma$	$\Delta$
0.650 - 0.658	3.06$\times$10$^{-4}$	$\cdots$
0.652 - 0.656	3.06$\times$10$^{-4}$	0.0%
0.653 - 0.655	3.04$\times$10$^{-4}$	0.6%
0.6532 - 0.6545	2.92$\times$10$^{-4}$	4.6%
0.6535 - 0.6543	2.77$\times$10$^{-4}$	9.5%