Differentiation Unfolding of Proton Recoil Spectra

The lower limit of the integral is set equal to E because at any energy E, only neutrons with energy E E can contribute to M(E). Equation 14.31 may be solved by differentiation to give 

The evaluation of the derivative in Eq. 14.32 is performed by numerical techniques, since it is not the spectrum M(E) that is measured but its binned equivalent, 

An improved differentiation technique consists of first smoothing the true spectrum (p(E) to obtain a smoothed true spectrum p (E), given by 

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