.. index:: GramCharlierComptonProfile
The GramCharlierComptonProfile function calculates the Compton profile of a nucleus using a Gram-Charlier approximation convoluted with an instrument resolution function. The Gram-Charlier expansion of the Neutron Compton profile, J(y) is given by [1] as an expansion of Hermite polynomials,
J(y) = \frac{e^{-y^2/2\sigma^2}}{\sqrt{2\pi}\sigma}\left[ 1+ \sum_{n=2}^{\infty}\frac{a_n}{2^{2n}n!}H_{2n}\left(\frac{y}{\sqrt{2}\sigma}\right)\right]\label{a}
where, \sigma is the standard deviation (Gaussian width parameter), a_n the hermite coefficients and H_n the Hermite polynomial terms. As well as the even polynomial terms, a third order factor is included of the form,
\frac{A}{\sqrt{2\pi} \sigma} \times FSE \times \exp(-z^2) \times H_3 (z) \label{b}
where z=y/\sqrt{2\pi\sigma^2} and FSE is an input ampltiude scaling parameter. The Hermite coefficients, a_n, are supplied to the function in the parameters C_0, C_2 and C_4. The attribute HermiteCoeffs may be used to determine which polynomial terms are active, e.g "1 0 1" will cause C_0 and C_4 to be active.
The instrument resolution, R_M, is approximated by a :ref:`Voigt <func-Voigt>` function.
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[1] Pantalei C, Pietropaolo A, Senesi R, Imberti S, Andreani C, Mayers J, et al. Proton Momentum Distribution of Liquid Water from Room Temperature to the Supercritical Phase. Phys Rev Lett 2008;100. https://doi.org/10.1103/physrevlett.100.177801.
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