  We have carried out first-principles calculations of the Compton scattering
spectra to demonstrate that the filling of the hole Fermi surface in
LaO$_{1-x}$F$_{x}$FeAs produces a distinct signature in the Fourier transformed
Compton spectrum when the momentum transfer vector lies along the [100]
direction. We thus show how the critical concentration $x_c$, where hole Fermi
surface pieces are filled up and the superconductivity mediated by
antiferromagnetic spin fluctuations is expected to be suppressed, can be
obtained in a bulk-sensitive manner.
