  We analyze a recent work of Mayers and Abdul-Redah,[J.Phys.: Condens. Matter
{\bf 16}, 4811 (2004)] in which the autors report the existence of anomalous
neutron cross sections in several systems. In the present work we show that the
Deep Inelastic Neutron Scattering (DINS) results presented by the authors are
affected by an inaccurate formalism employed for obtaining nuclear momentum
distributions, and therefore definitive conclusions cannot be drawn on the
subject of anomalous cross sections. We also show the reasons why the exact
formalism for obtaining momentum distributions that we recently published must
be employed for analysing the experimental data instead of the approximations
performed in the mentioned work. We also point out serious inconsistencies
between different results reported in the mentioned work, as well as
incompatibilities with previous results published by the authors. These
inconsistencies, as well as experimental evidence against the existence of
anomalous cross sections not considered by the authors, reinforce the need to
revise critically the procedures on which the usual DINS data analysis is based
as well as the proper characterisation of the experimental set-up.
