  The Coulomb-like backward peak of the neutron-proton scattering differential
cross section is due to one-pion exchange. Extrapolation to the pion pole of
precise data should allow to obtain the value of the charged pion-nucleon
coupling constant. This was classically attempted by the use of a smooth
physical function, the Chew function, built from the cross section. To improve
accuracy of such an extrapolation one has introduced a difference method. It
consists of extrapolating the difference between the Chew function based on
experimental data and that built from a model where the pion-nucleon coupling
is exactly known. Here we cross-check to which precision can work this novel
extrapolation method by applying it to differences between models and between
data and models. With good reference models and for the 162 MeV neutron-proton
Uppsala single energy precise data with a normalisation error of 2.3 %, the
value of the charged pion-nucleon coupling constant is obtained with an
accuracy close to 1.8 %.
