  In the analysis of experimental data on $p p$ (or $\bar p p$) elastic
differential cross section it is customary to define an average forward slope
$b$ in the form $\exp{(-b|t|)}$, where $t$ is the momentum transfer. Taking as
working example the results of experiments at Tevatron and SPS, we will show
with the help of the impact picture approach, that this simplifying assumption
hides interesting information on the complex non-flip scattering amplitude, and
that the slope $b$ is not a constant. We investigate the variation of this
slope parameter, including a model-independent way to extract this information
from an accurate measurement of the elastic differential cross section. An
extension of our results to the LHC energy domain is presented in view of
future experiments.
