  We show that collider data on elastic pp (and p\bar{p}) scattering, including
the LHC TOTEM data at 7 TeV, can be well described by a 3-channel eikonal model
with only one Pomeron, with parameters that are naturally linked to the
perturbative QCD (BFKL) framework. The proton opacity, determined in this way,
is then used to account for sizeable absorptive effects. We study the recent
measurements of d\sigma/d\Delta\eta made by the ATLAS collaboration, where they
select events with large rapidity gaps \Delta\eta. We demonstrate that the
absorptive corrections noticeably change both the value and the \Delta\eta
dependence of the cross section. We find that our parameter-free calculation is
in agreement with these ATLAS data.
