The basic idea of scattering cross-section is to connect the part of
the incoming beam which strikes a given area 
of the
scatterer with the solid angles 
into which the scattered
objects go. Imagine that a steady and uniform flux density of J
particles per unit area per unit along 
is incident on the
reflector. Into what range of angles 
and 
will
all the particles of the beam which impact the reflector in the
annulus defined by 
scatter? ( terms to first
order in db only.) Do you expect the particles to be scattered
evenly among these angles?