  The Nakanishi perturbative integral representation of the four-dimensional
T-matrix is investigated in order to get a workable treatment for scattering
states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski
space. The projection onto the null-plane of the four-dimensional inhomogeneous
Bethe-Salpeter Equation plays a key role for devising an equation for the
Nakanishi weight function (a real function), as in the homogeneous case that
corresponds to bound states and it has been already studied within different
frameworks. In this paper, the whole formal development is illustrated in
detail and applied to a system, composed by two massive scalars interacting
through the exchange of a massive scalar. The explicit expression of the
scattering integral equations are also obtained in ladder approximation, and,
as simple applications of our formalism, some limiting cases, like the
zero-energy limit and the Wick-Cutkosky model in the continuum, are presented.
