The method of Green's functions is employed within quantum field theory to derive model-independent expressions for the T matrix describing inelastic nucleon scattering on an even-even nucleus and formulas for the relevant differential cross section that follow from these expressions. In the problem under consideration, an exact determination of the quantities that appear in these expressions and which carry information about nuclear structure (such as the single-particle Green's function and the single-particle mass operator) is equivalent to taking into account the contributions of both direct processes and all processes of nucleon-nucleus scattering that proceed through the formation of a compound nucleus. Upon going over to relevant model approximations for the above quantities, it is therefore possible to use the resulting formulas in describing scattering processes in a wide range of incident-nucleon energies.