  For systems of unstable particles that mix with each other, an approximation
of the fully momentum-dependent propagator matrix is presented in terms of a
sum of simple Breit-Wigner propagators that are multiplied with finite on-shell
wave function normalisation factors. The latter are evaluated at the complex
poles of the propagators. The pole structure of general propagator matrices is
carefully analysed, and it is demonstrated that in the proposed approximation
imaginary parts arising from absorptive parts of loop integrals are properly
taken into account. Applying the formalism to the neutral MSSM Higgs sector
with complex parameters, very good numerical agreement is found between cross
sections based on the full propagators and the corresponding cross sections
based on the described approximation. The proposed approach does not only
technically simplify the treatment of propagators with non-vanishing
off-diagonal contributions, it is shown that it can also facilitate an improved
theoretical prediction of the considered observables via a more precise
implementation of the total widths of the involved particles. It is also
well-suited for the incorporation of interference effects arising from
overlapping resonances.
