  In this paper we extend the work synthetically presented in Ref.[1] and give
theoretical details and complete tables of numerical results. We exploit
calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order
to extract an ``experimental'' strong coupling \alpha_s^{exp}(Q^2) below 1 GeV
by comparison with the meson spectrum. The BS potential follows from a proper
ansatz on the Wilson loop to encode confinement and is the sum of a
one-gluon-exchange and a confinement terms. Besides, the common perturbative
strong coupling is replaced by the ghost-free expression \alpha_E(Q^2)
according to the prescription of Analytic Perturbation Theory (APT). The
agreement of \alpha_s^{exp}(Q^2) with the APT coupling \alpha_E(Q^2) turns out
to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming
quantitatively the validity of the APT prescription. Below this scale, the
experimental points could give a hint on the vanishing of \alpha_s(Q^2) as Q
approaches zero. This infrared behaviour would be consistent with some lattice
results and a ``massive'' generalization of the APT approach. As a main result,
we claim that the combined BS-APT theoretical scheme provides us with a rather
satisfactory correlated understanding of very high and rather low energy
phenomena from few hundreds MeV to few hundreds GeV.
