  The large set of accurate data on differential cross section and analyzing
power from the CERN LEAR experiment on $\bar pp \to \pi^+\pi^-$ in the range
from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation
approach. The initial $\bar pp$ scattering wave functions originate from a
recent $\bar N N$ model. The transition operator is obtained from a combination
of the $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms. A good fit
to the data, in particular the reproduction of the double dip structure
observed in the analyzing powers, requires quark wave functions for proton,
antiproton, and pions with radii slightly larger than the respective measured
charge radii. This corresponds to an increase in range of the annihilation
mechanisms and consequently the amplitudes for total angular momentum J=2 and
higher are much larger than in previous approaches. The final state $\pi\pi$
wave functions, parameterized in terms of $\pi\pi$ phase shifts and
inelasticities, are also a very important ingredient for the fine tuning of the
fit to the observables.
