  Experimental values of the lifetime of the 1s level of pionium and of the
difference between the energies of the 2s and 2p levels yield values of the
a(0c) and a(cc) elements of the s-wave scattering matrix for the 2-channel (pi+
pi-, pi0 pi0) system at the pi+ pi- threshold. We develop a method for
obtaining the isospin invariant quanties a20 - a00 and 2a00 + a20 from a(0c)
and a(cc). We emphasize that the isospin invariant scattering lengths a00 and
a20 universally used in the literature cannot be considered to be purely
hadronic quantities.
