  The reversal of the time evolution of the local polarization in an
interacting spin system involves a sign change of the effective dipolar
Hamiltonian which refocuses the 'spin diffusion' process generating a
polarization echo. Here, the attenuation of these echo amplitudes as a function
of evolution time is presented for cymantrene and ferrocene polycrystalline
samples, involving one and two five spin rings per molecule respectively. We
calculate the fraction of polarization which is not refocused because only the
secular part of the dipolar Hamiltonian is inverted. The results indicate that,
as long as the spin dynamics is restricted to a single ring, the non-inverted
part of the Hamiltonian is notable by itself to explain the whole decay of the
polarization echoes. A cross over from exponential (cymantrene) to Gaussian
(ferrocene) attenuation is experimentally observed. This is attributed to an
increase of the relative importance of the spin dynamics, as compared with
irreversible interactions, which favors dynamical irreversibility.
