  We study the fragmentation of very large dimers into two singly charged ions
caused by absorption of a photon. In this process a photo electron emitted from
one atom of the dimer has certain chances to hit the other atom knocking out
one of its electrons. This results in the production of two singly charged ions
and the consequent Coulomb explosion of the residual doubly charged system. We
develop a theory of this process and apply it to calculate the fragmentation of
$^4$He$_2$, $^7$Li - $^4$He and $^6$Li - $^4$He dimers. Our results for the
helium dimer are in good agreement with available experimental data. For the
Li-He dimers (where experimental data are still absent) our results predict
that this fragmentation mechanism becomes much more efficient than in the case
of He$_2$. We also show that, provided the recoil effects are of minor
importance, the so called reflection approximation is very accurate also for
large dimers.
