  In this work, considering the impact of a SNR with a neutral magnetized cloud
we derived analytically a set of conditions which are favorable for driving
gravitational instability in the cloud and thus star formation. We have built
diagrams of the SNR radius, versus the cloud density, that constrain a domain
in the parameter space where star formation is allowed. The diagrams are also
tested with fully 3-D MHD simulations involving a SNR and a self-gravitating
cloud and we find that the numerical analysis is consistent with the results
predicted by the diagrams. While the inclusion of a homogeneous magnetic field
approximately perpendicular to the impact velocity of the SNR with an intensity
~1 $ mu$G results only a small shrinking of the star formation triggering zone
in the diagrams, a larger magnetic field (~10 $ mu$G) causes a significant
shrinking, as expected. Applications of the diagrams to a few regions of our
own galaxy have revealed that star formation in those sites could have been
triggered by shock waves from SNRs. Finally, we have evaluated the effective
star formation efficiency for this sort of interaction and found that it is
smaller than the observed values in our own Galaxy (sfe ~0.01-0.3). This result
is consistent with previous work in the literature and also suggests that the
mechanism presently investigated, though very powerful to drive structure
formation, supersonic turbulence and eventually, local star formation, does not
seem to be sufficient to drive global star formation in normal star forming
galaxies, not even when the magnetic field in the neutral clouds is neglected.
(abridged)
