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 SN
R 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)
