Considering the physical conditions that are relevant for triggering star formation in interactions involving SN shocks and neutral clouds, we have built diagrams of the SNR radius versus the cloud density in which these conditions constrain a shaded zone where star formation is allowed. The diagrams are also tested with fully 3-D MHD radiative cooling 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 zone in the diagrams, a larger magnetic field (~10 $mu$G) causes a significant shrinking, as expected. Applications of our results to real star formation regions in our own galaxy have revealed that their formation could have been triggered by a SN shock wave. Finally, we have evaluated the effective global star formation efficiency of this sort of interactions and found that it is smaller than the observed values in our 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.
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