  Recent hydrodynamical simulations of the late stages of supernova remnant
(SNR) evolution have revealed that as they merge with the ambient medium, SNRs
implode, leading to the formation of dense clouds in their center. While being
highly chemically enriched by their host SNR, these clouds appear to have
similar properties as giant molecular clouds, which are believed to be the main
site of star formation. Here, we develop a simple model, in order to estimate
the efficiency of the star formation that might be triggered by the implosion
of SNRs. We separately consider two cases, cyclic star formation, maintained by
the episodic driving of feedback from new generations of stars; and a single
burst of star formation, triggered by a single explosion. We find that in the
cyclic case, star formation is inefficient, with implosion-triggered
star-formation contributing a few percent of the observed star-formation
efficiency per free-fall timescale. In the single-burst case, higher
star-formation efficiencies can be obtained. However, while the
implosion-triggered process might not contribute much to the overall
star-formation, due to the high chemical enrichment of the birth clouds, it can
explain the formation of a significant fraction of metal-rich stars.
