  The presence and abundance of the short-lived radioisotopes (SLRs) $^{26}$Al
and $^{60}$Fe during the formation of the Solar System is difficult to explain
unless the Sun formed in the vicinity of one or more massive star(s) that
exploded as supernovae. Two different scenarios have been proposed to explain
the delivery of SLRs to the protosolar nebula: (i) direct pollution of the
protosolar disc by supernova ejecta and (ii) the formation of the Sun in a
sequential star formation event in which supernovae shockwaves trigger further
star formation which is enriched in SLRs.
  The sequentially triggered model has been suggested as being more
astrophysically likely than the direct pollution scenario. In this paper we
investigate this claim by analysing a combination of $N$-body and SPH
simulations of star formation. We find that sequential star formation would
result in large age spreads (or even bi-modal age distributions for spatially
coincident events) due to the dynamical relaxation of the first star-formation
event(s). Secondly, we discuss the probability of triggering spatially and
temporally discrete populations of stars and find this to be only possible in
very contrived situations. Taken together, these results suggest that the
formation of the Solar System in a triggered star formation event is as
improbable, if not more so, than the direct pollution of the protosolar disc by
a supernova.
