  Cosmochemical evaluations of the initial meteoritical abundance of the
short-lived radioisotope (SLRI) $^{26}$Al have remained fairly constant since
1976, while estimates for the initial abundance of the SLRI $^{60}$Fe have
varied widely recently. At the high end of this range, $^{60}$Fe initial
abundances have seemed to require $^{60}$Fe nucleosynthesis in a core collapse
supernova, followed by incorporation into primitive meteoritical components
within $\sim$ 1 Myr. This paper continues the detailed exploration of this
classical scenario, using models of the self-gravitational collapse of
molecular cloud cores that have been struck by suitable shock fronts, leading
to the injection of shock front gas into the collapsing cloud through
Rayleigh-Taylor fingers formed at the shock-cloud interface. As before, these
models are calculated using the FLASH three dimensional, adaptive mesh
refinement (AMR), gravitational hydrodynamical code. While the previous models
used FLASH 2.5, the new models employ FLASH 4.3, which allows sink particles to
be introduced to represent the newly formed protostellar object. Sink particles
permit the models to be pushed forward farther in time to the phase where a
$\sim 1 M_\odot$ protostar has formed, orbited by a rotating protoplanetary
disk. These models are thus able to define what type of target cloud core is
necessary for the supernova triggering scenario to produce a plausible scheme
for the injection of SLRIs into the presolar cloud core: a $\sim 3 M_\odot$
cloud core rotating at a rate of $\sim 3 \times 10^{-14}$ rad s$^{-1}$ or
higher.
