  Recent meteoritical analyses support an initial abundance of the short-lived
radioisotope $^{60}$Fe that may be high enough to require nucleosynthesis in a
core collapse supernova, followed by rapid incorporation into primitive
meteoritical components, rather than a scenario where such isotopes were
inherited from a well-mixed region of a giant molecular cloud polluted by a
variety of supernovae remnants and massive star winds. This paper continues to
explore the former scenario, by calculating three dimensional, adaptive mesh
refinement, hydrodynamical code (FLASH 2.5) models of the self-gravitational,
dynamical collapse of a molecular cloud core that has been struck by a thin
shock front with a speed of 40 km/sec, leading to the injection of shock front
matter into the collapsing cloud through the formation of Rayleigh-Taylor
fingers at the shock-cloud intersection. These models extend the previous work
into the nonisothermal collapse regime using a polytropic approximation to
represent compressional heating in the optically thick protostar. The models
show that the injection efficiencies of shock front material are enhanced
compared to previous models, which were not carried into the nonisothermal
regime and so did not reach such high densities. The new models, combined with
the recent estimates of initial $^{60}$Fe abundances, imply that the supernova
triggering and injection scenario remains as a plausible explanation for the
origin of the short-lived radioisotopes involved in the formation of our solar
system.
