  Several lines of evidence, from isotopic analyses of meteorites to studies of
the Sun's elemental and isotopic composition, indicate that the solar system
was contaminated early in its evolution by ejecta from a nearby supernova (SN).
Previous models have invoked SN material being injected into an extant
protoplanetary disk, or isotropically expanding ejecta sweeping over a distant
(>10 pc) cloud core, simultaneously enriching it and triggering its collapse.
Here we consider a new astrophysical setting: the injection of clumpy SN
ejecta, as observed in the Cas A SN remnant, into the molecular gas at the
periphery of an HII region created by the SN's progenitor star. To track these
interactions we have conducted a suite of high-resolution (1500^3 effective) 3D
simulations that follow the evolution of individual clumps as they move into
molecular gas. Even at these high resolutions, our simulations do not quite
achieve numerical convergence, due to the challenge of properly resolving the
small-scale mixing of ejecta and molecular gas, although they do allow some
robust conclusions to be drawn. Isotropically exploding ejecta do not penetrate
into the molecular cloud, but, if cooling is properly accounted for, clumpy
ejecta penetrate to distances ~10^18 cm and mix effectively with star-forming
molecular gas. The ~2 M_\odot high-metallicity ejecta from a core-collapse SN
is likely to mix with ~2 \times 10^4 M_\odot of molecular gas. Thus all stars
forming late (~5 Myr) in the evolution of an HII region may be contaminated by
SN ejecta at a level ~10^-4. This level of contamination is consistent with the
abundances of short-lived radionuclides and possibly some stable isotopic
shifts in the early solar system, and is potentially consistent with the
observed variability in stellar elemental abundances. SN contamination of
forming planetary systems may be a common, universal process.
