The Galactic supernova remnant (SNR) IC443 is one of the most studied core-collapse SNRs for its interaction with molecular clouds. However, the ambient molecular clouds with which IC443 is interacting have not been thoroughly studied and remain poorly understood. Using Five College Radio Astronomy Observatory 14m telescope, we obtained fully sampled maps of ~ 1{deg} times 1{deg} region toward IC443 in the 12CO J=1-0 and HCO+ J=1-0 lines. In addition to the previously known molecular clouds in the velocity range v_lsr = -6 to -1 km/s (-3 km/s clouds), our observations reveal two new ambient molecular cloud components: small (~ 1) bright clouds in v_lsr = -8 to -3 km/s (SCs), and diffuse clouds in v_lsr = +3 to +10 km/s (+5 km/s clouds). Our data also reveal the detailed kinematics of the shocked molecular gas in IC443, however the focus of this paper is the physical relationship between the shocked clumps and the ambient cloud components. We find strong evidence that the SCs are associated with the shocked clumps. This is supported by the positional coincidence of the SCs with shocked clumps and other tracers of shocks. Furthermore, the kinematic features of some shocked clumps suggest that these are the ablated material from the SCs upon the impact of the SNR shock. The SCs are interpreted as dense cores of parental molecular clouds that survived the destruction by the pre-supernova evolution of the progenitor star or its nearby stars. We propose that the expanding SNR shock is now impacting some of the remaining cores and the gas is being ablated and accelerated producing the shocked molecular gas. The morphology of the +5 km/s clouds suggests an association with IC443. On the other hand, the -3 km/s clouds show no evidence for interaction.
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