  RX J1713.7-3946 is one of the TeV {\gamma}-ray supernova remnants (SNRs)
emitting synchrotron X rays. The SNR is associated with molecular gas located
at ~1 kpc. We made new molecular observations toward the dense cloud cores,
peaks A, C and D, in the SNR in the 12CO(J=2-1) and 13CO(J=2-1) transitions at
angular resolution of 90". The most intense core in 13CO, peak C, was also
mapped in the 12CO(J=4-3) transition at angular resolution of 38". Peak C shows
strong signs of active star formation including bipolar outflow and a
far-infrared protostellar source and has a steep gradient with a
r^{-2.2$\pm$0.4} variation in the average density within radius r. Peak C and
the other dense cloud cores are rim-brightened in synchrotron X rays,
suggesting that the dense cloud cores are embedded within or on the outer
boundary of the SNR shell. This confirms the earlier suggestion that the X rays
are physically associated with the molecular gas (Fukui et al. 2003). We
present a scenario where the densest molecular core, peak C, survived against
the blast wave and is now embedded within the SNR. Numerical simulations of the
shock-cloud interaction indicate that a dense clump can indeed survive shock
erosion, since shock propagation speed is stalled in the dense clump.
Additionally, the shock-cloud interaction induces turbulence and magnetic field
amplification around the dense clump that may facilitate particle acceleration
in the lower-density inter-clump space leading to the enhanced synchrotron X
rays around dense cores.
