  We present new, spatially resolved [CI]1-0, [CI]2-1, CO(7-6), and dust
continuum observations of 4C 41.17 at $z=3.8$ obtained with the IRAM NOEMA
interferometer. This is one of the best-studied radio galaxies in this epoch
and is arguably the best candidate of jet-triggered star formation at high
redshift currently known in the literature. 4C 41.17 shows a narrow ridge of
dust continuum extending over 15 kpc near the radio jet axis. Line emission is
found within the galaxy in the region with signatures of positive feedback.
Using the [CI]1-0 line as a molecular gas tracer, and multifrequency
observations of the far-infrared dust heated by star formation, we find a total
gas mass of $7.6\times 10^{10}$ M$_{\odot}$, which is somewhat greater than
that previously found from CO(4-3). The gas mass surface density of $10^3$
M$_{\odot}$ yr$^{-1}$ pc$^{-2}$ and the star formation rate surface density of
10 M$_{\odot}$ yr$^{-1}$ kpc$^{-2}$ were derived over the 12 kpc$\times$8 kpc
area, where signatures of positive feedback have previously been found. These
densities are comparable to those in other populations of massive, dusty
star-forming galaxies in this redshift range, suggesting that the jet does not
currently enhance the efficiency with which stars form from the gas. This is
consistent with expectations from simulations, whereby radio jets may
facilitate the onset of star formation in galaxies without boosting its
efficiency over longer timescales, in particular after the jet has broken out
of the interstellar medium, as is the case in 4C 41.17.
