  The onset of gravitational collapse in cluster-forming clouds is still poorly
known. Our goal is to use the Class 0 protostar IRAS 4A, which is undergoing
collapse in the active molecular cloud NGC 1333, to set constraints on this
process. In particular we want to measure the mass infall rate and investigate
whether the collapse could have been triggered by a strong external
perturbation. We analyze existing continuum observations to derive the density
structure of the envelope, and use our new molecular line observations done
with the IRAM 30m telescope to probe its velocity structure. We perform a
detailed comparison of this set of data with a numerical model of collapse
triggered by a fast external compression. Both the density and velocity
structures of the envelope can be well fitted by this model of collapse induced
by a fast external compression for a time elapsed since point mass formation of
1-2 x 10**4 yr. We deduce a large mass infall rate of 0.7-2 x 10**-4 Msun/yr.
The momentum required for the perturbation to produce this large mass infall
rate is of the same order as the momenta measured for the NGC 1333 numerous
outflows. Our analysis shows also that the turbulence is highly non uniform in
the envelope, dropping from supersonic to subsonic values toward the center.
The inner subsonic turbulence is most likely a relic of the conditions
prevailing in the dense core before the onset of collapse. The vigorous
collapse undergone by IRAS 4A was triggered by a fast external compression,
probably related to the expansion of a nearby cavity, which could have
triggered the collapse of the nearby Class 0 protostar IRAS 4B simultaneously.
This cavity could have been generated by an outflow but we have not found a
good protostellar candidate yet.
