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The onset of gravitational collapse in cluster-forming clouds is still poorlyknown. Our goal is to use the Class 0 protostar IRAS 4A, which is undergoingcollapse in the active molecular cloud NGC 1333, to set constraints on thisprocess. In particular we want to measure the mass infall rate and investigatewhether the collapse could have been triggered by a strong externalperturbation. We analyze existing continuum observations to derive the densitystructure of the envelope, and use our new molecular line observations donewith the IRAM 30m telescope to probe its velocity structure. We perform adetailed comparison of this set of data with a numerical model of collapsetriggered by a fast external compression. Both the density and velocitystructures of the envelope can be well fitted by this model of collapse inducedby a fast external compression for a time elapsed since point mass formation of1-2 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 infallrate is of the same order as the momenta measured for the NGC 1333 numerousoutflows. Our analysis shows also that the turbulence is highly non uniform inthe envelope, dropping from supersonic to subsonic values toward the center.The inner subsonic turbulence is most likely a relic of the conditionsprevailing in the dense core before the onset of collapse. The vigorouscollapse undergone by IRAS 4A was triggered by a fast external compression,probably related to the expansion of a nearby cavity, which could havetriggered 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 agood protostellar candidate yet.Comment: Accepted by A&A. 12 pages, 10 figure

Strongly induced collapse in the Class 0 protostar NGC 1333 IRAS 4A