Star-forming regions presenting a density gradient experience a higher star formation rate than if they were of uniform density. We refer to the ratio between the star formation rate of a spherical centrally-concentrated gas clump and the star formation rate that this clump would experience if it were of uniform density as the magnification factor $zeta$. We map $zeta$ as a function of clump mass, radius, initial volume density profile and star formation time-span. For clumps with a steep density profile (i.e. power-law slope ranging from $-3$ to $-4$, as observed in some high-density regions of Galactic molecular clouds), we find the star formation rate to be at least an order of magnitude higher than its top-hat equivalent. This implies that such clumps experience faster and more efficient star formation than expected based on their mean free-fall time. This also implies that measurements of the star formation efficiency per free-fall time of clumps based on their global properties, namely, mass, mean volume density and star formation rate, present wide fluctuations. These reflect the diversity in the density profile of star-forming clumps, not necessarily variations in the physics of star formation. Steep density profiles inside star-cluster progenitors may be instrumental in the formation of multiple stellar populations, such as those routinely observed in old globular clusters.
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