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 .