Molecular clumps disguising their star formation efficiency per freefall time: What we can do not to be fooled

The presence of a volume density gradient in molecular clumps allow them to raise their star formation rate compared to what they would experience were their gas uniform in density. This higher star formation rate yields in turn a higher value for the star formation efficiency per freefall time that we measure. The measured star formation efficiency per freefall time $\epsilon_{\rm ff, meas}$ of clumps is therefore plagued by a degeneracy, as two factors contribute to it: one is the density gradient of the clump gas, the other is the intrinsic star formation efficiency per freefall time $\epsilon_{\rm ff, int}$ with which the clump would form stars should there be no gas density gradient. This paper presents a method allowing one to recover the intrinsic efficiency of a centrally-concentrated clump. It hinges on the relation between the surface densities in stars and gas measured locally from clump center to clump edge. Knowledge of the initial density profile of the clump gas is not required. A step-by-step description of the method is provided as a tool in hand for observers. Once $\epsilon_{\rm ff, int}$ has been estimated, it can be compared with its measured, clump-averaged, counterpart $\epsilon_{\rm ff, meas}$ to quantify the impact that the initial gas density profile of a clump has had on its star formation history.