  There is increasing interest in using high-energy collisions to probe the
structure of nuclei, in particular with the high-precision data made possible
by collisions performed with pairs of isobaric species. A systematic study
requires a variation of parameters representing nuclear properties such as
radius, skin thickness, angular deformation, and short-range correlations, to
determine the sensitivity of the various observables on each of these
properties. In this work we propose a method for efficiently carrying out such
study, based on the shifting of positions of nucleons in Monte-Carlo samples.
We show that by using this method, statistical demands can be dramatically
reduced -- potentially reducing the required number of simulated events by
orders of magnitude -- paving the way for systematic study of nuclear structure
in high-energy collisions,
