  In high-energy heavy-ion collisions, the initial condition of the produced
quark-gluon plasma (QGP) and its evolution are sensitive to collective nuclear
structure parameters describing the shape and radial profiles of the nuclei. We
find a general scaling relation between these parameters and many experimental
observables such as elliptic flow, triangular flow, and particle multiplicity
distribution. In particular, the ratios of observables between two isobar
systems depend only on the differences of these parameters, but not on the
details of the final state interactions, hence offering a new way to constrain
the QGP initial condition. Using this scaling relation, we show how the
structure parameters of $^{96}_{44}$Ru and $^{96}_{40}$Zr conspire to produce
the rich centrality dependences of these ratios, as measured by the STAR
Collaboration. Our scaling approach demonstrates that isobar collisions are a
precision tool to probe the initial condition of heavy-ion collisions, as well
as the collective nuclear structures, including the neutron skin, of the atomic
nuclei across energy scales.
