  Nuclei with equal number of baryons but varying proton number (isobars) have
many commonalities, but differ in both electric charge and nuclear structure.
Relativistic collisions of such isobars provide unique opportunities to study
the variation of the magnetic field, provided the nuclear structure is well
understood. In this Letter we simulate collisions using several
state-of-the-art parametrizations of the $^{96}_{40}$Zr and $^{96}_{44}$Ru
isobars and show that a comparison with the exciting STAR measurement
arXiv:2109.00131 of ultrarelativistic collisions can uniquely identify the
structure of both isobars. This not only provides an urgently needed
understanding of the structure of the Zirconium and Ruthenium isobars, but also
paves the way for more detailed studies of nuclear structure using relativistic
heavy ion collisions.
