  The quasi-fission mechanism hinders fusion in heavy systems through breakup
within zeptoseconds into two fragments with partial mass equilibration. Its
dependence on the structure of both the collision partners and the final
fragments is a key question. Our original approach is to combine an
experimental measurement of the fragments' mass-angle correlations in
$^{40}$Ca$+^{238}$U with microscopic quantum calculations. We demonstrate an
unexpected interplay between the orientation of the prolate deformed $^{238}$U
with quantum shell effects in the fragments. In particular, calculations show
that only collisions with the tip of $^{238}$U produce quasi-fission fragments
in the magic $Z=82$ region, whilst collisions with the side are the only one
which may result in fusion.
