  We differentiate the event-by-event n-$\gamma$ multiplicity data from
\ce{^{252}Cf}(sf) with respect to the energies of the emitted particles as well
as their relative angles of emission. We determine that neutron emission
enhances $\gamma$-ray emission around $0.7$ and $1.2$ MeV, but the only
directional alignment was observed for $E_\gamma \leq 0.7$ MeV and tended to be
parallel and antiparallel to neutrons emitted in the same event. The emission
of $\gamma$ rays at other energies was determined to be nearly isotropic. The
presence of the emission and alignment enhancements is explained by positive
correlations between neutron emission and quadrupole $\gamma$-ray emission
along rotational bands in the de-exciting fragments. This observation
corroborates the hypothesis of positive correlations between the angular
momentum of a fragment and its intrinsic excitation energy. The results of this
work are especially relevant in view of the recent theoretical and experimental
interest in the generation of angular momentum in fission. Specifically, we
have determined an alignment of the fragments angular momenta in a direction
perpendicular to the direction of motion. We interpret the lack of $n$-$\gamma$
angular correlations for fission fragments near closed shells as a weakening of
the alignment process for spherical nuclei. Lastly, we have observed that
statistical $\gamma$ rays are emitted isotropically, indicating that the
average angular momentum removed by this radiation is small. These results, and
the analysis tools presented in this work, represent a stepping stone for
future analysis of $n$-$\gamma$ emission correlations and their connection to
angular momentum properties.
