  A candidate of a neutron-halo nucleus, $^{31}$Ne, contains a single neutron
in the $pf$ shell. Within the Glauber and eikonal models, we analyze reactions
used to study $^{31}$Ne. We show in a $^{30}$Ne+n model that the magnitudes of
the total reaction and above all of the one-neutron removal cross sections of
$^{31}$Ne on $^{12}$C and $^{208}$Pb targets strongly depend on the orbital
angular momentum of the neutron, thereby providing us with efficient ways to
determine both the spin-parity and structure of the ground state of $^{31}$Ne.
Besides these inclusive observables, we also calculate energy and
parallel-momentum distributions for the breakup of $^{31}$Ne, and show their
strong dependence upon the orbital of the valence neutron in the bound state of
$^{31}$Ne.
