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Probing the weakly-bound neutron orbit of $^{31}$Ne with total reaction and one-neutron removal cross sections

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.