  Using the Glauber theory, we calculate reaction cross sections for the
deformed halo nucleus $^{31}$Ne. To this end, we assume that the $^{31}$Ne
nucleus takes the $^{30}$Ne + $n$ structure. In order to take into account the
rotational excitation of the core nucleus $^{30}$Ne, we employ the
particle-rotor model (PRM). We compare the results to those in the adiabatic
limit of PRM, that is, the Nilsson model, and show that the Nilsson model works
reasonably well for the reaction cross sections of $^{31}$Ne. We also
investigate the dependence of the reaction cross sections on the ground state
properties of $^{31}$Ne, such as the deformation parameter and the p-wave
component in the ground state wave function.
