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Coulomb dissociation of the deformed halo nucleus 31Ne

The recently observed large cross sections for the Coulomb dissociation of $^{31}$Ne nucleus indicate that this nucleus takes a halo structure in the ground state. We analyse these experimental data using the particle-rotor model, that takes into account the rotational excitation of the core nucleus $^{30}$Ne. We show that the experimental data can be well reproduced when the quadrupole deformation parameter of $^{30}$Ne is around $β_2=0.2\sim0.3$, at which the ground state takes the spin and parity of $I^π$=3/2$^-$. This state corresponds to the Nilsson level [330 1/2] in the adiabatic limit of the particle-rotor model. On the other hand, the state corresponding to the Nilsson level [321 3/2] with $β_2\sim 0.55$ can be excluded when the finite excitation energy of the core is taken into account, even though this configuration is a candidate for the ground state of $^{31}$Ne in the Nilsson model analysis. We discuss briefly also a possibility of the $I^π$=1/2$^+$ configuration with $β_2\sim 1$ and $β_2\sim -0.4$.