The ground state properties of odd-$Z$ superheavy nuclei in the mass range of $Z=97\mathrm{}–115$ and $N=140\mathrm{}–190$ are systematically investigated in deformed relativistic mean-field (RMF) theory. Special emphasis is placed on nuclear shell effect around $N=184.\mathrm{}$ Calculations clearly show that the RMF model can reliably reproduce the data of binding energy and $\alpha$ decay energy of known nuclei and can also be used to predict the binding energy of unknown nuclei. It is found that deformation plays an important role for many superheavy nuclei. For $N=184\mathrm{}$ isotones, the lighter ones are approximately spherical but the heavier ones are deformed. The $\alpha$-decay energies of $N=184\mathrm{}$ isotones are lower than those of neighboring nuclei in some cases and higher in other cases. This demonstrates that there is a complicated structural behavior for $N=184\mathrm{}$ isotones.

• Received 21 January 2003

DOI:https://doi.org/10.1103/PhysRevC.67.064302