Study of exotic nuclei is one of the important frontiers in nuclear physics. The coupling of weakly bound states and resonant states, deformation, and pairings play important roles at the formation of exotic phenomena. To deal with these uniformly, we develop the deformed relativistic mean field theory in complex momentum representations with BCS pairings. ${}^{44}\mathrm{Mg}$ is chosen as an illustration example. The calculated binding energy indicates that ${}^{44}\mathrm{Mg}$ is a weakly bound nucleus. There are several broad resonant states with low orbital angular momentum near the Fermi surface, and the occupation of these levels is responsible for the halo structure in ${}^{44}\mathrm{Mg}$. The available density distributions suggest that ${}^{44}\mathrm{Mg}$ is a deformed halo nucleus with prolate core and oblate halo, which agree with the deformed relativistic Hartree-Bogoliubov in continuum calculations. In particular, the role of resonances is clearly demonstrated in the halo formation, which is helpful to understand the physical mechanism of deformed exotic nuclei.

• Received 12 January 2023
• Accepted 18 August 2023

DOI:https://doi.org/10.1103/PhysRevC.108.024320