A deformed relativistic Hartree Bogoliubov (RHB) theory in continuum is developed aiming at a proper description of exotic nuclei, particularly those with a large spatial extension. In order to give an adequate consideration of both the contribution of the continuum and the large spatial distribution in exotic nuclei, the deformed RHB equations are solved in a Woods-Saxon (WS) basis in which the radial wave functions have a proper asymptotic behavior at large distance from the nuclear center. This is crucial for the proper description of a possible halo. The formalism of deformed RHB theory in continuum is presented. A stable nucleus, ${}^{20}$Mg and a weakly bound nucleus ${}^{42}$Mg are taken as examples to present numerical details and to carry out necessary numerical checks. In addition, the ground-state properties of even-even magnesium isotopes are investigated. The generic conditions of the formation of a halo in weakly bound deformed systems and the shape of the halo in deformed nuclei are discussed. We show that the existence and the deformation of a possible neutron halo depend essentially on the quantum numbers of the main components of the single particle orbitals in the vicinity of the Fermi surface.

• Received 22 November 2011

DOI:https://doi.org/10.1103/PhysRevC.85.024312