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A deformed relativistic Hartree Bogoliubov (RHB) theory in continuum isdeveloped aiming at a proper description of exotic nuclei, particularly thosewith a large spatial extension. In order to give an adequate consideration ofboth the contribution of the continuum and the large spatial distribution inexotic nuclei, the deformed RHB equations are solved in a Woods-Saxon (WS)basis in which the radial wave functions have a proper asymptotic behavior atlarge distance from the nuclear center. This is crucial for the properdescription of a possible halo. The formalism of deformed RHB theory incontinuum is presented. A stable nucleus, 20Mg and a weakly-bound nucleus,42Mg, are taken as examples to present numerical details and to carry outnecessary numerical checks. In addition, the ground state properties ofeven-even magnesium isotopes are investigated. The generic conditions of theformation of a halo in weakly bound deformed systems and the shape of the haloin deformed nuclei are discussed. We show that the existence and thedeformation of a possible neutron halo depend essentially on the quantumnumbers of the main components of the single particle orbitals in the vicinityof the Fermi surface.

Deformed relativistic Hartree Bogoliubov theory in continuum