Coupled-channel Green's function approach to deformed continuum Hartree-Fock-Bogoliubov theory

The Rl-beam facilities in the new generation will enable us to approach the neutron drip-line in the 10 ≤ Z ≤ 20 and N ≥ 20 region, where we can expect a new physics situation that neutrons are weakly bound in a deformed nuclear potential under the influence of the pair correlation. A promising theoretical framework to describe this situation may be the Hartree-Fock-Bogoliubov (HFB) method. But an important requirement is that one has to install proper asymptotic behaviours of the nucleon wave function of weakly bound and unbound continuum orbits in order to describe, for instance, the width of the unbound ground state (resonance) of an odd N nucleus next to the drip-line, e.g. 39Mg. We have succeeded in giving a new formulation of the deformed continuum HFB method satisfying this condition, and we shall report it in the present contribution. The new formulation is based on the coordinate-space Green's function technique[l], and we have extended it to deformed nuclei for the first time. A coupled-channel representation[2,3] is adopted to achieve this. We shall present also some numerical examples, for which we adopt nuclei near 38Mg. For simplicity, we use a deformed Woods-Saxon potential to replace the Hartree-Fock mean-field, but we perform the self consistent pairing calculation employing a density-dependent delta interaction. The method has several new features. It produces a continuous spectra for the quasiparticle states (Fig.l). This enables us to argue, for instance, how the width of the quasiparticle states are affected by the pair correlation, the deformation, and the weak binding. This is demonstrated for the [310]| orbit relevant for 39Mg (Fig.l inset). We can also analyze in detail the structure of the continuum quasiparticle states, e.g. by decomposing contributions of the partial waves. It is found that the contribution of the non-resonant continuum orbits including large-/ continuum states have a sizable contributions to the pair correlation. We shall revisit the discussion[2] on the role of Ω = 12 orbits in the pair correlation.(author)