Dominance of low-ℓcomponent in weakly bound deformed single-neutron orbits

Abstract

Calculating single-particle (Nilsson) levels in axially symmetric quadrupole-deformed potentials in coordinate space, the structure of weakly bound neutron orbits is studied in the absence of pair correlation. It is shown that in the wave functions of ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1∕{2}^{+}$ orbits, where $\ensuremath{\Omega}$ expresses the projection of the particle angular momentum along the symmetry axis, the $\ensuremath{\ell}=0\phantom{\rule{0.3em}{0ex}}({s}_{1∕2})$ component becomes overwhelmingly dominant as the binding energy of the orbits approaches zero, irrespective of the size of the deformation and the kind of Nilsson orbits. Consequently, all ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1∕{2}^{+}$ levels become practically unavailable for both deformation and many-body pair correlation, when the levels approach continuum or lie in the continuum.