Role of low-$l$ component in deformed wave functions near the continuum threshold

Abstract

The structure of deformed single-particle wave functions in the vicinity of zero energy limit is studied using a schematic model with a quadrupole deformed finite square-well potential. For this purpose, we expand the single-particle wave functions in multipoles and seek for the bound state and the Gamow resonance solutions. We find that, for the $K^{\pi }=0^{+}$ states, where $K$ is the $z$-component of the orbital angular momentum, the probability of each multipole components in the deformed wave function is connected between the negative energy and the positive energy regions asymptotically, although it has a discontinuity around the threshold. This implies that the $K^{\pi }=0^{+}$ resonant level exists physically unless the $l=0$ component is inherently large when extrapolated to the well bound region. The dependence of the multipole components on deformation is also discussed.

References in corpus (3)

• Deformed nuclear halos
• Kinetic energy and spin-orbit splitting in nuclei near neutron drip line
• From bound states to resonances: analytic continuation of the wave function

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• Pairing and continuum effects on low-frequency quadrupole vibrations in deformed Mg isotopes close to the neutron drip line
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