One-particle resonant levels in a deformed potential

Abstract

Solving the Schr\"odinger equation in coordinate space with the appropriate asymptotic boundary conditions, neutron one-particle resonant levels in ${Y}_{20}$-deformed Woods-Saxon potentials are studied. These resonance levels are the natural extension of one-particle bound levels to the continuum and are defined in terms of eigenphase. For one-particle bound levels with ${\ensuremath{\Omega}}^{\ensuremath{\pi}}\ensuremath{\ne}1/{2}^{+}$ the corresponding one-particle resonant levels can be always found for small positive energies. For one-particle bound levels with ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1/{2}^{+}$ the corresponding one-particle resonant levels are either absent or disappearing quickly as energy increases, when we use well-deformed potentials with a realistic size of diffuseness. The possible presence of ${\ensuremath{\Omega}}^{\ensuremath{\pi}}=1/{2}^{+}$ one-particle resonant levels, in which $\ensuremath{\ell}=0$ components in the wave functions play a crucial role, is further studied using a simplified model without spin-orbit potential.