One-particle resonant levels in a deformed potential

(S)olving the Schrodinger 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 Omega(pi)not equal 1/2(+) the corresponding one-particle resonant levels can be always found for small positive energies. For one-particle bound levels with Omega(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 Omega(pi)=1/2(+) one-particle resonant levels, in which epsilon=0 components in the wave functions play a crucial role, is further studied using a simplified model without spin-orbit potential.