Positive-energy one-particle levels in quadrupole-deformed Woods-Saxon potentials

Positive-energy one-particle levels for neutrons in Y20 deformed Woods-Saxon potentials are examined using the eigenphase representation. Taking the example of =1/2+ levels, not only one-particle resonant levels but also all solutions in the eigenphase representation within a model space are studied. It is shown that a particular eigenphase solution among an infinite number of eigenphase solutions at a given energy plays a crucial role in producing low-lying one-particle resonance, whereas for the excitation energy lower than a few MeV the eigenphase sum is almost equal to the particular eigenphase when the sum is expressed by the value mod n. Some one-particle resonant levels defined in terms of eigenphase, which have no correspondence to any bound one-particle levels, are found and discussed. It is shown that the relative probability of the s1/2 component estimated using the probabilities inside the Woods-Saxon potentials is a decisive factor for obtaining one-particle resonant levels as a continuation of weakly bound =1/2+ levels