Phase-shift parametrization and extraction of asymptotic normalization constants from elastic-scattering data

摘要

We introduce a simplified effective-range function for charged nuclei, related to the modified K matrix but differing from it in several respects. Negative-energy zeros of this function correspond to bound states. Positive-energy zeros correspond to resonances and "echo poles" appearing in elastic-scattering phase-shifts, while its poles correspond to multiple-of-π phase shifts. Padé expansions of this function allowone to parametrize phase shifts on large energy ranges and to calculate resonance and bound-state properties in a very simple way, independently of any potential model. The method is first tested on a d-wave ~(12)C + α potential model. It is shown to lead to a correct estimate of the subthreshold-bound-state asymptotic normalization constant (ANC) starting from the elastic-scattering phase shifts only. Next, the ~(12)C + α experimental p-wave and d-wave phase shifts are analyzed. For the d wave, the relatively large error bars on the phase shifts do not allow one to improve the ANC estimate with respect to existing methods. For the p wave, a value agreeing with the ~(12)C(~6Li,d)~(16)O transfer-reaction measurement and with the recent remeasurement of the ~(16)N β-delayed α decay is obtained, with improved accuracy. However, the method displays two difficulties: the results are sensitive to the Padé-expansion order and the simplest fits correspond to an imaginary ANC, i.e., to a negative-energy "echo pole," the physical meaning of which is still debatable.