The effective-range function in nuclear physics: a method to parameterize phase shifts and extract ANCs

The connection between phase shifts and the ANC has been explored in the frame of the effective range theory. The main result is that, in practice and under rather simple requirements, scattering states (phases shifts) can be correctly described and connected with bound states via the effective range function, and therefore, ANCs can be accurately determined thanks to the analytic properties of this function. This result has an important impact in stellar evolution due to the ANC and phases shifts are directly connected with capture cross sections which, for instance, determine partially the stage and evolution of stars.As a first step, the effective range function is approximated via the effective range expansion which shows that a successful phase-shift description depends on how precise the effective range parameters are determined. Thus, a technique to compute accurately these parameters is developed here. Its construction is based on a set of recurrence relations at low energy, that allows a compact and general description of the truncatedeffective range expansion. Several potential models are used to illustrate the effectivenessof this technique and to discuss its numerical limitations. The results shows that a very good precision of the effective-range parameters can be achieved; nevertheless, to describe experimental phase shifts several effective-range parameters can be needed, which shows a limitation for practical applications.As a second step, the effective range function is analyzed theoretically in an arbitrary energy range. This analysis shows that this function can be decomposed in such a way that contributions of bound states, resonances and background can be separated in a similar way as in the phenomenological R-matrix. In this new form experimental data can be better fitted because the free parameter space is reduced considerably,and therefore, extrapolations are better handled. By construction, the method agrees with the scattering matrix properties which allows a simple calculation of resonances (locations and widths) and asymptotic normalization constants (ANCs). Several tests are successfully performed via potential models. Phase shifts for the 2 + partial wave of the 12C+α are analyzed with this method. They are correctly described including bothresonances at Ec.m. = 2.7 and 4.4 MeV. For the 6.92 MeV (2+) exited state of 16O, the ANC estimation 112(8) × 10 3 fm^−1/2 is obtained taking into account statistical errors.Doctorat en Sciences