C-12+C-12 ELASTIC-SCATTERING POTENTIALS OBTAINED BY UNIFYING PHASE-SHIFT ANALYSIS WITH THE MODIFIED NEWTON-SABATIER INVERSE METHOD

A procedure to connect a model-independent phase-shift analysis with the solution of the inverse quantum scattering problem has been developed and applied to experimental differential cross sections of C-12 + C-12 elastic scattering in the energy range E(c.m.) = 8-12 MeV. The minimization of the error square function chi2 is performed with respect to the spectral coefficients involved in the inverse procedure. Input quantities are measured differential cross sections; output results are complex potentials. The real part of the potentials, so obtained, is characterized by a pronounced minimum value of -(7-14) MeV at relative distances in the range 2.4-3 fm and by a Coulomb barrier of height 6-7 MeV in the outer region around r almost-equal-to 8-9 fm. In addition a second minimum, very shallow or vanishing at some incident energies, is found to exist in the region 5-6 fm. The imaginary part of the potential exhibits positive maxima in those regions of radial distances where the real part has minimum values indicating a possible feedback effect of flux to the elastic channel. The overall energy dependence of the potentials shows a shape transition resulting in diminishing the outer potential minimum between E(c.m.) of 9 and 12 MeV. The inverted (real) potentials yield phase shifts of pi/2 in those partial waves where resonances are known to exist. The procedure is tested by recalculating differential cross sections from the inverted energy-dependent potentials with the result that consistent agreement with the experimental input data is found.