B. Apagyi et al., C-12-12 ELASTIC-SCATTERING POTENTIALS OBTAINED BY UNIFYING PHASE-SHIFT ANALYSIS WITH THE MODIFIED NEWTON-SABATIER INVERSE METHOD(C), Physical review. C. Nuclear physics, 49(5), 1994, pp. 2608-2617
A procedure to connect a model-independent phase-shift analysis with t
he solution of the inverse quantum scattering problem has been develop
ed 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 min
imization 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 ar
e complex potentials. The real part of the potentials, so obtained, is
characterized by a pronounced minimum value of -(7-14) MeV at relativ
e 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 additio
n a second minimum, very shallow or vanishing at some incident energie
s, is found to exist in the region 5-6 fm. The imaginary part of the p
otential 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 th
e outer potential minimum between E(c.m.) of 9 and 12 MeV. The inverte
d (real) potentials yield phase shifts of pi/2 in those partial waves
where resonances are known to exist. The procedure is tested by recalc
ulating differential cross sections from the inverted energy-dependent
potentials with the result that consistent agreement with the experim
ental input data is found.