Determination of the effectiveC12+C12potential from the sub-Coulomb single-particle resonances

The sub-Coulomb resonances observed in the total reaction yield of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system at 4.9, 5.6, and 6.2 MeV are explained as single-particle resonances. The "true" effective ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ potential is determined directly as the real potential which reproduces best the position and the spacing of the observed sub-Coulomb resonances. This potential is found from a parametrization of the two limiting adiabatic and sudden potentials.