C12+C12Coulomb barrier resonances: Direct determination of resonance parameters from elastic scattering measurements

${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering angular distributions have been measured between $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.50\mathrm{} \mathrm{and} 7.05$ MeV at intervals of 0.05 MeV. Resonances were observed in these yields at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{} \mathrm{and} 6.83$ MeV. A phase shift analysis of these data was carried out which resulted in assignments of $J^{\pi }=2^{+}$ ($E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{}$ MeV) and $J^{\pi }=4^{+}$ ($E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.83\mathrm{}$ MeV) for the resonances. Carbon partial widths were determined by parametrizing the deduced phase shifts in terms of isolated Breit-Wigner resonances. The results, ${\Gamma }_c={29}_{-9\mathrm{}}^{+6\mathrm{}}$ keV at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.64\mathrm{}$ MeV and ${\Gamma }_c=11\mathrm{}\pm 3$ keV at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=6.83\mathrm{}$ MeV, demonstrate unambiguously the quasimolecular nature of the resonances.