Optical-model analysis of 14N+12C and 12C+12C elastic scattering in the range Ec.m.=35 to 63 MeV.

Abstract

Optical-model analyses have been performed with an optical-model code for $^{12}\mathrm{C}$${+}^{12}$C elastic scattering in the center-of-mass energy range ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=35--63 MeV. A total of 125 parameter sets have been found and a taxonomy of potential families is proposed on the basis of volume integrals and rms radii. To complement this study four parameter sets at ${\mathit{E}}_{\mathrm{lab}}$=81 and 100 MeV for $^{14}\mathrm{N}$${+}^{12}$C found in a previous report are also discussed. Conventional Woods-Saxon parameters of different real well depth and with either a volume or surface absorption predict the observed differential cross sections at six energies in the $^{12}\mathrm{C}$${+}^{12}$C case. The potentials found form discrete families corresponding to the quantum mechanical requirement for the allowed number of wavelengths of distorted waves in the interior region of the potential. Excitation functions for $^{12}\mathrm{C}$${+}^{12}$C elastic scattering were calculated with these parameters in the center-of-mass energy range ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=15--95 MeV and four families of potentials of different real well depth predict gross structure at 90\ifmmode^\circ\else\textdegree\fi{} that persists undiminished throughout this energy range. Inspection of the predicted cross-section surface shown as a function of energy and angle revealed important features which are in good qualitative agreement with experiment. Color contour visualizations of such surfaces gave new insights into the regularity of cross-section structures in different angular regions.