Failure of the Woods-Saxon nuclear potential to simultaneously reproduce precise fusion and elastic scattering measurements

A precise fusion excitation function has been measured for the ${}^{12}\mathrm{C}$+${}^{208}\mathrm{Pb}$ reaction at energies around the barrier, allowing the fusion barrier distribution to be extracted. The fusion cross sections at high energies differ significantly from existing fusion data. Coupled reaction channels calculations have been carried out with the code FRESCO. A bare potential previously claimed to uniquely describe a wide range of ${}^{12}\mathrm{C}$+${}^{208}\mathrm{Pb}$ near-barrier reaction channels failed to reproduce the new fusion data. The nuclear potential diffuseness of 0.95 fm which fits the fusion excitation function over a broad energy range fails to reproduce the elastic scattering. A diffuseness of 0.55 fm reproduces the fusion barrier distribution and elastic scattering data, but significantly overpredicts the fusion cross sections at high energies. This may be due to physical processes not included in the calculations. To constrain calculations, it is desirable to have precisely measured fusion cross sections, especially at energies around the barrier.

Figure 1

(a) The evaporation residue (ER) and fission cross sections as a function of center-of-mass energy for the ${}^{12}\mathrm{C}$+${}^{208}\mathrm{Pb}$ reaction. (b) The ratio of the fission to ER cross sections for the present measurement. The line is drawn to guide the eye.

Figure 2

Measured and calculated fusion excitation functions and barrier distributions for the ${}^{12}\mathrm{C}$+${}^{208}\mathrm{Pb}$ reaction. The lines show the FRESCO calculations using different potential parameter sets. See text for details.

Figure 3

The elastic scattering angular distribution at laboratory energies of (a) 69.9 MeV and (b) 84.9 MeV. The data are taken from Ref. [16]. The lines show the FRESCO calculations using different sets of potential parameters. See text for details.

Figure 4

As Fig. 2, for potential parameters fitting the elastic scattering data. See text for details.