H. Esbensen, X. Tang, C. L. Jiang
Fusion data for $^{13}$C+$^{13}$C, $^{12}$C+$^{13}$C and $^{12}$C+$^{12}$C
are analyzed by coupled-channels calculations that are based on the
M3Y+repulsion, double-folding potential. The fusion is determined by
ingoing-wave-boundary conditions (IWBC) that are imposed at the minimum of the
pocket in the entrance channel potential. Quadrupole and octupole transitions
to low-lying states in projectile and target are included in the calculations,
as well as mutual excitations of these states. The effect of one-neutron
transfer is also considered but the effect is small in the measured energy
regime. It is shown that mutual excitations to high-lying states play a very
important role in developing a comprehensive and consistent description of the
measurements. Thus the shapes of the calculated cross sections for
$^{12}$C+$^{13}$C and $^{13}$C+$^{13}$C are in good agreement with the data.
The fusion cross sections for $^{12}$C+$^{12}$C determined by the IWBC are
generally larger than the measured cross sections but they are consistent with
the maxima of some of the observed peak cross sections. They are therefore
expected to provide an upper limit for the extrapolation into the low-energy
regime of interest to astrophysics.
View original:
http://arxiv.org/abs/1112.0496
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