Quantitative analysis of precise heavy-ion fusion data at above-barrier energies using Skyrme-Hartree-Fock nuclear densities

Abstract

We calculate the capture (fusion) cross sections for nine reactions involving spherical nuclei: $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, $^{92}\mathrm{Zr}$, $^{144}\mathrm{Sm}$, $^{208}\mathrm{Pb}$; $^{28}\mathrm{Si}$ + $^{28}\mathrm{Si}$, $^{92}\mathrm{Zr}$, $^{208}\mathrm{Pb}$; $^{32}\mathrm{S}$ + $^{208}\mathrm{Pb}$. For six of them precision data are available in the literature. Analysis of these precision data within the framework of the single-barrier penetration model based on the Woods-Saxon profile for the strong nucleus-nucleus interaction potential (SnnP) gave rise to the problem of the apparently large diffuseness of the SnnP [Newton et al., Phys. Rev. C 70, 024605 (2004)]. Our fluctuation-dissipation trajectory model is based on the double-folding approach with the density-dependent M3Y NN forces including the finite-range exchange part. For the nuclear matter density the Skyrme-Hartree-Fock approach including the tensor interaction is applied. The resulting nucleus-nucleus potential possesses rather small (normal) diffuseness. The strength of the radial friction ${K}_{R}$ is used as the free parameter of the model. It turns out that for four of the five reactions induced by $^{16}\mathrm{O}$ (except $^{16}\mathrm{O}$ + $^{208}\mathrm{Pb}$) the calculated cross sections cannot be brought into agreement with the data within the experimental errors. This suggests that the calculated nuclear density is incorrect for $^{16}\mathrm{O}$. For the reactions not involving $^{16}\mathrm{O}$ and, surprisingly, for the $^{16}\mathrm{O}$ + $^{208}\mathrm{Pb}$ reaction the agreement with the data within 2-5% is achieved at ${K}_{R}=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ to $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{0.28em}{0ex}}{\mathrm{MeV}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{zs}$ which is in accord with the previous works.