Fusion ofSi28+Si28,30: Different trends at sub-barrier energies

Abstract

Background: The fusion excitation function of the system $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ at energies near and below the Coulomb barrier is known only down to $\ensuremath{\simeq}15$ mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ even if the fusion cross section is measured down to $\ensuremath{\simeq}50$ $\ensuremath{\mu}\mathrm{b}$, the evidence of hindrance is marginal. Both systems have positive fusion $Q$ values. While $^{28}\mathrm{Si}$ has a deformed oblate shape, $^{30}\mathrm{Si}$ is spherical.Purpose: We investigate 1. the possible influence of the different structure of the two Si isotopes on the fusion excitation functions in the deep sub-barrier region and 2. whether hindrance exists in the $\text{Si}\phantom{\rule{4.pt}{0ex}}+\phantom{\rule{4.pt}{0ex}}\text{Si}$ systems and whether it is strong enough to generate an $S$-factor maximum, thus allowing a comparison with lighter heavy-ion systems of astrophysical interest.Methods: $^{28}\mathrm{Si}$ beams from the XTU Tandem accelerator of the INFN Laboratori Nazionali di Legnaro were used. The setup was based on an electrostatic beam separator, and fusion evaporation residues (ER) were detected at very forward angles. Angular distributions of ER were measured.Results: Fusion cross sections of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ have been obtained down to $\ensuremath{\simeq}600$ nb. The slope of the excitation function has a clear irregularity below the barrier, but no indication of a $S$-factor maximum is found. For $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ the previous data have been confirmed and two smaller cross sections have been measured down to $\ensuremath{\simeq}4$ $\ensuremath{\mu}\mathrm{b}$. The trend of the $S$-factor reinforces the previous weak evidence of hindrance.Conclusions: The sub-barrier cross sections for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$ and the existing $^{30}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$ data. An additional weak imaginary potential (probably simulating the effect of the oblate $^{28}\mathrm{Si}$ deformation) is required to fit the low-energy trend of $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{28}\mathrm{Si}$. The parameters of these calculations are applied to predict the ion-ion potential for $^{28}\mathrm{Si}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{30}\mathrm{Si}$. Its cross sections are well reproduced by also including one- and successive two-neutron transfer channels, besides the low-lying surface excitations.