Sub-barrier fusion of Si+Si systems

The near- and sub-barrier fusion excitation function has been measured for the system ³⁰Si+³⁰Si at the Laboratori Nazionali di Legnaro of INFN, using the ³⁰Si beam of the XTU Tandem accelerator in the energy range 47 - 90 MeV. A set-up based on a beam electrostatic deflector was used for detecting fusion evaporation residues. The measured cross sections have been compared to previous data on ²⁸Si+²⁸Si and Coupled Channels (CC) calculations have been performed using M3Y+repulsion and Woods-Saxon potentials, where the lowlying 2⁺ and 3^- excitations have been included. A weak imaginary potential was found to be necessary to reproduce the low energy ²⁸Si+²⁸Si data. This probably simulates the effect of the oblate deformation of this nucleus. On the contrary, ³⁰Si is a spherical nucleus, ³⁰Si+³⁰Si is nicely fit by CC calculations and no imaginary potential is needed. For this system, no maximum shows up for the astrophysical S-factor so that we have no evidence for hindrance, as confirmed by the comparison with CC calculations. The logarithmic derivative of the two symmetric systems highlights their different low energy trend. A difference can also be noted in the two barrier distributions, where the high-energy peak present in ²⁸Si+²⁸Si is not observed for ³⁰Si+³⁰Si, probably due to the weaker couplings in last case.