Isotopic Effects in Sub-Barrier Fusion of Si + Si Systems

Background: Recent measurements of fusion cross sections for the Si-28 + Si-28 system revealed a rather Si-28 + Si-28 cross sections at low energies, unless a weak imaginary potential is applied, probably simulating the deformation. Si-30 has no permanent deformation and its low-energy excitations are of a vibrational nature. Previous measurements of this system reached only 4 mb, which is not sufficient to obtain information on effects that should show up at lower energies. Purpose: The aim of the present experiment was twofold: (i) to clarify the underlying fusion dynamics by measuring the symmetric case Si-30 + Si-30 in an energy range from around the Coulomb barrier to deep sub-barrier energies, and (ii) to compare the results with the behavior of Si-28 + Si-28 involving two deformed nuclei. Methods: Si-30 beams from the XTU tandem accelerator of the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare were used, bombarding thin metallic Si-30 targets (50 mu g/cm(2)) enriched to 99.64% in mass 30. An electrostatic beam deflector allowed the detection of fusion evaporation residues (ERs) at very forward angles, and angular distributions of ERs were measured. Results: The excitation function of Si-30 + Si-30 was measured down to the level of a few microbarns. It has a regular shape, at variance with the unusual trend of Si-28 + Si-28. The extracted logarithmic derivative does not reach the LCS limit at low energies, so that no maximum of the S factor shows up. CC calculations were performed including the low-lying 2(+) and 3(-) excitations. Conclusions: Using a Woods-Saxon potential the experimental cross sections at low energies are overpredicted, and this is a clear sign of hindrance, while the calculations performed with a M3Y + repulsion potential nicely fit the data at low energies, without the need of an imaginary potential. The comparison with the results for Si-28 + Si-28 strengthens the explanation of the oblate shape of Si-28 being the reason for the irregular behavior of that system.