Isotopic effects in sub-barrier fusion of Si + Si systems

Abstract

Background: Recent measurements of fusion cross sections for the 28 Si + 28 Si system revealed a rather unsystematic behavior; i.e., they drop faster near the barrier than at lower energies. This was tentatively attributed to the large oblate deformation of 28 Si because coupled-channels (CC) calculations largely underestimate the 28 Si + 28 Si cross sections at low energies, unless a weak imaginary potential is applied, probably simulating the deformation. 30 Si 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 30 Si + 30 Si in an energy range from around the Coulomb barrier to deep sub-barrier energies, and (ii) to compare the results with the behavior of 28 Si + 28 Si involving two deformed nuclei. Methods:30 Si beams from the XTU tandem accelerator of the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare were used, bombarding thin metallic 30 Si targets (50 μg/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 30 Si + 30 Si was measured down to the level of a few microbarns. It has a regular shape, at variance with the unusual trend of 28 Si + 28 Si. The extracted logarithmic derivative does not reach the L CS 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 28 Si + 28 Si strengthens the explanation of the oblate shape of 28 Si being the reason for the irregular behavior of that system.