Fusion hindrance for the positive Q -value system C12+Si30

Abstract

Background: The fusion reaction 12 C + 30 Si is a link between heavier cases studied in recent years, and the light heavy-ion systems e.g. 12 C + 12 C, 16 O + 16 O that have a prominent role in the dynamics of stellar evolution. 12 C + 30 Si fusion itself is not a relevant process for astrophysics, but it is important to establish its behaviour below the barrier, where couplings to low-lying collective modes and the hindrance phenomenon may determine the cross sections. The excitation function is presently completely unknown below the barrier for the 12 C + 30 Si reaction, thus no reliable extrapolation into the astrophysical regime for the C+C and O+O cases, can be performed.Purpose: Our aim was to carry out a complete measurement of the fusion excitation function of 12 C + 30 Si from well below to above the Coulomb barrier, so as to clear up the consequence of couplings to low-lying states of 30 Si, and whether the hindrance effect appears in this relatively light system which has a positive Q-value for fusion. This would have consequences for the extrapolated behaviour to even lighter systems.Methods: The inverse kinematics was used by sending 30 Si beams delivered from the XTU Tandem accelerator of INFN-Laboratori Nazionali di Legnaro onto thin 12 C (50µg/cm 2 ) targets enriched to 99.9% in mass 12. The fusion evaporation residues (ER) were detected at very forward angles, following beam separation by means of an electrostatic deflector. Angular distributions of ER were measured at E beam = 45, 59 and 80 MeV, and they were angle-integrated to derive total fusion cross sections. Results:The fusion excitation function of 12 C + 30 Si has been measured with high statistical accuracy, covering more than five orders of magnitude down to a lowest cross section ≃3µb. The logarithmic slope and the S factor have been extracted and we have a convincing phenomenological evidence of the hindrance effect. These results have been compared with the calculations performed within the model that considers a damping of the coupling strength well inside the Coulomb barrier. Conclusions:The experimental data are consistent with the coupled-channels calculations. A better fit is obtained by using the Yukawa-plus-exponential potential and a damping of the coupling strengths inside the barrier. The degree of hindrance is much smaller than the one in heavier systems. Also a phenomenological estimate reproduces quite closely the hindrance threshold for 12 C + 30 Si, so that an extrapolation to the C+C and O+O cases can be reliably performed.

Fusion hindrance in light and heavy systems

“…This is shown in Fig. 3 and is supported by CC calculations within the adiabatic model [14], using both the WS and the YPE potentials [15]. A damping of the coupling strengths improves the data fit at low energies and, overall, the YPE potential gives better results.…”

“…The red dots are extracted from experimental data while the blue ones are extrapolated from data at higher energies. The red diamond is the value for 12 C + 30 Si [15]. The dashed line is the curve resulting from the systematics discussed in Ref.…”

Fusion of 16O+165Ho at deep sub-barrier energies

“…The systems involving 165 Ho target nucleus, for which sub-barrier fusion cross sections have been reported in literature are 19 F+ 165 Ho [44] and 7 Li+ 165 Ho [46]. The projectile 16 O in the present system is a stiff nucleus, while 19 F is relatively heavier and less bound than 16 O, and 7 Li is a well known weakly bound stable nucleus. For comparison of different projectile-target systems, the fusion excitation functions have been plotted in a reduced scale.…”

“…On extending the measurements from sub-barrier down to deep sub-barrier energies, for a wide range of reactions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], a steep fall-off of fusion excitation function has been observed compared to the standard coupled channels calculations, although fusion cross sections are still enhanced with respect to single-barrier penetration model calculations. This phenomenon of change of slope in the fusion excitation function at deep sub-barrier energies is termed as "fusion hindrance".…”

A Fast Ionization Chamber for the Study of Fusion Reactions Induced by Radioactive Beams

“…The experimental set-up PISOLO at LNL has been largely employed in fusion reaction studies near and below the Coulomb barrier [1]. Fusion cross section is determined by the direct detection of the fusion-evaporation residues (ER) at small angles by separating out the beam and beam-like particles using an electrostatic beam deflector.…”