Measurements of Fusion Reactions of Low-Intensity Radioactive Carbon Beams on ${}^{12}\mathrm{C}$ and their Implications for the Understanding of X-Ray Bursts

The interaction between neutron-rich nuclei plays an important role for understanding the reaction mechanism of the fusion process as well as for the energy production through pycnonuclear reactions in the crust of neutron stars. We have performed the first measurements of the total fusion cross sections in the systems ${}^{10,14,15}\mathrm{C}+{}^{12}\mathrm{C}$ using a new active target-detector system. In the energy region accessible with existing radioactive beams, a good agreement between the experimental and theoretical cross sections is observed. This gives confidence in our ability to calculate fusion cross sections for systems which are outside the range of today’s radioactive beam facilities.

Figure 1

Top: Energy loss signals from the MUSIC for various reactions induced by ${}^{15}\mathrm{C}$ and ${}^{15}\mathrm{N}$ particles. Black: Energy-loss signals measured in the 18 strips for ${}^{15}\mathrm{C}$ beam particles passing through the MUSIC detector. Red: Energy-loss values measured for evaporation residues (ER) produced by ${}^{15}\mathrm{C}$ particles in anode strip 4. Green: Energy-loss values measured for evaporation residues produced by ${}^{15}\mathrm{N}$ particles in anode strip 10. Bottom: Schematic of the anode structure. See text for details.

Figure 2

Solid points: Experimental data for the $S$ factors in the fusion reactions ${}^{10,12,13,14,15}\mathrm{C}+{}^{12}\mathrm{C}$ as measured with the MUSIC detector. Open circles: Experimental data for ${}^{12,13}\mathrm{C}+{}^{12}\mathrm{C}$ from Refs. [21, 22]. Solid lines: Theoretical $S$ factors for the systems ${}^{10,12,13,14,15}\mathrm{C}+{}^{12}\mathrm{C}$ taken from the calculations of Yakovlev et al. [7]. Dashed line: Theoretical $S$ factor for the system ${}^{19}\mathrm{C}+{}^{12}\mathrm{C}$.

Figure 3

Comparison of the experimental averaged cross sections for ${}^{10,12,13,14,15}\mathrm{C}+{}^{12}\mathrm{C}$ (circles) with theoretical predictions. Solid points: Cross sections averaged in the energy range $E_{\text{c.m.}}=14–17\mathrm{MeV}$ for the fusion reactions ${}^{10,12,13,14,15}\mathrm{C}+{}^{12}\mathrm{C}$ as measured with the MUSIC detector and plotted as a function of the neutron excess $N-Z$. Open symbols: Experimental data for ${}^{12,13}\mathrm{C}+{}^{12}\mathrm{C}$ (red circles) from Ref. [21]. Solid line: cross sections prediction taken from the calculations of Yakovlev et al. [7] using the Sao Paulo (SP) potential, dashed line: cross section predicted by coupled-channel (CC) calculations from Ref. [24], dotted line: cross section predicted by TDHF calculations [23].