${}^{16–18}\mathrm{O}+{}^{16}\mathrm{O}$ and ${}^{16,18}\mathrm{O}+{}^{12,13}\mathrm{C}$ fusion-evaporation reactions at near-Coulomb-barrier energies from statistical model calculations

Fusion-evaporation reactions of carbon and oxygen isotopes at near-Coulomb-barrier energies are important subjects in nuclear-reaction studies. They are closely related to nucleosynthesis in astrophysics and may provide novel opportunities to study the $\alpha$-clustering effect in light nuclei. In this work, the ${}^{16-18}\mathrm{O}+{}^{16}\mathrm{O}$ and ${}^{16,18}\mathrm{O}+{}^{12,13}\mathrm{C}$ fusion-evaporation reactions are studied by using the statistical model based on the Hauser-Feshbach formalism. It is found that the statistical model with the original Gilbert-Cameron level-density formula typically underestimates the $\alpha$-emission cross sections. To overcome this problem, we introduce for the residual nuclei a new level-density formula with the correction term inspired by theoretical considerations on the $\alpha$-clustering effect. Compared with the original Gilbert-Cameron level-density formula, our statistical-model calculations with the new level-density formula show significant improvements.

Figure 1

The level densities of the residual nuclei as a function of the excited energy $E^{*}$ for the oxygen $+$ oxygen system. The solid red lines are the modified Gilbert-Cameron level densities ${\rho }_{\text{MGC}}$ and the dashed green lines are the original Gilbert-Cameron level densities ${\rho }_{\text{OGC}}$.

Figure 2

The level densities of the residual nuclei as a function of the excited energy $E^{*}$ for the oxygen $+$ carbon system. The solid red lines are the modified Gilbert-Cameron level densities ${\rho }_{\text{MGC}}$ and the dashed green lines are the original Gilbert-Cameron level densities ${\rho }_{\text{OGC}}$.

Figure 3

The $\alpha$-emission cross sections versus the center-of-mass incident energies $E_{\text{c.m.}}$ for the ${}^{16-18}\mathrm{O}+{}^{16}\mathrm{O}$ fusion-evaporation reactions. Solid points are the experimental data taken from Refs. [49, 50]. The dashed red lines are the theoretical results given by the statistical-model calculations with the original Gilbert-Cameron level-density formula, while the solid green lines are theoretical results given by the statistical-model calculations with the new level-density formula inspired by the $\alpha$-clustering effect.

Figure 4

The cross sections of the residual nuclei from the exit channels without $\alpha$ emissions versus the center-of-mass incident energies $E_{\text{c.m.}}$ for the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ fusion-evaporation reaction. Solid points are the experimental data taken from Ref. [49]. The dashed red lines are the theoretical results given by the statistical-model calculations with the original Gilbert-Cameron level-density formula, while the solid green lines are theoretical results given by the statistical-model calculations with the new level-density formula inspired by the $\alpha$-clustering effect.

Figure 5

The cross sections of the residual nuclei from the exit channels with $\alpha$ emissions versus the center-of-mass incident energies $E_{\text{c.m.}}$ for the ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ fusion-evaporation reaction. Solid points are the experimental data taken from Ref. [49]. The dashed red lines are the theoretical results given by the statistical-model calculations with the original Gilbert-Cameron level-density formula, while the solid green lines are theoretical results given by the statistical-model calculations with the new level-density formula inspired by the $\alpha$-clustering effect.

Figure 6

The $\alpha$-emission cross sections versus the center-of-mass incident energies $E_{\text{c.m.}}$ for the ${}^{16,18}\mathrm{O}+{}^{12,13}\mathrm{C}$ fusion-evaporation reactions. Solid points are the experimental data taken from Refs. [40, 43, 51, 52]. The dashed red lines are the theoretical results given by the statistical-model calculations with the original Gilbert-Cameron level-density formula, while the solid green lines are theoretical results given by the statistical-model calculations with the new level-density formula inspired by the $\alpha$-clustering effect.